XXX -X-XXXX -XXXX -XXXXX.00 20XX I EEE Experimental Evaluation of AoA Algorithms using [626972]

XXX -X-XXXX -XXXX -X/XX/$XX.00 ©20XX I EEE Experimental Evaluation of AoA Algorithms using
NI USRP Software Defined Radios

Buta Rares
Departament of Communications
Technical University of Cluj -Napoca
Cluj-Napoca , Romania
[anonimizat] j.ro
Tudor Palade
Departament of Communications
Technical University of Cluj -Napoca
Cluj-Napoca, Romania
[anonimizat] Cristian Codau
Departament of Communications
Technical University of Cl uj-Napoca
Cluj-Napoca , Romania
[anonimizat]
Horia Hedesiu
National Instruments
Cluj-Napoca, Romania
[anonimizat]
Emanuel Puschita
Departament of Communications
Technical University of Cluj -Napoca
Cluj-Napoca
[anonimizat] Pastrav
Departament of Communications
Technical University of Cluj -Napoca
Cluj-Napoca, R omania
[anonimizat]
Bogdan Balauta
National Instruments
Cluj-Napoca, Romania
[anonimizat]
Abstract—In the process of designing an access point with
beamforming capabilities, the first step is to implement an
accurate direction -finding method which determines the
position of the targeted user and acts on the adaptive radiation
pattern. As such, this paper presents a feasible solution to
implement and test two Angle o f Arrival algorithms: MUSIC
and ESPRIT. The deployed testbed comprises five sub –
systems: the transmitter, the uniform linear array antenna, the
synchronization sub -system, the receiver and the data
processing unit. The two algorithms are evaluated in six
measurement scenarios employing linear arrays antennas of 4,
6 or 8 elements, with a target transmitter located at different
measurement points. The measurement results show that
MUSIC provides more accurate results when est imating the
Angle of Arrival .
Keywords —AoA, MUSIC, ESPRIT, LabView, USRP
I. INTRODUCTION
As new ways of maximizing the network spectral
efficiency are needed, an effective method of improving the
wireless transmissions performance is to estimate the
directio n of a transceiver and focus the transmission only in
that direction. As such, the digital signal processing
capability of smart antenna arrays may improve the
performance of the transmitter by means of spatial
processing techniques like beamforming.
The principle of beamforming is essentially to weight the
transmit signals in such a way that the transmitter exhibits a
constructive superposition in a predetermined direction. In
other words, the system exhibits an adaptive radiation pattern
depending on cer tain variables of the control algorithm [1].
However, before performing the spatial processing
techniques leading to beamforming, the location of the target
user (source signals) must be determined in a direction
finding process. This is achieved by means of smart antenna
arrays with the capability to estimate the Direction of Arrival
(DoA) of the incoming signals. Certainly, the effectiveness
of this method depends to a large extent on the performance
of the employed algorithm, which is inherently depende nt on
the size of the antenna array, the number of the impinging
signals, the spacing between the elements and the number of
samples used in the process [2]. The scope of this work is to deploy a feasible solution
capable to indicate the direction of an in coming target signal
expressed by its Angle of Arrival (AoA) .
The laboratory set -up consist s of the following
constructive sub -systems: (1) the transmitting sub -system (1
x NI USRP 2954R) , (2) the uniform linear antenna array sub –
system (4 to 8 array elem ents), (3) the synchronization sub-
system (1 x NI Octoclock CDA -2990 and 1 x NI USRP
N2900), (4) the receiving sub -system (4 x NI USRP 2954R) ,
and (5) the data processing unit sub -system (1 x NI PXIe
8880 host controller and 1 x NI CPS-8910 switch ).
For t he above described hardware infrastructure, two
AoA algorithms , were implemented and integrated in
LabVIEW Communications System Design Suite 2.0 ,
namely Multiple Signal Classification (MUSIC) and
Estimation of Signal Parameters via Rotational Invariance
(ESPRIT) .
The ability of the deployed solution to indicate the target
signal AoA was confirmed by a set of laboratory
experimental test scenarios. A total of six test scenarios were
set-up by varying the AoA algorithm (MUSIC and ESPRIT)
and the number of t he array’s elements (4, 6 or 8 antennas).
For each test scenario, the AoA values were measured for a
number of 35 predefined points (i.e., different angles and
distances of the target signal with respect to the reference
antenna array element ).
The work p resented in this paper was performed in the
context of the “Retrodirective antenna array for wireless
systems operating in the IEEE 802.11 and IEEE 802.16
frequency bands” (RDAntenna) research project aimed to
design a beamforming -capable access point that improves
the quality of transmission for target users .
The rest of the paper is organized as follows. Section 2
presents the mathematical approach for the implemented
AoA algorithms (MUSIC and ESPRIT ), Section 3 describes
the experimental set -up scenario s, and Section 4 indicate the
measurements methodology and presents the results. Finally,
Section 5 concludes the paper, emphasizing on the
capabilities of the envisaged deployed solution .

