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ISSN: 2278 – 1323
International Journal of Advanced Research in Computer Engineering & Technology
Volume 1, Issue 4, June 2012

Comparative Study on Performance Analysis of
High Resolution Direction of Arrival Estimation
Algorithms
Chetan.L.Srinidhi, Dr.S.A.Hariprasad

Abstract-Array processing involves manipulation of The application of the array processing requires
signals induced on various antenna elements. Its either the knowledge of a reference signal or the
capabilities of steering nulls to reduce co channel direction of the desired signal source to achieve its
interferences and pointing independent beams toward desired objectives. There exists a range of schemes to
various mobiles, as well as its ability to provide estimates
of directions of radiating sources, make it attractive to a
estimate the direction of arrival with conflicting
mobile communications system designer. This paper demands of accuracy and processing power.
presents a performance evaluation of robust and high-
resolution direction-of-arrival (DOA) estimation The technique used for estimating directions of
algorithms such as MUSIC, ESPRIT and Q-MUSIC used arrival of signals using an antenna array has been
in the design of smart antenna systems. A comparative study of interest in recent years. Direction of arrival
study is carried out by evaluating the performance of methods has been widely studied in the literature and
these DOA algorithms for a set of input parameters that can be grouped into two categories. In the first
include the size of the sensor array, number and angular category, they are called as classical methods which
separation of incident signals from the mobile terminals, provides a representation of the sources field (power
as well as noise characteristics of the mobile and angular positions of the sources) by projecting
communication channel. MUSIC, ESPRIT and Q-
MUSIC algorithms provide high angular resolution
the model vector (directional vector) on the space of
among the other current DOA estimation techniques and observation without considering the determination of
hence they are explored in detail. The simulation results the number of sources. However, these conventional
shows that Q-MUSIC algorithm is highly accurate, stable methods do not get a good resolution. The second
and provides high angular resolution even for category is known as "parametric" or high-resolution
multidimensional complex data signals compared to method which requires prior knowledge of the
ESPRIT and MUSIC. number of uncorrelated sources before estimating
their characteristics (angular position, power). The
Index Terms - Direction of arrival (DOA), MUSIC, estimation problem is first solved by estimation
ESPRIT, Quaternion MUSIC.
methods of the number of sources. Then a high-
resolution method is applied to estimate the angular
1. INTRODUCTION position of these sources. These high-resolution
methods are known to be more robust than
The application of antenna array processing has conventional techniques.
been in extensive research in recent years for mobile
communication systems to cope up with the problem The origin of high-resolution methods was first
of limited channel bandwidth and to satisfy an ever proposed by Prony .This approach has been modified
growing demand that a large number of mobiles put by Pisarenko to estimate the sinusoids [1]. Both these
on the channel. methods are based on linear prediction technique
which characterizes the signal model. The modern
high-resolution method is based on the concept of
Manuscript received May, 2012. subspace, such as MUSIC developed by Schmidt [2],
Chetan.L.Srinidhi is with the Department of Electronics and
Communication Engineering, Visvesvaraya Technological
which requires a comprehensive search algorithm to
University Belgaum India, R.V.College of Engineering, Bangalore, determine the largest peaks for the estimated
India (srinidhipy@gmail.com). direction which is a computationally intensive
Dr.S.A.Hariprasad is with the Department of Electronics and process. MUSIC fails to resolve coherent sources,
Communication Engineering, Visvesvaraya Technological
University Belgaum India, R.V.College of Engineering, Bangalore,
sources with less number of snapshots and with low
India (hariprasad@rvce.edu.in). SNR conditions. To overcome these drawbacks Root-

