 Open Access
 Total Downloads : 593
 Authors : M. H. Bhede, D. G. Ganage, S. A. Wagh
 Paper ID : IJERTV4IS070201
 Volume & Issue : Volume 04, Issue 07 (July 2015)
 DOI : http://dx.doi.org/10.17577/IJERTV4IS070201
 Published (First Online): 08072015
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Performance Evaluation of Capon and Caponlike Algorithm for Direction of Arrival Estimation
M. H. Bhede E&TC Dept. SCOE, Pune,
D. G. Ganage E&TC Dept. SCOE, Pune,
Maharashtra, India
S. A. Wagh
E&TC Dept.
SITS, Narhe, Pune, India
Abstract: Wireless communications is one of the most active areas of technology development, since it is satisfying the demand for increasing system capacity.The system capability is improved using DirectionofArrival (DOA) estimation algorithm that corresponds to seek out the direction during which desired user and therefore the interference lie for antenna array. This paper investigates and compares Capon and Caponlike DOA estimation algorithm on the uniform linear array (ULA) which are used in design of smart antenna system. The Caponlike algorithm is based on Capon algorithm through the introduction of a new optimization problem, in order that which aims to maintain the array gain in the look direction is constant, usually unity. To verify the performance of the proposed algorithm, simulations are performed and then the results obtained are compared with the Capon algorithm.
KeywordsWireless Communication, DOA,Capon, Capon like, Smart Antenna System, ULA.

INTRODUCTION
In array signal processing Direction of Arrival estimation (DOA) stands for estimating the angles of arrivals of received signals by an array of antennas [1].The applications of this DOA estimation are such as in audio processing, wireless communication, radar and sonar, seismology, and wireless emergency call locating [3]. A smart antenna, is a system that combines multiple antenna elements with a signal processing capability to optimize its radiation pattern automatically in response to the system signal environment.In smart antenna systems, DOA estimation is anecessary process to find out the direction of incoming signals and thus to direct the beam of the antenna array towards the estimated direction and placing null towards interference signals.
Many resolution algorithms for DOA estimation are proposed such as Conventional spectralbased method and subspaced based and statistical method [3]. Conventional method for DOA estimation is based on the beamforming and nullsteering concept, is straightforward, depends on physical size of array and requires low computation complexity. This technique steer beams in all directions and look for the maximum peaks in the output power. The sum and delay or Bartlett and Minimum Variance Distortionless Response (MVDR) or Capon etc. are conventional spectral based methods. Conventional methods have some limited resolution leads to subspaced
based methods. Higher angular resolutions Multiple Signal Classification (MUSIC)[8] and Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT)

are subspaced based methods having higher accuracy than conventional based methods. In real applications, when the number of sources is incorrectly estimated and the coherent signals existed due to multipath fading, the performance of subspacebased methods will degenerate significantly. To avoid the problem of source estimation of high computational complexity, Capon algorithm can be applied in DOA estimation but with the cost of lower resolution compared with subspacebased method [3].
In this paper, Capon algorithm, which has less computational complexity than subspacebased methods, is used as the basis to derive the proposed algorithm (Capon like) algorithm. The proposed algorithm is similar to the Capon algorithm in one aspect, which is to minimize power from all direction subject to specific gain in the look direction; hence it is named Caponlike algorithm [3].
Capon and Caponlike algorithms were developed and simulated in MATLAB software. The organization of this paper is as follows firstly receiving signal model is developed for direction of arrival estimation in Section II. The Capon algorithm is described in detail in Section III. The Proposed Caponlike algorithm is described in detail in Section IV. In section V simulation results and discussion of Capon and Caponlike are presented. Finally conclusions are presented in further Section.


SIGNAL MODEL
Figure1 shows a uniform linear array (ULA) of N equispaced sensors. The array consists in a set of antenna elements connected to a receiver through amplitude and phase shift weights.
Figure1. Uniform Linear Array
Consider, D signals which are incident on ULA and the received input data vector at Melements that are separated by a distance. Now, distance d can be expressed
The output power of the array as a function of DOA is as shown below.
as a linear combination of N incident waveforms and noise. The signal vector u (t) can be defined as
PCapon
= 1
aH Ruu 1a
(7)
D1
x t = a l sl t + n t (1)
l=0
sl t
By computing and plotting MVDR spectrums over the whole range of, the DOA can be estimated by locating the peaks in the spectrum [12].

