International Journal of Engineering Trends and Technology (IJETT) – Volume 14 Number 5 – Aug 2014
Estimation of Direction of Arrival Algorithms
for Adaptive Array Smart Antenna in Wireless
Communication
1
K.N.Srinivasa Kumar, 2R.Satish, 3Dr.M.Siva Ganga Prasad
1
2
Department of ECE, C.R.Reddy college of Engineering& Technology, Eluru, A.P, India.
Assistant Professor Department of ECE, C.R.Reddy college of Engineering& Technology, Eluru, A.P, India.
3
professor Department of ECE, K.L.University, Vijayawada, A.P, India.
Abstract
This paper proposes the direction-of-arrival estimation
of fully correlated signals in mobile communications. In
adaptive array smart antenna, to locate the desired
signal, various directions of arrival (DOA) estimation
algorithms are used. In the past, conventional MUSIC
algorithm has high resolution and accurate method but
high percentage error in smart antenna systems. In this
work, comparison of different MUSIC algorithms
and ESPIRIT and hence ESPIRIT is high accurate and
less percentage error compare to MUSIC algorithm
techniques. The experimental result shows to
comparing different previous MUSIC techniques and
ESPIRIT algorithm.
Keywords- MUSIC, ESPRIT, Smart antenna, DOA.
I. INTRODUCTION
One of the most promising techniques in
wireless applications with smart antenna growing
exponentially. 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. The DOA algorithms are
classified as quadratic type and subspace type [1].
The Barltett and Capon (Minimum Variance
Distortion less Response) [1] are quadratic type
algorithms. The both methods are highly dependent
on physical size of array aperture, which results in
poor resolution and accuracy,[2],[3],[4].
The direction of interest is also known as
Direction of Arrival (DOA) of the incident signals.
Hence accurate estimation of Direction of Arrival
(DOA) plays significant role in smart antenna
systems. There are several algorithms those have the
ability in calculating the DOA of the incidents
signals. The most popular among those algorithms
ISSN: 2231-5381
are the Multiple Signal Classification (MUSIC) and
Estimation of signal Parameters via Rotational
Invariance Technique (ESPRIT).
Efficient source and channel coding as well
as reduction in transmission power or transmission
bandwidth or both are possible solutions to the
challenging issue. With the advances in digital
techniques, the frequency efficiency can be
improved by multiple access technique (MAT),
which gives mobile users access to scarce resource
(base station) and hence improves the system’s
capacity [5]. Family of existing Frequency
Division Multiple Access (FDMA), Time Division
Multiple Access (TDMA) and Code Division
Multiple Access (CDMA) can be enlarged by
adding a new parameter „space„ or „angle„ [6],
which results in MAT known as ‘’ Space Division
Multiple Access‟ (SDMA).
II. MUSIC TECHNIQUES
MUSIC stands for Multiple Signal
Classification. It is high resolution subspace DOA
algorithms and estimation of number of signals
arrived, hence their direction of arrival. In this paper,
we consider the two types of MUSIC algorithms are
used. They are spatial music and Conventional music.
A. music with spatial smoothing
Spatial smoothing is a widely used in
direction-of-arrival (DOA) estimation of more than
one source from a single snapshot in a smart antenna
systems. It has high resolution and accurate method.
It is very attractive in Communication, radar, sonar
fields.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 14 Number 5 – Aug 2014
The received signal is given by
( )=
(
)
(
)+ (
)
Where N is the number of received signals, θn is
direction of arrival of signal n and gn(tm) is the
waveform of signal n. v is the zero-mean spatially
and temporally white complex Gaussian vector with
second moment and can be written as
( )
=
( ) =
,
δ is the Kronecker delta and H is hermitage complex
conjugate. The direction of arrival of signal can be
written as
then estimate DOAs by local maxima of the
spectrum. This method suffer from lack of angular
resolution.
The vector of the received signals at the kth sub
array is expressed as:
( )=
)
()
,…,
)
⋮
(
( )+
The diagonal of kth matrix can be written as
=
(
)=
)
Where D is the kth power of the diagonal matrix and
n is the additive white Gaussian noise. S denotes an L
by N matrix with its N columns being the
eigenvectors corresponding to the N largest Eigen
values.
1
(
(
(
A is the direction of arrival of signal can be written as
)
1
Where k is the wave number given by 2πdλ, d is the
element interspaces, λ is the wavelength and L is the
number of elements. The waveform gn(tm) of signal
n is given by
(
(
)=
)
⋮
(
)
(
)
The correlation matrix of the array is given by
Gn(tm) = [0, Ø1, Ø2, Ø3, ØL-1];
= ⋀
Where Ø is the direction angles of desire signals
+ ⋀
The correlation matrix of the array is given by
= ⋀
The MUSIC spectrum is an all-pole function of the
form:
+ ⋀
Where S denotes an L by N matrix with its N
columns being the eigenvectors corresponding to the
N largest Eigen values of the array correlation matrix
R.
Λs is a diagonal matrix that contains the relevant
Eigen values at its diagonal.
E denotes an L by L − N matrix with its L − N
columns being the eigenvectors corresponding to the
L − N smallest Eigen values of the array correlation
matrix R.
Λe is a diagonal matrix contains the corresponding
Eigen values at its diagonal.
