International Journal of Scientific & Engineering Research, Volume 6, Issue 7, July-2015 594
ISSN 2229-5518
Study of DOA Estimation Using Music
Algorithm
Bindu Sharma
1
, Ghanshyam Singh
2
, Indranil Sarkar
3
Abstract— Wireless communication systems utilize smart antennas. Smart antenna have digital signal processing unit. Smart
antennas have ability to locate and track signals. Smart antenna performance depends on efficiency of digital signal processing
algorithms. The Angle of Arrival (AOA) estimation algorithms is used for estimate the number of incidents signals on the antenna
array and their angle of incidence. This paper based on MUSIC DOA estimation method. The simulation results show classical
MUSIC algorithm, different parameters effect on estimation and methods for improvisation of MUSIC algorithm.
Index Terms—
Smart antenna, digital signal processing, white Gaussian noise, DOA, MUSIC.
——————————
——————————
1 INTRODUCTION
In the last decade, wireless communication services
have known an explosive growth. According to the
International Telecommunication Union (ITU) [1];
number of mobile cellular subscriptions worldwide
increases in last few years. The important factors of
research in the wireless communication are public
demand for the improvement in the capacity, coverage
and quality. The ever increasing number of mobile
subscribers and limited available bandwidth
introduces major challenges for the wireless
technology, especially in heavily populated areas.
Wireless communication techniques have to improve
the capacity of the network and reduce co-channel
interference. Over the years, a number of technologies
have emerged that, very effectively, deal with these
high demands.
As the number of wireless user increases and with
the recent shift in emphasis from voice to multimedia
applications and research towards smart antennas
(SAs) or adaptive array technology emerged to attain
an even higher system capacity. Smart Antenna is a
combination of multiple antennas and forming an
antenna array [2].Smart Antenna has mainly two
functions one of them is DOA estimation. DOA
estimation can detect the arrival signal direction and
angle of incidence. Various DOA estimation techniques
present but this paper based on the MUSIC algorithm.
2
DIRECTION-OF-ARRIVAL
In order for the smart antenna to be able provide the
required functionality and optimization of the
transmission and reception; they need to be able to
detect the direction of arrival of the required incoming
signal. The signal processing unit within the antenna
and this provides the needed analysis result after
receiving data from antenna array.
Direction-of-arrival (DOA) estimation has also
been known as spectral estimation, angle-of-arrival
(AOA) estimation, or bearing estimation. One of the
important signal processing blocks in smart antenna
systems is the direction of arrival (DOA) algorithm.
The main use of the DOA algorithm is to estimate the
direction of incoming or arrival signals based on
samples of received signals [3] [4].
3 MUSIC DOA ESTIMATION
MUSIC is an acronym which stands for Multiple Signal
classification MUSIC algorithm was given by Schmidt
in 1979 and this higher resolution technique is based on
exploiting the eigen-structure of input covariance
matrix. This method is to decompose the covariance
matrix into eigenvectors in both signal and noise
subspaces. The direction of sources is calculated from
steering vectors that orthogonal to the noise subspace.
Which detect the peak in spatial power spectrum [5].
Bindu Sharma is currently pursuing master’s degree program in Digital
Communication engineering in Sobhasaria Engineering College, Rajasthan,
India. E-mail: bindus[email protected]om
Ghanshyam Singh is Asst. Prof. in Sobhasaria Engineering College, Sikar,
Rajasthan, India. E-mail: kaviya01singh@gmail.com
Indranil Sarkar is Asst. Prof. in Sobhasaria Engineering College, Sikar,
Rajasthan, India. E-mail: iindranilsarkar@gmail.com
IJSER
International Journal of Scientific & Engineering Research, Volume 6, Issue 7, July-2015 595
ISSN 2229-5518
IJSER © 2015
http://www.ijser.org
Fig.1. N element antenna array with D arriving signals
If D is the number of signal eigenvalues or eigenvectors
and number of noise eigenvalues or eigenvectors is N-
D, the array correlation matrix with uncorrelated noise
and equal variances is than given by:
Rxx = A*Rss*A
H
+σ
n
2
*I (1)
Where A = [a(θ
1
) a(θ
2
) a(θ
3
) --- a(θ
D
)] is N x D array
steering matrix
Rss = [s
1
(k) s
2
(k) s
3
(k) ---- s
D
(k)]T is D x D source
correlation matrix
Rxx has D eigenvectors associated with signals and
N – D eigenvectors are associated with noise, we can
then construct the N x (N-D) subspace spanned
through the noise eigenvectors such that
VN = [v
1
v
2
v
3
------- v
N-D
] (2)
The noise subspace eigenvectors are orthogonal to
array steering vectors at the angles of arrivals θ1, θ2, θ3,
θD and Pseudospectrum of the MUSIC given as:
P
(
θ
)
=
((
(
θ
)
(
θ
)
)
(3)
However when signal sources are coherent or
noise variances vary the resolution of MUSIC
diminishes [6] [7], we must collect many time samples
of received signal plus noise; we assume ergodicity and
estimate the correlation matrices via time averaging as:
R
=
(
)
()
(4)
And Rxx = A*Rss*AH + A*Rsn + Rns *AH + Rnn (5)
The MUSIC Pseudospectrum using equation (5.3)
with time averages now provides high angular
resolution for coherent signals.