All Rights Reserved © 2012 IJARCET 67

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MUSIC [3] was proposed which has better II. SIGNAL MODEL
probability of resolution than MUSIC and also
estimates coherent sources, but not applicable for all In this section, we present the general-rank signal
array geometry. Further ESPRIT [4] was developed models which frequently appear in array signal
which has identical performance as Root-MUSIC, but processing for communication. The following signal
is less computationally intensive than the other two model is applicable for MUSIC and ESPRIT, later
algorithms because of the selection of sub arrays. the polarization signal model for Q-MUSIC is
However in all these methods, the multidimensional
discussed in Section V. The conventional data model
collection of an EM vector sensor array is organized
into a long vector to enable matrix formulation. As a assumes that the signal impinging upon an array of
result, the relevant DOA estimators somehow destroy sensors to be narrow-band and emitted from a point
the vector nature of the incident signals carrying source in the far field region. The far field wave is
multidimensional information in space, time and incident at a DOA upon a uniform linear array
polarization. consisting of M identical antenna elements. Consider
K narrowband signals S1(t), S2(t), ..., SK(t) at
To overcome this drawback in array signal
processing, recently quaternion based algorithms frequency f0 arriving with directions qk (k = 1,.., K)
were proposed [5]. This quaternion model based and received by a linear array of M identical elements
algorithms use vector sensors for multidimensional (M > K) spaced by a distance d, in an additive white
complex data signals, for recovery of vector nature of Gaussian noise, Fig.1. These signals can be fully
incident signals and also for polarization estimates of correlated as in the case of multiple paths or not
EM waves. As vector sensors become more and more correlated as in the case of multiple users.
reliable, polarization has been added to estimation
process as an essential attribute to characterize Depending on the analytical representation, the
sources, in addition to their DOAs. In recent years, received signal in baseband can be written as:
MUSIC-like methods for polarized arrays are
presented in [6], [7] and ESPRIT techniques [8], [9],
[10] which can be used to estimate spatially coherent
sources, whereas MUSIC and ESPRIT is only for
(1)
uncorrelated sources. In this paper we discuss
quaternion based MUSIC algorithm for vector sensor
array which exploits spatial and polarization diversity Where is the
for multi-component complex data signals. It also reception signal or observation vector signal of (M-1)
results in accurate estimation of signal subspace on a dimension representing the measured complex
two component vector sensor array. The quaternion envelopes of K signals on each antenna.
MUSIC provides more robust resolution than the
other subspace method even at low SNR conditions
and also with less number of samples. Q-MUSIC
allows a more accurate estimation of the noise
subspace for a two component data, compensating for
the loss of performance due to the reduction of data
covariance matrix size.

This paper is organized as follows. Section II,
describes receiving signal model. Section III,
presents description of the MUSIC algorithm along
with the simulation results. Section IV, discusses the
ESPRIT algorithm. A short description of
quaternion’s and polarization model along with
QUATERNION MUSIC is introduced in Section V.
Section VI, presents the Comparison of MUSIC,
ESPRIT and Q-MUSIC. Finally Section VII, presents
the conclusion of the work.
Fig.1 Network of M antennas and receiver system
with K incident signals.


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Where N is the number of samples or observation
Symbol T denotes transpose. is the steering or vectors, and X is the N×K complex envelopes matrix
direction vector of the kth source defined at the central of K measured signals.
frequency: From the decomposition of this autocorrelation
matrix of observation vectors into orthogonal
subspaces, we will compare the performance of the
(2) two methods (MUSIC, ESPRIT) of high resolution
based on the concept of subspace.
With m=1... where III. MUSIC ALGORITHM
M is the geometric phase shift introduced at the
element m of the network and the kth signal A. Algorithm
depending on the angle of arrival. Sk is the complex
envelope of the analytic signal of the kth source MUSIC exploits the technique of eigenvectors
emitted and is the Gaussian vector of noise on the decomposition and eigenvalues of the covariance
network. It is noted that noises are stochastic matrix of the antenna array for estimating directions-
processes assumed to be stationary with zero mean. of-arrival of sources based on the properties of the
signal and noise subspaces. For this, the initial
Using matrix notation, the matrix of observations
can be expressed as:
(3) hypothesis is that the covariance matrix ܴ is not
Where:

singular. This assumption physically means that
sources are totally uncorrelated between them.
MUSIC algorithm assumes that signal and noise
A is a MxK matrix formed by M steering vectors of subspaces are orthogonal. The signal subspace
sources , S is the Kx1 vector of complex envelopes of consists of phase shift vectors between antennas
K sources, and is the noise vector on the network. depending on the angle of arrival. All orthogonal
vectors to constitute a subspace called noise
If the number of sources K is less than the number subspace.
of elements M of the network, then K directional
vectors are linearly independent and generate a vector MUSIC algorithm being based on the properties of
subspace of the observation space of dimension M signal and noise subspaces, vectors derived from
assuming that signals and noises are stationary and generate a signal subspace collinear with steering
uncorrelated. The correlation matrix or covariance of vectors of sources and vectors derived
signals will be given by:
from generate a noise subspace orthogonal to
steering vectors of these sources.
(4)
Noisy observation = Signal space + Noise space If the number of signals impinging on M element
array is D, the number of signal eigenvalues and
Where is the conjugate transpose of X, eigenvectors is D and number of noise eigenvalues
is the MxM correlation matrix of the and eigenvectors is M-D. The array correlation
noise vector, I is the identity matrix and σ² is the matrix with uncorrelated noise and equal variances is
noise power identical for each element of network. then given by:
is the KxK square matrix of covariance of the (6)
signal vector given by is a
diagonal of full rank. However, it becomes singular Where
when at least two sources are totally correlated. is array steering matrix.