CAPONLIKE ALGORITHM
x t = a 0 . . a D1
.
. + n t (2)
.
The proposed algorithm is based on modified Capon algorithm; the steering vector can be expressed
sl t
Where a , sl t and n t are the steering vector, desiredsignal and noise signal respectively
asfollows
A() = g 1 a 1 g 2 a(2
) . . a N g N
(8)
T
u t = A s t + n t (3)
Where, sT t = s0 t s1 t . . sD1 t
is the vector of incident signals,
= [0 1 . . 1 ] is the noise vector, and
a j is the array steering vector. In terms of the above data
Where g is the array gain in a specific direction . Since the array response is affected by the gainpattern in a
look direction, the constraint in Caponlikealgorithm can be given by [3] –
min E y k 2 = min wH R w
model, the input covariance matrix Ruu can be expressed w w uu
as [6]
Ruu = A E ssH AH + E nnH (4)
Where Rss is the signal correlation matrix E ssH .


CAPON ALGORITHM
Introduced by J. Capon [3], Capon algorithm is a conventional spectralbased method which is used to improve resolution of Bartlett Algorithm.The main idea of Capon algorithmis to minimize the received power of the
Subject to wH a 0 = g()(9)
Applying Lagrange optimization technique to the constraint yields the Lagrange multiplier , and the optimized weight w given by,
=
aH Ruu 1a (10)
Ruu 1a
incoming signal in all direction while maintaining a unity gain in look direction [3].The constrained imposed on this
algorithm is given as:
w = aH Ruu
1a (11)
min E y k 2 = min wH Ruu w
Finally, the power spectrum of the Caponlike algorithm is
given as
w w
Subject to wH a 0 = 1(5)
PCaponlike
= 1
aH Ruu 1a
(12)
The weight w vector obtained by solving (5) is often called Capon beam former weights or minimum variance distortion less response (MVDR). Applying Lagrange optimization method to the constraint yields the optimized weight,
Ruu 1a
uu
w = aH R 1a (6)

SIMULATION RESULTS
The Capon and Caponlike algorithm of DOA estimation are simulated using MATLAB. In these simulations, it is considered a uniform linear array antenna formed by elements with the equally spaced distance of 2. The noise is Gaussian white noise, SNR=2dB and number of snapshots is 500. The simulation has been run for three independent narrow band signals;angle of arrival is 200, 300 and 700. The performance has been analyzed for different array elementsand SNR.

SIMULATION RESULTS OF CAPON ALGORITHM
Case.1: Capon spectrum for varying number of array elements
The effect of varying the number of array elementswith two different values M1=30, M2= 100 and other condition remains unchanged are as shown in Figure2. It is clear that as number of array elements increases, the peaks of spectrum become narrower and if number of array element decreases, then angular resolution of Capon algorithm decrease.
Figure2. MVDR spectrum for varying number of array elements
Case.2: Capon spectrum for varying signal to noise ratio.
The effect of varying the signal to noise ratio with two different values SNR1= 10, SNR2= 20 and other condition remains unchanged are as shown in Figure3. It is clear that as the value of SNR increases, precise detection of incoming signal and angular resolution capacity increases also the spectral beam width becomes narrower. The value of SNR can affect the performance of the Capon algorithm.
Figure3. MVDR spectrum for varying SNR

SIMULATION RESULTS OF CAPONLIKE ALGORITHM
Case.1: MUSIC spectrum for varying number of array elements
The effect of varying the number of array elements with two different values M1=30, M2= 100 and other condition remains unchanged are as shown in Figure4. It is clear that as number of array elements increases, the peaks of spectrum become narrower and if number of array element decreases, then angular resolution of Capon algorithm decrease.
Figure4. MUSIC spectrum for varying number of array elements
Case.3: Caponlike spectrum for varying signal to noise ratio.
The effect of varying the signal to noise ratio with two different values SNR1= 10, SNR2= 20 and other condition remains unchanged are as shown in Figure5. It is clear that as the value of SNR increases, precise detection of incoming signal and angular resolution capacity increases also the spectral beam width becomes narrower. The value of SNR can affect the performance of the Capon like algorithm.
Figure5. Caponlike spectrum for varying SNR

SIMULATION RESULTS FOR COMPARISON OF ALGORITHM
In these simulations, it is considered a linear array antenna formed by 10 elements that are equally spaced with the distance of / 2. The noise is Gaussian white noise, SNR=20dB and number of snapshots is 500. The simulation has been run for threeindependent narrow band signals;direction of arrival is 200, 300 and 700.
Figure6.Comparison ofCapon and Caponlike spectrum.
CONCLUSION
In this paper a new algorithmCaponlike is proposed from Conventional based Capon DOA estimation algorithm. The two algorithms are sensitive to the number of array elements and signaltonoise ratio. The angular resolution of the algorithm is improved with increasing the number of array elements, number of snapshots, signalto noise ratio. Caponlike algorithm gives more accurate DOA estimation than Capon algorithm for same specification.
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