MUSIC’s Spatial Spectrum
P
=
(
θ
)
(θ)
(6)
Where a(θ) is steering vector and En is noise subspace
eigenvectors.
FaF3.1 Factors affecting MUSIC DOA Estimation
Many parameters affect DOA estimation results. The
results are affected by the source of the incoming signal
and actual application environment. Some factors are
given here and such effects are also shown thought
simulation results [8].
• Number of array elements: If array elements
increases with condition of other parameters
remaining unchanged then it gives improved
estimation performance for resolution
algorithm.
• Array element spacing: The performance of
DOA estimation algorithm is affected by array
element spacing. When the spacing of the
array elements is larger than half the
wavelength, the estimated spectrum, except
for the signal source direction, shows false
peaks, that gives poor estimation accuracy.
IJSER
International Journal of Scientific & Engineering Research, Volume 6, Issue 7, July-2015 596
ISSN 2229-5518
IJSER © 2015
http://www.ijser.org
• Snapshots: Snapshot also affects the
performance of the system. Snapshot is given
by number of samples for time domain and in
frequency domain and it is given by sub
segments of DFT.
• SNR: The performance of DOA estimation
algorithm is directly affected by SNR. With
lower noise, the beam width of spectrum
becomes sharper, the direction of the signal
becomes clearer, and the accuracy is also
increased. At low SNR, algorithm performance
would drop. Hence, the studies are focused on
how to get good results at low SNR.
• Angle Spacing: The performance of DOA
estimation algorithm depends on angle
spacing, when angle space is small; it is hard
to estimate number of sources clearly. With
large angle space, the estimation is clear,
sharper and provides good resolution.
• Coherence of the signal source: If signal source
is a coherent signal, then signal covariance
matrix is no longer for the non-singular
matrix. For this condition, the original super-
resolution algorithm will not suitable. This
would affect performance of estimation.
3.2 Improvisation Methods
• Modified MUSIC Algorithm
MUSIC algorithm is limited to uncorrelated signals.
When signal sources are coherence correlated signal or
a signal with low SNR then the estimated performance
of the MUSIC algorithm deteriorates or even
completely loses. Hence, if we want to estimate the
coherent signal DOA accurately, we have to eliminate
the correlation between the signals. The modified
MUSIC overcomes the problem by conjugate
reconstruction of the data matrix of the MUSIC
algorithm [9].
Make a transformation matrix J (J is an Mth-order
anti-matrix, known as the transition matrix).
J =
0 1
1 0
Let Y=JX*, where X* is the complex conjugate of X,
then the covariance of data matrix Y is
Ry=E[YY
H
]=JRX*J (7)
From the sum of Rx and Ry, the reconstructed
conjugate matrix can be obtained.
R= Rx+ Ry=AR
s
A
H
+ J[ AR
s
A
H
]*J + 2I
2
(8)
The formula shows derivation process, the essence
of the modified music algorithm is the special situation
of the spatial before and after smoothing algorithm,
which equals the length of sub-array with the number
of array elements [10].
• Forward Spatial Smoothing Techniques
The spatial smoothing given by J.E. Evans initially and
improve by D.F. Suns. A spatial smoothing
preprocessing method for resolving issue of
encountered in direction-of-arrival estimation of
completely correlated signals is analyzed.
