Enhancement of Mobile Radio [600500]
Enhancement of Mobile Radio
Channel Using Diversity Techniques
A Thesis
Submitted to the Department of Electrical &
Electronic Engineering
University of Technology
In Partial Fulfillment of the Requirements for the
Degree of Master of Science in
Communication Engineering
By
Mohannad Mohammed Abdul-Hussien
Supervised By
Dr. Wa’il A.H. Hadi
January 2010
Republic of Iraq
Ministry of Higher Education and Scientific Research
University of Technology
Electrical and Electronic Engineering Department
ﻴﻢﹺ ﺣ ﻦﹺ ﺍﻟﺮ ﲪ ﻢﹺ ﺍﷲِ ﺍﻟﺮ ﺑﹺﺴ
ﺎ ﺇﹺﻻ ﻣ ﺎﻥ ﺴ ﻺﻧ ﻟ ﺲ ﺃﹶﻥﹾ ﻟﹶﻴ ﻭ
ﻰ ﻌ ﺳ﴿39﴾ ﻑ ﻮ ﺳ ﻪ ﻴ ﻌ ﺃﹶﻥﱠ ﺳ ﻭ
ﻯ ﺮ ﻳ﴿40﴾ ﺍﺀَ ﺰ ﺍﻟﹾﺠ ﺍﻩ ﺰ ﺠ ﻳ ﺛﹸﻢ
ﻓﹶﻰ ﺍﻷَﻭ ﴿41﴾
ﺃﷲ ﻕ ﺪ ﺻ ﻢ ﻴ ﻈ ﺃﻟﻌ
﴿اﻟﻨﺠﻢﺳﻮرة ﴾
Dedication
To Whom Had Made Me
of What I am… To My
Family, the Cause of My
Success.
Mohannad
Thanks to Allah for providing me the great willingness
and strength to finish this work.
I would like to express my deepest thanks and sincere
gratitude to my supervisor Dr. Wa’il A.H. Hadi for his
continuing guidance, encouragement, and supports during this
study.
My thanks are expressed to the Department of Electrical
and Electronic Engineering for providing facilities to do this
work.
I wish to express my deepest thanks to my loving family,
thanks to my mother, my father, my brothers and Sister whom
without their unlimited patience this work might never see the
light.
Finally, special words of thanks with gratitude are
devoted to all my friends who provided me any kind of help
during the period of the study, and I couldn’t mention them all
in these few lines.
Mohannad Mohammed Abdul-Hussien
December 2009
اﻟﺨﻼﺻﺔ
اﻟﺘﻨﻮﯾﻊﯾُﻌﺘَﺒﺮ diversity) ( ﺧﻞَاﻗﻨﻮاتِ اﻟﺘﺪرﺳﺎل ﻓﻲاﻹاﻟﻄﺮق ﻓﺎﻋﻠﯿﺔِ ﻟﺘَﺤﺴﯿﻦ أداءِأﺣﺪ أﻛﺜﺮ
(interference) واﻟﺨﻔﻮت (fading) .أَويﺘﺮدداﻟأواﻟﻤﺠﺎل اﻟﺰﻣﻨﻲ،ﻓﻲﯾُﺴﺘَﻐﻞﱠأَنْﻟﻠﺘﻨﻮﯾﻊﻦﯾُﻤْﻜ
ﺋﻲﻔﻀﺎاﻟ)ﻤﻜﺎﻧﻲاﻟ (. ﻓﻲأﺳﺘﺨﺪماﻟﺬياﻟﺘﻨﻮﯾﻊﻧﻮعﻓﺎن اﻟﻨﻈﺎمِ،ردﺎﻣﺼاﺳﺘﺨﺪامﻧﺎﺣﯿﺔﻣﻦﻛﻔﺎءﺗِﮫﺑﺴﺒﺐ
اﻟﻤﺮﺳﻞِﻓﻲﻄﺒﻖ ﻋﻠﻰ ﻋﺪة ھﻮاﺋﯿﺎت ﻣﻔﺼﻮﻟﺔ ﻣﻜﺎﻧﯿﺎ ﯾُاﻟﺬيوﻤﻜﺎﻧﻲاﻟﺘﻨﻮﯾﻊُھﻮ اﻟاﻷﻃﺮوﺣﺔھﺬهﻛﻞّ
و/ﻧﻈﺎم أﺣﺎديﻣﺜﻞاﻟﮭﻮاﺋﯿﺎت اﻟﻤﺘﻌﺪدة ﺑﺄﻧﻈﻤﺔِاﻟﻤﻌﺮوفوﻘﺒﻞاﻟﻤﺴﺘﻓﻲ أَو – اﻹدﺧﺎل ﻣﺘﻌﺪد – اﻹﺧﺮاج
(SIMO) ، ﻧﻈﺎم ﻣﺘﻌﺪد – اﻹدﺧﺎل أﺣﺎدي – اﻹﺧﺮاج (MISO) وﻧﻈﺎم ﻣﺘﻌﺪد – اﻹدﺧﺎل ﻣﺘﻌﺪد – اﻹﺧﺮاج
(MIMO) .ﻋﺪة ھﻮاﺋﯿﺎت ﻓﻲ اﻹرﺳﺎل واﻻﺳﺘﻘﺒﺎل ماﺳﺘﺨﺪاإنّ )ﻧﻈﺎم MIMO ( ﻧﺤﻮﻋﻠﻰﺒَﻞﻛﺎن ﻗﺪ ﻗ
ﻧِﺴَﺐِﻹﻧْﺠﺎزﻗﺪرﺗِﮫﺑﺴﺒﺐ،ﻲاﻟﻤﺴﺘﻘﺒﻠﻠﻜﻲاﻟﻼﺳﻟﻼﺗﺼﺎلوَاﻋِﺪةﻛﺘﻘﻨﯿﺔاﻷﺧﯿﺮةاﻟﺴَﻨَﻮاتﻓﻲواﺳﻊ
ﺔﯿﻗﻣﻮﺛﻮﺗَﺤﺴﯿﻦﻋﻠﻰ ﻗﺪرﺗَﮫإﻟﻰﺑﺎﻷﺿﺎﻓﺔاﻹرﺳﺎلَ،ﻧﻄﺎق ﺗﺮددوﺪرةﻗزﯾَﺎْدَةﺑﺪوناﻷﻋﻠﻰاﻟﺒﯿﺎﻧﺎتِ
ﻊ اﻟﺘﻨﻮﯾزﯾَﺎْدَةﺧﻼلﻣﻦ اﻟﻨﻈﺎم diversity)( .ﺗﺤﺴﯿﻨﺎتﺤﺴﺎب ﻟﻣﻘﺎرﻧﺔدِراﺳﺎتاﻟﻌﻤﻞھﺬاﯾُﻘﺪّم
اﻟﮭﻮاﺋﯿﺎت اﻟﻤﺘﻌﺪدةأﻧﻈﻤﺔاﻟﻨﺎﺗﺠﺔ ﻣﻦ اﺳﺘﺨﺪام واﻟﺴﻌﺔ اﻟﺘﻨﻮﯾﻊ اﻟﻤﻌﺮوفوأﺣﺎدي اﻟﮭﻮاﺋﻲﻋﻠﻰ ﻧﻈﺎم
ﺑﻨﻈﺎم أﺣﺎدي – اﻹدﺧﺎل أﺣﺎدي – اﻹﺧﺮاج (SISO) .اﻟﺨﻄﺄﻧﺴﺒﺔأداءﺑﺪﻻﻟﺔﺘﺤﺴﯿﻨﺎتاﻟھﺬهﻠﺖﻋُﻤ
() BERاﻟﺘﻮاﻟﻲﻋﻠﻰ،اﻟﺴﻌﺔ واﻟﺘﻨﻮﯾﻊﺗﺤﺴﯿﻨﺎتﻨﺴﺒﺔ اﻟﻰﺑﺎﻟاﻟﺒﯿﺎﻧﺎترﺳﺎلإﻧﺴﺒﺔأداءو .
ﻗﻨﻮاتﻟﺘَﻮﻟﯿﺪ، واﻟﺬي ﯾﻤﻜﻦ أن ﯾﺴﺘﺨﺪمرﻣﻄﻮﻗﻨﺎة ﻣﻮﺑﺎﯾﻞﻣﻮدﯾﻞﺗﺼﻤﯿﻢﺗﻢ،ﺒﺤﺚاﻟھﺬاﻓﻲ
راﯾﻠﻲ ذات اﻟﺨﻔﻮت ﻣﻦ ﻧﻮع (SISO)، (SIMO)، MISO)(و (MIMO)ﺑﻌﺪ ذﻟﻚ، ﻓﺎن ﺗﻘﻨﯿﺎت ،
ﺟﺎﻣﻊ اﻷﺧﺘﯿﺎر (SC) وﺟﺎﻣﻊ اﻟﻤﻜﺴﺐ اﻟﻤﺘﺴﺎوي (EGC) وﺟﺎﻣﻊ اﻟﻨﺴﺒﺔ اﻟﻘﺼﻮى (MRC) ﻛﺎﻧﺖ ﻗﺪ
درﺳﺖ وﺣﻠﻠﺖ ﻟﻨﻈﺎم ﺗﻨﻮﯾﻊ اﻷﺳﺘﻼم (SIMO system) . ﻛﺬﻟﻚ ﻓﺎن اﻟﻨﺴﺒﺔ اﻟﻘﺼﻮى ﻛﺎﻧﺖ ﻗﺪ درﺳﺖ
ﻟﻨﻈﺎم ﺗﻨﻮﯾﻊ اﻻرﺳﺎل (MISO system)اﻷﻋﻠﻰاﻟﻨﺴﺒﺔِﺑﺈرﺳﺎلِواﻟﻤﻌﺮوﻓﺔ ، (MRT) .اﻟﻨﺎﺣﯿﺔﻣﻦ
ﻣﺘﻌﺪدﻧﻈﺎمِﻋﻠﻰﻤﺴﺘﻨﺪاﻟاﻟﺘﻨﻮﯾﻊأداءﻓﺎناﻷﺧﺮى، – اﻹدﺧﺎل ﻣﺘﻌﺪد- اﻹﺧﺮاج ( MIMO)ﺳﺘﺨﺪام ﺑﺈ
اﻟﺘﺼﻔﯿﺮإﺟْﺒﺎرﺗﻘﻨﯿﺔ (ZF)ﺧﻄﺄﻣﺮﺑّﻊﻣﻌﺪلأدﻧﻰﺗﻘﻨﯿﺔ و، ( MMSE)أﺧﺘﺒﺮودرسﻗﺪﻛﺎن . أﺿﺎﻓﺔ
ﺗﻘﻨﯿﺔ اﻟﺘﺮﻣﯿﺰ اﻟﻤﻜﺎﻧﻲﻓﺎنذﻟﻚ،إﻟﻰ – أﻟﺰﻣﺎﻧﻲ (STBC) ﻧﻈﺎم ﻣﺘﻌﺪدﻣﻦ ﻟﻜﻞﺖﺳردﻛﺎﻧﺖ ﻗﺪ – اﻹدﺧﺎل
أﺣﺎدي- اﻹﺧﺮاج ) MISO ( وﻧﻈﺎم ﻣﺘﻌﺪد – اﻹدﺧﺎل ﻣﺘﻌﺪد – اﻹﺧﺮاج () MIMO .ﺖ دراﺳﺔﺗﻤأﺧﯿﺮاً
أﻧﻈﻤﺔﻣﻘﺎرﻧﺔو (SISO)، (SIMO)، MISO)(و( ) MIMO، ﻋﻨﺪ اﻟﻘﻨﺎةﺳﻌﺔﺗﺤﺴﯿﻦِﻧﺎﺣﯿﺔﻣﻦ
اﻟﻘﻨﺎةﻇﺮوفﻣﺨﺘﻠﻒ اﻟﺤﺎﻻت وﻣﺨﺘﻠﻒ .
ﺗﻢ اﺳﺘﺨﺪام ﺑﺮﻧﺎﻣﺞ (MATLAB R2007a) ﻟﺘﻨﻔﯿﺬ ﺟﻤﯿﻊ اﻟﻤﺤﺎﻛﯿﺎت واﻟﻘﯿﺎﺳﺎت اﻟﻤﺴﺘﺨﺪﻣﺔ
ﻓﻲ ھﺬا اﻟﻌﻤﻞ. ﻟﻘﺼﻮى اﺔاﻟﻨﺴﺒﺑﺎن ﻃﺮﯾﻘﺔ اﻟﺮﺋﯿﺴﯿﺔُاﻟﻨَﺘﺎﺋِﺞُأﻇﮭﺮت (MRC) ﺑﯿﻦأداءِأﻓﻀﻞﺣﻘﻘﺖ
ﻧﻈﺎم أﺣﺎديﻧﻈﺎمﻓﻲاﻷﺧﺮىاﻟﺘﻨﻮﯾﻊِﺗﻘﻨﯿﺎتﺟﻤﯿﻊ – اﻹدﺧﺎل ﻣﺘﻌﺪد – اﻹﺧﺮاج (SIMO). أنﱠﺣﯿﺚ
ﺗﺤﺴﯿﻨﺎ ﺑﺤﻮاﻟﻲ 34.023 dB ﻋﻠﻰ ﻧﻈﺎم أﺣﺎدي- اﻹدﺧﺎل أﺣﺎدي- اﻹﺧﺮاج () SISO ﻛﺎن ﻗﺪ ﺗﺤﻘﻖ ﻋﻨﺪ
ﻧﺴﺒﺔ ﺧﻄﺄ BER=10-5، ﻋﻨﺪ اﺳﺘﺨﺪام أرﺑﻌﺔ ھﻮاﺋﯿﺎت اﺳﺘﻼم) أرﺳﺎل ذو1×4( .ﻛﺎﻧﺖ ﻗﺪ ﺔاﻟﻨﺘﯿﺠﻧﻔﺲ
اﻟﻘﺼﻮىاﻟﻨﺴﺒﺔِرﺳﺎلِﻹﻧﺘﺠﺖ (MRT) ﻣﺘﻌﺪدﻧﻈﺎمﻓﻲ – اﻹدﺧﺎل أﺣﺎدي- اﻹﺧﺮاج ( MISO)) أرﺳﺎل
ذو1×4(اﻟﻘﻨﺎةﻣﻌﻠﻮﻣﺎتﺗﻮﻓﺮ ﺣﺎﻟﺔﻓﻲ (CSI) ﺑﺸﻜﻞ ﻛﺎﻣﻞ ﻋﻨﺪ اﻟﻤﺮﺳﻞ. ﻓﺎناﻷﺧﺮى،اﻟﻨﺎﺣﯿﺔﻣﻦ
ﺗﻘﻨﯿﺔ اﻟﺘﺮﻣﯿﺰ اﻟﻤﻜﺎﻧﻲ- أﻟﺰﻣﺎﻧﻲ (STBC) ﻛﺎﻧﺖ ﻗﺪ ﺣﻘﻘﺖ أﺣﺴﻦ أداء ﻣﻦ ﻧﺎﺣﯿﺔ ﻧﺴﺒﺔ اﻟﺨﻄﺄ (BER)
ﻓﻲ ﻧﻈﺎم MIMO ، ﺣﯿﺚ ﺗﻢ ﺗﺤﻘﯿﻖ ﻣﻘﺪار ﺗﺤﺴﯿﻦ ﺑﺤﻮاﻟﻲ 37.198 dB ﻋﻠﻰ ﻧﻈﺎم أﺣﺎدي- اﻹدﺧﺎل
أﺣﺎدي- اﻹﺧﺮاج () SISO ﻋﻨﺪ ﻧﺴﺒﺔ ﺧﻄﺄ BER = 10-5 ھﻮاﺋﯿﺎت اﻹرﺳﺎل ﻋﺪدﯾﻜﻮن ﻋﻨﺪﻣﺎ،
اﻟﺘﻮاﻟﻲﻋﻠﻰ،وأرﺑﻌﺔاﺛﻨﺎنواﻻﺳﺘﻼم ) ذوأرﺳﺎل4×2( . أﻋﻠﻰ اﻣﺎ ﺑﺎﻟﻨﺴﺒﺔ ﻟﻘﯿﺎﺳﺎت ﺳﻌﺔ اﻟﻘﻨﺎة ﻓﺎن
ﺳﻌﺔ ﻗﻨﺎة ﻛﺎﻧﺖ ﺑﺤﻮاﻟﻲ 19.95 bit/s/Hz ﺿﻮﺿﺎءإﻟﻰﺷﺎرة أﻧﺴﺒﺔ ﻋﻨﺪ ) SNR ( SNR=18 واﻟﺘﻲ
ﻛﺎﻧﺖ ﻗﺪ ﺗﺤﻘﻘﺖ ﺑﺎﺳﺘﺨﺪام ﻧﻈﺎم ﻣﺘﻌﺪد – اﻹدﺧﺎل ﻣﺘﻌﺪد – اﻹﺧﺮاج () MIMOذورﺳﺎلﻷ)4×4(
ﺗﻘﻨﯿﺔ ﻏﻤﻮر اﻟﻤﺎء ﺑﺎﺳﺘﺨﺪام )WF( اﻟﻜﺎﻣﻠﺔ ﻋﻦ اﻟﻘﻨﺎة ت، ﻓﻲ ﺣﺎﻟﺔ ﺗﻮﻓﺮ اﻟﻤﻌﻠﻮﻣﺎ (CSI) ﻋﻨﺪ اﻟﻤﺮﺳﻞ.
I
Abstract
Diversity is considered one of most effective way s to improve the
performance of transmission in the fading and interference channels. It can be
exploited under, time, frequency or space (spatial ) domain. Due to its efficiency
in terms of system resource usage, the diversity type, utilized in the whole of
this thesis is spatial diversity which is applied to a multiple spatially separate d
antennas at the transmitter and/or the receiver known as multiple antenna s
system s such as Single -Input Multiple -Output (SIMO ) system, Multiple -Input
Single -Output (MISO) system , and Multiple -Input Multiple -Output (MIMO)
system . The use of multiple transm it and receive antennas (MIMO system ) is
widely accepted in recent years , as a promising technology for future wireless
communication, due to its ability to achieve higher data rates without
increasing the transmission power and bandwidth, in addition to its ability t o
improve system reliability through increasing diversity . This work introduces a
comparative stud ies that determines the diversity and channel capacity
enhancements , result ing from using multiple antennas systems over single
antenna system, which is known as Single -Input Single -Output (SISO) system.
These enhancements were done in term of Bit Error Rate (BER) and bit rate of
data transmission for the diversity and capacity enhancements, respectively.
In this work , a develop ed mobile channel model has been design ed,
which can be used to generate SISO, SIMO, MISO, and MIMO Rayleigh
fading channels. Then, Selection Combining (SC), Equal Gain Combining
(EGC), and M aximal Ratio Combining (MRC) techniques have been studied
and analyzed for receiv ing diversity (SIMO system). Furthermore , maximal
ratio has been studied for transmitting diversity (MISO system) , which is
known as M aximal Ratio Transmission (MRT) . On the other hand, the
performance of diversity based on MIMO system by using, Z ero Forcing (ZF),
and Minimum Mean Square Error (MMSE) techniques have been studied and
tested . In addition to that, S pace-T ime Block Codes (STBC) have been studied
and analyzed for both MISO and MIMO systems . Finally , comparison s
II
between SISO, SIMO, MISO and MIMO systems , in terms of channel capacity ,
have been studied and analyzed under different cases and channel conditions .
All the simulations and measurements were carried out by using
MATLAB R2007a. The main results showed tha t the (MRC) diversity
technique provides the best BER performance between all other diversity
techniques in SIMO system, where an SNR improvement , by about 34.023 dB ,
is achieved over SISO system, at BER=10-5, when the number of receive
antennas is four (1×4 transmission). The same result is obtained for MRT in
MISO system (4×1 transmission) , in case of full Channel State Information
(CSI) is available at the transmitter. On the other hand, STBC provides the best
BER performance in MIMO system, where an SNR improvement by about 37.198 dB is achieved over SISO system, at BER = 10
-5, when the number of
transmit and receive antennas is two and four, respectively (2×4 transmission) .
For channel capacity measurements, a maximum capacity of about 19.95
bit/s/Hz at SNR=18 dB was achieved with MIMO system for 4×4 transmission
by using Water-Filling (WF) method when CSI is available at the transmitter.