In practice, the correlation matrix or covariance is (7)
estimated by an average over N observations as
following:
(5)


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has D eigenvectors associated with signals For the set of input parameters, MUSIC algorithm
and M – D eigenvectors associated with the noise. has been tested for the following cases.
We can then construct the M x (M-D) subspace
spanned by the noise eigenvectors such that: Case.1. Varying number of array elements

MUSIC algorithm has been tested in MATLAB for
(8) two different sizes of array elements (8 and 16)
considering previously defined set of input
The noise subspace eigenvectors are orthogonal to parameters.
array steering vectors at the angles of arrivals θ1, θ2,
θ3, θD and the MUSIC Pseudo spectrum is given as: 4
x 10 MUSIC SPECTRUM
6
m-- array elements=8
b b array elements=16
5
(9)
4

pseudospectrum(db)
However when signal sources are coherent or noise
variances vary the resolution of MUSIC diminishes. 3
To overcome this we must collect several time
samples of received signal plus noise, assuming 2
ergodicity and estimate the correlation matrices via
time averaging as: 1

0
-100 -80 -60 -40 -20 0 20 40 60 80 100
angle in degrees

(10) Fig.2: Music spectrum for array elements 8 and 16.
(SNR= 25 db and number of snapshots = 200)
and
From Fig.2 it is observed that with the increase in
number of array elements, peak becomes more sharp
(11)
indicating an increase in ability to resolve two closely
spaced targets and hence resulting in an enhanced
We find the ‘D’ largest peaks of PMUSIC ( ) in DOA estimation.
eqn(9) to obtain DOA estimates.
Estimated DOA
B. Simulation Results
Actual DOA Array Array
DOA estimation using MUSIC algorithm is elements=8 elements=16
performed based on a set of input parameters viz. 25 25 25
Angle of arrival, inter element spacing, number of 80 80 80
elements in an array, SNR range and number of
snapshots. The input parameters for simulation of Table 2: DOA estimation for arrays elements 8 and
MUSIC algorithm is given in Table 1. 16 (SNR= 25 db and number of snapshots = 200)

Parameter Value Table.2 depicts the case where SNR is 25 dB and
Angle of arrival of 25 , 80 hence the DOA estimation is equal for both array
signals elements. For a lesser SNR value accurate angular
Inter element spacing estimation is possible for higher number of array
(d) elements.
Number of elements in 8 ,16
an array Case.2. Varying number of SNR values
SNR range (dB) 0 to 25
Number of snapshots 200,1000 DOA estimation varies with respect to variations in
SNR values. Here MUSIC algorithm has been tested
for different values of SNR (0dB and 25dB).
Table 1: Input parameters for music algorithm


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4 5 MUSIC SPECTRUM
x 10 MUSIC SPECTRUM x 10
6 6
m-- SNR=0dB m-- Snapshots=200
b SNR=25dB b Snapshots=1000
5 5

4

pseudospectrum(db)
4
pseudospectrum(db)