Forward smoothing of spatial smoothing is based
on averaging the covariance matrix of identical
overlapping arrays and requires an array of identical
elements built with some form of periodic structure,
such as the uniform linear array.
The signal covariance matrix Rxx is a full-rank
matrix as long as the incident signals on the sensor
arrays are uncorrelated, which is the key to the MUSIC
IJSER
International Journal of Scientific & Engineering Research, Volume 6, Issue 7, July-2015 597
ISSN 2229-5518
IJSER © 2015
http://www.ijser.org
eigenvalues decomposition. If the incoming signals
become highly correlated then the matrix Rxx will lose
its non-singularity property and performance of
MUSIC will reduce. In this case, spatial smoothing
must be used to overcome the correlation between the
incoming signals by dividing the main sensor array
into forward overlapping subarrays and introducing
phase shifts between these sub-arrays.
The vector of received signals at the kth forward
sub-array is given by:
x
(
t
)
= AD
(
)
S
(
t
)
+ n
(t) (9)
Where (k-1) is kth power of the diagonal matrix D
is expressed as:
D = diag{e
, … … , e
} (10)
The spatial correlation matrix R is given by:
R =
R
(11)
L is number of overlapping subarrays. When
applying forward spatial smoothing the N-element
array can detect up to N/2 correlated signals [11].
• Toeplitz Approximation Method
S. Y. Kung et al. gives Toeplitz approximation method,
TAM based on a reduced order Toepitz approximation
of an estimated spatial conariance matrix. When source
are uncorrelated and statistically stationary then the
estimated covariance matrix is Toeplitz. In a multipath
environment, where the source paths are fully
correlated then covariance matrix is not Toeplitz. The
Toeplize structure can be guaranteed by employing
spatial smoothing, which destroys cross correlation
between directional components. The TAM is designed
for robustness in an arbitrary ambient noise
environment [11].
When the signals are coherent with each other, the
value of R matrix’s rank is rank-deficient, and then
correlation matrix will be no longer Toeplitz.
We can structure a TAM:
R
T
(-n) =
R
()
, n = 0,1, … … , N 1 (12)
R
(n) = R
(n) (13)
Toeplitz approximation method can well
distinguish and estimate DOA of the coherent signals.
Comparing with the spatial smoothing technology [12].
4 DIRECTION OF ARRIVAL SIMULATION
This section compounds the MATLAB simulation by
studying and changing various parameters e.g. N
number elements used in array, each element is spaced
by d and number of iterations used for computations.
The simulations are carried out to analyze the various
features of estimation. It illustrates as to how it will
affect on the digital beam forming by changing the
parameters.
Fig.2. Simulation of Classical MUSIC algorithm
0 10 20 30 40 50 60 70 80 90
-10
0
10
20
30
40
50
60
Classical MUSIC
angle
θ
in degree
spectrum function P(
θ
) in dB
IJSER
International Journal of Scientific & Engineering Research, Volume 6, Issue 7, July-2015 598
ISSN 2229-5518
IJSER © 2015
http://www.ijser.org
The simulation shows how four signals are recognized
by the classical MUSIC algorithm. We have taken four
independent narrow band signals, whose incident
angle is 20, 30, 45 and 60 degrees respectively and these
four signals are not correlated. Ideal Gaussian white
noise is used, with SNR of 30dB. The element spacing is
half of the input signal wavelength, array element
number is 8 and the number of snapshots is 100.
Effect of Number of Array Elements:
We have performed the second simulation with array
elements 8, 16, 20 and have taken all the previous
parameters same i.e. incident angle - 20, 30, 45 and 60
degrees respectively, Noise - ideal Gaussian white
noise with SNR is 30dB, element spacing - half of the
input signal wavelength and snapshots - 100. The
simulation results are shown in Figure 3.
Fig.3. Simulation for effect of number of array elements
According to Figure 3, we can say that increase in the
number of array elements, DOA estimation spectral
beam width becomes sharper and gives better
directivity. Increased number of elements provides
more accurate estimations but more the number of
array elements the more the data need processing; and
more amount of computation, resulting in lower speed.