III
Abbreviation Definition
2G Second Generation
3G Third Generation
4G Fourth Generation
AMPS Advanced Mobile Phone Service
AWGN Additive White Gaussian Noise
BEP Bit Error Probability
BER Bit Error Rate
BLAST Bell Labs Layered Space -Time
BPSK Binary Phase Shift Keying
CDMA Code Division Multiple Access
CSI Channel State Information
D-AMPS Digital AMPS
dB Decibels
D-BLAST Diagonal -Bell Labs Layered Space -Time
DOA Direction -of-Arrival
DSL Digital Subscriber Line
EGC Equal Gain Combining
EVD Eigen Value Decomposition
FDMA Frequency Division Multiple Access
GSM Global System for Mobile Communication
I.I.D. Independent and Identically Distributed
IEEE Institute of Electrical and Electronic Engineers
IMT-2000 International Mobile Communications -2000
IP Internet Protocol
ISI Inter Symbol Interference
ITU International Telecommunication Union
LOS Line of Sight
MIMO Multiple -Input Multiple -Output
IV
MISO Multiple -Input Single -Output
MMSE Minimum Mean Square Error
MRC Maximal Ratio Combining
MRT Maximal Ratio Transmission
MS Mobile Station
OFDM Orthogonal Frequency Division Multiplexing
PDF Probability Density Function
QoS Quality of Service
SC Selection Combining
SIMO Single -Input Multiple -Output
SISO Single -Input Single – Output
SM Spatial Multiplexing
SMS Short Message Service
SNR Signal to Noise Ratio
SOS Sum of Sinusoidal
STBC Space -Time Block Code
STC Space -Time Coding
SVD Singular Value Decomposition
TDMA Time Division Multiple Access
UMTS Universal Mobile Telecommunication System
V-BLAST Vertical Bell Labs layered Space -Time
WCDMA Wideband Code Division Multiple Access
WF Water -Filling
WLAN Wireless Local Area Networks
WMAN Wireless Metropolitan Area Networks
ZF Zero Forcing
V
Symbol Definition
B Channel coherence bandwidth C
B Bandwidth W
T Symbol duration s
T Coherence time of the channel C
v Speed of mobile
c Speed of light
C Channel capacity
f Sampling frequency s
f Carrier frequency c
f Doppler frequency d
N Noise power spectral density o
Eb/N Bit energy to noise ratio o
𝛾𝛾𝑏𝑏 Effective bit energy to noise ratio
K Ricean K -factor : power ratio between line –
of-sight and scattered components
I0Zero order modified Bessel function of the
first kind (.)
M Number of paths for fading channel
M The number of receive antennas R
M The number of transmit antennas T
erfc(.) Complementary error function
P Bit error probability b
h Vector of Channel Coefficients
H A MIMO flat -fading channel
I m × m Identity matrix m
𝜏𝜏𝑚𝑚𝑚𝑚𝑚𝑚 Maximum Delay Spread of Channel
λ Wavelength
(.) Conjugate of a matrix *
(.) Transpose of a matrix T
VI
(.) Conjugate transpose (Hermitian) of a matrix
H
(.) Pseudo -inverse of a matrix P
λ(.) Eigen values of matrix
|a| Absolute value of scalar a
||.|| Norm of a vector or a matrix
||.||Norm of matrix (sum of squared
magnitudes of elements) 2
diag( .) Elements placed along the diagonal of a
matrix
log 2 Base 2 logarithm (.)
𝑚𝑚� Estimate of signal x
VII
List of Contents
Subject Page
No.
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I
List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III
List of S ymbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V
List of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII
Chapt er One: Introduction
1.1 Overview of Cellular Communication System . . . . . . . . . . . . 1
1.2 General Concept of Spatial Diversity . . . . . . . . . . . . . . . . . . . 3
1.3 Multiple -Input Multiple -Output (MIMO) System . . . . . . . . . . 4
1.4 Literature Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Aim of the Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Chapter Two: Mobile Channel Characteristics
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Multipath Propagation Mechanisms . . . . . . . . . . . . . . . . . . . . 10
2.3 Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.1 Large -Scale Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.2 Small -Scale Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.2.1 Delay Spread and Coherence Bandwidth . . . . . . 15
2.3.2.2 Doppler Spread and Coherence Time . . . . . . . . . 16
2.4 Types of Fading Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.1 Rayleigh Fading Distribution . . . . . . . . . . . . . . . . . . . . . 19
2.4.2 Ricean Fading Distribution . . . . . . . . . . . . . . . . . . . . . . . 19
2.5 Jakes Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6 Improved Sum -of-Sinusoids (SOS) Model . . . . . . . . . . . . . . . 24
Chapter Three: Diversity Techniques
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Types of Diversity Techniques . . . . . . . . . . . . . . . . . . . . . . . . 26
VIII
3.3 Multiple Antennas in Wireless System . . . . . . . . . . . . . . . . . . 28
3.4 Modeling of Single -Input Single -Output (SISO) Fading
Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4.1 Bit Error Probability (BEP) Expression of SISO
System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.5 Diversity Combining Methods . . . . . . . . . . . . . . . . . . . . . . . . 31
3.5.1 Receive Diversity (SIMO) Systems . . . . . . . . . . . . . . . 31
3.5.1.1 Selection Combining (SC) . . . . . . . . . . . . . . . . . 32
3.5.1. 2 Maximal Ratio Combining (MRC) . . . . . . . . . . . 33
3.5.1. 3 Equal Gain Combining (EGC) . . . . . . . . . . . . . . 35
3.6 Transmit Diversity (MISO) Systems . . . . . . . . . . . . . . . . . . . . 36
3.6.1 Maxim al Ratio Transmission (MRT) . . . . . . . . . . . . . . . 37
3.6.2 Alamouti Space -Time Block Code Transmit Diversity . 38
3.6.2.1 Summary of Alamouti’s Scheme . . . . . . . . . . . . 41
Chapter Four: MIMO Wireless Communication
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2 Benefits of MIMO Technology . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3 MIMO Fading Channel Model . . . . . . . . . . . . . . . . . . . . . . . . 44
4.4 MIMO Transceiver Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.5 Spatial Multiplexing (SM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.6 Transmitter and Receiver Structure . . . . . . . . . . . . . . . . . . . . . 47
4.7 Zero-Forcing (ZF) method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.8 Minimum Mean -Square Error (MMSE) Method . . . . . . . . . . . 49
4.9 Space-Time Block Coding (STBC) Method . . . . . . . . . . . . . . 50
4.9.1 Space -Time Block Coding (STBC) with Multiple
Receive Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.10 Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.11 SISO Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.12 SIMO Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.13 MISO Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.14 MIMO Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.14.1 Channel Unknown to the Transmitter . . . . . . . . . . . . . 57
4.14.2 Channel Known to the Transmitter . . . . . . . . . . . . . . . 59
IX
4.14.2 .1 Water -Filling (WF) Method . . . . . . . . . . . . . 60
Chapter Five: Simulation Results and Discussions
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2 Developed Design of the Improved Sum -of-Sinusoids (SOS)
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.3 Performance of SISO S ystem . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.4 Performance of SIMO and MISO Systems . . . . . . . . . . . . . . . 70
5.4.1 Selection Combining (SC) Performance . . . . . . . . . . . . . 70
5.4.2 Equal Gain Combining (EGC) Performance . . . . . . . . . 73
5.4.3 MRC and MRT Diversity Performance . . . . . . . . . . . . . 76
5.4.4 Comparison Between Diversity Combining Techniques 79
5.5 MIMO Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.6 MIMO Techniques Performance . . . . . . . . . . . . . . . . . . . . . . . 84
5.6.1 ZF Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.6.2 MMSE Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.6.3 STBC Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.6.4 Performance Comparison for MIMO Techniques . . . . . 90
5.7 Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.7.1 Channel Capacity of SISO system . . . . . . . . . . . . . . . . . 93
5.7.2 Channel Capacity of SIMO system . . . . . . . . . . . . . . . . 93
5.7.3 Channel Capacity of MISO system . . . . . . . . . . . . . . . . 94
5.7.4 SIMO and MISO Channel Capacity Comparison . . . . . 96
5.7.5 MIMO Capacity with N o CSI at the Transmitter . . . . . 96
5.7.6 MIMO Capacity with CSI at the Transmitter (Water –
Filling (WF) Method ) . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Chapter Six: Conclusions and Suggestions for Future Work
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.1.1 Error Rate Performance Improvement . . . . . . . . . . . . . . 101
6.1.2 Channel Capacity Improvement . . . . . . . . . . . . . . . . . . . 103
6.2 Suggestions for Future Work . . . . . . . . . . . . . . . . . . . . . . . . . 104
References 105
Chapter One: Introduction 1
1.1 Overview of Cellular Communication Systems
Wireless communications is, by any criterion, the fastest growing
part of the communications industry. As it has captured the attention of
the media and the imagination of the public [ 1]. In recent years,
communications researches have seen an unprecedented growth,
especially related with cellular phones, due to the increasing demand for the wide variety of end user applications. In additi on to accommodating
standard voice, personal mobile communication services must now be able to satisfy the consumer demand for text, audio, video, multimedia and Internet services [ 2]. To meet these demands, there have been many
different generations of mo bile communication networks that have
evolved from analog to digital [ 3].
The first generations (1G) systems were introduced in the mid
1980s, and can be characterized by the use of analog transmission techniques, and the use of simple multiple access tech niques such as
Frequency Division Multiple Access (FDMA) to divide the bandwidth into specific frequencies that are assigned to individual calls. First generation telecommunications systems such as Advanced Mobile Phone
Service (AMPS), only provided voice communications and they are not
sufficient for high user densities in cities . They also suffered from a low
user capacity at a rate of 2.4 kbps, and security problems due to the
simple radio interface used [ 4,5].
Chapter One: Introduction 2
In the early 1990s, second generation (2G) systems based on
digital transmission techniques were introduced to provide more robust
communications. The major improvements offered by the digital transmission of the 2G systems over 1G systems were better speech quality, increased capacity, global roam ing, and data services like the
Short Message Service (SMS). The second generation (2G) systems provided low -rate circuit and packet data at a rate of 9.6 and 14.4 kbps,
and medium -rate packet data up to 76.8 kbps [6]. The second generation
consists of the first digital mobile communication systems such as the Time Division Multiple Access (TDMA) based on GSM system , D-
AMPS (Digital AMPS), and Code Division Multiple Access (CDMA)
based on systems such as IS -95 [5].
The third generation (3G) started in October 2001 when Wideband
CDMA or WCDMA network was launched in Japan [ 3]. The 3G has
become an umbrella term to describe cellular data communications with
a target data rate of 2 M bps (actually 64
∼ 384 Kbps) [ 4]. which enables
many new services, including streaming video, web browsing and file
transfer to be of interest to the customers, the new services should be
cheap and of high quality. An important step for achieving these goals is
the selection of the multiple access method. WCDMA has been selected as the air interface for these networks. The 3G system in Europe is called
the Universal Mobile Telecommunication System (UMTS) [ 7].
The fourth generation (4G) systems may become available even
before 3G is fully develope d because 3G is a confusing mix of standards.
In 4G systems, it is expected that the target data rate will be up to 1 Gbps
for indoor and 100 Mbps for outdoor environments. The 4G will require s
a channel capacity above 10 times that of 3G systems and must also fully support Internet Protocol (IP). High data rates are a result of advances in
Chapter One: Introduction 3
signal processors, new modulation techniques, such as Orthogonal
Frequency Division Multiplexing (OFDM), and it will have M ultiple –
Input-Multiple Output (MIMO) technolog y at its foundation. The
combination of the above is the promising scheme that can provide
extremely high wireless data rates [ 8,4].
1.2 General Concept of Spatial Diversity
Due to the inhospitable nature of the radio propagation
environment, i.e. multipath propagation, time variation, and so on, the
wireless channel is unfriendly to reliable communication [9]. However, transmission over wireless channel using single transmitter and single receiver , which is known as, Single -Input Single -Output (SISO) system
is not reliable due to its high sensitivity to multipath fading [10]. In fact,
multipath fading, which is typically caused by a reflection from any physical structure, is a n unavoidable phenomenon in wireless
communication environments, because the signals are usually propagated
through a multipath. When passing through a multipath, the signals are
delayed and a phase difference are expected to occur with the signals
passing through a direct path, this causes random fluctuations in received
signal level known as fading which causes severely degradation in the
receiving quality of the wireless link [4,11].
To combat the impact of fading on the error rate, multiple
antennas hav e been employed at the receiver end only. This technique is
known as spatial diversity or Single -Input Multiple -Output (SIMO)
system, and it refers to the basic principle of picking up multiple copies of the same signal at different locations in space. The separation between the multiple antennas is chosen so that the diversity branches experience
independent fading. [ 12,1,13].
Chapter One: Introduction 4
The exploitation of the spatial dimension may take place at the
transmitter as well, known as transmit diversity or Multiple -Input Single –
Output (MISO) system [ 8]. Spatial diversity provides a diversity gain or
a significantly reduction in the signal- to-noise ratio (SNR) variations
owing to fading, leading to much smaller error probabilities [ 14]
1.3 Multiple -Input Multiple -Output (MIMO) System
The great potential of using multiple antennas for wireless
communications has only become apparent during the last decade, which
is witnessed new proposals for using multiple antennas systems to increase the capacity of wireless links, creating enormous opportunities beyond just diversity [ 15,16]. In recent years , and due to the increasing
demand for higher data transmission rate, a lot of research based on an exploitation of the multiple antennas at both transmitter and receiver which is known as Multiple -Input Multiple -Output (MIMO) systems
were established. They were shown that MIMO systems can provide a
novel means to achi eve both higher bit rates and smaller error rates
without requiring extra bandwidth or extra transmission power [17,18].
Whilst spatial diversity protects the communication system from the
effects of multipath propagation when multiple antennas are used at
either the transmitter or receiver, significant capacity increases can be
achieved by using multiple antennas at both ends of the link. In fact, by using multiple transmit and receive antennas, the multipath propagation can be effectively converted into a benefit for the communication system
by creating a multiplicity of parallel links within the same frequency band, and thereby to either increase the rate of data transmission through Spatial Multiplexing (SM) gain or to improve system reliability through
the increased diversity gain [19, 16].
Chapter One: Introduction 5
1.4 Literature Survey
In 1993, A. Wittneben [20] proposed one of the earliest form of
spatial transmit diversity, called delay diversity scheme, where a signal is
transmitted from one antenna, then delayed one time slot, and transmitted from the other antenna. Signal processing is used at the receiver to decode the superposition of the original and time- delayed
signals.
In 1996, Q. H. Spencer [ 21] presented a statistical model for the
indoor multipath channel, that includes the angle of arrival and its correlation with time of arrival, in order to be used, in simulating and analyzing the performance of array processing or diversity combining. He also presented his results with two different buildings depending on
simu ltaneous collecting for time and angle of arrival at 7 GHz.
In 1998, S. M. Alamouti [ 22] presented a simple two -branch
transmit diversity scheme. Using two transmit antennas and one receive
antenna, the scheme provides the same diversity order as maximal -ratio
combining (MRC) at the receiver, with one transmit an tenna, and two
receive antennas . The new scheme does not require any bandwidth
expansion, any feedback from the receiver to the transmitter, and its
computation complexity is similar to MRC.
In 2002, K. Kalliola [ 23] developed a new systems for radio
channel measurements including space and polarization dimensions for
studying the radio propagation in wideband mobile communication
systems. He demonstrated the usefulness of the developed measurement
systems by performing channel measurements at 2 GHz and analyzing
the experimental data. He also analyzed the spatial channels of both the
Chapter One: Introduction 6
mobile and base stations, as well as the double- directional channel that
fully characterizes the propagation between two antennas.
In 2004, A. H. Al -Hassan [ 24] studied the data transmission over
mobile radio channel. He introduced a software radio receiver design and
simulation, then he attempted to develop this software over mobile radio channel. He also used many tech niques to improve the performance of
the data transmission like equalization and diversity. Selection Switching
Combining (SSC) d iversity technique was used in his simulation test.
In 2005, S. H. Krishnamurthy [ 25] studied the dependence of
capacity on the electromagnetic (EM) waves properties of antennas and
the scattering environment, the limits on performance of parameter
estimation algorithms at the receiver and finally, the fundamental limits
on the capacity that volume- limited multiple -antenna systems can
achieve. He used the theory methods to derive a channel propagation
model for multiple antennas in a discrete -multipath channel environment.
In 2006, M. R. Mckay [ 26] considers the analysis of current and
future wireless communication systems. The mai n focus is on M ultiple –
Input Multiple -Output (MIMO) antenna technologies. The goal of his
work is to characterize the fundamental MIMO capacity limits, as well as
to analyze the performance of practical MIMO transmission strategies, in
realistic propagati on environments.
In 2007 P. Zhan [ 9] studied the performance of a Maximum SNR
(Max -SNR) scheduler, which schedules the strongest user for service,
with the effects of channel estimation error, the Modulation and Coding
Scheme (MCS), channel feedback delay, and Doppler shift, all taken into
account.
Chapter One: Introduction 7
In 2008, D. Q. Trung, N. Prayongpun, and K. Raoof [17]
considered two schemes of antenna selection in correlated Rayleigh
channels, i.e. the Maximal Ratio Transmission (MRT) and Orthogonal
Space- Time Block Code technique (OSTBC). The simulation results
illustrate that, the new antenna selection scheme can obtain performance
close to the optimum selection with low computational complexity.
In 2009, A. Lozano, and N. Jindal [27] provided a contemporary
perspective on the tradeoff between transmit antenna diversity and spatial multiplexing. They showed the difference between the
transmission techniques that utilizing all available spatial degrees of
freedom for multiplexing and the techniques that explicitly sacrifice
spatial multiplexing of MIMO communication for diversity.
1.5 Aim of the Work
The aim of this thesis can be summarized by the following:
1. Enhancement the performance of mobile radio channel by
exploiting spatial diversity , through the use of multiple antennas in
the transmission and/or reception.
2. Design a developed mobile channel model, which can be used to
generate SISO, SIMO, MISO, and MIMO channels , and to be the
dependent channel model in all the simulations of this thesis.
3. Study and analyze the improvement of capacity gained from using
SIMO, MISO, and especially from MIMO systems.
Chapter One: Introduction 8
1.6 Thesis Outline
This thesis is arranged in six chapters as follows :
Chapter one presents an introduction with literature survey and aim of
this thesis.
Chapter two gives a description of wireless fading channel character –
istics including , multipath propagation mechanisms , large scale fading
and small scale fading, then, channel simulator models which are
frequently used in mobile communication system such as, Jakes and
improved Sum-of-Sinusoids (SOS) models are studied .
Chapter three gives an overview of time, frequency, spatial diversity,
channel modeling of SISO system, and diversity combining techniques
in receiver (SIMO system) are introduced using, S election Combining
(SC), Equal Gain Combining (EGC), and M aximal Ratio Combining
(MRC) techniques. Finally, Transmit diversity techniques (MISO
system), using Maximal Ratio Transmission ( MRT ), and Space- Time
Block Code (STBC ) are studied and analyzed .
Chapter four begins with a brief description of MIMO communication
system. Then, methods of transmission from multiple antennas are introduced. Later, STBC diversity technique is introduced for MIMO
system . Finally, capacity enhancements from using multiple antennas are
studied and analyzed. Chapter five presents the simulation results and discussions using the
develop ed design that proposed for mobile channel modeling , which is
used in all the simulations and measurements.
Chapter six includes the conclusions and suggestions for future work.
Chapter Two: Mobile Channel Character istics 9
2.1 Introduction
Radio channel is the link between the transmitter and the receiver
that carries information bearing signal in the form of electromagnetic
waves. In an ideal radio channel, the received signal would consist of only a single direct path signal, which would be a perfect reconstruction of the transmitted signal [5]. However, a real mobile radio channel
experiences a lot of limitations on the performance of wireless syst ems.
The transmission path can vary from L ine-of-Sight (LOS) to complex
environments with obstruction from mountains, foliage, and man -made
objects such as buildings . Unlike fixed or wired channels , which are
stationary and predictable, wireless channels exhibit an extremely random nature and are often difficult to characterize and analyze. The speed of motion, for example, impacts on how the signal level fades as the mobile terminal moves in space. Therefore , the detailed knowledge
of radio propagation characteristics is an essential issue to develop a
successful wireless system [ 28, 29].
This chapter is organized as follows : A brief qualitative
description of the main propagation mechanism character istics of fading
channels, fading, large -scale fading, small -Scale fading , types of fading
channels. Finally Jakes model and improved Sum-of-Sinusoids (SOS)
models are presented .
Chapter Two: Mobile Channel Character istics 10
2.2 Multipath Propagation Mechanisms
The mechanisms behind electromagnetic wave propagation
through the mobile channel are wide and varied, however , they can be
generally classified as reflection, diffraction and scattering [30]. They
can be described as follows:
1. Reflection: This occurs when electromagnetic waves bounce off
objects whose dimensions are large compared with the wavelength
of the propagating wave. They usually occur from the surface of
the earth and buildings and walls as shown in Fig. (2.1- a). If the
surface of the object is smo oth, the angle of reflection is equal to
the angle of incidence [ 28].
2. Diffraction: Diffraction occurs when the electromagnetic signal
strikes an edge or corner of a structure that is large in terms of
wavelength , such as building corners, causing energy to reach
shadowed regions that have no LOS component from the transmitter as shown in Fig. (2.1-b). The received power for a
vertically polarized wave diffracted over round hills is stronger than that diffracted o ver a knife- edge, but the received power for a
horizontal polarization wave over the round hills is weaker than that over a knife- edge [31].