3
3

2
2

1
1

0
-100 -80 -60 -40 -20 0 20 40 60 80 100
0 angle in degrees
-100 -80 -60 -40 -20 0 20 40 60 80 100
angle in degrees
Fig.4: MUSIC spectrum for snapshots 200 and 1000.
Fig. 3: MUSIC spectrum for SNR of 0dB and 25dB. (SNR= 25 db and number of arrays elements=8)
(Number of array elements = 8 and number of
snapshots =200) From the Fig.4 it is clearly observed that accuracy
of DOA estimates is directly proportional to the
From Fig.3 it is observed that as SNR value number of snapshots. The estimated DOA for two
increases, DOA estimates of MUSIC are more different snapshots is as shown in Table.4.
accurate and almost near to estimated DOA. When
SNR is very low (close to 0dB) accurate estimation Estimated DOA
of DOA fails. The actual and estimated DOA’s are Actual DOA Snapshots=200 Snapshots=1000
shown in Table 3.
25 24.82 25
Estimated DOA
Actual DOA 80 79.29 80
SNR=0dB SNR=25dB
Table 4: DOA estimation for snapshots 200 and 1000
25 24.70 25 (SNR= 25 db and number of arrays elements=8)
80 79.41 80
VI. ESPRIT ALGORITHM
Table 3: DOA estimation for SNR 0dB and 25dB
(Number of array elements = 8 and number of A. Algorithm
snapshots =200)
ESPRIT (Estimation of Signal Parameters via
Case.3. Varying number of snapshots Rotational Invariance Techniques) was developed by
Roy and Kailath in 1989 [4]. It is based on the
Simulations are carried out for two different rotational invariance property of the signal space to
snapshots viz. 200 and 1000 keeping other input make a direct estimation of the DOA and obtain the
parameters specified in Table 1 constant. angles of arrival without the calculation of a pseudo-
spectrum on the extent of space, nor even the search
for roots of a polynomial.

This method exploits the property of translational
invariance of the antenna array by decomposing the
main network into two sub-networks of identical
antennas which one can be obtained by a translation
of the other, Fig.5


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i=0,1,2,…D (21)

DOA can be calculated by

(22)

B. Simulation Results

DOA estimation using ESPRIT algorithm is
performed based on the same set of input parameters
specified for MUSIC algorithm and are shown in
Fig.5 Principle of the ESPRIT algorithm Table 5.

The main advantage of this method is that it avoids Parameter Value
the heavy research of maxima of a pseudo-spectrum Angle of arrival of 25 , 80
or a cost function (therefore a gain calculation) and signals
the simplicity of its implementation. In addition, this Inter element spacing
technique is less sensitive to noise than MUSIC. It is (d)
based on the array elements placed in identical Number of elements in 8 ,16
displacement forming matched pairs, with M array an array
elements, resulting in m=M/2 array pairs called SNR range (dB) 0 to 25
“doublets”. Number of snapshots 200,1000
Computation of signal subspace for the two sub
Table 5: Input parameters for ESPRIT algorithm
arrays, P1 and P2, results in two vectors V1 and V2,
such that Range[S]=Range[B]. Also, there should DOA estimation using ESPRIT technique has been
exist a non singular matrix T of D×D such that tested for the following cases.
, where can be decomposed into V1 and
V2. Case.1. Varying number of array elements

, (16) ESPRIT algorithm has been tested for two
different sizes of array elements (8 and 16) by
considering other parameters as shown in Table 5.
(17) ESPRIT
4
If D×D is diagonal,unitary matrix with phase shifts
pseudospectrum (dB)

between doublets for each DOA , there exists a
unique rank D matrix FεC such that 3

V1W1+V2W2=BTW1+B TW2=0 (18)
2
Rearranging eqn(18), we get:
1
BT =B T (19)

With B as full rank and sources are having distinct 0
0 50 100 150
DOA, then angle in degree
(20) Fig.6: ESPRIT spectrum for array elements 8 and 16.
(SNR= 25 db and number of snapshots = 200)
Eqn(20) indicates that if we are able to find out
eigenvalues of, which are diagonal elements of ,we
can estimate DOA as where


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ESPRIT spectrum provides almost similar DOA
estimates for different array elements with lesser Table 7: DOA estimation for SNR 0dB and 25dB
variance than MUSIC algorithm. (Number of array elements = 8 and number of
snapshots =200)

From Table 7 it is observed that ESPRIT provides
better resolution than MUSIC even at lower SNR.

Estimated DOA Case.3. Varying number of snapshots
Actual DOA Array Array
elements=8 elements=16 ESPRIT algorithm has been tested for two different
25 25.0031 25.0010 snapshots 200 and 1000 by considering input
parameters as shown in Table 5.
80 79.9565 79.9873
ESPRIT
Table 6: DOA estimation for arrays elements 8 and 5
16 (SNR= 25 db and number of snapshots = 200)

pseudospectrum (dB)
From Table 6 it is observed that as array size
4
increases from 8 to 16, DOA estimates of signals are
almost close to actual DOA which is superior to
3
performance of MUSIC.
2
Case.2. Varying number of SNR values
1
ESPRIT technique has been tested for two different
SNR values 0dB and 25dB as in the case of MUSIC 0
algorithm.
0 50 100 150
angle in degree
ESPRIT
Fig.8: ESPRIT spectrum for two different snapshots
1
200 and 1000. (SNR= 25 db and number of arrays
pseudospectrum (dB)

