performance analysis of MUSIC and ESPRIT DOA estimation used in adaptive array smart antenna.

T. B. Lavate, V. K. Kokate & A. M. Sapkal
International Journal of Computer Netwoks (IJCN), Volume(2):Issue(3) 152
Performance Analysis of MUSIC and ESPRIT DOA Estimation
Algorithms for Adaptive Array Smart Antenna in Mobile
Communication
T.B.LAVATE lavate.tb@rediffmail.com
Department of E&T/C,College of Engineering Pune,
Pune University
Pune-411005, India
Prof. V. K. Kokate vkkokateetc@gmail.com
Department of E&T/C,
IndiraCollege of Engineering and management Pune.
Pune University
Pune, 411017,India.
Prof. Dr. A.M. Sapkal ams.extc@coep.ac.in
Department of E&T/C,College of Engineering Pune,
Pune University
Pune-411005, India
Abstract
Adaptive array smart antenna involves the array processing to manipulate the
signals induced on various antenna elements in such way that the main beam
directing towards the desired signal and forming the nulls towards the interferers.
Such smart antennas are widely used in wireless mobile communications as they
can increase the channel capacity and coverage range. In adaptive array smart
antenna, to locate the desired signal, various direction of arrival (DOA) estimation
algorithms are used. This paper investigates and compares MUSIC and ESPRIT,
DOA estimation algorithms which are widely used in the design of smart antenna
system. MUSIC and ESPRIT algorithms provide high angular resolution and
hence they are explored much in detail by varying various parameters of smart
antenna system .However simulation in this paper shows that MUSIC algorithm
is highly accurate and stable and provides high angular resolution compared to
ESPRIT and hence MUSIC algorithm can be widely used in mobile
communication to estimate the DOA of the arriving signals.
Keywords: MUSIC, ESPRIT, Smart antenna, DOA.
1. INTRODUCTION
One of the most promising techniques for increasing the capacity in 3G cellular is the adaptive
array smart antenna. The smart antenna technology is based on antenna arrays where the
radiation pattern is altered by adjusting the amplitude and relative phase on the different
elements. If several transmitters are operating simultaneously, each source creates many
multipath components at the receiver and hence receive array must be able to estimate the
angles of arrival in order to decipher which emitters are present and what are their angular

locations. This information in turn can be used by the smart antenna to eliminate or combine
signals for greater fidelity or suppress interferers to improve the capacity of cellular mobile
communication . The various DOA estimation algorithms are Bartlett, Capon, Min-norm, MUSIC
and ESPRIT. But MUSIC and ESPRIT algorithms are high resolution and accurate methods
which are widely used in the design of smart antennas and hence their performance is evaluated
in following sections. With use of MUSIC algorithms smart antennas add a new possibility of user
separation by space through space division multiple access (SDMA).
2. DOA ESTIMATION ALGORITHMS
The purpose of DOA estimation is to use the data received by the array to estimate the direction
of arrival of the signal. As shown in Fig. 1, the results of DOA estimation are then used by the
array to design the adaptive beam former in such way as to maximize the power radiated towards
the users and to suppress the interference. In short the successful design of adaptive array
smart antenna depends highly on the performance of DOA estimation algorithm. In the design of
adaptive array smart antenna for mobile communication the performance of DOA estimation
algorithm depends on many parameters such as number of mobile users and their space
distribution , the number of array elements and their spacing, the number of signal samples and
SNR. Number of DOA estimation algorithms have been developed and categorized into two
methods viz. conventional and subspace methods. Conventional methods also called classical
methods which first compute a spatial spectrum and then estimate DOAs by local maxima of the
spectrum. Methods that fall under this class are Bartlett, Capon methods. But these methods
suffer from lack of angular resolution. For this reason high angular resolution subspace methods
such as MUSIC and ESPRIT algorithms are most used.
2.1 Music Algorithm
MUSIC is an acronym which stands for Multiple Signal classification. It is high resolution
technique based on exploiting the eigenstructure of input covariance matrix. MUSIC makes
assumption that the noise in each channel is uncorrelated making correlation matrix diagonal.
The incident signals are somewhat correlated creating non diagonal signal correlation matrix.
ω1
ω2
ωM
Beamformer
Source
Estimation
Processor
∑ Mobilelocation
data
DOA Estimation
Algorithms
eg; Music, ESPRIT
X1(k)
X2(k)
XM(k)
Ѳ1
Ѳ2
ѲD
M signal ports
FIGURE 1: M element antenna array with D arriving signals.
If the number of signals impinging on M element array is D, the number of signal eigenvalues
and eigenvectors is D and number of noise eigenvalues and eigenvectors is M-D. The array
correlation matrix with uncorrelated noise and equal variances is then given by
Rxx = A*Rss*AH
+σn
2
*I (1)
where A= [a(θ1) a(θ2) a(θ3) --- a(θD)] is M x D array steering matrix