Effect of array element spacing:
We have performed the third simulation by changing
the array spacing as λ/4, λ/2, 1.2λ. have taken all the
previous parameters same i.e. incident angle - 20, 30, 45
and 60 degrees respectively, Noise - ideal Gaussian
white noise with SNR is 30dB, array elements number -
8 and snapshots - 100. The simulation results are shown
in Figure 4.
Fig.4. Simulation for effect of array element spacing
According to figure 4, we can say that when the array
element spacing is not more than half the wavelength,
with increasing array element spacing, the beam width
of spectrum becomes sharper, the direction of the array
elements becomes better; that is to say, the resolution of
MUSIC algorithm improves with the increase in the
spacing of array elements, but when the spacing of the
array elements is larger than half the wavelength, the
estimated spectrum, except for the signal source
direction, shows false peaks, that gives poor estimation
accuracy. Hence, in practical applications, the spacing
of the array elements must not exceed half the
wavelength.
0
10
20
30
40
50
60
70
80
90
-20
-10
0
10
20
30
40
50
60
70
angle
θ in degree
spectrum function P(
θ
) in dB
Effect of Number of Array Elements
N1-8
N2-16
N3-20
0 10 20 30 40
50 60
70 80 90
-10
0
10
20
30
40
50
60
angle
θ
in degree
spectrum function P(
θ
) in dB
Effect of Array Elements Spacing
d-lambda/4
d-lambda/2
d-1.2*lambda
IJSER
International Journal of Scientific & Engineering Research, Volume 6, Issue 7, July-2015 599
ISSN 2229-5518
IJSER © 2015
http://www.ijser.org
Effect of Number of Snapshots:
We have performed the fourth simulation by changing
number of snapshots as 50, 100 and 2000. We have
taken all the previous parameters same i.e. incident
angle - 20, 30, 45 and 60 degrees respectively, Noise -
ideal Gaussian white noise with SNR is 30dB, array
elements number – 8 and element spacing - half of the
input signal wavelength. The simulation results are
shown in Figure 5.
Fig.5. Simulation for effect of number of snapshots
According to figure 5 we can say that increase in the
number of snapshots, the beam width of spectrum
becomes sharper, the direction of the array element
becomes better and the accuracy is also increased.
Increased number of snapshots provides more accurate
estimations but the more the number of snapshots the
more the data needs processing; and the more amount
of computation, resulting lower speed.
Effect of SNR:
We have performed the fifth simulation the SNR is
0dB, 30dB and 50dB. We have taken all the previous
parameters same i.e. incident angle - 20, 30, 45 and 60
degrees respectively, Noise - ideal Gaussian white
noise, array elements number – 8, element spacing -
half of the input signal wavelength and snapshots -
100.The simulation results are shown in Figure 6.
Fig.6. Simulation for effect of SNR
According to figure 6 we can say that increase in the
number of SNR, the beam width of spectrum becomes
sharper, the direction of the signal becomes clearer, and
the accuracy is also increased. The value of SNR can
affect the performance of high resolution DOA
estimation algorithm directly.
Effect of Angle Spacing:
We have performed the simulation angle of arrivals [20
30 45 60], [25 30 45 50], [20 30 31 85] and have taken all
the previous parameters same i.e. incident angle - 20,
30, 45 and 60 degrees respectively, Noise - ideal
Gaussian white noise with SNR is 30dB, element
spacing - half of the input signal wavelength, array
elements number – 8and snapshots - 100. The
simulation results are shown in Figure.
0
10
20
30
40
50
60
70
80
90
-10
0
10
20
30
40
50
60
70
80
angle
θ
in degree
spectrum function P(
θ
) in dB
Effect of Number of Snapshots
M-2000
M2-100
M3-50
0 10
20 30
40 50
60
70
80 90
-10
0
10
20
30
40
50
60
70
80
angle
θ
in degree
spectrum function P(
θ
) in dB
Effect of SNR
SNR1-0
SNR2-30
SNR3-50
IJSER
International Journal of Scientific & Engineering Research, Volume 6, Issue 7, July-2015 600
ISSN 2229-5518
IJSER © 2015
http://www.ijser.org
Fig.7. Simulation for Effect of Angle Spaceing
According to simulation result we can say that when
angle space is small, it is hard to estimate number of
sources clearly. It also shows that when angle space is
large then the estimation is clear, sharper and provides
good resolution.