elements=8)
0.8
From Fig.8 it is observed that DOA estimates for
0.6 ESPRIT technique are almost close to actual DOA
even at lesser number of snapshots and hence it
0.4 outperforms MUSIC algorithm.
0.2 Table 8: DOA estimation for snapshots 200 and 1000
(SNR= 25 db and number of arrays elements=8)
0
0 50 100 150
angle in degree Estimated DOA
Actual DOA Snapshots=200 Snapshots=1000
Fig.7: ESPRIT spectrum for SNR of 0dB and 25dB. 25 25.0056 25.0047
(Number of array elements = 8 and number of 80 80.1840 80.0013
snapshots =200)
The observation made from Table 8 clearly
Pseudo spectrum obtained using ESPRIT technique indicates that ESPRIT provides more precise
for different S.N.R values is shown in Fig.7 and their estimation of DOA than MUSIC.
DOA estimates are shown in Table 7.
VI. QUATERNION MUSIC ALGORITHM
Actual DOA Estimated DOA
SNR=0dB SNR=25dB A. Quaternions
25 24.92 24.9658
80 79.1016 80.0026


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Quaternions are a four dimensional hyper complex polarized signal quaternion model proposed in the
number system. Discovered by Sir R.W. Hamilton in next section.
1843 [11], they are an extension of complex numbers
to 4D space. A quaternion q is described by four B. Polarization model
components (one real and three imaginaries). It can
be expressed in its Cartesian form as: Consider a scenario with one polarized source,
assumed to be a centred, stationary stochastic
process, emitting a wave field in an isotropic,
(23) homogenous medium. This wave field is recorded on
a two-component noise free sensor, resulting in two
Where highly correlated temporal series , . In this
case, the two signals are linked by phase and
amplitude coefficient called polarization parameters
(supposed constant in time and frequency). Consider
that the two signals in time are transformed in the
Fourier domain as
,with and
then the two-component signal recorded on
a vector –sensor can be expressed in the frequency
Several properties of complex numbers can be
domain such as:
extended to quaternions. Some of them are given
below:
(28)
- The conjugate of q, noted , is given by:
This signal is pure quaternion valued. Taking the
- A pure quaternion is a quaternion which real part is first component as reference and with the
null: previous assumptions on polarization parameters,
can be rewritten as:

- The modulus of a quaternion q is = = = (1+ (29)
= = and its inverse is
Where , and are the amplitude
given by
ratios and the phase shifts for the second and third
component respectively, with respect to the first one.
(24) In the following, the working frequency will be
omitted, assuming that we consider narrowband
- A quaternion is said to be null if a = b = c = d = 0; signals or that we work independently at each
frequency.
- The set of quaternion’s, denoted by , forms a
non-commutative normed division algebra, that C. Quaternion-MUSIC
means that given two quaternion’s q1 and q2:
(25) MUSIC-like methods are based on the projection of
a steering vector on the estimated noise subspace.
Here we discuss a new approach based on
- Conjugation over is an anti-involution:
hypercomplex number system discovered by
(26) Hamilton[11],they are an extension of complex
numbers to four-dimensional(4-D) space. This new
It is that a quaternion is uniquely expressed
approach improves the signal subspace estimation
as: , where = and = accuracy and reduces the computational burden.
.This is known as the Cayley-Dickson form. It Additionally, the discussed algorithm presents a
is also possible to express q in an alternate Cayley- better resolution power for direction of arrival (DOA)
Dickson form. Thus, any quaternion q can be written estimation than the long-vector approach, for
as: , where = and equivalent statistical performances and also results in
This notation will be used in the


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a reduction by half of memory requirements for expression of the quaternion spectral matrix
representation of data covariance model. becomes:

The Quaternion Music can be summarized as (33)
follows [12]:

Step1: Consider a linear, uniform vector-sensor array
of N sensors .Assume that the far-field waves from K Where and is a
sources (K-known, K < N) impinge on an antenna as matrix containing noise second order statistics.
shown in Fig.9. Sources are supposed to be
decorrelated, spatially coherent and confined in the Step6: We associate the first K eigenvalues to the
array plane. Their polarizations are also stationary in signal part of the observation and the rest of N-K to
time and space (distance). Noise is spatially white the noise part. Thus, the projector on the noise
and not polarized. subspace is defined as:

(34)