3. Scattering: Scattering occurs when the wave travels through or
reflected from an object with dimensions smaller tha n the
wavelength. If the surface of the scattering object is random, the signal energy is scattered in many directions as shown in Fig. (2.1-
c). Rough surfaces, small objects, or other irregularities in the
channel cause scattering [31,32].
Chapter Two: Mobile Channel Character istics 11
All of these phenomena occur in a typical wireless channel as
waves propagate and interact with surrounding objects [14,28 ].
LOS Component
Ground Plane
(a) Reflection
(b) Diffraction Building
(c) Scattering Random Surface
Fig. (2.1) Multipath propagation mechanisms
Chapter Two: Mobile Channel Character istics 12
2.3 Fading
Cellular systems usually operate in urban areas, where there is no
direct line -of-sight (LOS) path between the transmitter and receiver [ 28].
In such locations and due to multiple reflections from various objects,
the electromagnetic waves propagate along various paths of differing lengths. The presence of several paths by which a signal can travel between transmitter and receiver is known as multipath propagation. At
the receiver, the incoming waves arrive from many different directions
with different propagation delays. The signal received at any point in
space may consist of a large number of plane waves with random distributed amplitudes, phases, and angles of arrival. The received signal
will typically be a superposition of these many multipath components
thereby creating a rapid fluctuation in signal strength at the receiver,
known as multipath fading [30]. Fig. (2.2) shows a scenario wit h
multipath fading [ 33].
LOS Component
TX RX Diffraction
Fig. (2. 2) Multipath propagation Environment
Reflection
Reflection
Scattering
Chapter Two: Mobile Channel Character istics 13
Two different scales of fading have been defined, large scale
fading and small scale fading. Large- scale fading characterizes average
signal strength over large transmitter -receiver (T X-RX) separation
distances (several hundred or thousands of wavelengths), and small -scale
fading characterizes the rapid fluctuations of the received signal over a
short distance (a few wavelengths) or a short time duration [ 34].
2.3.1 Large -Scale Fading
This phenomenon is affected by promin ent terrain contours (hills,
forests, billboards, buildings, etc.) over large transmitter -receiver (T X-
RX
Small -scale fading or simply fading is used to describe the rapid
fluctuations of the amplitude, phases, or multipath delays of a radio
signal over a short period of time or travel distance (a few wavelengths), so that large -scale path loss effects may be ignored. Small -scale fading
is caus ed by a number of signals (two or more) arriving at the reception
point through different paths, giving rise to constructive (strengthening) or destructive (weakening) of the received signal, depending on their ) separation distances (several hundred or thousands of wavelengths)
[34,35 ]. The receiver is often represented as being shadowed by such
obstacles and the mobile station should move over a large distance to
overcom e the effects of shadowing [ 36].
The large- scale effects are described by their probability density
functions (pdf), whose parameters differ for the different radio
environments [ 19].
More d etails of this phenomenon is available in [34, 36, 28, 37]
and will not be described in this work.
2.3.2 S mall-Scale Fading
Chapter Two: Mobile Channel Character istics 14
phase and amplitude values. These different s ignals other than the main
signal are called multipath waves. Multipath in a radio channel is the
cause of the small scale fading, and the three most important effects are
[36, 28, 9]:-
a. Rapid fluctuation in the signal strength over a short distance or time
interval.
b. Random frequency modulation due to different Doppler shifts on various propagation paths , if there is a relative motion between the
transmitter and receiver.
c. Time dispersion (echoes) caused by multipath propagation delays.
Many physi cal factors can affect the small -scale fading. The most
important factors include multiple propagation paths, relative motion between the transmitter and receiver, motion of the scatterers in the
environment, transmitted signal bandwidth, etc. In the typic al mobile
communication setup, due to the relatively lower height of the mobile receiver, there is usually no L ine of -Sight (LOS) path. In this scenario,
when the number of independent electromagnetic waves is assumed to be
large, the distribution of the r eceived signal can be considered as a
complex Gaussian process in both its in -phase and quadrature
components [9]. The envelope of the received signal is consequently
Rayleigh distributed . On the other hand, if there is a Line of -Sight (LOS)
path between the transmitter and receiver, the signal envelope is no
longer Rayleigh and the distribution of the signal is Ricean [28]. In this
work, only small -scale fading with Rayleigh distribution is considered.
Small -scale fading is categorized by its spectral properties (flat or
frequency -selective) and its rate of variation (fast or slow). The spectral
properties of the channel are determined by the amount of delay on the
Chapter Two: Mobile Channel Character istics 15
various reflected signals that arrive at the receiver. This effect is called
delay spread and causes spreading and smearing of the signal in time.
The temporal properties of the channel (i.e., the speed of variation) are
caused by relative motion in the channel and the concomitant Doppler
shift. This is called Doppler spread and causes spreading or smearing of
the signal spectrum [ 32]. This will classified in the following sections .
2.3.2.1 Delay Spread and Coherence Bandwidth
Delay spread causes frequency selective fading as the channel acts
like a tapped delay line filter [28]. It is resulting from the difference in
propagation delays among the multiple paths, and it is the amount of time that elapses between the first arriving path an d the last arriving path
[34]. The reciprocal of delay spread is a measure of channel’s coherence
bandwidth. The coherence bandwidth B
C, is the maximum frequency
difference for which the signals are still strongly correlated , and it is
inversely proportional to the delay spread (i.e., the smaller the delay
spread the larger the coherence ban dwidth). In general, the coherence
bandwidth B C
On the other hand, if the spectral components of the transmitted
signal are affected by different amplitude gains and phase shifts, the fading is said to be frequency selective. This applies to wideband systems , is related to the maximum delay spread 𝜏𝜏𝑚𝑚𝑚𝑚𝑚𝑚 by [28, 29].
𝐵𝐵𝐶𝐶≈1
𝜏𝜏𝑚𝑚𝑚𝑚𝑚𝑚 (2.1)
If all the spectral components of the transmitted signal are affected
in a similar manner, the fading is said to be frequency nonselective or,
equivalently, frequency flat. This is the case for narrowband systems in
which the transmitted signal bandwidth is much smaller than the channel ’s coherence bandwidth 𝐵𝐵
𝐶𝐶 [38].
Chapter Two: Mobile Channel Character istics 16
in which the transmitted bandwidth is bigger than the channel’s
coherence bandwidth 𝐵𝐵𝐶𝐶 [38].
2.3.2.2 Doppler Spread and Coherence Time
Relative motion between the transmitter and receiver imparts a
Doppler shift on the signal, where the entire signal spectrum is shifted in
frequency. When multipath is combined with relative motion, the
electromagnetic wave may experience both positive and negative
Doppler shift, smearing or spreading the signal in frequency. This effect is called Doppler spread. Fig. (2.3) shows how this spreading could
occur in an urban mobile telecommunications environment [32]. In this
figure, as the car moves to the ri ght, the reflections toward the vehicle’s
front end will have a positive Doppler shift and the signal from the tower
will have negative Doppler shift. The magnitude of the Doppler shifts depends upon the transmitted frequency and the relative velocity of the
mobile station [32].
Fig. ( 2.3) Illustration of how Doppler spreading can occur.
Chapter Two: Mobile Channel Character istics 17
In general the Doppler shift of the received signal denoted by f d, is
given by [ 39]:
𝑓𝑓𝑑𝑑=𝑣𝑣𝑓𝑓𝐶𝐶
𝑐𝑐cos𝜃𝜃 (2.2)
where 𝑣𝑣 is the vehicle speed, 𝑓𝑓𝐶𝐶 is the carrier frequency, θ is the
inciden ce angle with respect to the direction of the vehicle motion , and c
is the speed of light.
The Doppler shift in a multipath propagation environment spreads
the bandwidth of the multipath waves within the range of 𝑓𝑓𝐶𝐶 ±𝑓𝑓𝑑𝑑𝑚𝑚𝑚𝑚𝑚𝑚,
where 𝑓𝑓𝑑𝑑𝑚𝑚𝑚𝑚𝑚𝑚 is the maximum Doppler shift when 𝜃𝜃=0 which is given
by[39,40]:
𝑓𝑓𝑑𝑑𝑚𝑚𝑚𝑚𝑚𝑚=𝑣𝑣𝑓𝑓𝐶𝐶
𝑐𝑐 (2.3)
A related parameter to 𝑓𝑓 𝑑𝑑𝑚𝑚𝑚𝑚𝑚𝑚, called coherence time, 𝑇𝑇𝐶𝐶, is defined
as the time over which the channel is assumed to be constant [ 29,32].
𝑇𝑇𝐶𝐶≈1
𝑓𝑓𝑑𝑑𝑚𝑚𝑚𝑚𝑚𝑚 (2.4)
Comparing the coherence time TC with the symbol time Ts
provides two general concepts, that is t he fading is said to be slow if the
symbol time duration T S is smaller than the channel’s coherence time 𝑇𝑇𝐶𝐶,
otherwise, it is considered to be fast [32,38]. Fig. (2.4) shows a tree of
the four different types of fading [41].
Chapter Two: Mobile Channel Character istics 18
2.4 Types of Fading Channel
As discussed earlier, m ultipath fading is due to the constructive
and destructive combination of randomly delayed, reflected, scattered,
and signal components. This type of fading is relatively fast and is
therefore responsible for the small -scale fading. Depending on the nature
of the radio propagation environment, there are different models describing the statistical behavior of the multipath fading envelope .
Some of these methods ar e summarized below [38, 42].
Small -Scale Fading
(Based on multipath time delay spread)
Flat Fading
1- BW of signal < BW of channel .
2- Delay spread < symbol period. Frequency Selective Fading
1- BW of signal < BW of channel .
2- Delay spread < symbol period.
Small -Scale Fading
(Based on Doppler spread)
Fast Fading
1- High Doppler spread.
2- Coherence time < Symbol period .
3- Channel variation faster than base
band signal variation . Slow Fading
1- Low Doppler spread .
2- Coherence time >Symbol period.
3- Channel variation slower than base
band signal variation .
Fig. (2. 4) Types of small -scale fading
Chapter Two: Mobile Channel Character istics 19
2.4.1 Rayleigh Fading Distribution
The Rayleigh distribution is frequently used to model the
multipath fading channels with no direct line -of-sight (LOS) path
between the transmitter and receiver. In this case, the channel samples
amplitudes has a Probability Density Functions (PDF) given by
[43,38,44]
𝑝𝑝(𝑟𝑟)=𝑟𝑟
𝜎𝜎2𝑒𝑒𝑚𝑚𝑝𝑝�−𝑟𝑟
2𝜎𝜎2�, 𝑟𝑟≥0 (2.5)
where r is the fading magnitude, 𝑟𝑟=�𝑚𝑚2+𝑦𝑦2, x and y are
random variables representing the real and imaginary parts of channel
samples. The parameter σ is the standard deviation of the real and
imaginary parts of the channel samples, and 𝜎𝜎2 denotes the average
power of the channel samples [ 44,43]
2.4.2 Ricean Fading Distribution
In the LOS situation, the received signal is composed of a random
multipath components whose amplitude s are described by the Rayleigh
distribution, plus a direct LOS component that has essentially constant
power . The theoretical PDF distribution, which applies in this case, was
derived and proved by Ricean and it is called Ricean distribution. It is
given by [45, 40].
𝑝𝑝(𝑟𝑟)=𝑟𝑟
𝜎𝜎2𝑒𝑒𝑚𝑚𝑝𝑝−(𝑟𝑟2+𝐴𝐴2)
2𝜎𝜎2𝐼𝐼𝑂𝑂�𝐴𝐴𝑟𝑟
𝜎𝜎2�, 𝑟𝑟≥0 (2.6)
where A2 is the LOS signal power and 𝐼𝐼𝑂𝑂(.) is the modified Bessel
function of the first kind and zero -order. The Ricean channel is
sometimes described using the K-factor , which is the ratio between the
Chapter Two: Mobile Channel Character istics 20
power of the LOS component and the multipath power component s, or
Rayleigh components. The Rician factor is given by [ 46,40]
𝐾𝐾=𝐴𝐴2
2𝜎𝜎2 (2.7)
Observe that when K = 0, the Ricean distribution becomes the
Rayleigh distribution [ 46].
2.5 Jakes Model
Signal fading due to multipath propagation in wireless channels is
widely modeled using mobile channel simulators. Many approaches have
been proposed for the modeling and simulation of these channels.
Among them, the Jakes model, which has been widely used to simulate Rayleigh fading channels [ 47]. Jakes has introduced a realization for the
simulation of fading channel model, which generates real and imaginary parts of the channel taps coefficients as a superposition of a finite number of sinusoids, usually known as a Sum -of-Sinusoids (SOS)
model. [20, 40]
Jakes starts with an expression representing the received signal as
a superposition of waves which is given by[ 48]
𝑅𝑅
𝐷𝐷(𝑡𝑡)=𝐸𝐸𝑂𝑂�𝐶𝐶𝑛𝑛𝑐𝑐𝑐𝑐𝑐𝑐(𝜔𝜔𝑐𝑐𝑡𝑡+𝜔𝜔𝑑𝑑𝑡𝑡𝑁𝑁
𝑛𝑛=1𝑐𝑐𝑐𝑐𝑐𝑐𝛼𝛼𝑛𝑛+𝜙𝜙𝑛𝑛) (2.8)
where 𝐸𝐸𝑂𝑂 is the amplitude of the transmitted cosine wave, 𝐶𝐶 𝑛𝑛 is the
random path gain, N is the number of arriving waves, 𝛼𝛼 𝑛𝑛 and 𝜙𝜙𝑛𝑛 are
random variables representing the angle of incoming ray and the initial
phase associated with the 𝑛𝑛𝑡𝑡ℎ propagation path, respectively, 𝜔𝜔 𝑐𝑐 is the
transmitted cosine’s radian frequency, 𝜔𝜔𝑑𝑑 is the maximum Doppler
radian frequency shift, i.e., 𝜔𝜔𝑑𝑑=2𝜋𝜋𝑣𝑣/𝜆𝜆𝑐𝑐 where v is the relative speed
Chapter Two: Mobile Channel Character istics 21
of the receiver and 𝜆𝜆𝑐𝑐 is the wavelength of the transmitted cosine wave
[48].
The signal 𝑅𝑅 𝐷𝐷(𝑡𝑡) can be normalized such that it has unit power
and thus Eq. (2.8) becomes [48]:
𝑅𝑅(𝑡𝑡)=√2�𝐶𝐶𝑛𝑛𝑐𝑐𝑐𝑐𝑐𝑐(𝜔𝜔𝑐𝑐𝑡𝑡+𝜔𝜔𝑑𝑑𝑡𝑡𝑁𝑁
𝑛𝑛=1𝑐𝑐𝑐𝑐𝑐𝑐𝛼𝛼𝑛𝑛+𝜙𝜙𝑛𝑛) (2.9)
where 𝑅𝑅(𝑡𝑡) is the normalized received signal which can be taken
as a reference model.
In the development of this simulator, Jakes makes some
assumptions which have the goal of reducing the number of low
frequency oscillators needed to generate the flat fading signal of Eq.
(2.9). Thus, he sele cts [48]
𝐶𝐶𝑛𝑛=1
√𝑁𝑁, 𝑛𝑛=1,…,𝑁𝑁 (2.10)
and
𝛼𝛼𝑛𝑛=2𝜋𝜋𝑛𝑛
𝑁𝑁, 𝑛𝑛=1,…,𝑁𝑁 (2.11)
𝜙𝜙𝑛𝑛=0, 𝑛𝑛=1,…,𝑁𝑁 (2.12)
Furthermore, Jakes chooses N of the form N=4M+2 so that the
number of distinct Doppler frequency shifts is reduced from N to M+1.
Thus, the fading signal may be generated through the use of only M+1
low-frequency oscillators. The block diagram of the simulator is given in
Fig. (2.5) [48]. From the block diagram of the simulator , the simulator
Chapter Two: Mobile Channel Character istics 22
output signal can be written in terms of quadrature components as
follows [48]:
𝑅𝑅�(𝑡𝑡)=𝑋𝑋�𝑐𝑐(𝑡𝑡)cos𝜔𝜔𝑐𝑐𝑡𝑡+𝑗𝑗𝑋𝑋�𝑐𝑐(𝑡𝑡)sin𝜔𝜔𝑐𝑐𝑡𝑡, (2.13)
where
𝑋𝑋�𝑐𝑐(𝑡𝑡)=2
√𝑁𝑁�√2 cos𝛽𝛽𝑀𝑀+1cos𝜔𝜔𝑑𝑑𝑡𝑡+2�𝑐𝑐𝑐𝑐𝑐𝑐𝛽𝛽𝑛𝑛𝑐𝑐𝑐𝑐𝑐𝑐𝜔𝜔𝑛𝑛𝑡𝑡𝑀𝑀
𝑛𝑛=1�, (2.14)
and
𝑋𝑋�𝑐𝑐(𝑡𝑡)=2
√𝑁𝑁�√2 𝑐𝑐𝑠𝑠𝑛𝑛𝛽𝛽𝑀𝑀+1cos𝜔𝜔𝑑𝑑𝑡𝑡+2�𝑐𝑐𝑠𝑠𝑛𝑛𝛽𝛽𝑛𝑛𝑐𝑐𝑐𝑐𝑐𝑐𝜔𝜔𝑛𝑛𝑡𝑡𝑀𝑀
𝑛𝑛=1�, (2.15)
𝛽𝛽𝑛𝑛=𝜋𝜋𝑛𝑛
𝑀𝑀 𝑛𝑛=1,2,…,𝑀𝑀, (2.16)
𝜔𝜔𝑛𝑛=𝜔𝜔𝑑𝑑𝑐𝑐𝑐𝑐𝑐𝑐2𝜋𝜋𝑛𝑛
𝑀𝑀 𝑛𝑛=1,2,…,𝑀𝑀 (2.17)
Chapter Two: Mobile Channel Character istics 23
𝑋𝑋�𝑐𝑐(𝑡𝑡)
𝑅𝑅�(𝑡𝑡) 𝑋𝑋�𝑐𝑐(𝑡𝑡) cos𝜔𝜔1𝑡𝑡
cos𝜔𝜔𝑐𝑐𝑡𝑡
1
√2cos𝜔𝜔𝑚𝑚𝑡𝑡
….…
….…
•
•
•
•
•
•
∑ ∑
∑
−90°
Fig. (2. 5) Jakes Rayleigh fading channel simulator
2𝑐𝑐𝑠𝑠𝑛𝑛𝛽𝛽𝑀𝑀+1 2cos𝛽𝛽𝑀𝑀+1 2𝑐𝑐𝑠𝑠𝑛𝑛𝛽𝛽𝑀𝑀 2cos𝛽𝛽𝑀𝑀 cos𝜔𝜔𝑚𝑚𝑡𝑡
2𝑐𝑐𝑠𝑠𝑛𝑛𝛽𝛽1 2cos𝛽𝛽1
Chapter Two: Mobile Channel Character istics 24
2.6 Improved Sum -of-Sinusoids (SOS) Model
Despite its widespread acceptance, the Jakes model has some
important limitations. As a deterministic model, Zheng and Xiao
proposed an improved sum -of-sinusoids model in [ 49]. By introducing
randomness to path gain 𝐶𝐶𝑛𝑛, Doppler frequency 𝛼𝛼 𝑛𝑛 and initial phase 𝜙𝜙 𝑛𝑛,
it was proved that this new model matches the desired statistical
properties of Rayleigh channel .
The normalized low -pass fading process of a new statistical S um-
of-Sinusoids (SOS) simulation model is defined by [49]:
𝑅𝑅�(𝑡𝑡)=𝑋𝑋�𝑐𝑐(𝑡𝑡)𝑐𝑐𝑐𝑐𝑐𝑐𝜔𝜔𝑐𝑐𝑡𝑡+𝑗𝑗𝑋𝑋�𝑐𝑐(𝑡𝑡)𝑐𝑐𝑠𝑠𝑛𝑛𝜔𝜔𝑐𝑐𝑡𝑡, (2.18)
𝑋𝑋�𝑐𝑐(𝑡𝑡)=2
√𝑀𝑀�cos(𝜓𝜓𝑛𝑛).cos(𝜔𝜔𝑛𝑛𝑡𝑡𝑐𝑐𝑐𝑐𝑐𝑐𝛼𝛼𝑛𝑛+𝜙𝜙)𝑀𝑀
𝑛𝑛=1 (2.19)
𝑋𝑋�𝑐𝑐(𝑡𝑡)=2
√𝑀𝑀�sin(𝜓𝜓𝑛𝑛).cos(𝜔𝜔𝑛𝑛𝑡𝑡𝑐𝑐𝑐𝑐𝑐𝑐𝛼𝛼𝑛𝑛+𝜙𝜙)𝑀𝑀
𝑛𝑛=1 (2.20)
with
𝛼𝛼𝑛𝑛=2𝜋𝜋𝑛𝑛−𝜋𝜋+𝜃𝜃
4𝑀𝑀, 𝑛𝑛=1,2,…,𝑀𝑀 (2.21)
where 𝑀𝑀=𝑁𝑁/4, 𝜔𝜔𝑛𝑛=𝜔𝜔𝑑𝑑𝑐𝑐𝑐𝑐𝑐𝑐𝛼𝛼𝑛𝑛, 𝜃𝜃,𝜙𝜙 and 𝜓𝜓𝑛𝑛 are statistically
independent and uniformly distributed over [−𝜋𝜋,𝜋𝜋] for all 𝑛𝑛. In this work
an improved Sum -of-Sinusoids (SOS) model is considered.