MUSIC algorithm and modified MUSIC algorithm
for coherent signals:
The simulations show how four signals are recognized
by the MUSIC algorithm and modified MUSIC
algorithm. If the signals are coherent and the incident
angle be 20, 30, 45 and 60 degrees respectively, ideal
Gaussian white noise is used, the SNR is 30dB, the
element spacing is half of the input signal wavelength,
array element number is 8, and the number of
snapshots is 100. The simulation results are shown in
Figure 6.7 for MUSIC algorithm and Figure 6.8 for
modified MUSIC algorithm (both when the signals are
coherent).
Fig.8. Simulation for MUSIC algorithm when the
signals are coherent
Fig.9. Simulation for the modified MUSIC algorithm
when the signals are coherent
As shown in Figure 8 and Figure 9, for coherent
signals, classical MUSIC algorithm has lost
effectiveness, while modified MUSIC algorithm can be
better applied to remove the signal correlation feature,
which can distinguish the coherent signals, and
estimate the angle of arrival more precisely. Under the
right model, using MUSIC algorithm to estimate DOA
can get any high resolution. But MUSIC algorithm only
concentrates on uncorrelated signals. The MUSIC
algorithm estimation performance deteriorates or fails
completely when the signal source is correlation signal.
0 10 20 30 40 50 60 70 80 90
-10
0
10
20
30
40
50
60
70
angle
θ
in degree
spectrum function P(
θ
) in dB
Effect of Angle
DOA1-[20 30 45 60]
DOA2-[25 30 45 50]
DOA3-[20 30 31 85]
0
10
20
30
40
50
60
70
80
90
-10
-8
-6
-4
-2
0
2
4
MUSIC Algorithm when the signals are coherent
angle
θ
in degree
spectrum function P(
θ
) in dB
0 10
20 30 40 50 60 70 80
90
-10
0
10
20
30
40
50
60
70
Modified MUSIC Algorithm when the signals are coherent
angle
θ
in degree
spectrum function P(
θ
) in dB
IJSER
International Journal of Scientific & Engineering Research, Volume 6, Issue 7, July-2015 601
ISSN 2229-5518
IJSER © 2015
http://www.ijser.org
This modified MUSIC algorithm can make DOA
estimation more effective.
Forward Smoothness MUSIC Algorithm:
We have taken all the previous parameters same i.e.
incident angle - 20, 30, 45 and 60 degrees respectively,
Noise - ideal Gaussian white noise, array elements
number – 8, element spacing - half of the input signal
wavelength and snapshots - 100.
Fig.10. Forward Smoothness Music Algorithm
As shown in Figure 10, Smooth MUSIC is better that
MUSIC. The performance can be improved with more
elements in the array, with greater number of samples
or snapshots of signals and greater angular separation
between the signals. These are responsible for the form
of sharper peaks in MUSIC spectrum and smaller
errors in angle detection.
Toeplitz Approximation MUSIC Algorithm:
We have taken all the previous parameters same i.e.
incident angle - 20, 30, 45 and 60 degrees respectively,
Noise - ideal Gaussian white noise, array elements
number – 8, element spacing - half of the input signal
wavelength and snapshots - 100.
Fig.11. Toeplitz Approximation Music Algorithm
As shown in Figure 11, Toeplitz MUSIC is better that
smooth MUSIC. The performance can be improved
with more elements in the array, with larger number of
samples or snapshots of signals and greater angular
separation between the signals. These are responsible
for formation of sharper peaks in MUSIC spectrum and
smaller errors in angle detection.
5 CONCLUSION
In this paper we have vary parameters of MUSIC DOA
estimation algorithm and the simulations show that
when snapshots are increased, the accuracy increases,
similarly when the number of array elements are
increased, the accuracy increases but the speed
reduces. When the array element spacing is less than
half the wavelength, the MUSIC algorithm resolution
increases in accord with the increase of array element
spacing, however when the array element spacing is
0
10
20
30
40
50
60
70
80
90
-40
-20
0
20
40
60
80
100
Forward Smoothness Music Algorithm
angle
θ in degree
spectrum function P(
θ
) in dB
0
10
20
30
40
50
60
70
80
90
-40
-20
0
20
40
60
80
100
120
Toeplitz Music Algorithm
angle
θ
in degree
spectrum function P(
θ
) in dB
IJSER
International Journal of Scientific & Engineering Research, Volume 6, Issue 7, July-2015 602
ISSN 2229-5518
IJSER © 2015
http://www.ijser.org
greater than the half of wavelength, except the
direction of signal source, other directions as false
peaks in the spatial spectrum. Simulation result of SNR
shows that with lower noise, the beam width of
spectrum becomes sharper, the direction of the signal
becomes clearer, and the accuracy is also increased.