II. ANGLE OF ARIVAL ALGORITHMS
The algorithms for estimating AoA can be divided in two
categories. On the one hand, beam -scan algorithms form a
conventional beam which is scanned over the desired region
and plot the magnitude squared of the output. The Minimum
Variance Distortion -less Beamformer (MVDR) is such an
algorithm , in which the weights used in the beamformer are
adaptively calculated based on the environmental conditions,
to keep the desired signals undistorted while suppressing
interferences. On the other hand, subspace algorithms exploit
the orthogonality between the signal and noise subspaces.
MUSIC and ESPRIT are among the most efficient
subspace algorithms. MUSIC is based on the eigen value
decomposition of the received signal covariance matrix,
isolating the signal and noise subspaces. ESPRIT is based on
the rotational invariance property of the signal space for
directly estimating the AoA.
Several conclusions can be made based on the
simulations results indicated in the literature [3] – [6]:
• the performance of the AoA algorithm (i.e. the
accuracy in the estim ation of A oA) is improved in
case of an increased number of elements in the array,
a greater number of samples/snapshots taken , and an
inter-element distance closer to half the impinging
signal’s wavelength ;
• MUSIC algorithm is suitable for an array with fe w
elements in an environment with high SNR and
average number of snapshots ;
• ESPRIT is less dependent on the array size and
behaves better than the other two algorithms in an
environment with low SNR.
To the best of our knowledge, only in [7] the authors
deployed a hardware infrastructure for evaluating MUSIC
and ESPRIT algorithms using National Instruments (NI)
tools (i.e., LabView implementation environment and
USRP/PXI hardware platform s) as one presented in this
paper . The experimental results are shown for a single source
lying in the far -field region of the ULA at two different
arbitrary angles, i.e. 1000 and 700. In the first case, MUSIC
estimated an angle of 101.480 and ESPRIT estimated 99.960,
whereas for the second case MUSIC computed an angle of
67.330 and ESPRIT computed 71.370.
In this context, the laboratory testbed and measurements
results presented in this paper constituted an objective
evaluation method for the for aforementioned AoA
algorithms , by extending the number of test scenarios and
measurement points while varying the number of the array’s
elements.
Next , the mathematical approach of MUSIC and ESPRIT
algorithms is presented .
A. MUSIC Algorithm
For a uniform linear array (ULA) with K elements, and
M signals
arriving from di rections
, the received signal x(t) is given in (1):
(1)
where
(2)
is the array steering vector, with the propagation phase delay
for the ith direction displaced on the ith column , for the mth
antenna array element represented on the mth line, and n(t)
the gaussian noise. The autocorrelation matrix of the
received signal is