Chapter Three: Diversity Techniques 25
3.1 Introduction
Chapter two described how the multipath channel causes
significant impairments to the signal quality in mobile radio
communication systems. As signals travel between the transmitter and receiver, they get reflected, scattered, and diffracted . In addition, user’s
mobility gives rise to Doppler shift in the carrier frequency. As a result,
those signals experience fading (i.e., they fluctuate in their strength).
When the signal power drops significantly, the channel is said to be in
fade. This gives rise to high Bit Error Rates ( BER) [29,28].
To combat the impact of fading on the error rate, diversity
techniques are usually employed which is applied to multi-antenna
systems (the use of multiple antennas at the transmitter and/or the
receiver) [ 19,42]. The principle of diversity is to provide the receiver
with multiple versions of the same transmitted signal. Each of these versions is defined as a diversity branch. If these versions are affected by
independent fading conditions, the probability that all branches are in
fade at the same time is reduced dramatically [ 19].
In a wireless communication s system, this results in an
improvement in the required SNR or E
s/No
In this chapter, types of d iversity techniques will be introduced ,
then, receive diversity combining techniques which are, Selection
Combining (SC), Maximal Ratio Combining (MRC) and Equal Gain is necessary to achieve a
given quality of service in terms Bit Error Rate (BER).[ 29]
Chapter Three: Diversity Techniques 26
Combining (EGC) will be studied and analyzed. Finally, transmit
diversity combining techniques such as, Maximal Ratio Transmission
(MRT) and Space -Time Block Code s (STBC) will be presented .
3.2 Types of Diversity Techniques
Diversity involves providing replicas of the transmitted signal over
time, frequency, or space. Therefore , three types of diversity schemes
can be found in wireless communications [ 28].
a. Time diversity: In this case, replicas of the transmitted signal are
provided across time by a combination of channel coding and time
interleaving strategies. The key requirement here for this form of diversity to be effective is that the channel must provide sufficient variations in time. It is applicable in cases where the coherence time of the channel is small compared with the desired interleaving symbol duration. In such an event, it is assured that the interleaved
symbol is independent of the previous symbol. This makes it a completely new replica of the original symbol [28].
b. Frequency diversity: This type of diversity provides replicas of
the original signal in the frequency domain. This is applicable in cases where the coherence bandwidth of the channel is small
compared with the bandwidth of the signal [28]. This will assure
that different parts of the relevant spectrum will suffer independent
fades. Frequency dive rsity can be utilized through spread spectrum
techniques or through interleaving techniques in combination with multicarrier modulation. For example, Code -Division Multiple –
Access (CDMA) systems such as the Direct -Sequence CDMA and
Frequency -Hopping CDMA a s well as the Orthogonal Frequency –
Division Multiplexing (OFDM) systems are based on frequency
diversity , however frequency diversity techniques use much more
Chapter Three: Diversity Techniques 27
expensive frequency spectrum and require a separate transmitter for
each carrier [ 30,25].
c. Space diversity: Recently, systems using multiple antennas at
transmitter and/or receiver gained much interest [50]. The spatial
separation between the multiple antennas is chosen so that the diversity branches experience uncorrelated fading [ 12]. Unlike time
and frequency diversity, space diversity does not induce any loss in
bandwidth efficiency. This property is very attractive for high data
rate wireless communications [39]. In space , various combining
techniques, i.e., Maximum -Ratio Combining (MRC), E qual Gain
Combining (EGC) and S election Combining (SC), may be used at
the receiver . Space -time codes which exploit diversity across space
and time can also be used at the transmitter side [28].
The diversity type which utilize d in this thesis is the spatial
diversity and all the combining techniques m entioned above will be
examined in this c hapter .
In the category of spatial diversity , there are two more types of
diversity that must be consider ed:
i. Polarization diversity: In this type of diversity , horizontal and
vertical polarization signals are transmitted by two different polarized antennas and received correspondingly by two different polarized antennas at the receiver. The benefit of different
polarizations is to ensure that there is no correlation between the
data streams [ 39]. In addition to that, the two polarization antennas
can be installed at the same place and no worry ha s to be taken
about the antenna separation. However, polarization diversity can achieve only two branches of diversity . The drawback of this
scheme is that a 3 dB extra power has to be transmitted because
Chapter Three: Diversity Techniques 28
the transmitted signal must be fed to both polarized antennas at the
transmitter [ 45].
ii. Angle diversity : This applies at carrier frequencies in excess of 10
GHz. In this case, as the transmitted signals are highly scattered in
space, the received signals from different directions are independent to each other. Thus, two or more directional antennas can be pointed in different directions at the receiver site to provide uncorrelated replicas of the transmitted signals [ 39].
3.3 Multiple A ntennas in Wireless System
A wireless system may be classified in terms of the number of
antennas used for transmission and reception. The mo st traditional
configuration uses a single transmit antenna and a single receive antenna, in which case the system is defined as a Single -Input Single -Output
(SISO) system. With multiple antennas at the receiver, the system is classified as a Single -Input Multiple -Output (SIMO) system. Similarly,
with multiple transmit antennas and a single receive antenna, the system is a Multiple -Input Single -Output (MISO) system. Finally, if multiple
antennas are employed at both sides of the link, the system is classified
as a Multiple -Input Multiple -Output (MIMO) system [ 13]. The full study
of MIMO communication will be the subject of c hapter four.
3.4 Modeling of Single -Input Single -Output (SISO) Fading Channel
The principle objective of a channel model in communications is
to relate the received signal to the transmitted signal. Let x (t) represent
the baseband signal to be transmitted at time t, then the received signal
y(t) at a stationary receiver is given by the convolution of the channel
impulse response, ℎ(𝜏𝜏,𝑡𝑡) and x(t) as [ 30].
Chapter Three: Diversity Techniques 29
𝑦𝑦(𝑡𝑡)=�ℎ(𝜏𝜏,𝑡𝑡)∞
−∞𝑥𝑥(𝑡𝑡−𝜏𝜏)𝑑𝑑𝜏𝜏+𝑛𝑛(𝑡𝑡) (3.1)
Where n(t) is the A dditive White Gaussian Noise (AWGN) at the
receiver. Here, it is assumed that the channel impulse response ℎ (𝜏𝜏,𝑡𝑡) is
a function of both time t , and delay 𝜏𝜏 of the channel.
Although the continuous channel representation given by Eq.
(3.1) is natural from an electromagnetic wave propagation point of view ,
it is often conceptually convenient to work with an equivale nt discrete –
time baseband model, As shown in Fig. (3.1) [51]. Consider the sampling
of the received signal at t = nT with period T , then, at y (n) = y (nT), the
signal at the receiver can be represented as [ 30,51]
𝑦𝑦(𝑛𝑛)=�𝒉𝒉(𝑛𝑛,𝑘𝑘)𝒙𝒙(𝑛𝑛−𝑘𝑘)+𝒏𝒏(𝑛𝑛)∞
𝑘𝑘=−∞ (3.2)
where ℎ(𝑛𝑛,𝑘𝑘) is the channel response at time n to an impulse
applied at time 𝑛𝑛−𝑘𝑘, n(n) is usually modeled as Additive White
Gaussian Noise (AWGN) with variance 𝜎𝜎𝑛𝑛2. When 𝒉𝒉(𝑛𝑛,𝑘𝑘) does not vary
with n, i.e. h (n,k) = h(0,k), the channel is called time- nonselective/time –
invariant. The input -output relation then becomes [ 51]:
𝑦𝑦(𝑛𝑛)=�𝒉𝒉(𝑘𝑘)𝒙𝒙(𝑛𝑛−𝑘𝑘)+𝒏𝒏(𝑛𝑛)∞
𝑘𝑘=−∞ (3.3)
𝒏𝒏(𝑛𝑛) 𝑦𝑦(𝑛𝑛)
𝒉𝒉(𝑛𝑛,𝑘𝑘) 𝒙𝒙(𝑛𝑛)
Fig. (3.1) Discrete -time baseband equivalent channel model
Chapter Three: Diversity Techniques 30
In this thesis, only narrowband frequency -flat systems will be
studied. In narrowband systems, where there is negligible delay, the
channel model can be simplified to [ 30,51].
𝑦𝑦=ℎ𝑥𝑥+𝑛𝑛 (3.4)
The phase of this type channel s is uniformly distributed in [0 , 2𝜋𝜋)
and the amplitude is Rayleigh distributed [51].
3.4.1 Bit Error Probability (BEP) Expression of SISO
System
Consider the simple case of Binary Phase Shift Keying (BPSK)
transmission through a SISO Rayleigh fading channel. In the absence of
fading, the Bit Error Probability (BEP) in an A dditive White Gaussian
Noise (AWGN) channel is given by [ 3,19,50]
𝑃𝑃𝑏𝑏=1
2.𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒��𝐸𝐸𝑏𝑏
𝑁𝑁𝑜𝑜� (3.5)
Where 𝐸𝐸𝑏𝑏
𝑁𝑁𝑜𝑜 is the bit energy to noise ratio , and erfc(x) , is the
complementary error function defined as [ 52,19,18]
𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 (𝑥𝑥)=1
√2𝜋𝜋�𝑒𝑒𝑡𝑡2𝑑𝑑𝑡𝑡∞
𝑥𝑥 (3.6)
When fading is considered, the average BEP of SISO system can
be determined by simulation or analytically by integrating over the
Rayleigh Probability Density Function (PDF) of the channel coefficient s,
the BEP is therefore given by [46,19].
𝑃𝑃𝑏𝑏,𝑒𝑒𝑓𝑓𝑑𝑑𝑓𝑓𝑛𝑛𝑓𝑓 =�1
2.𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒��𝛾𝛾𝑏𝑏�𝑝𝑝��𝛾𝛾𝑏𝑏�∞
0𝑑𝑑𝛾𝛾𝑏𝑏 (3.7)
Chapter Three: Diversity Techniques 31
Where 𝛾𝛾𝑏𝑏 is the effective bit energy to noise ratio of Rayleigh
fading channel h, and 𝑝𝑝��𝛾𝛾𝑏𝑏� is the Rayleigh fading distribution. For
BPSK, the integration in Eq. (3.7) reduces to the well -known form
[52,50,6]
𝑃𝑃𝑏𝑏,𝑒𝑒𝑓𝑓𝑑𝑑𝑓𝑓𝑛𝑛𝑓𝑓 =1
2�1−�𝛾𝛾𝑏𝑏
1+𝛾𝛾𝑏𝑏� (3.8)
For SISO system, the diversity gain (th e number of copies is often
referred to as the diversity gain or diversity order) is equal to one [46].
3.5 Diversity Combining Methods
In section ( 3.2), diversity techniques were classified according to
the domain where the diversity is introduced. The key feature of all
diversity techniques is a low probability of simultaneous deep fades in various diversity subchannels. In general, the performance of communication systems with diversity techniques depends on how multiple signal replicas are combined at the receiver to increase the
overall received SNR. Therefore, diversity schemes can also be classified according to the type of combining methods empl oyed [39].
3.5.1 Receive Diversity Techniques
Receive diversity or SIMO system techniques are applied in
systems with a single transmit antenna and multiple receive antennas (i.e., M
R ≥ 2). They perform a (linear) combining of the individual
received signals, in order to provide a diversity gain [ 15,19]. For a SIMO
system, the general input -output relation may be treated similar to that of
SISO system with, appropriately modified Signal to Noise Ratio (SNR),
and it is given by [ 53,19]
Chapter Three: Diversity Techniques 32
𝑦𝑦=�𝐸𝐸𝑠𝑠ℎ𝑥𝑥+𝑛𝑛 (3.9)
Where 𝐸𝐸𝑠𝑠 is the average signal energy per receive antenna and per
channel use, ℎ = [ℎ1,ℎ2 …,ℎ𝑀𝑀𝑅𝑅]𝑇𝑇, is the MR×1 channel vector for
SIMO system, x and n is the M R×1 vectors representing, the transmitted
signal and the Additive White Gaussian Noise (AWGN), respectively, at
the MR
In this section, three receive diversity combining techniques will
be studied and analyzed, which are, Selection Combini ng (SC), Equal
Gain Combining (EGC), and Maximal Ratio Combining (MRC). receivers [ 53,19].
3.5.1.1 Selection Combining (SC)
Selection combining is the simplest combining method, in which
the combiner selects the diversity branch with the highest instantaneous SNR at every symbol interval, whereas all other diversity branches are discarded. This is shown in Fig. (3.2) [28,1 9,15]. With this criterion of
selection, the effective bit energy -to-noise ratio at the output of the
combiner 𝛾𝛾
𝑏𝑏 is given by [ 12,28 ].
𝛾𝛾𝑏𝑏=max {𝛾𝛾1,𝛾𝛾2,…,𝛾𝛾𝑀𝑀𝑅𝑅} (3.10)
𝑛𝑛𝑀𝑀𝑅𝑅
𝑛𝑛2
𝑛𝑛1
𝑦𝑦�
𝑦𝑦2
𝑦𝑦1
𝑥𝑥 ℎ𝑀𝑀𝑅𝑅
ℎ2 ℎ1
•
•
•
Select
Best
Antenna
Fig. (3. 2) Block diagram of SC technique 𝑦𝑦𝑀𝑀𝑅𝑅
Chapter Three: Diversity Techniques 33
For BPSK and a two -branch diversity, the Bit Error Probability
(BEP) in a Rayleigh channel , is given by [ 19]
𝑃𝑃𝑏𝑏=1
2−�𝛾𝛾𝑏𝑏
1+𝛾𝛾𝑏𝑏+12�𝛾𝛾𝑏𝑏
2+𝛾𝛾𝑏𝑏 (3.11)
At high SNR,
𝑃𝑃𝑏𝑏≅3
8𝛾𝛾𝑏𝑏2 (3.12)
In general, the diversity gain of MR-branch selection diversity
scheme is equal to M R
, indicating that selection diversity extracts all the
possible diversity out of the channel [19].
3.5.1.2 Maxim al Ratio Combining (MRC)
Maximal or maximum ratio combining method relies on the
knowledge of the complex channel gains (i.e., it requires the knowledge
of amplitudes and phases of all involved channels), so that the signals from all of the M
R
Then, the received signal is [ 28,50,19] branches are weighted according to their individual
SNRs and then summe d, to achieve the maximum signal to noise ratio at
the receiver output. Fig . (3.3) shows a block diagram of a maximal ratio
combining technique [ 50]. If the signals are 𝑦𝑦 𝑓𝑓 from each branch, and
each branch has a combiner weight 𝑊𝑊𝑓𝑓𝑀𝑀𝑅𝑅𝑀𝑀 given by [28,1 9]
𝑊𝑊𝑓𝑓𝑀𝑀𝑅𝑅𝑀𝑀=ℎ𝑓𝑓∗, 𝑓𝑓=1,2,…,𝑀𝑀𝑅𝑅 (3.13)
Chapter Three: Diversity Techniques 34
𝑦𝑦�=�𝑊𝑊𝑓𝑓𝑀𝑀𝑅𝑅𝑀𝑀.𝑦𝑦𝑓𝑓𝑀𝑀𝑅𝑅
𝑓𝑓=1 =�ℎ𝑓𝑓∗𝑀𝑀𝑅𝑅
𝑓𝑓=1��𝐸𝐸𝑠𝑠ℎ𝑓𝑓𝑥𝑥+𝑛𝑛𝑓𝑓�
=��𝐸𝐸𝑠𝑠|ℎ𝑓𝑓|2𝑥𝑥+ℎ𝑓𝑓∗𝑛𝑛𝑓𝑓𝑀𝑀𝑅𝑅
𝑓𝑓=1 (3.14)
Where ℎ𝑓𝑓∗ is the complex channel gains, representing the weighting
factor of MRC at 𝑓𝑓𝑡𝑡ℎ receive antenna, 𝑥𝑥 is the transmitted signal, 𝑦𝑦𝑓𝑓and
𝑛𝑛𝑓𝑓 are the received signal and the AWGN at 𝑓𝑓𝑡𝑡ℎ receive antenn a,
respectively.
This method is called optimum combining since it can maximize
the output SNR , where the maximum output SNR is equal to the sum of
the instantaneous SNRs of all the diversity branches [11]. Exact
expression for the Bit Error Probability (BEP) using MRC with MR
Analogous to the SC case, the diversity gain is equal to the
number of receive branches M = 2
is given by [46]
𝑃𝑃𝑏𝑏=1
2−�𝛾𝛾𝑏𝑏
1+𝛾𝛾𝑏𝑏−14�𝛾𝛾𝑏𝑏
(2+𝛾𝛾𝑏𝑏)3 (3.15)
R
in Rayleigh fading channels [ 19].
ℎ𝑀𝑀𝑅𝑅∗ ℎ1∗
ℎ2∗
𝑛𝑛𝑀𝑀𝑅𝑅
𝑛𝑛2
𝑛𝑛1
𝑦𝑦�
𝑦𝑦𝑀𝑀𝑅𝑅
𝑦𝑦2
𝑦𝑦1
𝑥𝑥 ℎ𝑀𝑀𝑅𝑅
ℎ2 ℎ1
•
•
•
Fig. (3. 3) Block diagram of MRC technique ∑
Chapter Three: Diversity Techniques 35
3.5.1.3 Equal Gain Combining (EGC)
Equal gain combining is a suboptimal but simple linear combining
method. It does not require estimation of the complex channel gains for
each individual branch. Instead, the receiver sets the amplitudes of the weighting factors to be unity (|ℎ
𝑓𝑓|=1) [39].
In general, the EGC combiner weight 𝑊𝑊𝑓𝑓𝐸𝐸𝐸𝐸𝑀𝑀 for 𝑓𝑓𝑡𝑡ℎ receive
antenna is given by [39,19 ]
𝑊𝑊𝑓𝑓𝐸𝐸𝐸𝐸𝑀𝑀=|ℎ𝑓𝑓|𝑒𝑒−∠ℎ𝑓𝑓=𝑒𝑒−∠ℎ𝑓𝑓, 𝑓𝑓=1,2,…,𝑀𝑀𝑅𝑅 (3.16)
Then the received vector is written as [39 ,19]:
𝑦𝑦�=�𝑊𝑊𝑓𝑓𝐸𝐸𝐸𝐸𝑀𝑀.𝑦𝑦𝑓𝑓=𝑀𝑀𝑅𝑅
𝑓𝑓=1�𝑒𝑒−∠ℎ𝑓𝑓��𝐸𝐸𝑠𝑠ℎ𝑓𝑓𝑥𝑥+𝑛𝑛𝑓𝑓�𝑀𝑀𝑅𝑅
𝑓𝑓=1
=�𝑒𝑒−∠ℎ𝑓𝑓��𝐸𝐸𝑠𝑠|ℎ𝑓𝑓|𝑒𝑒∠ℎ𝑓𝑓𝑥𝑥+𝑛𝑛𝑓𝑓�𝑀𝑀𝑅𝑅
𝑓𝑓=1
=��𝐸𝐸𝑠𝑠|ℎ𝑓𝑓|𝑥𝑥+𝑒𝑒−∠ℎ𝑓𝑓𝑛𝑛𝑓𝑓 (3.17)𝑀𝑀𝑅𝑅
𝑓𝑓=1
In this way all the received signals are co -phased and then added
together with equal gain as shown in Fig. (3.4). The implementation
complexity for equal -gain combining is significantly less than the
maximal ratio combining [39].
Chapter Three: Diversity Techniques 36
The Bit Error Probability (BEP) with 2 -branch EGC diversity
combining BPSK modulation is given by [12].