Rss=[s1(k) s2(k) s3(k) ---- sD(k)]
T
is D x D source correlation matrix
Rxx has D eigenvectors associated with signals and M – D eigenvectors associated with the
noise. We can then construct the M x (M-D) subspace spanned by the noise eigenvectors such
that
VN =[v1 v2 v3 ------- vM-D] (2)
The noise subspace eigenvectors are orthogonal to array steering vectors at the angles of
arrivals θ1, θ2, θ3, θD and the MUSIC Pseudospectrum is given as
P MUSIC(θ) = 1/abs((a(θ)H
*VN *VN
H*
a(θ)) (3)
However when signal sources are coherent or noise variances vary the resolution of MUSIC
diminishes. To overcome this we must collect several time samples of received signal plus
noise, assume ergodicity and estimate the correlation matrices via time averaging as
1 K
Rxx = ∑x(k)*x(k)
H
(4)
K k=1
and
Rxx = A*Rss*AH
+ A*Rsn + Rns *AH
+ Rnn (5)
The MUSIC Pseudospectrum using equation (3) with time averages now provides high angular
resolution for coherent signals.
2.2 ESPRIT Algorithm
ESPRIT stands for Estimation of Signal Parameters via Rotational Invariance Techniques which
is another subspace based DOA estimation algorithm. It does not involve an exhaustive search
through all possible steering vectors to estimate DOA and dramatically reduces the computational
and storage requirements compared to MUSIC. The goal of the ESPRIT technique is to exploit
the rotational invariance in the signal subspace which is created by two arrays with a translational
invariance structure. ESPRIT assumes that there are D < M narrowband sources centered at the
centre frequency f0. ESPRIT further assumes multiple identical arrays called doublets and these
arrays are displaced translationally but not rotationally. Fig. 2 shows four element linear array
which is composed of two doublets.
d
y
x
Ar ray-1
Ar ray-2
Ѳ1
Ѳ2
ѲD
S2(k)
FIGURE 2: Four element linear array with two doublets.
The two subarrays , array-1 and array-2 are displaced by distance ‘d’. The signals induced on
each of the arrays are given by

x1(k) = A1*s(k) + n1(k)
and
x2(k) = A1*Λ*s(k) + n2(k)
where Λ = diag{ejkdsin(θ1)
ejkdsin(θ2)
----- ejkdsin(θD)
}
= D x D diagonal unitary matrix with phase shifts between
doublets for each DOA.
Creating the signal subspace for the two subarrays results in two matrices V1 & V2. Since the
arrays are translationally related, the subspaces of eigenvectors are related by a unique
nonsingular transformation matrix ф such that
V1ф =V2
There must also exist a unique nonsingular transformation matrix T such that
V1 = AT and V2 =AΛT and finally we can derive
T ФT
-1
= Λ (6)
Thus the eigenvalues of ф must be equal to the diagonal elements of Λ such that
λ1 = e
jkdsin(θ1)
, λ2 = e
jkdsin(θ2)
----- λD = e
jkdsin(θD)
Once the eigenvalues of ф, λ1 ,λ2, ------ λD are calculated, we can estimate the angles of
arrivals as
θi =sin-1
(arg(λi)/kd) (7)
Clearly the ESPRIT eliminates the search procedure & produces the DOA estimation directly in
terms of the eigenvalues without much computational and storage requirements. This
eigenstructure method has shown excellent accuracy and resolution in many experimental and
theoretical studies.
3. SIMULATION RESULTS
The MUSIC & ESPRIT methods of DOA estimation are simulated using MATLAB. A uniform
linear array with M elements has been considered here.
3.1 Simulation results of MUSIC DOA estimation algorithm
-30 -20 -10 0 10 20 30 40
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
AOA Degrees
|P()|db
M=5
M=11
M=5
M=11
FIGURE 3: MUSIC spectrum for DOA= -5, 10, 25 degrees