(3)
where
is the Hermitian matrix of A,
is the noise
variance,
is the identity matrix and
{} is the expe ctation
operation on the argument . The autocorrelation matrix of the
source signal is
(4)
However, it must be considered that it is a diagonal matrix
only if the signals are not correlated.
Rxx has N eigen values {
and N associated
eigenvectors, making a subspace E,
] (5)
Sorting the N eigen values from the smallest to the largest
ones, the E subspace can be divided in two subspaces,
(6)
where the first one is the noise subspace, composed of the
eigenvectors associated with the noise, and the latter is the
signal subspace composed of the eigenvectors associated
with the arriving signal. These two subspaces are orthogonal
at the angles of arrival of the M incident signals, with the
MUSIC Spectrum being calcula ted as
(7)
exhibiting sharp peaks at the angle of arrival.
B. ESPRIT Algorithm
The Total Least Squared (TLS) ESPRIT algorithm
involves splitting a K elements array in two subarrays, of the
same dimension, for instance an array from the first element
to the (K -1)th element, and another array from the second
element to the Kth element. The received signals at these
subarrays are expressed in (9)
and
(9)
where
is an M x M diagonal matrix called the rotation
operator

(10)
where
and (11)

The eigen decomposition of the autocorrelation matrices R11
and R22 will give two signal subspaces, E1 and E2,
respectively . These subspaces will compute a matrix C,

(12)
where EC is a 2Mx2M matrix obtained after C has been
eigenvalue decomposed such that λ1≥ λ 2≥ … ≥ λ 2M and
Λ=diag{ λ 1, λ2, …, λ2M}.
Partitioning E C into four MxM submatrices such that
(13)
the rotation operator is estimated as

Finally, fro m M eigenvalues of
, the AoA are estimated
as
(14)
III. EXPERIMENTAL SETUP
The experimental set up deployed to perform the AoA
measurements while implementing the MUSIC and ESPRIT
algorithms, consists of the following constructive sub –
systems: (1) the transmitting sub -system , (2) the uniform
linear antenna array (ULA) sub-system, (3) the
synchronization sub -system, (4) the receiving sub -system ,
and (5) the data processing unit sub -system . The conceptual
architectural design of the experimental t estbed is illustrated
in Figure 1.
Next , the hardware platform’s sub -systems are presented. A. The receiving sub -system
The receiving sub -system comprises 4 x NI USRP
2954Rs connected to the host computer (NI PXI 1083 ) via a
switch using 4 x PCIe cables as illustrated in Figure 1.

Fig. 1. The r eceiving sub -system : front and rear view of NI USPRs
connections
The NI USRP 2954R is a 10MHz to 6GHz tunable RF
transceiver. Each USRP device has a 2×2 MIMO RF
transceiver with a programmable DSP oriented Kintex 7
FPGA and integrates two RF modules (RF0 and RF1) . Each
TX1/RX1 input connect s an element of the antenna array.
These inputs are on the front of the USRP device , while on
the back REF In, PPS (Pulse Per Second ) In, PCIe cable , and
Power Supply input s are connected. An external reference
source can be fed to the REF In and PPS inputs. The
maximum instantaneous real -time bandwidth is of 160MHz,
the maximum sampling rate is of 200MS/s, the resolution of
the DAC is of 16 bits, and the noise figure ranges from 5 to
7dB.
RIO1
RF0:RX1
RF1:RX1
RIO2
RF0:RX1
RF1:RX1
RIO3
RF0:RX1
RF1:RX1
RIO4
RF0:RX1
RF1:RX1
OCTOCLOCK
CDA-2990NI2900
Ref. Signal
RF0:RX1HOST
COMPUTERSMA Cables
PPS InRef InRIO0 Target
RF0:TX1
RF1:TX1
CPS-8910 PCI x4 SwitchMXI Cable s
SMA Cables(4). Receiving
sub-system
(3). Synchronization
sub-system(2). ULA Antenna Array
sub-system
(1). Transmitting
sub-system(5). Data Processing Unit
sub-system

Fig. 2. Conceptual systems architecture deployed to indicate the direction of an incoming target signal expressed by its AoA

B. ULA antenna array sub-system
The ULA array comprises 8 x VERT2450 omni –
directional vertical 3 dBi antennas attached to each TX1/RX1
input of the USRPs. The antennas were mounted on a
support board in a linear configuration, with a spacing of half
of the wavelength of the operating frequency (2.415GHz) .
Figure 3 illustrates the antenna support board for the uniform
linear antenna array.