𝑃𝑃𝑏𝑏=1
2�1−�1−𝜇𝜇𝑏𝑏2� (3.18)
Where
𝜇𝜇𝑏𝑏=1
1+𝛾𝛾𝑏𝑏 (3.19)
For EGC and MRC, the array gain grows linearly with M R , and is
therefore larger than the array gain of selection combining. However , the
diversity gain of EGC is equal to M R
3.6 Transmit Diversity (MISO) Systems analogous to SC and MRC [19].
Multiple -Input Single -Output (MISO) systems exploit diversity at
the transmitter through the use of MT transmit antennas in combination
with pre -processing or precoding. A significant difference with receive
diversity is that the transmitter might not have the knowledge of the
MISO channel. Indeed, at the receiver, the channel is easily estimated. 𝑒𝑒−𝑗𝑗∠ℎ1
𝑒𝑒−𝑗𝑗∠ℎ𝑀𝑀𝑅𝑅 𝑒𝑒−𝑗𝑗∠ℎ2
𝑛𝑛𝑀𝑀𝑅𝑅
𝑛𝑛2
𝑛𝑛1
𝑦𝑦�
𝑦𝑦𝑀𝑀𝑅𝑅
𝑦𝑦2
𝑦𝑦1
𝑥𝑥 ℎ𝑀𝑀𝑅𝑅
ℎ2 ℎ1
•
•
•
Fig. (3. 4) Block diagram of EGC technique ∑
Chapter Three: Diversity Techniques 37
This is not the case at the transmit side, where feedback from the
receiver is required to inform the transmitter. However, there are
basically two different ways of achieving direct transmit diversity [19]:
1. when the transmitter h as a perfect channel knowledge,
beamforming can be performed using various optimization metrics to achieve both diversity and array gains
2. when the transmitter has no channel knowledge, pre -processing
known as space –time coding is used to achieve a diversit y gain,
but no array gain.
In this section, beamforming technique known as Maximal Ratio
Transmission (MRT) is evaluated and studied, then, Space- Time Block
Codes (STBC) technique known as , the Alamouti scheme is introduced
and analyzed .
3.6.1 Maxim al Ratio Transmission (MRT)
This technique, also known as transmit beamforming or Maximal
Ratio Transmission (MRT ), assumes that the transmitter has perfect
knowledge of the channel. To exploit diversity, the signal x is weighted
adequately before being transmitted on each antenna [19]. At the
receiver, the signal reads as [37,19 ]:
𝑦𝑦=�𝐸𝐸𝑠𝑠ℎ𝑤𝑤𝑥𝑥+𝑛𝑛 (3.20)
where ℎ= [ℎ1,…,ℎ𝑀𝑀𝑇𝑇 ], is the MT × 1 MISO channel vector ,
𝑤𝑤=[𝑤𝑤1,…,𝑤𝑤𝑀𝑀𝑇𝑇 ] is the beamforming weight vector , and 𝑥𝑥 is the
transmitted symbol over all transmitted antennas . The choice that
maximizes the receive SNR is given by [ 19,37,54]
𝑊𝑊𝑗𝑗𝑀𝑀𝑅𝑅𝑇𝑇 =ℎ𝑗𝑗∗
‖ℎ‖ , 𝑗𝑗=1,2,…,𝑀𝑀𝑇𝑇 (3.21)
Chapter Three: Diversity Techniques 38
where ℎ𝑗𝑗∗ is the complex conjugate channel of 𝑗𝑗𝑡𝑡ℎ transmit
antenna, ‖ℎ‖2=|ℎ1|2+|ℎ2|2+⋯+�ℎ𝑀𝑀𝑇𝑇�2is the beamforming gain
which guarantees the average total transmit energy remains equal to
𝐸𝐸𝑠𝑠 [37,54].
This choice comes to transmit along the direction of the matched
channel, hence it is also known as matched beamforming. Matched
beamforming presents the same performance as receive MRC, but
requires perfect transmit channel knowledge, which implies feedback
from the receiver as shown in Fig. (3.5) [19].
3.6.2 Alamouti Space -Time Block Code Transmit Diversity
Space- time block coding is a simple yet ingenious transmit
diversity which is proposed by Alamouti. It can be applied to both MISO
and MIMO systems with M T =2 and any number of receive antennas (in
this chapter only MISO system is considered) [ 16,55]. It is usually Fig. (3. 5) Block diagram of MRT technique ℎ𝑀𝑀𝑇𝑇
ℎ2 ℎ1
𝑥𝑥
𝑥𝑥
𝑥𝑥 𝑦𝑦
𝑤𝑤2 𝑤𝑤1
•
•
•
Estimate CSI parameter s
and feedback 𝑤𝑤𝑀𝑀𝑇𝑇
Chapter Three: Diversity Techniques 39
designed to capture the diversity in the spatial channel without requiring
Channel State Information (CSI) at the transmitter. A full- diversity code
achieves the maximum diversity order of MR×M T
This scheme can be described by considering the simple case, M available in the
channel. However, Not all STBCs offer full- diversity order . In addition
to the diversity gain , STBC can also be characterized by its spatial rate,
which is usually known as Spatial Multiplexing (SM) gain, and it is the
average number of distinct symbols sent per symbol time -period [28,16].
T
= 2, M R
= 1, which yields the scheme illustrated in Fig. (3.6) [56].
Assume that the flat fading channel remains constant over the two
successive symbol periods, thus the code matrix X has the form [19 ,56]:
𝑋𝑋=�𝑥𝑥1−𝑥𝑥2∗
𝑥𝑥2𝑥𝑥1∗� (3.22)
This means that during the first symbol interval, the signal 𝑥𝑥 1 is
transmitted from antenna 1, while signal 𝑥𝑥 2 is transmitted from antenna
2. During the next symbol period, antenna 1 transmits signal − 𝑥𝑥2∗, and
antenna 2 transmits signal 𝑥𝑥1∗ Thus, the signals received in two adjacent
time slots are [56] Fig. (3. 6) Alamouti transmit -diversity scheme with MT = 2 and MR = 1 𝑥𝑥1 −𝑥𝑥2∗
𝑥𝑥2 𝑥𝑥1∗ ℎ2 ℎ1
𝑥𝑥�1
𝑥𝑥�2 TX RX 𝑥𝑥1 ,𝑥𝑥2
Chapter Three: Diversity Techniques 40
𝑦𝑦1=�𝐸𝐸𝑠𝑠
2(ℎ1𝑥𝑥1+ℎ2𝑥𝑥2)+𝑛𝑛1 (3.23)
and
𝑦𝑦2=�𝐸𝐸𝑠𝑠
2(−ℎ1𝑥𝑥2∗+ℎ2𝑥𝑥1∗)+𝑛𝑛2 (3.24)
where the factor �𝐸𝐸𝑠𝑠
2 ensures that the total transmitted energy is 𝐸𝐸𝑠𝑠,
ℎ1 and ℎ2 denote the channel gains from the two transmit antennas to the
receive antenna. The combiner of Fig. (3 .6), which has perfect CSI and
hence knows the values of the channel gains, generates the signals
𝑥𝑥�1=ℎ1∗𝑦𝑦1+ℎ2𝑦𝑦2∗ (3.25)
and
𝑥𝑥�2=ℎ2∗𝑦𝑦1−ℎ1𝑦𝑦2∗ (3.26)
So that
𝑥𝑥�1=ℎ1∗��𝐸𝐸𝑠𝑠
2( ℎ1𝑥𝑥1+ℎ2𝑥𝑥2)+𝑛𝑛1�+ℎ2��𝐸𝐸𝑠𝑠
2(−ℎ1𝑥𝑥2∗+ℎ2𝑥𝑥1∗)+𝑛𝑛2∗�
=�𝐸𝐸𝑠𝑠
2�|ℎ1|2+|ℎ2|2�𝑥𝑥1+ℎ1∗𝑛𝑛1+ℎ2𝑛𝑛2∗ (3.27)
and similarly
𝑥𝑥�2=�𝐸𝐸𝑠𝑠
2(|ℎ1|2+|ℎ2|2)𝑥𝑥2+ℎ2∗𝑛𝑛1−ℎ1𝑛𝑛2∗ (3.28)
Thus, 𝑥𝑥1 is separated from 𝑥𝑥2 [56].
Chapter Three: Diversity Techniques 41
3.6.2.1 Summary of Alamouti’s Scheme
The characteristics of this scheme is given by [28,19 ]:
1) No feedback from receiver to transmitter is required for CSI to
obtain full transmit diversity.
2) No bandwidth expansion (as redundancy is applied in space across
multiple antennas, not in time or frequency).
3) Low complexity decoders.
4) Identical performance as MRC if the total radiated power is
doubled from that used in MRC. This is because, if the transmit power is kept constant, this scheme suffers a 3 -dB penalty in
performance, since the transmit power is divided in half across
two transmit antennas.
5) No need for complete redesign of existing systems to incorporate
this diversity scheme. Hence, it is very popular as a candidate for improving link quality based on dual transmit antenna techniques,
without any drastic system modifications.
Chapter Four: MIMO Wireles s Communication 42
4.1 Introduction
The use of multiple antennas at the transmitter and receiver in
wireless systems, popularly known as MIMO ( Multiple -Input Multiple –
Output) technology, has rapidly gained in popularity over the past decade
due to its powerful performance -enhancing capabilities. It has been
widely accepted as a promising technology to increase the transmission
rate and the strength of the received signal , with no additional increase i n
bandwidth or transmission power , as compared with traditional S ingle –
Input Single -Output (SISO) systems, [ 16,53,14].
MIMO technology constitutes a breakthrough in wireless
communication system design and now it’s considered the core of many
existing and emerging wireless standards such as IEEE 802.11 (for
Wireless Local Area Networks or WLAN), IEEE 802.16 (for Wireless
Metropolitan Area Networks or WMAN) and IEEE 802.20 (for M obile
Broadband Wireless Access or MBWA) [ 16].
In this chapter, Spatial Multiplexing (SM) techniques such as,
Zero Forcing (ZF) and Minimum Mean Squared Error (MMSE) will be
studied and analyzed . Then, STBC diversity technique will be introduced
for MIMO system . Finally, the c apacit ies of SISO, SIMO, MISO, and
MIMO system s will be introduced and studied over flat fading Rayleigh
channels with different situations (i.e., the case of channel knowledge or
not).
Chapter Four: MIMO Wireles s Communication 43
4.2 Benefits of MIMO T echnology
The benefits of MIMO technology that help achieve such
significant performance gains are array gain, spatial diversity gain,
spatial multiplexing gain and interference suppression . Some of these
gains are described in brief below [16].
1) Array gain : Array gain indicates the improvement of SNR at the
receiver compared to traditional systems with one transmit and
one receive antenna (SISO system ). Array gain improves
resistance to noise, thereby improving the coverage and the range
of a wireless network. The improvement can be achieved with
correct processing of the signals at the transmit or at the receive
side, so the transmitted signals are coherently combined at the receiver. [ 55,57].
2) Spatial diversity gain : As mentioned earlier, Multiple antennas
can also be used to combat the channel fading due to multipath
propagation. Sufficiently spaced multiple antennas at the receiver providing the receiver with multiple (ideally independent) copies of the transmitted signal in space that has propagated through
channels with different fading. The probability that all signal
copies are in a deep fade simultaneously is small , thereby
improving the quality and reliability of reception [ 55]
3) Spatial multiplexing gain : MIMO systems offer a linear increase
in data rate through spatial multiplexing, i.e., transmitting
multiple, independent data streams within the bandwidth of
operation. Under suitable channel conditions, such as rich
scattering environment, the receiver can separate the data streams.
Furthermore, each data stream experiences at least the same
channel quality that would be experienced by a SISO system,
Chapter Four: MIMO Wireles s Communication 44
effectively , enhancing the capacity by a multiplicative factor equal
to the number of streams. In gen eral, the number of data streams
that can be reliably supported by a MIMO channel equals the
minimum of the number of transmit antennas and the number of
receive antennas, i.e., min {MT,MR}. The Spatial Multiplexing
(SM) gain increases the capacity of a wireless network [16].
4) Interference suppression : By using the spatial dimension
provided by multiple antenna elements, it is possible to suppress
interfering signals in a way that is not possible with a single antenna. Hence, the system can be tuned to be less susceptible to interference and the distance between base stations using the same
time/frequency channel can be reduced, which is beneficial in densely populated areas. This leads to a system capacity
improvement [55].
4.3 MIMO Fading Channel Model
For a Multiple -Input Multiple -Output (MIMO) communication
system , shown in Fig. (4.1) , with MT transmit and MR receive antennas ,
each of the receive antennas detects all of the transmitted signals. This
allows the SISO channel , given in Eq. (3.4), to be represented as a
MT×M R matrix [30]. For frequency -flat fading over the bandwidth of
interest, the MT×M R
where ℎ𝑖𝑖𝑖𝑖 is the S ingle -Input Single -Output (SISO) channel gain
between the i MIMO channel matrix at a given time instant may
be represented as [30 ,16]
𝐻𝐻=
⎣⎢⎢⎡ℎ1,1ℎ1,2
ℎ2,1ℎ2,2…ℎ1,𝑀𝑀𝑇𝑇
…ℎ2,𝑀𝑀𝑇𝑇
⋮⋮
ℎ𝑀𝑀𝑅𝑅,1ℎ𝑀𝑀𝑅𝑅,2⋱⋮
…ℎ𝑀𝑀𝑅𝑅,𝑀𝑀𝑇𝑇⎦⎥⎥⎤
(4.1)
th receive and jth transmit antenna pair. The jth column of H
Chapter Four: MIMO Wireles s Communication 45
is often referred to as the spatial signature of the jth
As for the case of SISO channels, the individual channel gains
comprising the MIMO channel are commonly modeled as zero -mean
Additive White Gaussian N oise (AWGN ). Consequently, the amplitudes
of ℎ𝑖𝑖𝑖𝑖 are Rayleigh distributed random variables [16]. Hence, the
received signal can be represented as in the following equation [47,58].
𝑦𝑦=�𝐸𝐸𝑠𝑠
𝑀𝑀𝑇𝑇𝐻𝐻𝐻𝐻+𝑛𝑛 (4.2) transmit antenna
across the receive antenna array.
where y is the M R×1 received signal vector, x is the M T×1
transmitted signal vector, 𝑛𝑛 is the AWGN , and the factor �𝐸𝐸𝑠𝑠
𝑀𝑀𝑇𝑇 ensures
that the total transmitted energy is E s
. The MIMO channel in Fig. (4.1) is
presumed to be a rich scattering environment. Each transmit receive
antenna pair can be treated as parallel sub channels (i.e., SISO channel).
Since the data is being transmitted over parallel channels, one channel for each antenna pair, the channel capacity increases in proportion to the number of transmit -receive pairs [44]. Thi s will become clearer when the
analysis of the MIMO channel is discussed .
RX TX 𝐻𝐻1
𝐻𝐻2
𝐻𝐻𝑀𝑀𝑇𝑇 •
•
•
•
•
•
𝑦𝑦2
𝑦𝑦𝑀𝑀𝑅𝑅 𝑦𝑦1
Fig. (4.1) Block diagram of a MIMO system with MT
transmit antennas and M R receive antennas
MIMO
Channel
Chapter Four: MIMO Wireles s Communication 46
4.4 MIMO T ransceiver D esign
Transceiver algorithms for MIMO systems may be broadly
classified into two categories: rate maximization schemes and diversity
maximization schemes. MIMO systems within the two categories are known as Spatial Multiplexing (SM) techniques and spatial divers ity
techniques , respectively. A s patial multiplexing techniques such as Bell
Labs layered Space -Time (BLAST ) predominantly aim at a multiplexing
gain, (i.e., a n increas ing in bit rates as compared to a SISO system ). In
spatial diversity techniques a maximum diversity gain are provided, for
fixed transmission rate, (i.e., decreasing error rates ) such as , space -time
coding techniques [16,15]. which are based on the principle of
appropriately sending redundant symbols over the channel, from
different antennas to increase reliability of transmission [ 59].
4.5 Spatial M ultiplexing (SM)
Spatial Multiplexing (SM) techniques simultaneously transmit
independent data streams, often called layers, over M T transmit antennas .
The overall bit rate compared to a single- antenna system is thus
enhanced by a factor of MT
The earliest known spatial -multiplexing receiver was invented and
prototyped in Bell Labs and is called Bell Labs l ayered Space-Time
(BLAST) [60, 43]. There are two different BLAST architectures, the
Diagonal BLAST (D-BLAST) and its subsequent version, V ertical
BLAST (V-BLAST). The encoder of the D -BLAST is very similar to that
of V-BLAST. However, the main difference is in the way the signals are without requiring extra bandwidth or extra
transmission power. The achieved gain in terms of bit rate (in
comparison to a single antenna system) is called multiplexing gain
[15,16].
Chapter Four: MIMO Wireles s Communication 47
transmitted from different antennas. In V -BLAST, all signals from each
layer are transmitted from the same antenna, whereas in D -BLAST, they
are shifted in time before transmission. This shifting increases the
decoding complexity. V -BLAST was subsequently addressed in order to
reduce the inefficiency and complexity of D -BLAS T [59]. In this work
only V -BLAST is considered. More details about D -BLAST are
available in [ 60,43,59], and it is not considered in this work.
4.6 Transmitter and Receiver Structure
The basic principle of all Spatial Multiplexing (SM) schemes is as
follows. At the transmitter, the information bit sequence is split into M T
The signals transmitted from various antennas propagate over
independent ly scattered paths and interfere with each other upon
reception at the receiver [ 39]. There are several options for the detection
algorithm at the receiver, which are characterized by different trade- offs
between performance and complexity.
sub-sequences (demultiplexing), that are modulated and transmitted
simultaneously over the transmit antennas using the same frequency
band. At the receiver, the transm itted sequences are separated by
employing an interference -cancellation type of algorithm [ 15]. The basic
structure of a Spatial Multiplexing (SM) scheme is illustrated in Fig.
(4.2).
A low -complexity choice is to use a linear receiver, e.g., based on
the Zero Forcing (ZF) or the M inimum -Mean-Squared -Error (MMSE)
criterion. However, the error performance is typically poor, especially when the ZF approach is used (unless a favorable chan nel is given or the
number of receive antennas significantly exceeds the number of transmit antennas). In general, it is required that M
R ≥ MT in order to reliably
Chapter Four: MIMO Wireles s Communication 48
separate the received data streams . However, if the number of receive
antennas exceeds the n umber of transmit antennas ( MR >M T
) case, is
satisfied, a spatial diversity gain is accomplished [ 16,57].
4.7 Zero -Forcing (ZF) M ethod
The most simple, but also the least efficient decoding method is
matrix inversion. As matrix inversion exists only for square matrices,
there is a more general expression known as, p seudo -inverse matrix,
which can be used for a square and non square matrices . The i nterference
is removed by multiplying the received signal y given in Eq. (4.2) with
the pseudo inverse of the channel matrix. This i s also called Z ero Forcing
(ZF) method . Hence, the ZF combiner weight G ZF
Where H is given by [57,60,19].
𝐺𝐺𝑍𝑍𝑍𝑍=�𝑀𝑀𝑇𝑇
𝐸𝐸𝑠𝑠𝐻𝐻𝑃𝑃=�𝑀𝑀𝑇𝑇
𝐸𝐸𝑠𝑠(𝐻𝐻𝐻𝐻𝐻𝐻)−1𝐻𝐻𝐻𝐻 (4.3)
P=(HHH)-1HH, is a pseudo inverse of the channel matrix ,
H is the channel matrix, and HH is the complex conjugate transpose of
the channel H . For 2 × 2 channel, the HHInformation
H term is given by [ 50] bit sequence
Demultiplexing TX RX
•
•
•
MT MR •
•
•
Detection
Algorithm Estimated
bit sequence MIMO
Channel
Fig. (4. 2) Basic pr inciple of Spatial Multiplexing (SM)
MT Sub-sequences
Chapter Four: MIMO Wireles s Communication 49
𝐻𝐻𝐻𝐻𝐻𝐻 =�ℎ11∗ℎ21∗
ℎ12∗ℎ22∗��ℎ11ℎ12
ℎ21ℎ22�
=�|ℎ11|2+|ℎ21|2ℎ11∗ℎ12+ℎ21∗ℎ22
ℎ12∗ℎ11+ℎ22∗ℎ21 |ℎ12|2+|ℎ22|2� (4.4)
As stated above, the interfering signals is totally suppresse d by
multiplying the received signal y given in Eq. (4.2) with the ZF weight
GZF
The main drawback of the zero -forcing solution is the
amplification of the noise. If the matrix H, giving an estimated received vector 𝐻𝐻 � [14,43].
𝐻𝐻�=𝐺𝐺𝑍𝑍𝑍𝑍𝑦𝑦=𝐺𝐺𝑍𝑍𝑍𝑍��𝐸𝐸𝑠𝑠
𝑀𝑀𝑇𝑇𝐻𝐻𝐻𝐻+𝑛𝑛�
=𝐻𝐻+𝐺𝐺𝑍𝑍𝑍𝑍𝑛𝑛 (4.5)
HH has very small eigenvalues,
its inverse may contain very large values that enhance the noise samples
[14]. The diversity gain (diversity order) achieved using this detection
method is just MR – MT
4.8 Minimum Mean -Square Error (MMSE) Method +1 [57,43]. A bit better performance is achieved
using similar method called Minimum Mean -Square Error (MMSE),
where the SNR is taken into account when calculating the matrix
inversion to achieve MMSE [ 57].