Step7: The quaternion steering-vector is
then generated:

 1 + i ρ e jϕ 
Fig.  
9 Acquisition Scheme q (θ , ρ , ϕ ) = N (1 + ρ ) 2
e + i ρ e j (ϕ −θ )
− jθ

 e − j ( N −1)θ + i ρ e j (ϕ − N −1)θ 
 
Step2: The source direction of arrival (DOA) can
then be calculated using the following formula:
(35)

(30) Where q is a three-parameter unitary vector,
modelling the arrival of a source of DOA and
Where is the inter-sensors distance, is the polarization parameters on a 2C sensor array.
wave propagation velocity and v is the working
Step8: Quaternion-MUSIC estimator (Q-MUSIC) is
frequency.
then computed by projecting the steering-vector
step3: The output of the vector-sensor array is given on the noise subspace:
by a column quaternion vector equal to the
sum of the K sources contributions (added with a
noise term): (36)

eqn (36) for Q-MUSIC estimator similar to the well-
known form of MUSIC algorithm for scalar-sensor
(31) array. The functional in (36) has maxima for sets of
( corresponding to sources present in the
Step4: We introduce the equivalent second order signal.
representation for a vector-sensor array using
quaternion formalism. Quaternion spectral matrix D. Simulation Results
is defined as:
DOA estimation using Q-MUSIC algorithm has
been tested for one polarized source impinging on a
(32)
two component (2C) - sensor array for input
Step5: Assuming the decorrelation between the noise parameters shown in Table 9.
and the sources and between sources themselves, the


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Parameter Value Table 10: DOA estimation for array of sensor 8 and
Angle of arrival of 0.44rad 25 16 (SNR= 25 db, number of snapshots = 200, =3
signals and )
Inter element spacing
(d) Case.2. Varying number of SNR values
Number of elements in 8 ,16
an array Q-MUSIC algorithm simulation has been carried
SNR range (dB) 0 to 25 out for two different SNR values 0dB and 25dB for
Number of snapshots 200,1000 input parameters shown in Table 9.
constant modulus ratio 3
QMUSIC
( ) 0.4
m-- snr=25dB
constant phase shift 0.27rad 0.35 r snr=0dB

( )
0.3

Pseudospectrum(dB)
Table 9: Input parameters for Q-MUSIC algorithm 0.25

0.2
Q-Music algorithm has been tested for the following
cases. 0.15

0.1
Case.1. Varying number of array elements
0.05

For two different array elements 8 and 16 Q-
0
MUSIC algorithm has been tested with input 0 0.2 0.4 0.6 0.8
Angle in radians
1 1.2 1.4 1.6

parameters shown in Table 9.

QMUSIC
Fig.11: QMUSIC spectrum for S.N.R values 0dB and
0.5
m-- array=16
25dB. (Number of array elements = 8 and number of
0.45 r array=8 snapshots =200)
0.4

0.35 From Fig.11 it is observed that even when SNR is
Pseudospectrum(dB)

0.3
0dB, Q-MUSIC still provides better estimation of
0.25
DOA of signals when compared to MUSIC. The
estimates are provided in Table 11.
0.2

0.15
0.1 SNR=0dB SNR=25dB
0.05
25 25.0675 25
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Angle in radians
Table 11: DOA estimation for two different SNR
Fig.10: Q-MUSIC spectrum for two different array of 0dB and 25dB (array of sensor=8, number of
sensor 8 and 16. (SNR= 25 db and number of snapshots = 200, =3 and )
snapshots = 200)
Case.3. Varying number of snapshots
From the Fig.10 it is observed that as array
elements increases from 8 to 16 the 3dB detection Q-MUSIC algorithm has been tested for two
lobe width for Q-MUSIC becomes narrower different snapshots 200 and 1000 by considering
compared to MUSIC and ESPRIT and hence input parameters shown in Table 9.
provides accurate DOA and polarized estimates for
multidimensional signals.