Fig. 3. The support board for the ULA antenna array sub-system
C. Synchronization sub-system
The operation of the hardware platform requires phase,
frequency, and time synchronization. Thus, it is utterly
important to implement synchronizatio n and calibration
methods so that the system to operate as a phase aligned
network.
The implemented solution uses a high accuracy external
module of time and frequency reference ( NI CDA -2990
Octoclock) that generates a signal for the frequency
synchroniza tion of the local oscillators (REF In) and a pulse
per second signal (PPS In) for the time synchronization of
AD convertors. Thus, each USRP device receives a 10MHz
REF In signal and a 1PPS In PPS signal, guaranteeing in this
way frequency and time synchro nization. However, it is not enough for ensuring a phase aligned
system. At each reconfiguration of the LO a new phase shift
is produced between the channels. For applications that have
phase aligned antenna arrays, where the phase difference is
critical, this problem must be eliminated for each new set of
collected data. An additional calibration step for eliminating
the induced phase shift at each reconfiguration command of
the USRP device would be inefficient. Therefore, the
solution uses an external RF synchronization signal
generated by an external USRP (N290 0) device. This signal
is delivered to each RX2 port of each USRP device and is
used for estimating the phase shift and later for phase
correction and establishing a synchronized system network.
The signal used for phase synchronisation is separated from
the one coming target by using a digital filter .
D. Receiving sub -system
An additional NI USRP 2954R device is used to generate
the target signal. It is connected to the same host computer
via a switch . A continuous sine wave with the tone of 10kHz
was transmitted, at the frequency of 2.415GHz. The antenna
used for transmitting was of the same with the ones used at
the receiving system, a VERT2450 omnidirectional vertical
antenna . It was connected to th e TX1/RX1 port of NI USRP .
E. Data processing unit sub-system
The entity responsible with the command of the system is
the host computer, namely the NI PXIe -8880 . It has a 16
core Intel (Xeon) CPU processor, at frequency of 2.3GHz,
running on Windows 7 and ha ving 24GB RAM installed. It
runs the LabVIEW Communication System Design Suite 2.0
software, in which the MUSIC algorithm is integrated, and
the ESPRIT algorithm is implemented [8]. All the 5 USRPs
used in the experiment are connected to the host computer
via the CPS -8910 switch and PCIe x4 cables. The USRP
used at the synchronization system is connected to the host
by a USB cable.

Fig. 4. Hardware platform deployed to indicate the direction of an incoming target signal expressed by its AoA

IV. MEASUREMENTS RESULTS
The evaluation scenarios of the implemented AoA
algorithms consider 35 positions of the target transmitter at
different angles (i.e., ∡0, ∡±15, ∡±30, and ∡±45) and
distances ( 0.5m, 1m, 1.5m, 2m and 2.5m ) with respect to the
reference antenna array element , as illustrated in Figure 5.