A logical alternative to the zero forcing receiver is the MMSE
receiver, which attempts to strike a balance between spatial interference
suppression and noise enhancement by minimizing the expected value of
the mean square error between the transmitted vector x and a linear
combination of the received vector GMMSE y [60,39,14]
min𝐸𝐸{(𝐻𝐻−𝐺𝐺𝑀𝑀𝑀𝑀𝑀𝑀𝐸𝐸𝑦𝑦)2} (4.6)
Chapter Four: MIMO Wireles s Communication 50
where 𝐺𝐺𝑀𝑀𝑀𝑀𝑀𝑀𝐸𝐸 is an M R×MT
Where E matrix representing the MMSE
combiner weight and it is given by [19,39 ]
𝐺𝐺𝑀𝑀𝑀𝑀𝑀𝑀𝐸𝐸 =�𝑀𝑀𝑇𝑇
𝐸𝐸𝑠𝑠�𝐻𝐻𝐻𝐻𝐻𝐻+𝑁𝑁𝑜𝑜
𝐸𝐸𝑠𝑠𝐼𝐼𝑀𝑀𝑇𝑇�−1
𝐻𝐻𝐻𝐻 (4.7)
s is the transmitted energy , No is the noise energy and IMT
is an MT×MT
As the SNR grows large, the MMSE detector converges to the ZF
detector, but at low SNR, it prevents the worst eigenvalues from being
inverted [60]. identity matrix. An estimated received vector 𝐻𝐻� is
therefore given by [19].
𝐻𝐻�=𝐺𝐺𝑀𝑀𝑀𝑀𝑀𝑀𝐸𝐸𝑦𝑦=𝐻𝐻+𝐺𝐺𝑀𝑀𝑀𝑀𝑀𝑀𝐸𝐸𝑛𝑛 (4.8)
4.9 Space -Time B lock C oding (STBC) Method
In this section the example of Alamouti scheme of 2×1 MISO
transmission (given in chapter three) is extend ed to 2×2 MIMO
transmission . Analogous to the MISO case, consider that two symbols 𝐻𝐻 1
and 𝐻𝐻2 are transmitted simultaneously from transmit antennas 1 and 2
during the first symbol period, while symbols − 𝐻𝐻2∗ and 𝐻𝐻1∗ are transmitted
from antennas 1 and 2 during the next symbol period , see Fig. (4. 3) [19].
ℎ22 ℎ21 ℎ11
ℎ12
𝐻𝐻1 ,𝐻𝐻2
𝐻𝐻2 𝐻𝐻1∗ 𝐻𝐻�1
𝐻𝐻�2 𝐻𝐻1 −𝐻𝐻2∗
TX RX
Fig. (4. 3) Alamouti scheme with MT = 2 and MR = 2
Chapter Four: MIMO Wireles s Communication 51
Assume that the flat fading channel remains constant over the two
successive symbol periods, thus the code matrix X has the form [19,56 ]
𝑋𝑋=�𝐻𝐻1−𝐻𝐻2∗
𝐻𝐻2𝐻𝐻1∗� (4.9)
and that the 2 ×2 channel matrix reads as [56]
𝐻𝐻=�ℎ11ℎ12
ℎ21ℎ22� (4.10)
If y11, y12, y21, and y22
denote the signals received by antenna 1 at
time 1, by antenna 1 at time 2, by antenna 2 at time 1, and by antenna 2
at time 2, respectively,[ 56]
�𝑦𝑦11𝑦𝑦12
𝑦𝑦21𝑦𝑦22�=�𝐸𝐸𝑠𝑠
2�ℎ11ℎ12
ℎ21ℎ22��𝐻𝐻1−𝐻𝐻2∗
𝐻𝐻2𝐻𝐻1∗�+�𝑛𝑛11𝑛𝑛12
𝑛𝑛21𝑛𝑛22�
=
⎣⎢⎢⎢⎢⎡�𝐸𝐸𝑠𝑠
2(ℎ11𝐻𝐻1+ℎ12𝐻𝐻2)+𝑛𝑛11�𝐸𝐸𝑠𝑠
2(−ℎ11𝐻𝐻2∗+ℎ12𝐻𝐻1∗)+𝑛𝑛12
�𝐸𝐸𝑠𝑠
2(ℎ21𝐻𝐻1+ℎ22𝐻𝐻2)+𝑛𝑛21�𝐸𝐸𝑠𝑠
2(−ℎ21𝐻𝐻2∗+ℎ22𝐻𝐻1∗)+𝑛𝑛22
⎦⎥⎥⎥⎥⎤
(4.11)
At the receiver , the combiner generates [56].
𝐻𝐻�1=ℎ11∗𝑦𝑦11+ℎ12𝑦𝑦12∗+ℎ21∗𝑦𝑦21+ℎ22𝑦𝑦22∗ (4.12)
and
𝐻𝐻�2=ℎ12∗𝑦𝑦11−ℎ11𝑦𝑦12∗+ℎ22∗𝑦𝑦21−ℎ21𝑦𝑦22∗ (4.13)
Chapter Four: MIMO Wireles s Communication 52
Which yields
𝐻𝐻�1=�𝐸𝐸𝑠𝑠
2(|ℎ11|2+|ℎ12|2+|ℎ21|2+|ℎ22|2)𝐻𝐻1+𝑛𝑛1′ (4.14)
and
𝐻𝐻�2=�𝐸𝐸𝑠𝑠
2(|ℎ11|2+|ℎ12|2+|ℎ21|2+|ℎ22|2)𝐻𝐻2+𝑛𝑛2′ (4.15)
Where n1′ and n2′ are noise terms that are linear combinations of
the elements in n11, n12, n21, and n 22
4.9.1 Space -Time Block Coding (STBC) with Multiple
Receive Antennas . It is n oted that the detection
becomes completely decoupled, that is, the detection of 𝐻𝐻1 is
independent of the detection of 𝐻𝐻 2 [55].
The Alamouti scheme can be applied for a system with two
transmit and M R receive antennas. The encoding and transmission for
this configuration is identical to the case of a single receive antenna. It is
assumed that 𝑟𝑟 1𝑖𝑖 and 𝑟𝑟 2𝑖𝑖 are the received sig nals at the ih
where h receive antenna
at the first and second symbol period , respectively [39] .
𝑟𝑟 1𝑖𝑖=�𝐸𝐸𝑠𝑠
2�ℎ𝑖𝑖,1𝐻𝐻1+ℎ𝑖𝑖,2𝐻𝐻2�+𝑛𝑛 1𝑖𝑖 (4.16)
𝑟𝑟 2𝑖𝑖=�𝐸𝐸𝑠𝑠
2�−ℎ𝑖𝑖,1𝐻𝐻2∗+ℎ𝑖𝑖,2𝐻𝐻1∗�+𝑛𝑛 2𝑖𝑖 (4.17)
i, j ( j = 1, 2 ; i = 1, 2, . . . , M R ) is the fading coefficient
for the path from transmit antenna j to receive antenna i , and 𝑛𝑛 1𝑖𝑖 and 𝑛𝑛 2𝑖𝑖
Chapter Four: MIMO Wireles s Communication 53
are the noise signals for receive antenna i at the first and second symbol
periods , respectively [ 39].
The receiver combiner generates two decision statistics based on
the linear combination of the received signals. The decision statistics,
denoted by 𝐻𝐻 �1 and 𝐻𝐻�2, are given by [39,9]
𝐻𝐻�1=�ℎ𝑖𝑖,1∗𝑀𝑀𝑅𝑅
𝑖𝑖=1𝑟𝑟 1𝑖𝑖+ℎ𝑖𝑖,2�𝑟𝑟 2𝑖𝑖�∗ (4.18)
𝐻𝐻�2=�ℎ𝑖𝑖,2∗𝑀𝑀𝑅𝑅
𝑖𝑖=1𝑟𝑟 1𝑖𝑖−ℎ𝑖𝑖,1�𝑟𝑟 2𝑖𝑖�∗ (4.19)
4.10 Channel Capacity
As known, the channel capacity is defined as the maximum
possible transmission rate such that the probability of error is arbitrary
small [ 28,47]. In 1948, the mathematical foundations of information
transmission were established by Shannon. In his work, he demonstrated that, by proper encoding of the information, errors induced by a noisy channel can be reduced to any desired level without sacrificing the rate of information transfer. In case of , Additive White Gaussian Noise
(AWGN) channel, he derived the most famous formula of channel
capacity, which is given by [ 45,7,33].
𝐶𝐶=𝐵𝐵
𝑊𝑊log 2�1+𝐸𝐸𝑠𝑠
𝑁𝑁𝑜𝑜� (4.20)
where C is the channel capacity in bits per second [bit/s], BW is the
channel bandwidth in Hertz [Hz], Es is the total transmitted energy , and
No is the noise power spectral density, which equivalent to the total noise
power divided by the noise equivalent bandwidth (i.e, N o=N/BW). In
Chapter Four: MIMO Wireles s Communication 54
addition to white Gaussian noise, the mobile wireless channels are under
other impairments (i.e., channel fading) as mentioned in chapter two,
which reduces the channel capacity significantly . Thus, channel capacity
becomes as follows [33,44]
𝐶𝐶=𝐵𝐵𝑊𝑊log 2�1+𝐸𝐸𝑠𝑠
𝑁𝑁𝑜𝑜|ℎ|2� (4.21)
where |ℎ|2 is the average channel fading gain. For deep fading
conditions, the channel capacity degrades significantly. The capacity in
Eq. (4. 21) depends on Channel State Information (CSI) which is defined
by whether the value of instantaneous channel gain h is known to the
transmitter and receiver or not. Channel State Information (CSI) at
transmitter plays an important role to maximize the chann el capacity in
MISO and MIMO systems, but it is difficult to be obtained. However, channel state information at receiver can be obtained through the transmission of a training sequence [ 33]. Throughout this section , CSI is
assumed to be known to the receiv er. On the other hand, the transmitter
CSI is studied for two cases (i.e. known and un known CSI) .
In th e next section s, channel capacity of Rayleigh fading channels
for various system architectures such as SISO, SIMO, MISO and MIMO is studied. Then, the analytical model that analyzes the behavior of these systems over fl at fading channel is presented.
4.11 SISO Channel Capacity
In Single -Input Single -Output (SISO) systems , the normalized
Shannon capacity formula per unit bandwidth (i.e., BW =1Hz) of such
system s is given by [ 29,42,44].
𝐶𝐶=log 2�1+𝐸𝐸𝑠𝑠
𝑁𝑁𝑜𝑜|ℎ|2� (4.22)
Chapter Four: MIMO Wireles s Communication 55
where C is the capacity in bit per second per Hertz [bit/sec/Hz].
The limitation of SISO systems is that the capacity increases very slowly
with the log of S NR and in general it is low. Moreover, fading can cause
large fluctuations in the signal power level. Only temporal and frequency domain processing are possible for SISO system. Spatial domain
processing cannot be applied for this system [29].
4.12 SIMO Channel Capacity
Single -Input Multiple -Output (SIMO) systems have a single
antenna at the transmitter and multiple antennas at the receiver. While SIMO system includes only a single transmit antenna, the Channel State Information (CSI) at the transmitter provides no capacity increase. Thus,
the capacity can be derived as follows [ 33,30]
𝐶𝐶=log 2𝑑𝑑𝑑𝑑𝑑𝑑�𝐼𝐼𝑀𝑀𝑅𝑅+𝐸𝐸𝑠𝑠
𝑁𝑁𝑜𝑜𝐻𝐻𝐻𝐻𝐻𝐻�
=log 2�1+𝐸𝐸𝑠𝑠
𝑁𝑁𝑜𝑜�|ℎ𝑖𝑖|2𝑀𝑀𝑅𝑅
𝑖𝑖=1� (4.23)
where, 𝐻𝐻𝐻𝐻𝐻𝐻=∑ |ℎ𝑖𝑖|2 𝑀𝑀𝑅𝑅
𝑖𝑖=1 , which is the summation of channel
gains for all receive antennas [ 30,28]. If the channel matrix elements are
equal and normalized as |ℎ1|2=|ℎ2|2=⋯ |ℎ𝑀𝑀𝑅𝑅|2=1, then channel
capacity becomes [28]
𝐶𝐶=log 2𝑑𝑑𝑑𝑑𝑑𝑑�1+𝑀𝑀𝑅𝑅𝐸𝐸𝑠𝑠
𝑁𝑁𝑜𝑜� (4.24)
Chapter Four: MIMO Wireles s Communication 56
Therefore, by using multiple receive antennas, the system can
achieves a capacity increases of MR
relative to the SISO case. this
increment of SNR is known as array gain [ 33,28].
4.13 MISO Channel Capacity
Multiple -Input Single -Output (MISO) systems have multiple
antennas at the transmitter and single antenna at the receiver. When the
transmitter does not have the CSI, the transmission power is equally
divided among all the transmit antennas ( MT
) [33]. Hence, the capacity
is give n by [ 33,30 ]
𝐶𝐶=log 2�1+𝐸𝐸𝑠𝑠
𝑀𝑀𝑇𝑇𝑁𝑁𝑜𝑜��ℎ𝑖𝑖�2𝑀𝑀𝑇𝑇
𝑖𝑖=1� (4.25)
where ∑�ℎ𝑖𝑖�2 𝑀𝑀𝑇𝑇
𝑖𝑖=1 is the summation of channel gains for all transmit
antennas. In Eq. (4. 25), the power is equally divided among MT
transmit
antennas, if the channel coefficients are equal and normalized as
∑�ℎ𝑖𝑖�2 𝑀𝑀𝑇𝑇
𝑖𝑖=1=𝑀𝑀𝑇𝑇, then the maximum value of MISO capacity approaches
the ideal AWGN channel with single antenna at both the transmitter and
receiver (SISO system) [ 33,28].
It is important to note here there is no array gain in transmit
diversity . Unlike the receive diversity case (SIMO system) where the
total received SNR is increased due to array gain [ 30]. However, when
Chapter Four: MIMO Wireles s Communication 57
the CSI is known to the transmitter , the capacity of MISO system
becomes [ 29,39]
𝐶𝐶=log 2�1+𝐸𝐸𝑠𝑠
𝑁𝑁𝑜𝑜��ℎ𝑖𝑖�2𝑀𝑀𝑇𝑇
𝑖𝑖=1� (4.26)
Therefore, the MISO capacity equals the SIMO capacity when the
CSI is known at transmitter [ 33].
4.14 MIMO Channel Capacity
With the advent of the Internet and rapid proliferation of
computational and communication devices, the demand for higher data
rates is ever growing. In many circumstances, the wireless medium is an effective means of delivering a high data rate at a cost lower than that of wire line techniques (such as cable modems and digital subscriber line
(DSL) modems) [16]. Limited bandwidth and power makes the use of
multiple antennas at both ends of the link (i.e. MIMO system)
indispensable in meeting the increasing dem and for data and it offers a
significant capacity gains over single antenna systems, or transmit/receive diversity systems [30]. In this section , detailed studies
and analysis of MIMO capacity is covered, with channel unknown to the
transmitter and with channel known to the t ransmitter.
4.14.1 Channel Unknown to the Transmitter
When there is no feedback in the system , and the channel is
known at the receiver but unknown at the transmitter. The transmitted
power is divided equally likely into M T transmit antennas [ 30,8], and the
MIMO channel capacity is given by [ 30,29].
Chapter Four: MIMO Wireles s Communication 58
𝐶𝐶=log 2𝑑𝑑𝑑𝑑𝑑𝑑�𝐼𝐼𝑀𝑀𝑅𝑅+𝐸𝐸𝑠𝑠
𝑀𝑀𝑇𝑇𝑁𝑁𝑜𝑜𝐻𝐻𝐻𝐻𝐻𝐻� (4.27)
The MIMO channel is usually interpreted as a set of parallel
eigen -channels, by using the eigenvalues of the MIMO channel matrix H
[44]. The matrix HHH with MR×M R
The eigen value decomposition (EVD) of such a matrix is given
by QΛQ dimensions is usually diagonalized
using eigen value decomposition (EVD) to find its eigenvalues [ 44,28].
H (i.e., HHH= QΛQH
Where Q is a matrix of eigenvectors of M). Based on this fact, Eq. (4.27) can be
rewritten as [ 8]
𝐶𝐶=log 2𝑑𝑑𝑑𝑑𝑑𝑑�𝐼𝐼𝑀𝑀𝑅𝑅+𝐸𝐸𝑠𝑠
𝑀𝑀𝑇𝑇𝑁𝑁𝑜𝑜𝑄𝑄Λ𝑄𝑄𝐻𝐻� (4.28)
R×M R dimensions
satisfying, QQH=QHQ=I MR, while Λ=diag{λ1, λ2,…, λMR}, is a diagonal
matrix with a non -negative square roots of the eigenvalues. These
eigenvalues are ordered so that , λi ≥ λi+1
By u sing the identity property, det(I + AB) = det(I + BA) , and the
property of eigenvectors , QQ [8,28,44].
H =IMR
where r is the rank of the channel , which implies that, r ≤ min
(M, Eq. (4.28) can be reduced to [2,28] :
𝐶𝐶=log 2𝑑𝑑𝑑𝑑𝑑𝑑�𝐼𝐼𝑀𝑀𝑅𝑅+𝐸𝐸𝑠𝑠
𝑀𝑀𝑇𝑇𝑁𝑁𝑜𝑜Λ�
=�𝑙𝑙𝑜𝑜𝑙𝑙 2�1+𝐸𝐸𝑠𝑠
𝑀𝑀𝑇𝑇𝑁𝑁𝑜𝑜 𝜆𝜆𝑖𝑖�𝑟𝑟
𝑖𝑖=1 (4.29)
R,MT) and 𝜆𝜆𝑖𝑖 (i = 1, 2, . . . , r) are the positive eigenvalues of HHH.
Eq. ( 4.29) expresses the capacity of the MIMO channel as a sum of the
capacities of r SISO channels as illustrated in Fig. (4. 4), each having a
power gain of 𝜆𝜆𝑖𝑖 (i = 1, 2, . . . , r) and transmit energy of Es/MT [28,8].
Chapter Four: MIMO Wireles s Communication 59
4.14.2 Channel Known to the Transmitter
If the channel is known at both transmitter side and receiver side,
then Singular Value Decomposition (SVD) can be used to transform the
MIMO channel into a set of parallel subchannels [ 61]. Hence, the MIMO
channel matrix H given in Eq. ( 4.2) can be written as [ 61,39]
𝐻𝐻=𝑈𝑈Σ𝑉𝑉𝐻𝐻 (4.30)
Where Σ is an MR×M T non-negative and diagonal matrix, U and
V are MR×MR, and MT×MT, unitary matrices, respectively. That is,
UUH=IMR, and VVH= IMT. The diagonal entries of Σ are the non-negative
square roots of the eigenvalues of matrix HHH. The eigenvalues on the
diagonal are positive numbers with a descending order , such that λ i ≥ λi+1
By multiplying the inverse of U and V at the receiver side and
transmitter side respectively, the channel with interferences can be
transformed into a set of independent singular value channels, as shown
[39,8] MR
•
•
•
•
•
•
1
2
r = min(M R,MT) MT RX TX
Fig. ( 4.4) Conversion of the MIMO channel into r SISO subchannels
Chapter Four: MIMO Wireles s Communication 60
in Fig. (4.5 ) [28], and the input -output relationship given in Eq. ( 4.2)
changes to [ 61,59].
𝑦𝑦�=�𝐸𝐸𝑠𝑠
𝑀𝑀𝑇𝑇𝑈𝑈𝐻𝐻𝐻𝐻𝑉𝑉𝐻𝐻�+𝑈𝑈𝐻𝐻𝑛𝑛=�𝐸𝐸𝑠𝑠
𝑀𝑀𝑇𝑇∑𝐻𝐻�+𝑛𝑛� (4.31)
where 𝑦𝑦� is the transformed received signal vector of size 𝑟𝑟×
1 and 𝑛𝑛� is the transformed AWGN vector with size of 𝑟𝑟×1. The rank of
the channel H is r. Eq. (4. 31) shows that with the channel knowledge at
the transmitter, H can be explicitly decomposed into r parallel SISO
channels satisfying [ 58,28].
𝑦𝑦�𝑖𝑖=�𝐸𝐸𝑠𝑠
𝑀𝑀𝑇𝑇� 𝜆𝜆𝑖𝑖𝐻𝐻�𝑖𝑖+𝑛𝑛�𝑖𝑖 , 𝑖𝑖=1,2,…,𝑟𝑟 (4.32)
4.14.2.1 Water -Filling (WF) Method
When the channel parameters are known at the transmitter, the
capacity given by Eq. (4. 29) can be increased by assigning the
transmitted energy to various antennas according to the “ Water-Filling”
rule [ 39]. WF is an energy dis tribution strategy based on SVD , derived to n
𝑦𝑦� 𝑦𝑦 𝐻𝐻 𝐻𝐻� Receiver
V UH H Channel Transmitt er
Fig. (4. 5) Decomposition of H when the channel is known to the
transmitter and receiver.
