 Open Access
 Total Downloads : 753
 Authors : Iffath Fawad, Aaquib Nawaz. S, Syed Younus
 Paper ID : IJERTV1IS8346
 Volume & Issue : Volume 01, Issue 08 (October 2012)
 Published (First Online): 29102012
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Reduced Complexity Sign Beamforming Algorithms for Mobile Communication Systems
(1) Iffath Fawad (2) Aaquib Nawaz. S (3) Syed Younus
(1)Assistant Professor, Islamiah Institute of Technology, Bangalore
(2)Software Engineer ACI Pvt Limited, Bangalore
(3) M.Tech, Dept of Telecommunication, RVCE, Bangalore
Abstract: The increasing capacity and quality demands for mobile communication services without a corresponding increase in RF spectrum allocation motivate the need for new techniques to improve spectrum utilization. Smart Antenna shows real promise for increasing spectrum efficiency. Smart Antenna comprises of two functions viz. Angle Of Arrival (AOA) and Adaptive Beamforming (ABF). The function of AOA is to get the directions of signals having maximum power and that of Beamforming is to direct beam towards look direction and nulls in the unwanted directions.
In this paper existing LMS algorithm is modified to obtain better execution speed and computational complexity by using sign algorithms. Beamforming algorithms namely Least Mean Square (LMS), Sign Error LMS (SELMS), Sign Data LMS (SDLMS), Sign Sign LMS (SSLMS)
algorithms were simulated for various look directions and jammer configurations and their MSE characteristics and phase transients are compared. Performance of SDLMS algorithm is studied by varying the step size. SSBeamforming algorithm is also implemented on DSP kit TMS320C6713 and compared with simulation result.
KeywordsAdaptive array beamforming, LMS algorithm, sign algorithms, MSE

INTRODUCTION
SMART antenna systems employing multiple antennas promises increased system capacity, extended radio coverage and improved quality of service through the ability to steer the antenna pattern in the direction of desired user while placing nulls at interferer locations [1][3]. Adding more antennas to the array gives higher angle resolution while steering the beam and more degrees
of freedom in placing the nulls, but it results in increase of computational complexity and latency in calculating the weight vectors, which are used to process the received signals at the antennas. In Switchedbeam approach a set of weight vectors are precalculated and stored for different angles, hence there is less computational complexity. In fully adaptive systems, however, a new weight vector is calculated adaptively with the change in the angle of the user and/or an interferer. The adaptive approach, therefore, offers accurate tracing of the user angle at the cost of increased computational complexity.
The computational requirements of conventional LMS algorithm is high, therefore we need to devise methods to reduce complexity of beamforming algorithm without considerable degradation in performance.
In this paper well Known LMS algorithm is modified to make it suitable for high speed digital communication systems by reducing the complexity in the weight vector updation. The LMS algorithm is modified to obtain SELMS, SDLMS and SSLMS algorithms.

FORMULATION OF ADAPTIVE BEAMFORMING
Figure1: Uniform Linear Array
A uniform linear array is as shown in Figure(1), which consists of L equispaced omni directional sensors with interelement spacing of .
2
It receives M narrowband interference signals, one The array weight coefficients of LMS are
desired signal
s(n)
and noise signal
n(n) .The
modified by applying sign operator to error e(n)
received data vector x(n) is given by
M
given by
x(n) a(0 )s(n) a(i ) i(n) n(n)
i1
(1)
w(n 1) w(n) x(n) sgn(e(n))
Where, sgn(e(n)) is given by
(6)
Where, a(0 ) is the desired steering vector
1 e(n) 0
and
a(i ) is the steering vector for the ith
sgn(e(n)) 0 e(n) 0
1 e(n) 0
(7)
interference signal [3].
If w(n) is the complex weight then the
The SELMS algorithm is also known as
output of a linear beamformer is
y(n) w(n)T x (n)
(2)
Least Mean Absolute Value (LMAV) algorithm. The sign error algorithm can be viewed as the result of applying two level quantizer to error e(n).

SIGN DATA LMS ALGORITHM (SDLMS)
w(n)
are usually estimated through the
This is similar to SELMS, instead of using
minimization of error e(n) given by
e(n) s(n) y(n)
(3)
the sgn operator for error, the computational requirement of the LMS algorithm may be simplified by applying sgn operator to the data as
III. LEAST MEAN SQUARE ALGORITHM (LMS)
w(n 1) w(n) sgn(x(n)) e(n)
Where, sgn(x(n)) is sign of data vector given by
(8)
The LMS algorithm is the most widely used adaptive beamforming algorithm, being employed in
sgn(x(n))
x(n)
x(n)
(9)
several communication applications. The LMS algorithm changes the weight vector w(n) along the direction of the estimated gradient based on the steepest descent method. The weight vector updation
for LMS algorithm is given by
The disadvantage of SDLMS algorithm is that it sometimes alters the direction of weight vectors.

SIGN SIGN LMS ALGORITHM (SSLMS)
w(n 1)
w(n) e(n) x* (n)
(4)
In this algorithm we quantize both error and data by applying sgn operator. The weight update
Where, is the step size controlling the
convergence characteristics of beamforming algorithm given by
equation is
w(n 1) w(n) sgn( x(n)) sgn(e(n))
(10)
0
2
3tr( Rxx )
(5)

SIMULATION RESULTS
tr(Rxx ) is the trace of auto correlation matrix.