-30 -20 -10 0 10 20 30 40
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
AOA Degrees
|P()|db K=10
K=100
K=10
K=100
FIGURE 4: MUSIC spectrum for varying number of snapshots
SNR (dB) MUSIC (θ) ESPRIT(θ)
-20 21.66 -39.08
-19 24.00 23.47
0 24.66 26.02
9 25.00 25.67
20 25.00 25.21
21 25.00 24.99
TABLE 1: DOA Estimation by MUSIC & ESPRIT for varying SNR.
(Input θ =25 deg, M=4, k=100)
Fig. 3 shows the MUSIC spectrum for uniform linear array with varying elements and SNR=20
dB, K=100 for direction of arrivals -5, 10, 25 degrees. Spacing between elements is assumed to
be 0.5λ.When number of elements in array is increased to 11 MUSIC spectrum takes the form of
sharper peaks in which angular resolution is improved. The number of signal snapshots used to
generate realistic signal model is a key factor in the realization of practical antennas . Fig.4 shows
the music spectrum obtained for snapshots equal to 10 and 1000. Increased snapshots leads to
sharper MUSIC spectrum peaks indicating more accurate detection and better resolution.
3.2 Simulation results of ESPRIT DOA estimation algorithm
Simulation of ESPRIT algorithm for linear uniform array with four elements is carried out by
varying different parameters of linear array.
TABLE 2: DOA Estimation Using ESPRIT For varying Angular Separation (M=4, SNR=20 dB, K=100)
Sr,no, θ Input (deg) θ ESPRIT (deg)
10 9.431
25 23.94
20 20.022
80 80.27

TABLE 3: DOA Estimation using ESPRIT for Varying Number of Snapshots K. (M=4, SNR=20 dB)
TABLE 4: DOA estimation using ESPRIT for varying number of signals.(M=4, SNR=20dB,K=100)
Table 2 illustrates that the percentage error in DOA detection using ESPRIT algorithm decreases
as angular separation between arriving signals increases. Table 3 illustrates that when number of
samples are increased the error becomes small. Table 4 illustrates how the ESPRIT algorithm
can successfully detects 2 incident signals on array of 4 elements and how it completely fails if
the number of incident signals increased to 4. Table 1 indicates DOA estimation by both MUSIC
and ESPRIT with respect to SNR. This table clearly indicates that MUSIC provides high
resolution and accurate detection of an angle of arrival than that of ESPRIT.
4. CONCLUSION
This paper presents the results of direction of arrival estimation using ESPRIT & MUSIC. These
two methods have greater resolution and accuracy and hence these are investigated much in
detail. The simulation results of both MUSIC and ESPRIT show that their performance improves
with more elements in the array, with large snapshots of signals and greater angular separation
between the signals. These improvements are seen in form of the sharper peaks in the MUSIC
and smaller errors in angle detection in the ESPRIT. However Table 1 shows that there are more
errors in DOA estimation by using ESPRIT compared to the MUSIC algorithm. Clearly MUSIC is
more stable and accurate and provides high resolution and this adds new possibility of user
separation through SDMA and can be widely used in the design of smart antenna system.
5. REFERENCES
1. L.C.Godara.“Application of antenna arrays to mobile communication II: Beamforming &
direction of arrival considerations”, Proceedings of IEEE, volume 85,issue 8,August 1997,
pages 1195-1245.
2. Lal. C. Godara.“Limitations and capabilities of directions of arrival estimation techniques
using an array of antennas: A Mobile communications perspective ,” proceedings of IEEE,
pp 327-333,1996.
K=10
θ Input (deg) θ ESPRIT (deg)
80 79.39
20 19.92
K=1000
80 80.04
20 20.00
No. of signals θ Input (deg) θ ESPRIT (deg)
20 20.08
2
40 39.96
10 24.46
30 32.34
50 -44.524
70 -18.82

3. Paulraj and T. Kailath.“Eigenstructure methods for direction of arrival estimation in the
presence of unknown noise field”, IEEE Transaction Acoustic, speech and signal processing,
Vol.Assp. 34, No.1, pp. 1302, Feb. 1986.
4. J. C. Liberti, T. S. Rappaport.“ Smart antenna for wireless communications,” Prentice Hall
India,1999.
5. Frank Gross .“ Smart antennas for wireless communication,” McGraw Hill. New York, 2005
6. T. S. Rappaport, “Wireless Communications: Principles and Practice”, 2005 ,Prentice Hall .
7. Ahmed EI Zooghby, “Smart Antenna Engineering”, Artech House, 2005
8. Preeti Gupta, Munish Rattan,”Performance Analysis of direction of arrival estimation
algorithms for smart antennas”, Proceedings of second national conference on wireless and
optical communication, pp. 60-64,Chandigarh,India,December-2008.

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