Chapter Four: MIMO Wireles s Communication 61
provide the upper bound on data throughput across the MIMO channel
[61,53]. It allocat es more energy when the channel is in good condition
and less when the channel state gets worse [ 39]. By using this method,
the capacity of the system is given by [ 28,58]
𝐶𝐶=max
∑𝛾𝛾𝑖𝑖r
i=1�log 2�1+𝐸𝐸𝑠𝑠𝛾𝛾𝑖𝑖
𝑀𝑀𝑇𝑇𝑁𝑁𝑜𝑜 𝜆𝜆𝑖𝑖�𝑟𝑟
𝑖𝑖=1 (4.33)
where 𝛾𝛾𝑖𝑖(𝑖𝑖 = 1,2,…,𝑟𝑟) is the transmitted energy amount in the
ith
Using Lagrangian method , the optimal energy allocation policy,
𝛾𝛾𝑖𝑖𝑜𝑜𝑜𝑜𝑑𝑑 , satisfies [ 28,58].
𝛾𝛾𝑖𝑖𝑜𝑜𝑜𝑜𝑑𝑑=�𝜇𝜇−𝑀𝑀𝑇𝑇𝑁𝑁𝑜𝑜
𝐸𝐸𝑠𝑠𝜆𝜆𝑖𝑖�+
,𝑖𝑖=1,2,…,𝑟𝑟 (4.35) subchannel such that [ 28].
�𝛾𝛾𝑖𝑖=𝑀𝑀𝑇𝑇𝑟𝑟
𝑖𝑖=1 (4.34)
where 𝜇𝜇 is chosen so that ∑𝛾𝛾𝑖𝑖𝑜𝑜𝑜𝑜𝑑𝑑=𝑀𝑀𝑇𝑇r
i=1 and (𝐻𝐻)+ implies
[28,58]
(𝐻𝐻)+=�𝐻𝐻 𝑖𝑖𝑖𝑖 𝐻𝐻≥0
0 𝑖𝑖𝑖𝑖 𝐻𝐻<0 (4.36)
The constant 𝜇𝜇 given in Eq. (4.35) is calculated by [28]
𝜇𝜇=𝑀𝑀𝑇𝑇
𝑟𝑟�1+𝑁𝑁𝑜𝑜
𝐸𝐸𝑠𝑠�1
𝜆𝜆𝑖𝑖𝑟𝑟
𝑖𝑖=1� (4.37)
Chapter Four: MIMO Wireles s Communication 62
Some remarks on W ater-Filling (WF) method [ 28,61]:
1. 𝜇𝜇 is often referred to as water level. It decides the power
distribution to all subchannels [ 61].
2. If the power allotted to the channel with the lowest gain is
negative (i.e. λi
3. since this algorithm only concentrates on good -quality channels
and rejects the bad ones during each channel realization, it is to be
expected that this method yields a capacity that is equal or better than the situatio n when the channel is unknown to the transmitter
[28]. < 0), this channel is discarded by setting 𝛾𝛾
𝑖𝑖𝑜𝑜𝑜𝑜𝑑𝑑=0.
The optimal power allocation strategy, therefore, allocates power to those spatial subchannels that are non -negative. Fig. (4. 6)
illustrates the WF algorithm [28].
𝑀𝑀𝑇𝑇𝑁𝑁𝑜𝑜
𝐸𝐸𝑀𝑀 𝜆𝜆1
𝑀𝑀𝑇𝑇𝑁𝑁𝑜𝑜
𝐸𝐸𝑀𝑀 𝜆𝜆2
𝑀𝑀𝑇𝑇𝑁𝑁𝑜𝑜
𝐸𝐸𝑀𝑀 𝜆𝜆𝑖𝑖−1
𝛾𝛾3𝑜𝑜𝑜𝑜𝑑𝑑
𝛾𝛾1𝑜𝑜𝑜𝑜𝑑𝑑
𝛾𝛾2𝑜𝑜𝑜𝑜𝑑𝑑
𝑀𝑀𝑇𝑇𝑁𝑁𝑜𝑜
𝐸𝐸𝑀𝑀 𝜆𝜆𝑖𝑖
• • •
𝑀𝑀𝑇𝑇𝑁𝑁𝑜𝑜
𝐸𝐸𝑀𝑀 𝜆𝜆3
𝜇𝜇 Discarded
subchannels Used
subchannel
Fig. (4. 6) Principle of Water -Filling (WF) algorithm
Chapter Five: Simulation Results and Discussions 63
5.1 Introduction
In this chapter, a development of the improved Jakes model has
been designed. Then, the Bit Error Rate (BER ) performance by using
different receive and transmit diversity techniques have been simulated
and tested for SIMO and MISO systems, respectively. Furthermore, different diversity techniques based on MIMO system have also been
simulated and tested. All of these techniques are compared numerically and graphically with the BER performance of SISO system, in addition
to their comparison with each other , by using various numbers of
antennas. These techniques can be s ummarized as follows: –
i. For SIMO system:
1. Selection Combining (SC).
2. Equal Gain Combining (EGC).
3. Maximal Ratio Combining (MRC).
ii. For MISO system:
1. Maximal Ratio Transmission (MRT).
2. Space -Time Block Codes (STBC) Transmit Diversity.
iii. For MIMO system:
1. Zero-Forcing (ZF).
2. Minimum Mean -Squared Error (MMSE).
3. Space -Time Block Coding (STBC).
Chapter Five: Simulation Results and Discussions 64
In addition to that , the capacity enhancement resulting from using
multiple antennas for SIMO, MISO, and MIMO systems are simulated in
different situations ( the case of channel knowledge or not) . Furthermore,
graphical with numerical compari son with SISO system is also
introduced .
All of the diversity techniques and capacity simulations mentioned
above are simulated and test ed by using the presented desig n of the
channel model in Rayleigh flat fading narrow -band channel .
5.2 Develop ed Design of the I mproved Sum-of-Sinusoids
(SOS) Channel Model
In chapter two, J akes and improved J akes models were discussed.
In this section, a description of the develop ed design of mobile channel
model is presented.
As discussed earlier, in an environment with no direct L ine-of-
Sight (LOS) between transmitter and receiver, multipath propagation
leading to Rayleigh distribution of the received signal envelope. Jakes
model have been widely used to simulate Rayleigh fading channels for
the last decades.
Despite its widespread acceptance, the Jakes model has some
important limitations. As a deterministic model, Jakes simulator is
unable to produce multiple channels with uncorrelated fading for
multiple antennas systems. Study of the simulator's statistical behavior also suggested that it is wide -sense non -stationary, which is due to the
fact that the simulated rays experiencing the same Doppler frequency
shift are correlated.
Chapter Five: Simulation Results and Discussions 65
To correct these problems, an improved S um-of-Sinusoids (SOS)
model i s proposed as discussed in chapter two. By introducing a
randomness to the path gain Cn, Doppler frequency 𝛼𝛼𝑛𝑛 and initial phase
ϕn, given in Eq. (2.19) and Eq. (2.20).
To evaluate the optimal performance of the multiple antennas
(SIMO, MISO, and MIMO) systems, multip le uncorrelated channels
must be generated. In this thesis, t he proposed design of the improved
Sum-of-Sinusoids (SOS) channel model introduce a randomness to the
number of arriving waves M, given in Eq. (2.19) and Eq. (2.20) , that is,
each subchannel in the multiple antennas systems depends on different
number of arriving waves M to ensure satisfying uncorrelation condition
between these subchannels. T he new number of arriving waves M is a
vector of M T×M R length with a lower and upper limit range s given by N 1
and N2
In addition , to generate SISO channel, the new simulator can also
be used directly to generate multiple uncorrelated fading channels for SIMO , MISO, and MIMO system s. Fig. (5.1) representing the program
flowchart of the developed design channel model. The parameters which
have been used in the simulation of the introduced channel model are shown in Table (5.1) . It is important here to mention that, all the
simulations of BER performance and capacity measurement s introduced
in this work w ere done with maximum velocity of mobile receiver set to
100 Km/hr and sampling frequency of f, respectively.
s
Fig. (5.2) shows a set of results for SISO channel response at a
mobile receiver , traveling with different speeds . From Fig. (5.2), it is
clear that the channel fading is increased with increasing mobile speed. = 10 kHz. Other measurements
depend on different values of these para meters, which will be stated for
each case.
Chapter Five: Simulation Results and Discussions 66
Fig. (5.3) represent s the simulated PDF of Fig. (5.2-c). The simulated
curve is seen to exhibit the expected Rayleigh distribution and it show s a
very good congruence (agreement) with the theoretical PDF curve .
parameter value
Carrier frequency f 900 MHz c
Sampling frequency f 10 KHz , 12 KHz s
No. of transmitted bits L 106 bit S
Modulation type BPSK
Lower limit number of arriving
waves N 140 related to each channel
Upper limit number of arriving
waves N280 related to each channel
Speed of mobile v 10, 40, 50, 80, 100 Km/hr
No. of transmit antennas M 1, 2 T
No. of receive antennas M 1, 2, 3, 4 , 10 R
Table (5.1) The developed design channel model parameters
Chapter Five: Simulation Results and Discussions 67
Fig. (5.1) F low chart of the developed design channel model j = j+1 Generate a random numbers of arriving waves vector 𝑁𝑁 for each
subchannel between two random integer numbers 𝑁𝑁1,𝑁𝑁2
𝑁𝑁 = randint(1, MR × MT ,[ N1 , N2]);
Initialize No. of paths counter j = 1
Calculate the inphase and quadrature components
of the kth channel in Eq. (2.19) and Eq. (2. 20)
j < M
Yes No
No k = k+1 Select M for each subchannel M = N(k)
Generate three random numbers between
𝜋𝜋 and −𝜋𝜋 for 𝜓𝜓𝑛𝑛,𝛼𝛼𝑛𝑛 and 𝜙𝜙 Initialize channel No. counter k = 1
k < MR × MT
Yes Set fc, fs
Set No. of transmitted bits LS
Set No. of transmit and receive
antennas MR and MT respectively
Reshape the generated channels in a form of
SISO, SIMO, MISO, or MIMO channel with a
specified dimensions by MR and MT antennas Calculate maximum Doppler frequency fd
End
Start
Chapter Five: Simulation Results and Discussions 68
(a)
(b)
(c)
Fig. (5.2) Signal level of mobile channel with fs = 10 kHz at
(a) speed 10 Km/hr (b) speed 4 0 Km/hr (c) speed 80 Km/hr
Chapter Five: Simulation Results and Discussions 69
5.3 Performance of SISO System
A SISO communication system provides the simplest description
of a communication link between one transmit antenna and one receive
antenna. This clearly implies that spatial diversity cannot be applied.
Fig. (5.4). represents the simulated BER of SISO system in a
Rayleigh fading channel with its theoretical result. The BER of such
systems have the worst performance among other systems, that depends
on the advantage of spatial diversity through the using of mul tiple
spatially separated antennas, These systems will be discussed and
simulated in the next sections.
Fig. (5.3) probability density function (PDF) of Rayleigh fading
channel with speed v = 80 Km/hr
Chapter Five: Simulation Results and Discussions 70
5.4 Performance of SIMO and MISO System s
In this section, three different receive diversity combining
techniques are tested and simulated for SIMO system, which are,
Selection Combining (SC), Equal Gain Combining (EGC), and Maximal Ratio Combining (MRC). For MISO system, Beamforing or Maximal Ratio Transmission (MRT) will be simulated, tested and compared with
the performance of Maximal Ratio Combining (MRC) for SIMO system.
5.4.1 Selection Combining (SC) Performance
The first test of this method is concerned with the variation of
signal level at the output of the selection diversity combiner with two receive antennas . The results will be compared graphically with single
receive antenna as a reference signal, this is shown in Fig. (5.5). The two
received signals have different deep fades, which occur at different
random times (uncorrelated signals). It can be seen that , the selection
diversity combiner selects the branch with the maximum instantaneous Fig. (5.4) BER for SISO system in Rayleigh fading channel
Chapter Five: Simulation Results and Discussions 71
SNR, and discard s the other branch at any instance of time . As a result ,
the deep fades can be a voided by using Selection Combining (SC)
technique . However, the selection diversity combiner has no array gain,
since it takes the advantage of single branch without exploiting the array
gain of the other branches. This is also clearly shown in Fig. (5.5).
The second test is the BER performance. Fig. (5.6) shows an SNR
gain over SISO system , at BER=10-5 by about 21.14 dB, 27.37 dB, and
30.66 dB , for MR
= 2, 3, and 4, respectively (i.e., 1×2, 1×3, and 1×4,
transmission cases, respectively). For comparison with the theoretical
results, the simulated 1×2 transmission case, shows a good agreeme nt
with its theoretical result. However, form simulation results, it can be
seen that, as the number of received antennas increases, the bi t error rate
decreases. The program flow chart of SC is shown in Fig. (5.7).
Fig. (5.5) Signal level of SC with two receive antennas
at v = 50 Km/hr and fs = 10KHz
Chapter Five: Simulation Results and Discussions 72
Fig. (5.7) SC flow chart Generate a random binary data x with length of LS
Modulate the generated binary data in BPSK modulation
Generate a SIMO channel using the developed
design channel model h = SIMO_Ch (𝑀𝑀𝑅𝑅,LS)
Passing the signal through channel 𝑦𝑦=ℎ𝑥𝑥
Set fc, fs, SNR
Set No. of received antenna 𝑀𝑀𝑅𝑅
Set No. of transmitted bits LS
Adding AWGN by the specified SNR
Initialize SNR counter i = 0
B A Start
Fig. (5.6) BER of SC with different number of receive antennas
Chapter Five: Simulation Results and Discussions 73
5.4.2 Equal Gain Combining (EGC) Performance
If the same signal s are received by using EGC , the signal level
variation at the output of the combiner will appear as shown in Fig. (5.8).
The received signals are co -phased (weighed equally) and added together
with equal gain (unity gain) in order to improve SNR at the output. Fig.
(5.8). clearly shows that this method can achieve a higher SNR gain than
Selection Combining (SC) diversity due to the array gain of EGC , which
result s in a better performance than selection combining diversity
technique.
The results of BER performance for M R =2, 3, and 4 are shown in
Fig. (5.9). From this figure, it can be seen that a gain of about 22.02 dB,
29.17 dB and 33.07 dB can be obtained for M R = 2, 3, and 4, Fig. (5.7) Continued Finding the power of the channels 𝑝𝑝=ℎ×ℎ∗
on all the received antennas
i = i +2
No Selecting the receiver which has the maximum power
Equalization, decoding the selected signal
Counting the errors
i < max SNR
Yes
BER calculation B A
End
Chapter Five: Simulation Results and Discussions 74
respectively, at BER=10-5
. As SC situation, the enhancement in
performance also increas es with increasing the number of the receive
antennas. The program flow chart of EGC is shown in Fig. (5.10).
Fig. (5.8) Signal level of EGC with two receive antennas at v = 50
Km/hr and fs = 10KHz
Fig. (5.9) BER of EGC with different number
of receive antennas
Chapter Five: Simulation Results and Discussions 75
Set fc, fs, SNR
Set No. of received antenna 𝑀𝑀𝑅𝑅
Set No. of transmitted bits LS
Generate a random binary data x with length of LS
Modulate the generated binary data in
BPSK modulation
Generate a SIMO channel using the developed
design channel model h = SIMO_Ch (𝑀𝑀𝑅𝑅,LS)
Initialize SNR counter i = 0
Passing the signal through channel 𝑦𝑦=ℎ𝑥𝑥
Adding AWGN by the specified SNR
Multiply each of the received signal with its
corresponding weight given in Eq. (3.16)
Make a summation for all the weighted signals
Decoding the resulted signal using hard decision decoding
Counting the errors
i < max SNR
Yes
No i = i +2
Fig. (5.10) EGC flow chart Start
End
BER calculation
Chapter Five: Simulation Results and Discussions 76
5.4.3 MRC and MRT Diversity Performance
As SC and EGC, the received signal level variation will be tested
at first. Figs.(5.11) shows the received signal level variation if M aximal
Ratio Combining (MRC) is used. This method achieves the maximum
signal to noise ratio at the receiver output by weighting each received
replica by the corresponding complex conjugate channel coefficient and then add ing the resulted signals to take the array gain advantages of all
the diversity branches . From figure, it is clearly seen that this method has
a higher SNR gain than SC and EGC, which makes this method to has
the best performance than other combining methods .
Fig. (5.12) presents the BER performance of MRC , which shows
an improvement over SISO system by about 22.02 dB, 30.14 dB and
34.023 dB for M
R
=2, 3and 4, respectively.
Fig. (5.11) Signal level of MRC with two receive antennas at
v = 50 Km/hr and fs = 10KHz
Chapter Five: Simulation Results and Discussions 77
The comparisons in BER performance between MRC and MRT is
shown in Fig. (5.13) for 2, 3, and 4 receive antennas. The results show a
very good agreement between the two methods in case of full CSI is
avaliable at the transnitter. The program flow chart of MRC is shown in
Fig. (5.14).
Fig. (5.13) BER performance comparison between MRC and MRT
Fig. (5.12) BER of MRC with different number of receive antennas
Chapter Five: Simulation Results and Discussions 78
Set fc, fs, SNR
Set No. of received antenna 𝑀𝑀𝑅𝑅
Set No. of transmitted bits LS
Generate a random binary data x with length of LS
Modulate the generated binary data in
BPSK modulation
Generate a SIMO channel using the developed
design channel model h =SIMO_Ch ( 𝑀𝑀𝑅𝑅,LS)
Initialize SNR counter i = 0
Passing the signal through channel 𝑦𝑦=ℎ𝑥𝑥
Adding AWGN by the specified SNR
Multiply each of the received signal with its complex
conjugate of the channel ℎ∗ given in Eq. (3.13)
Make a summation for all the weighted signals
decoding the resulted signal using hard decision decoding
Counting the errors
i < max SNR
Yes
No i = i +2
Fig. (5.14) MRC flow chart
Start
End
BER calculation
Chapter Five: Simulation Results and Discussions 79
5.4.4 Comparison Between Diversity Combining Techniques
Performance evaluations of the three receive diversity mentioned
above are presented in this section.
At first, comparisons of the signal level variation of the three
diversity techniques is depicted in Fig. (5.15) and Fig. (5.16) for MR
The performance of error rate for these techniques with M=4,
and 10, respectively . From these figure s, it can be seen that MRC method
has the best signal level gain, followed by EGC , which has a small
decreas e in signal level gain below MRC. On the other hand, SC
technique , has the lowest signal level gain as compared with the two
other diversity techniques. This difference increas es with increasing
number of received antennas, as shown in Fig. (5.16) . This happens
because SC technique depends on select ion of only one branch with the
highest instantaneous SNR , without exploiting the SNR gain introduced
from the other branches (i.e., the array gain) . However, these figures
clearly show that, an increasing in the number of antennas reduces the
number of deep fades of the received signal and also reduces the d uration
of fading. These are shared features for all of the diversity techniques
stated above.
R = 2
and 4 is shown in Fig. (5.17). At BER=10-5 with MR = 2, it is can be seen
that MRC provides the better performance by about 0.62 dB and 1.5 dB
as compared with EGC and SC, respectively , This is due to the MRC
method of combining, which depends on maximizing the SNR at the output of the combiner. Table ( 5.2) provides more details of comparison
between these methods with respect to SISO system at BER=10
-5
.
Chapter Five: Simulation Results and Discussions 80
Fig. (5.15) Signal level of SC, EGC and MRC with
four receive antennas at v = 50 Km/hr and fs = 10KHz
Fig. (5.16) Signal level of SC, EGC and MRC with ten receive
antennas at v = 50 Km/hr and fs = 10KHz
Chapter Five: Simulation Results and Discussions 81
For 1×2
transmission For 1×3
transmission For 1×4
transmission
SC 21.14 27.37 30.66
EGC 22.02 29.17 33.07
MRC 22.64 30.14 34.023
5.5 MIMO Channel
This section will focus on simulation measurements and models
aimed at realizing the MIMO channel. Fig. (5.18) shows the simulation
of 2×2 MIMO channel in a rich scattering environment between the
transmitter and receiver . The probability density function PDF is
depicted in Fig. (5.19) for each channel . It shows a very good
congruence between simulation and theoretical results. Method Improved SNR
in (dB)
Fig. (5.17) BER performance comparison of SC, EGC and
MRC with different number of receive antennas
Table (5.2) A comparison in the SNR improvement for SIMO
system over SISO system with different number of receive antennas
Chapter Five: Simulation Results and Discussions 82
Fig. (5.18) 2×2 MIMO channel at v = 80 Km/hr and fs = 12 kHz. Hij denotes
the channel gain between jth transmit antenna and ith receive antenna
Chapter Five: Simulation Results and Discussions 83
Fig. (5.19) The PDFs of 2 ×2 MIMO. Hij denotes the PDF of the channel
between jth transmit antenna and ith receive antenna
Chapter Five: Simulation Results and Discussions 84
5.6 MIMO Techniques Performance
In this section, ZF, MMSE, and STBC techniques will be tested
and simulated for MIMO system. In addition, these techniques will be
compared with each other, graphically and numerically in terms of BER
performance, by using different transmission types.