Sensors=8 Sensors=16
25 24.97 25


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0.8
QMUSIC Array elements=8
m-- Snapshots=200 Algorithm Actual Estimated % Error
0.7 r Snapshots=1000
DOA DOA
0.6 MUSIC
ESPRIT
Pseudospectrum(dB)

0.5
Q-
0.4 MUSIC
0.3 Array elements=16
Algorithm Actual Estimated % Error
0.2
DOA DOA
0.1 MUSIC
0
ESPRIT
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Angle in radians Q-
MUSIC
Fig.9: QMUSIC spectrum for snapshots 200 and
1000. (SNR= 25 db and number of arrays
Table 13: DOA estimation for array elements 8 and
elements=8)
16 (SNR= 25 db and number of snapshots = 200)
The estimation of DOA using Q-MUSIC algorithm From Table 13, it is clear that as the number of
is directly proportional to the number of snapshots array elements increase, accurate DOA estimation
similar to MUSIC. But from Fig.9, it is observed that
can be achieved. Amongst the three algorithms
Q-MUSIC provides better estimation of signal arrival discussed above, Q-MUSIC has a lesser % error and
even at lower number of samples than MUSIC and the estimated DOA is almost equal to the actual
the estimated DOA is equal to actual DOA as shown
DOA.
in Table 12.
Case.2. Varying number of SNR values

For SNR= 0 dB and 25dB, all the three discussed
algorithms have been simulated and results are
tabulated in Table 14.

SNR=0dB
Actual Estimated DOA Algorithm Actual Estimated % Error
DOA Snapshots=200 Snapshots=1000 DOA DOA
25 25.0092 25 MUSIC
ESPRIT
Table 12: DOA estimation for snapshots 200 and Q-
1000 (SNR= 25 db, number of sensors = 8, =3 MUSIC
and ) SNR=25dB
VII. COMPARISON OF MUSIC, ESPRIT AND Q- DOA DOA
MUSIC ALGORITHMS MUSIC
ESPRIT
Section IV, V and VI discussed the various Q-
algorithms used in smart antenna systems for robust MUSIC
DOA estimation. The performance analysis of
MUSIC, ESPRIT and Q-MUSIC algorithm based on Table 14: DOA estimation for SNR 0db and 25dB.
high resolution direction of arrival estimation is (Number of array elements=8 and number of
compared in this section for the following cases. snapshots = 200)
Case.1. Varying number of array elements In general, performance of DOA estimation
degrades as signal to noise ratio decreases. But Q-
For array elements 8and 16 all the three algorithms MUSIC accurately estimates DOA even at a very
have been simulated and results are tabulated in lower gain of 0dB.
Table 13.