Tables I to VI indicate the measurement results obtained
for the six test scenarios using either MU SIC or ESPRIT
AoA algorithms and varying the number of ULA antenna
elements (N = 4, 6, and 8).
TABLE I. MEASUREMENT SCENARIO 1 (MUSIC AND N=4)
Source position with respect to the reference element
-45 -35 -15 0 15 30 45
Distance Measured Angle of Arrival []
0.5m -45.5 -30.5 -17.5 -1.5 10 24 45
1m -45.5 -31 -15 0.5 14 28.5 46
1.5m -44.5 -28 -12.5 0.5 14.5 29.5 43
2m -46 -30 -15.5 -0.5 12 30 43.5
2.5m -43.5 -32 15.5 0 12.5 26.5 42.5
The MUSIC measurement results in Table I indicate that
the most accu rate results are obtained for the source target
placed 1m away from the ULA reference element, with an
average deviation of 0.79 . The most erroneous results are
obtained for the distance of 0.5m, with an average deviation
of 2.29, and a maximum of 5 – 6 for the 15 and 30
reference angles . All in all, the average deviation for the first
test scenario is of 1.38.
TABLE II. MEASUREMENT SCENARIO 2, ESPRIT AND N=4
Source position with respect to the reference element
-45 -35 -15 0 15 30 45
Distance Meas ured Angle of Arrival [ ]
0.5m -42.5 -32.5 -15.5 -2.5 13.5 26.5 44
1m -47 -26 -10 0.5 10.5 32.5 44.5
1.5m -45 -32 -10.5 0.5 16.5 30.5 44.5
2m -42 -25.5 -14.5 1 16 32.5 43
2.5m -45 -26.5 -14.5 0.5 14.5 33 42 The ESPRIT measurement results in Table I I indicate
that the most accurate results are obtained for the source
target placed 1.5m away from the ULA reference element,
with an average deviation of 1.36 . The most erroneous
results are obtained for the distance of 1m, with an average
deviation of 2.7 1, and a maximum of 5 for the -15
reference angle. The average deviation for the second test
scenario is of 1. 83, exceeding the MUSIC estimation error
by 0.45.
TABLE III. MEASUREMENT SCENARIO 3, MUSIC AND N=6
Source position with respect to the reference elemen t
-45 -35 -15 0 15 30 45
Distance Measured Angle of Arrival [ ]
0.5m -44.5 -33.5 -22.5 -12.5 0.5 14.5 31.5
1m -44.5 -29.5 -16 -2 10 26 44
1.5m -45 -30 -17 -2 12.5 25.5 45
2m -44.5 -30 -15.5 0.5 15.5 29.5 44.5
2.5m -45 -31 -13.5 2.5 14.5 30 46.5
The MUSIC measurement results in Table I II indicate
that the most accurate results are obtained for the source
target placed 2m away from the ULA reference element,
with an average deviation of 0. 43. As in the previous cases,
the most erroneous resul ts are obtained closer to the ULA
receiver, with an average deviation of 9.64  at 0.5m away
from the reference antenna , indicating that the 0.5m
measurement line falls within the reactive near field of the 6-
element ULA receiver . On the 1m measurement line the
average deviation decreases to 2. Excluding the
inconclusive measurement results in the reactive near field,
the average deviation is of 1.25, 0.13 less than the results
for MUSIC and a 4-element array .
TABLE IV. MEASUREMENT SCENARIO 4, ESPRIT AND N =6
Sourc e position with respect to the reference element
-45 -35 -15 0 15 30 45
Distance Measured Angle of Arrival [ ]
0.5m -45 -37.5 -28 -15 -2 15.5 31.5
1m -45.5 -30 -20 -2 10 25.5 41.5
1.5m -43.5 -30.5 -15 -1 13 28 44.5
2m -43 -30.5 -15.5 0 14 30 46
2.5m -46 -28 -14.5 -0.5 14.5 30 45
The ESPRIT measurement results in Table IV show the
best estimation results on the 2.5m measurement line away
from the ULA with an average deviation of 0.64 . As in the
case of the 6-element MUSIC scenario , the measu rements on
the 0.5m line provide the most erroneous results, with an
average deviation of 11.5  because of the reactive near field .
However, 1m away from the array the average deviation
decreases to 2.93. Discarding the indeterminate results
obtained in t he reactive near field , the average deviation for
the 6-element ESPRIT implementation is of 1.34, which is
0.49 less than the average deviation of the 4 -element
ESPRIT, but 0.09  greater than the average deviation of the
6-element MUSIC implementation .