5.6.1 ZF Performance
Fig. (5.20) shows the comparative simulation results for ZF
techniques by using M T = 2 and M R = 2, 3, and 4. From Fig. (5.20), it
can be seen that the BER performance of ZF with MT = MR = 2 (2×2
transmission case) is the same as SISO system. In fact, ZF combiner
perfectly separates the interference of cochannel signals at the cost of
noise enhancement, hence, it has a poor BER performance. Furthermore, this result is related with the diversity order of ZF, that is given by M
R –
MT + 1. When MR = MT , the diversit y order is 1, which is the same
diversity order of SISO system. Hence, ZF reception method, does not
offer any diversity advantage over SISO system when , MT = MR
The BER performance improved when M.
R > M T. For example, at
BER=10-5 , there is 22.77 dB and 30.01dB improvement for MR = 3 and
4, respectively. It can also be noted that ZF method with M R > MT has
the same BER performance of MRC method . For example, ZF with M R
= 3, has the same BER result of MRC method with M R = 2 (i.e. diversity
order of 2). This similarity in BER performance because that, the two
methods depend on multiplying the rec eived signal with the complex
conjugate of the channel h*
, and the two methods have the same diversity
order.
Chapter Five: Simulation Results and Discussions 85
5.6.2 MMSE Performance
The simulated BER performance of MMSE method , is illustrated
in Fig. (5.21). The figure clearly shows that the BER performance for MT
= MR = 2 is better than SISO system by about 3.18 dB, a t BER=10-5.
This improvement in BER performance will be increased when MR >
MT, which is by about, 32.81 dB and 30.66 dB, for MR
From the results of Figs. (5.20) and (5.2 1), it can be seen that
MMSE algorithm has a superior performance over the ZF. The MMSE
receiver suppresses both the interference and noise components, whereas
the ZF receiver removes only the interference components. This implies that the mean square error between the transmitt ed symbols and the
estimated symbol at the receiver is minimized. Hence, MMSE is superior
to ZF in the presence of noise. The program flow chart of ZF and MMSE
methods is shown in Fig. (5.22) = 3 and 4 ,
respectively. Fig. (5.20) BER performance of ZF with MT = 2 and MR = 2, 3, and 4
Chapter Five: Simulation Results and Discussions 86
Fig. (5.21) BER performance of MMSE with MT = 2 and MR =2, 3, and 4
Set fc, fs
Set SNR vector
Set No. of transmitted bits LS
Set No. of transmit and receive antennas
MT, M R respectively
Generate a random binary data x with length of LS
Modulate the generated binary data in BPSK modulation
Group the Modulate d data into pair of two symbols 𝑥𝑥1 ,𝑥𝑥2
and send each of two symbols in one time slot
Generate a MIMO channel using the developed
design channel model H = MIMO_Ch( 𝑀𝑀𝑅𝑅 ,𝑀𝑀𝑇𝑇, LS)
Passing the signal through MIMO channel
Initialize SNR counter i = 0
A Start
Fig. (5.22) ZF and MMSE flow chart
Chapter Five: Simulation Results and Discussions 87
5.6.3 STBC Performance
In this section, simulation results pertaining to the BER
performance of STBC method are discussed. Furthermore , a comparison
in BER performance between STBC and MRC method will be presented
graphically and numerically . In the STBC simulation , it is assumed that
the receiver has perfect CSI and the channel remain s constant over two
time slots for transmitting two symbol periods .
For STBC method with M T =2, the received antennas can be M R =
1, 2, 3, and 4, this is because, STBC can be used for both MISO and
MIMO systems, as described earlier in chapter three. The BER performance of STBC is shown in Fig. (5.23). From figure, it can be seen Multiply the received signal with the inverse
weight of the channel specified by Eq. (4.3) for ZF
method or E q. (4.7) for MMSE method
A
No Counting the errors
i < max SNR
Yes
BER calculation i = i +2 Decoding the resulted signal
Fig. (5.22) Continued
Adding AWGN by the specified SNR to the received signal
End
Chapter Five: Simulation Results and Discussions 88
that there is 19.56 dB, 31.3 dB, 35.001 dB, and 37. 189 dB improvement
for MR = 1, 2, 3, and 4, respectively, at BER=10-5
Fig. (5.24) shows BER performance c omparisons between MRC
and STBC methods. It is clear from Fig. (5.24 ) that STBC for 2× 1
tranmission scheme has around 3dB poorer performance than MRC for
1×2 tranmission scheme , at BER=10.
-5. This is because the power from
the STBC scheme is divided equally between the two transmit antennas
(i.e., 3 dB less per antenna than the power from the MRC scheme, which has only one antenna). The 2× 2 STBC method , on the other hand, shows
a better performance than either of these curves because the order of diversity in this case is 4 ( M
T MR
=2×2 = 4). Extending this logic
further, it is to be expected that a 2 ×2 STBC scheme will be 3 dB poorer
than 1 ×4 MRC scheme, since both have the same diversity order, but
there is a 3 dB power loss at the transmitter of the Alamouti scheme due to equal division of power between the transmitting antennas. The
program flow chart for ST BC method is shown in Fig. (5.25)
Fig. (5.23) BER performance of STBC with MT = 2 and MR =1, 2, 3, and 4
Chapter Five: Simulation Results and Discussions 89
Fig. (5.24) BER performance comparison between STBC and
MRC methods
Start
A Set fc, fs
Set SNR vector
Set No. of transmitted bits LS
Set No. of transmit and receive antenna
MT, MR respectively
Generate a random binary data x with length of LS
Modulate the generated binary data in BPSK modulation
Group the Modulate d data into pair of two symbols
𝑥𝑥 𝑥𝑥
Code each symbol pair by Alamouti code given in Eq. (3.22) and Eq. ( 4.9)
Passing the coded signals through MIMO channel
Fig. (5.25) STBC flow chart
Generate a MIMO channel using the developed
design channel model H = MIMO_Ch( 𝑀𝑀𝑅𝑅 ,𝑀𝑀𝑇𝑇, LS)
Chapter Five: Simulation Results and Discussions 90
5.6.4 Performance Comparison for MIMO Techniques
Fig. (5.26 ) shows the BER performance comparison of ZF, MMSE
and STBC methods with M T =1, 2 and M R
From Fig. (5.26), for all methods with M = 2 and 3.
T = 2 and MR = 2, it can
be seen that the ZF has the worst performance followed by MMSE and
STBC method , which has the better BER performance by about 28.12 dB
and 31.14 dB, than MMSE and ZF, respectively , at BER=10-5. The same
logical scinario can be extended for M R
This difference in performane is because the SM of ZF and
MMSE is depend on transmitting independent data streams from each of
the transmit antennas without coding , to achieve a maximum rate of
transmiision . The multiple transmitted data streams will interfere with = 3 receive antennas. Initialize SNR counter i = 0
Adding AWGN by the specified SNR to the received signal
Equalization, decoding the resulted signal
A
No Counting the errors
i < max SNR
Yes
BER calculation i = i +2
Fig. (5.25) Continued
End
Chapter Five: Simulation Results and Discussions 91
each other s at the receiver , which results in low BER pe rformance. On
the other hand, STBC method, exploit diversity, by sending a
redundancy of information bits across space and time to achieve a reliable transmission. However, due to the added redundancy bits, the effective bit rate of the channel is reduced . For more details, Table (5.3)
gives a numerical comparison for the improvement over SISO system,
between the three MIMO techniques mentioned above, at BER=10
-5
.
For 2×1
transmission For 2×2
transmission For 2×3
transmission For 2×4
transmission
ZF – 0.16 22.77 30.01
MMSE – 3.18 32.81 30.66
STBC 19.56 31.3 35.001 37.189 Improved SNR
in (dB)
Method Fig. (5.26) BER performance comparison of ZF, MMSE
and STBC methods for different transmission schemes
Table (5.3) A comparison in the SNR improvement over SISO
system using MIMO techni ques for different transmission schemes
Chapter Five: Simulation Results and Discussions 92
5.7 Channel Capacity
In this section, simulation results and tests of channel capacity for
SISO, SIMO, MISO, and MIMO systems will be discussed under various
assumptions with regards to the availability of CSI at the receiver and/or
the transmitter. In addition to that, it should be noted that the transmitted
signal bandwidth B W
The program of channel capacity for SISO, SIMO, MISO, and
MIMO systems has the same construction steps to be generated. Hence
these systems have a shared program flow chart , which is illustrated in
Fig. (5.27 ). is normalized to be 1Hz for all the abov e systems.
Fig. (5.27) SISO, SIMO, MISO, and MIMO
channel capacity flow chart
Generate either SISO, SIMO, MISO, or MIMO channel
using the developed design channel model
Initialize SNR counter i = 0
For each SNR, compute the capacity 𝐶𝐶 either for SISO, SIMO, MISO,
or MIMO channel using the suitable Eq. for the selected channel
i < max SNR
Yes
No
Plot the capacity curve i=i+2 Start
End
Set fc, fs
Set SNR vector
Set No. of transmitted bits LS
Set No. of transmit and receive antenna
MT, MR respectively
Chapter Five: Simulation Results and Discussions 93
5.7.1 Channel Capacity of SISO system
The channel capacity of SISO system versus SNR is illustrated in
Fig. (5.28). From Fig. (5.28), it can be seen that the limitation of SISO
system is that the capacity increases very slowly with the log of SNR and
in general it is low. The capacity of SISO s ystem at SNR = 18 dB is
about 5.245 bit/s/Hz. The SISO capacity curve will also be shown in the
next capacity figures for graphical comparison. It should be noted that
the capacity simulation results of all the above system will be
numerically compared with the other systems .
5.7.2 Channel Capacity of SIMO system
The addition of receive antennas yields a logarithmic increase in
capacity in SIMO channels , due to the array gain of the receive antennas .
However, knowledge of the channel at the transmitter for this system
provides no additional benefit. The channel capacity of SIMO system is
shown in Fig. (5.29 ) for MRFig. (5.28) SISO system capacity
= 2, 3 and 4. From Fig. (5.29), it can be seen
Chapter Five: Simulation Results and Discussions 94
that SIMO system has a channel capacit ies at SNR = 18 dB of about
6.572 bit/s/Hz, 7.3 bit/s/H z, and 7.822 bit/s/Hz for M R
= 2, 3, and 4,
respectively . The maximum capacity improvement for SIMO system
over SISO system was achieved by using 1×4 transmission, which is
about 2.577 bit/s/Hz at SNR = 18 dB .
5.7.3 Channel Capacity of MISO system
For MISO system, when CSI is unknown, the transmit power will
be equally divided between all the transmit antennas . This yields in a
very low capacity improvement over SISO system. If CSI is known to
the transmitter , MISO capacity channel will be improved . This is shown
in Fig. (5.30) .
From Fig. (5.30 ), it can be seen that, when the transmitter has no
CSI, MISO system achieves a capacity improvement over SISO system
at SNR = 18 dB by about 0.422 bit/s/Hz and 0.5 44 bit/s/Hz for M TFig. (5.29) SIMO channel capacity
= 2,
and 3, resp ectively . If CSI is available at the transmitter , these capacities
Chapter Five: Simulation Results and Discussions 95
can be farther improved over SISO system , and it will be about 1. 367
bit/s/Hz and 2. 072 bit/s/Hz for MT
= 2, and 3, respectively, when CSI is
available at the transmitter. Table (5.4) , presents a numerical results for
the achieved capacit ies by using different number s of transmit antennas
at SNR = 18 dB for both, known and unknown CSI.
For
unknown
CSI For
known
CSI
1×1 5.245 5.245
2×1 5.667 6.612
3×1 5.789 7.317
4×1 5.845 7.812 Transmission
type
Channel capacity
[bit/s/Hz ]
Fig. (5.30) MISO channel capacity
Table (5.4) Numerical results for the achieved capacity of
MISO system with differe nt numbers of transmit antennas
Chapter Five: Simulation Results and Discussions 96
5.7.4 SIMO and MISO Channel Capacity Comparison
The channel capacity comparison between SIMO and MISO
system for MT =2 and 4 MR
From Fig. (5.31), it can be seen that, when the transmitter has no
CSI, channel will not achieve a significant capacity improvement for
MISO system, Whereas , MISO channel capacity will be the same as
SIMO system, when CSI is available at the transmitter . However, these
syste ms have a s low logarithmic growth of capacity with increasing
number of antennas . = 2 and 4 is shown in Fig. (5.31).
5.7.5 MIMO Capacity with No CSI at the T ransmitter
By using multiple transmit and receive antennas, the channel
capacity can be much better than the earlier examined systems. This is
clearly shown in Fig. (5.32), which presents the MIMO channel capacity Fig. (5.31) SIMO and MISO channel capacity comparison
Chapter Five: Simulation Results and Discussions 97
for the case of unknown CSI at the transmitter. From Fig. (5.32), at SNR
= 18 dB, the MIMO channel capacities are about, 10.11 bit/s/Hz, 11.17
bit/s/Hz, 13.15 bit/s/Hz, and 19.63 bit/s/Hz for transmission schemes of 2×2, 4×2, 2×4, and 4×4 respectively. The maximum capacity improvement over SISO system is about 14.385 bit/s/Hz for 4×4
transmission, at SNR = 18 dB.
5.7.6 MIMO Capacity with CSI at the Transmitter ( Water –
Filling (WF) Method)
When CSI is available at the transmitter, the MIMO channel
capacity could be further increased by optimally allocating power to each
transmit antenna using Water -Filling (WF) principle. Fig. (5.33 ) shows
the program flow chart of WF Method. Fig. (5.32) MIMO channel capacity with
no CSI at the transmitter
Chapter Five: Simulation Results and Discussions 98
Compute the singular values of the MIMO channel
using singular value decomposition (SVD) method
Yes k = k+1 No Compute the power allocation constant 𝜇𝜇 specified in Eq. (4.37) Evaluate 𝑟𝑟=min [MT,MR]
Initialize SNR counter i = 0 Generate a MIMO channel using the developed design channel model
Compute the optimal power allocation constant 𝛾𝛾𝑜𝑜𝑝𝑝𝑜𝑜 for each
subchannel specified in Eq. (4.35)
Initialize k = 0
𝛾𝛾𝑘𝑘𝑜𝑜𝑝𝑝𝑜𝑜≤0
k <𝑟𝑟 Yes
No
Compute new optimal power allocation
𝛾𝛾𝑜𝑜𝑝𝑝𝑜𝑜 for positive values only by Eq. (4.35)
Calculate the capacity 𝐶𝐶 given in Eq. (4.33)
B A i=i+2 Start
Fig. (5.33) WF program flow chart
𝛾𝛾𝑘𝑘𝑜𝑜𝑝𝑝𝑜𝑜=0 Set fc, fs
Set SNR vector
Set No. of transmitted bits LS
Set No. of transmit and receive antenna
MT, MR respectively
Chapter Five: Simulation Results and Discussions 99
The comparison of MIMO system capacities for known and
unknown CSI at the transmitter is shown in Fig. (5.34), for 4×2, and 4×4
transmission cases. From Fig. (5.34), it can be seen that, there is a clear
difference in channel capacity between unknown and known CSI at the
transmitter for 4×2 transmission cases. The difference is decreased for 4×4 transmission cases. This is because that, for 4×2 transmission cases, the number of transmit antennas is more than the number of receive antennas (M
T = 2MR
), and h ence, the almost channel capacity will
depend on the transmitter, thus, the existence of CSI at the transmitter for
4×2 transmission will has an important role in increasing the MIMO
channel capacity and vice versa. For 4×4 transmission cases, the number of transmit antennas not exceeds the number of receive antennas and
hence, the MIMO channel capacity will not be of high dependence on the transmitter. For more details, Table (5.5) provides a numerical results comparison of MIMO channel capacities for unkn own and known CSI at
the transmitter , with different transmission cases . End
Fig. (5.33) Continued
A
i < max SNR
Yes B
No
Plot the capacity curve
Chapter Five: Simulation Results and Discussions 100
For
unknown
CSI For
known
CSI
1×1 5.245 5.245
2×2 10.11 10.14
2×3 11.18 12.08
2×4 13.15 13.2
4×2 11.17 13.13
4×4 19.63 19.95
Transmission
type
Channel capacity
[bit/s/Hz ]
Fig. (5.34) MIMO channel capacity comparison with
CSI (water filling) and without CSI at the transmitter
Table (5.5) Numerical results for the achieved capacity of MIMO
system with different numbers of transmit and receive antennas
Chapter Six: Conclusions and Suggestions for Future Wor k 101
6.1 Conclusion s
The effect of Rayleigh fading channel humiliates the performance
of SISO system and causes a significantly low error rate performance. In
addition to that, SISO system has a very limited channel capacity. The presented work in this thesis shows the enhanc ement gained from using
multiple antenna systems, which is divided into two parts :
a. The first part was related to error rate performance improvement
obtained from diversity through using multiple antennas systems.
b. The second part was concerned with c hannel capacity
improvement gained from using multiple antennas systems.
6.1.1 Error R ate P erformance Improvement
The conclusions obtained from the results of using diversity in
SIMO, MISO, and MIMO systems are summarized below, each system include s its own types of diversity techniques .
i. SIMO Diversity Techniques:
1. MRC method gives the be st performance compared with the two
EGC and SC methods, because it maximizes the output SNR,
relying on the knowledge of the amplitude and phase coefficients
Chapter Six: Conclusions and Suggestions for Future Wor k 102
of all involved channels , hence, it is considered the optimal
combining techniques.
2. EGC method has lower performance than MRC, because it
relies on the phase coefficients of the channel only, hence,
EGC is a suboptimal combining techniques.
3. SC method has t he worst performance as compared with the
two above methods, because it simply select s the branch with
the highest SNR and discards all other branch es.
ii. MISO Diversity Techniques:
1. MRT method gives the same performance of MRC in SIMO
system, because the transmitter has a full knowledge of CSI, and
the two methods depend on the same working concept.
2. STBC with 2×1 transmission, has a lower error rate performance
than MRT with 2×1 transmission , since, STBC transmission
method does not depends on the transmitter CSI knowledge as
compared with MRT .
iii. MIMO Diversity Techniques:
1. STBC has the better error rate performance, since it provides a diversity gain through coding across space and time to achieve a
reliable transmission.
2. The ZF method gives the worst BER performance as compared
with MMSE and STBC methods . This is due to the noise
enhancement in the received signal .
3. MMSE has a lower error rate performance than STBC, but it outperforms ZF performance, since the MMSE receiver combiner
Chapter Six: Conclusions and Suggestions for Future Wor k 103
can minimize the overall error caused by noise and mutual
interference between the cochannel signals.
The common result between all these multiple antennas systems
metods is that, the error rate performance is improved, when the number
of the transmit and/or receive antennas is increased.
6.1.2 C hannel C apacity I mprovement
The following conc lusions have been obtained from channel
capacity results of multiple antennas systems :
1. SIMO system provides a slight channel capacity enhancement
over SISO system, and its increases with the number of receive antennas. Furthermore, Since CSI is often easy to obtain at the
receiver, SIMO system usually has a higher channel capacity t han
MISO system.
2. MISO system has lower channel capacity than SIMO system ,
when the transmitter has no CSI, which is not easy to obtain as in
SIMO system, because it require s a feedback from the receiver to
inform the transmitter. If the transmitter has a full CSI, MISO
system has the same channel capacity of SIMO system.
3. MIMO s ystem has best channel capacity enhancement. Its
capacity increases linearly with increasing number of transmit and receive antennas. The MIMO capacity can bec ome optimal, if the
transmitter has a full CSI knowledge. In this case, Water-Filling
(WF) theorem is used to allocate the desired power in each
subchannel.
Chapter Six: Conclusions and Suggestions for Future Wor k 104
6.2 Suggestions for Future Work
For future work, there are few possible extensions to the presented
work, which are listed below:
1. MIMO channel models used in this work assume a flat fading
environment. However, in mobile channel, the signals usually
undergo frequency selective fading and various multipath
components can be resolved. It would be useful to extend the analysis on MIMO models in c hapter five to account the frequency
selective fading.
2. All diversity techniques analysis in this thesis has been restricted
to uncorrelated fading. These techniques can be studied in
correlated fading by using the presented channel model design.
3. Extending Water-Filling (WF) principle to error rate calculations
in MIMO system.
4. The MIMO -OFDM system is a promising technique in high data
rate wireless communications and t here are many issues for
MIMO -OFDM systems that need to be investigated.
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