ISSN: 2278 – 1323

Case.3. Varying number of snapshots snapshots than scalar techniques (MUSIC, ESPRIT).
Thus Q-MUSIC can be quite successfully used in
The comparison table for performance of three radar’s to improve clutter rejection and discriminate
discussed algorithms is shown in Table 15 for two between different types of target. It also provides
different snapshots 200 and 1000. more efficient spectrum utilization for mobile
communication systems.
Snapshots=200
DOA DOA REFERENCES
MUSIC
ESPRIT [1] V. F. Pisarenko, “The retrieval of harmonics from a
covariance function,” Geophysical J. of the Royal Astron.
Q- Soc., vol. 33, pp. 347–366, 1973.
MUSIC [2] R. O. Schmidt, “Multiple emitter location and signal
Snapshots=1000 parameter estimation,” IEEE Trans. Antennas Propagation,
Algorithm Actual Estimated % Error vol. 34, no. 3, pp. 276–280, Mar. 1986.
[3] A. J. Barabell, “Improving the resolution performance of
DOA DOA eigenstructure based direction-finding algorithms,” Proc. of
MUSIC ICASSP, Boston, MA, USA, pp. 336–339, 1983.
ESPRIT [4] Richard Roy and Thomas Kailath, “ESPRIT-Estimation of
signal parameters via rotational invariance techniques,”
Q- IEEE Transactions on Acoustics, Speech, and Signal
MUSIC Processing, vol. 37, N° 7, pp. 984-995, July 1989.
[5] H. D. Schutte and J. Wenzel, “Hypercomplex numbers in
Table 15: DOA estimation for snapshots 200 and digital signal processing,” Proc. IEEE Int. Symp. Circ. Syst.,
pp. 1557–1560, 1990.
1000 (SNR= 25 db and number of array elements=8) [6] K. T. Wong and M. D. Zoltowski, “Self- initiating MUSIC
direction finding and polarization estimation in spatio
From Table 15, it is observed that Q-Music polarizational beamspace,” IEEE Trans. Antennas
provides better detection capability for lower number Propagation, vol. 48, pp. 1235–1245, Sept. 2000.
of samples compared to the other two algorithms. [7] K. T. Wong and M. D. Zoltowski, “Diversely polarized root-
MUSIC for azimuth- elevation angle of arrival estimation,”
Hence Q-MUSIC algorithm is best suited in Digest of the 1996 IEEE Antennas Propagation Soc. Int.
multipath environment whereas the received signal is Symp., Baltimore, pp. 1352–1355, July 1996
difficult to estimate accurately. [8] M. D. Zoltowski and K. T. Wong, “ESPRIT-based 2D
direction finding with a sparse array of electromagnetic
vector-sensors,” IEEE Trans. Signal Processing, vol. 48, pp.
VIII. CONCLUSION 2195–2204, Aug. 2000.
[9] K. T. Wong and M. D. Zoltowski, “Uni-vector-sensor
In this paper, we discussed three high resolution ESPRIT for multi-source azimuth, elevation and polarization
direction finding algorithms based on their estimation,” IEEE Trans. Antennas Propagation, vol. 45, pp.
1467–1474, Oct. 1997.
performance for different number of array elements, [10] J. Li and J. R. Compton, “Angle and polarization estimation
snapshots and different SNR’s. From the simulated using ESPRIT with a polarization sensitive array,” IEEE
results, it is observed that MUSIC and ESPRIT Trans. Antennas Propagation, vol. 39, pp. 1376–1383, Sept.
provides an accurate estimation of DOA with 1991.
[11] W.R.Hamilton, “ On quaternions,” in Proc. Royal Irish
improved resolution power than the other direction Academy,1843
finding techniques. But in the case of diversely [12] Miron S., Bihan N.L. and Mars J. “Quaternion-MUSIC for
polarized antenna arrays where the SNR values and Vector-Sensor Array processing,” IEEE Trans. Signal
number of snapshots are less, these two algorithms Processing, 2006, 54(4):1218-1229.
[13] N. Le Bihan and J.Mars,” Singular value decomposition of
failed to achieve precise estimation of DOA of
matrices of quaternions: A new tool for vector-sensor signal
signals. To overcome these drawbacks we have processing.” Signal Process, vol.84, n0 7, pp 1177-1199,
discussed a new technique for vector sensor array 2004.
processing using Quaternion’s for diversely polarized [14] CUI Wei, “A Novel Quaternion DOA estimation algorithm
based on magnetic loop antenna”.
array. This Quaternion based algorithm (Q-MUSIC)
of EM vector sensors can achieve better performance [15] J.P. Ward, Quaternion's and Cayley Numbers, Algebra and
than scalar–sensor arrays, while occupying less space applications,Kluwer Academic, 1997
and cost for hardware implementation. However, the
processing requirements are somewhat higher for the [16] F. Zhang, “Quaternions and matrices of quaternions,” Linear
algebra and its applications, vol. 251, pp. 21–57, 1997.
diversely polarized array. Further we have shown that
Q-MUSIC provides higher direction finding accuracy [17] Kantor and A. Solodovnikov, Hypercomplex numbers, an
and higher resolving power even with lower SNR and elementary introduction to algebras. Springer-V erlag, 1989.


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[18] Kantor and A. Solodovnikov, Hypercomplex numbers, an
elementary introduction to algebras. Springer-V erlag, 1989.

[19] L.C. Godra, “Application of antenna arrays to mobile
communications-PartI: Performance improvement, feasibility
and system considerations,” Proc. IEEE, vol. 85, pp. 1031-
1060, Jul, 1997.

[20] L.C. Godra,”Application of antenna arrays to mobile
communications_Part II: Beam – forming and direction-of-
arrival considerations,” Proc. IEEE,vol. 85,pp.1195-1245,
Aug 1997.

BIOGRAPHIES

Chetan.L.Srinidhi graduated in Electronics
and Communication Engineering from Nitte
Meenakshi Institute of Technology,
Bangalore India. He is Currentlty pursuing his
M.Tech degree in Communication syatems, at
R.V.College of Engineering, Bangalore,
India. His research interests are in the fields
of digital Signal Processing, Antennas and
Digital Communication.

Dr.S.A.Hariprasad obtained his
PhD from Avinashilingam University for
Women, Coimbatore in the area of digital
controller’s .He is having teaching experience
of 22 years and five years of research
experience. He has published nearing 35
papers in international/national journals and
conferences. He has also published a text
book on advanced Microprocessor and
reviewed books on Microwave engineering
and won best teacher award (twice) from
RSST and appreciation award from ISTE. His
research areas of interest are embedded
systems and RF systems.


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