According to simulation result we can say that when
angle space is small, it is hard to estimate number of
sources clearly. It also shows that when angle space is
large then the estimation is clear, sharper and provides
good resolution. MUSIC method algorithm also have
some problems like channel mismatch and coherent
interface. When the signal is coherent, classical MUSIC
algorithm has lost effectiveness, and modified MUSIC
algorithm is able to effectively distinguish their DOA.
A spatial smoothing preprocessing scheme used for
solving problems encountered in direction-of-arrival
estimation of fully correlated signals is analyzed. The
Toeplitz structure can be guaranteed by employing
spatial smoothing, which destroys cross correlation
between directional components. The TAM is designed
for robustness in an arbitrary ambient noise
environment.
REFERENCES
[1] T. Union, \The world in 2010," tech. rep.,
International Telecommunication Union, 2010.
[2] Ahmed Mohamed Elmurtada Elameen, “SMART
ANTENNA SYSTEM”, Thesis, University of
Khartoum, Department of Electrical and Electronic
Engineering, September 2012.
[3] S. N. Shahi, M. Emadi, and K. Sadeghi “High
Resolution Doa Estimation In Fully Coherent
Environments”, Progress In Electromagnetics
Research C, Vol. 5, 135–148, 2008.
[4] Dhusar Kumar Mondal ”Studies of Different
Direction of Arrival (DOA) Estimation Algorithm
for Smart Antenna in Wireless Communication”,
IJECT Vo l. 4, Is s uEsp l- 1, Ja n- Ma rCh2013.
[5] Rias Muhamed”Direction of Arrival Estimation
using antenna array”, Virginia Polytechnic
Institute and State University, Blacksburg,
Virginia, Jan 1996.
[6] Revati Joshi, Ashwinikumar Dhande,
“DIRECTION OF ARRIVAL ESTIMATION USING
MUSIC ALGORITHM IJRET”, International
Journal of Research in Engineering and
Technology eISSN: 2319-1163 | pISSN: 2321-7308.
[7] T. B. Lavate, V. K. Kokate & A. M. Sapkal,
“Performance Analysis of MUSIC and ESPRIT
DOA Estimation Algorithms for Adaptive Array
Smart Antenna in Mobile Communication”,
International Journal of Computer Netwoks
(IJCN), Vol.2, Issue 3 PP.152-158.
[8] Tanuja S. Dhope (Shendkar), “Application of
MUSIC, ESPRIT and ROOT MUSIC in DOA
Estimation”, Faculty of Electrical Engineering and
Computing,University of Zagreb,Croatia.
[9] Zhao Qian, Zhen Ai, “An Iterative MUSIC
Algorithm Research Based On the DOA
Estimation”, International Conference on
Biological and Biomedical Sciences Advances in
Biomedical Engineering, Vol.9, 2012.
[10] Yan Gao, Wenjing Chang, Zeng Pei, Zhengjiang
Wu, “An Improved Music Algorithm for DOA
Estimation of Coherent Signals”, Sensors &
Transducers, Vol. 175, Issue 7, July 2014, pp. 75-82.
[11] Tithi Gunjan, Gaurav Chaitanya, “Comparative
Analysis of MUSIC Algorithm in Smart Antenna”,
International Journal of Digital Application &
Contemporary research , Volume 2, Issue 8, March
2014.
IJSER
International Journal of Scientific & Engineering Research, Volume 6, Issue 7, July-2015 603
ISSN 2229-5518
IJSER © 2015
http://www.ijser.org
[12] Yan Gao, Wenjing Chang, Zeng Pei, Zhengjiang
Wu, “An Improved Music Algorithm for DOA
Estimation of Coherent Signals” Sensors &
Transducers, Vol. 175, Issue 7, July 2014, pp. 75-82.
IJSER