TABLE V. MEASUREMENT SCENARIO 5, MUSIC AND N =8
Source position with respect to the reference element
-45 -35 -15 0 15 30 45
Distance Measured Angle of Arrival [ ]
0.5m -47.5 -39.5 -34 -21 -7 7 31
1m -41.5 -27.5 -17.5 -2.5 11.5 26.5 47.5
1.5m -42.5 -28.5 -14.5 -0.5 13.5 28.5 45.5
2m -42.5 -27.5 -14.5 -1.5 13.5 30 46.5
2.5m -40.5 -28.5 -14.5 0 14.5 33 47.5
The MUSIC measurements in Table V show that once
again the line situated at 0.5 m from the array exhibits the
most errors, having an average deviatio n of 15.86 . Farther,
at 1m away from the array the average deviation decreases to
2.93. The best AoA estimation was obtained for the line
situated at 1.5m from the array, with an average deviation of
1.21. Discarding the measurements in the reactive nea r field
(at 0.5m), the average deviation becomes 1.84, which is
greater than the average deviations obtained for the MUSIC
algorithm on 4 and 6 elements.
TABLE VI. MEASUREMENTS SCENARIO 6, ESPRIT AND N =8
Source position with respect to the reference element
-45 -35 -15 0 15 30 45
Distance Measured Angle of Arrival [ ]
0.5m -42 -35 -21 -15 0 13 34
1m -41.5 -29.5 -18 -4 8.5 23 42.5
1.5m -40.5 -30.5 -18.5 0 12 27.5 45.5
2m -42.5 -27.5 -15.5 -0.5 15.5 30.5 42.5
2.5m -40.5 -29 -16.5 0 15.5 33.5 47
The ES PRIT measurement results in Table VI show the
most accurate results on the 2m measurement line away from
the array, with an average deviation of 1.36 . Once again,
the reactive near field of the 8 -element ULA generates
inconclusive results on the 0.5m measurement line, the
average deviation being 10.29. At 1m away from the array,
the deviation decreases to 3.86. Discarding the uncertain
results obtained in the reactive near field, the 8-element
ESPRIT algorithm exhibit s an average deviation of 2.29 ,
which is 0.95  greater than 6-element ESPRIT and 0.45 
greater than the 8-element MUSIC implementation .
V. CONCLUSIONS
In the context of the RDAntenna research project, this
paper evaluates the AoA estimation capabilities of the
MUSIC and ESPRIT algorithms imple mented in LabVIEW
Communications System Design Suite 2. The deployed
feasible testbed solution comprises the receiving, ULA,
synchronization, transmitting and data processing unit sub –
systems. The six measurement scenarios employing ULA antennas
of 4, 6 o r 8 elements provide useful insights regarding the
performance of the algorithms, showing the impact of the
source positioning and of the size of the antenna array .
The overall measurement results show that the AoA
estimation using MUSIC is more accurate t han the ESPRIT
implementation. For the MUSIC algorithm, the average
deviation ranges from 1.25  to 1.84 while the ESPRIT
average deviation ranges from 1.34  to 2.29.
The measurements show erroneous results close to the
ULA (0.5m) due to the operation in the reactive near field
which increases with the number of elements in the array.
For the 4 -element ULA, MUSIC exhibited an average
accuracy of 0.46  greater than ESPRIT. For 6 antennas, the
MUSIC implementation was 0.09  more accurate than
ESPRIT, while for 8 elements the average deviation of
ESPRIT exceeded MUSIC by 0.45 .
As future work, the setup will be tested in an anechoic
chamber to eliminate the propagation environment
impairments. Moreover, the evaluation of a circular array
setup configuration w ill be studied .
ACKNOWLEDGMENT
This paper was supported by a grant of the Ministry of
Innovation and Research, UEFISCDI, project number 6 Sol /
2017 within PNCDI III .
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