B. Conventional music
Conventional music also called classical
music which first compute a spatial spectrum and
ISSN: 2231-5381
=
exp(−
2
cos )
exp(
2
cos )
III. ESPIRIT ALGORITHM
ESPRIT stands for Estimation of Signal
Parameters via Rotational Invariance Techniques
which is another subspace based DOA estimation
algorithm. ESPRIT is similar to MUSIC in that it
generates estimates that are asymptotically unbiased
and efficient. In addition, it has several important
advantages over MUSIC. In this algorithm is more
robust with respect to array imperfections than
MUSIC. It has high resolution, less percentage error,
Computation complexity and storage requirements
are lower than MUSIC. Figure 1 shows the spirit
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International Journal of Engineering Trends and Technology (IJETT) – Volume 14 Number 5 – Aug 2014
algorithm of four element linear array which is
composed of two doublets.
Eigenvalues without much computational and storage
requirements.
IV. EXPERIMENTAL RESULTS
The different MUSIC algorithms & ESPRIT methods
of DOA estimation are simulated using MATLAB. A
uniform linear array with M elements has been
considered here.
CONVENTIONAL MUSIC
10
smoothing music
conventional music
5
0
Figure1. Four element linear array which is composed of two
doublets using spirit algorithm.
The signals induced on each of the arrays are written
as
magnitude (dB)
-5
-10
-15
-20
-25
-30
-35
( )=
∗Λ∗ ( )+
( )
-40
-45
And
( )=
∗Λ∗ ( )+
( )
Where S denotes an L by N matrix with its N
columns being the eigenvectors corresponding to the
N largest Eigen values of the array correlation matrix
x.
-80
-60
-40
-20
0
20
angle (degree)
40
60
80
Fig. 2 Comparison of Conventional MUSIC with Spatial
Smoothing technique for the case of two coherent waves and one
incoherent wave received by an 8-element uniform linear array at
angles 30, -30, and -45 degrees, respectively.
10
smoothing music
conventional music
5
0
Λ = diag{ejkdsin(θ1) ejkdsin(θ2) ----- ejkdsin(θD)}
A is the direction of arrival of signal can be written as
-5
magnitude (dB)
Λs is a diagonal matrix that contains the relevant
Eigen values at its diagonal.
-10
-15
-20
-25
-30
A= [a(θ1) a(θ2) a(θ3) --- a(θD)]
-35
-40
Thus the eigenvalues of ф must be equal to the
diagonal elements of Λ such that
=
,
=
,…
=
Once the Eigen values of ф, λ1, λ2, ------ λD are
calculated, we can estimate the angles of arrivals as
= sin (
( )/
-45
-80
-60
-40
-20
0
20
angle (degree)
40
60
80
Fig. 3 Comparison of Conventional MUSIC with Spatial
Smoothing technique in coherent multipath environment. Four
coherent signals arrive at an 8-element linear uniform array at
angles 30, -43,70 and -81 degrees, respectively.
)
It is eliminates the search procedure and produces
the DOA estimation directly in terms of the
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International Journal of Engineering Trends and Technology (IJETT) – Volume 14 Number 5 – Aug 2014
REFERENCES
200
forwardmusic
[1] Harry Trees,” Optimum Array Processing, Detection,
Estimation and Modulation Part IV”, John Wiley and Sons, New
York, 2002.
backwardmusic
150
100
Pmusic
[2] Varade, S.W., Kulat, K.D,” Robust Algorithms for DOA
Estimation and Adaptive Beam forming for Smart Antenna
Application”,2nd international conference on Emerging Trends
in Engineering and Technology (ICETET), 2009 , pp: 1195 –
1200, Dec. 2009.
50
0
-50
-100
-80
-60
-40
-20
0
DOA
20
40
60
80
100
Fig. 4 Comparison of Forward Spatial Smoothing technique with
Forward/Backward method. Five coherent signals arrive at a 9element uniformly spaced array at angles - 81, -43, 30, 57’and 70
degrees, respectively.
Simulation of ESPRIT algorithm for linear uniform
array with four elements with SNR =20
Table 1 DOA ESTIMATION USING ESPRIT FOR VARYING
ANGULAR SEPARATION (M=4, SNR=20 dB, K=100)
Sr,no
1
2
θ Input
(deg)
10
25
20
80
[3] De Leon, F.A. Marciano, J.J.S. ,” Application of MUSIC,
ESPRIT and SAGE Algorithms for Narrowband Signal
Detection and Localization”, TENCON ,IEEE Region 10
Conference, pp 1-4, Nov. 2006.
[4] Sheng, W.X.; Zhou, J.; Fang, D.G.; Gu, Y.C.,” Super resolution
DOA Estimation in switched beam smart antenna”, Antennas,
Propagation and EM Theory, 2000. Proceedings. ISAPE 2000. 5th
International Symposium, pp 603-606, 2000.
[5] John Litva, Titus Lo,” Digital Beam forming in Wireless
Communication”, Artech House Bostan-London,1996.
[6] Shauerman, Ainur K. Shauerman, Alexander A.,” Spectralbased algorithms of direction-of-arrival estimation for adaptive
digital antenna arrays”, 9th international conference and seminar
on Micro/Nanotechnologies and Electron Devices (EDM)
2010, pp 251-255,Sept. 2010.
θ ESPRIT
(deg)
9.43
24.53
19.56
78.23
Table 1 illustrates that the percentage error in DOA
detection using ESPRIT algorithm decreases as
angular separation between arriving signals increases.
V. 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. But
ESPIRIT algorithm has low error percentage error
and less computation a complexity compare to
MUSIC algorithm
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