SIGN ERROR LMS ALGORITHM (SE LMS)
LMS algorithm is computationally efficient but the convergence rate is low and complexity is high. Therefore, the LMS algorithm is to be modified to achieve better convergence and reduced complexity by using SELMS.
The performance of all Beamforming algorithms stated has been studied by means of MATLAB simulation. For comparison purpose, result obtained with the conventional LMS algorithm is also presented.
For Simulation the following assumptions are considered

Mutual Coupling effects are zero between antenna elements

Distance between antenna elements is
2
an optimum value to avoid grating lobes

Look Direction and jammer directions have been determined aprior.

The propagation environment is stationary.

Number of array elements is 100.


Case (a): Beamforming Result for LMS
Look Direction=450
Interference Directions=100 and 300.
Figure (2): Polar Plot of LMS algorithm
From the Figure(2) it is clear that LMS algorithm is able to form the main beam in the look direction of 450 and nulls in the direction of interferers i.e 100 and 300.
Case (b) Beamforming Result for SELMS
Look Direction=600
Interference Directions=100,200,300 and 450
Figure (3): Polar Plot of SE LMS algorithm
From the Figure3 it is clear that SELMS algorithm is able to form the main beam in the look direction of 600 and nulls in the direction of interferers i.e 100,200,300 and 450.
Case(c) Beamforming Result for SDLMS algorithm
Look Direction=300
Interference Directions=100,450,550 and 600
Figure (4): Polar Plot of SD LMS algorithm
From the Figure(4) it is clear that SDLMS algorithm is able to orm the main beam in the look direction of 300 and nulls are diminishing in the direction of interferers. Hence SDLMS has an advantage of completely blocking the jammer directions.
Case (d) Beamforming Result for SSLMS
Look Direction=700
Interference Directions=100,200,300 and 600
Figure (5): Polar Plot of SS LMS algorithm
From the Figure (5) it is clear that SSLMS algorithm is able to form the main beam in the look direction of 700 and nulls are in the direction of interferers.
Case (e): Weight Vector Computation
The performance of various algorithms is compared in terms of phase variations applied to individual array elements by performing 100 runs.
LMS algorithm has the larger variations in phase shifts whereas sign algorithms have lesser variations in phase as depicted in simulation curves of Figure(6)
Figure(6): Array weigths ofBeamforming algorithms
Case(f): Effect of Change in Step Size on MSE
Case(g): Effect of Change in Step Size on weight magnitude
Figure(8): Step Size Variation Effects
The performance of SDLMS algorithm is studied by varying the step size.As the step size is incresed the weigth vector magnitude has large amount of variations. Hence it is good to choose smaller step size for better performance as shown in simulation curve of Figure(8).
Case (g): Error Vector Magnitude (EVM) measurement of Beamforming algorithms
For a complex signal, it is also convenient to make use of the Error Vector Magnitude (EVM) as an accurate measure of any distortion introduced by the adaptive scheme on the received signal [8].
The EVM is given by
EVM
1 S ( j) S ( j) 2
(11)
rms
KP0
r t
K
j 1
0
Where, K is the number of observations
used,
Sr ( j)
is the normalized jth output of the
beamformer and
St ( j)
is the jth transmit signal. P
Figure(7): MSE of SDLMS algorithm
The performance of SDLMS is studied by varying the step size. From the simulation curve of Figure(7) it is clear that as the step size increses the the algorithm takes more iterations to converge.
is the normalized transmit signal power. K= Number of observations= 100.
Table (1): Simulation Results of EVM
Algorithm 
EVM 
LMS 
0.9870 
SELMS 
0.9760 
SDLMS 
0.9582 
SSLMS 
0.9844 
From the MATLAB simulation results of Table(1) it is clear that the EVM of SDLMS algorithm is less as compared to other algorithms.
Case (h): Computation Complexity & Execution Speed
Computation complexity is also a good performance index to measure the efficiency of Beamforming algorithms. If L is number of array elements and N is number of iterations.
Table (2): Computation Complexity of Beamforming
Algorithm 
Number of Additions 
Number of Multiplications 
LMS 
N (L+1) 
N(L+2) 
SELMS 
N 
N 
SDLMS 
N(2L+4) 
N(2L2) 
SSLMS 
N 
NL 
From the Table(2) SELMS requires least number of multiplications and additions followed by SSLMS where as conventional LMS requires large amount of multiplications.
Table(3): Execution Speed of Beamforming
Beamforming algorithm 
Execution Time in seconds 
L.M.S 
0. 8541 
SDLMS 
0.3084 
SELMS 
0.2297 
SSLMS 
0.4780 
From the Table (3) it is clear that SELMS takes least amount of execution time followed by SDLMS as compared to conventional LMS.
VIII.IMPLEMENTATION RESULTS ON TMSC3206713
In this section graphs for real and imaginary phase shifts obtained using DSP kit for SSLMS algorithm are presented.
Table (4): Input to SSLMS Beamformer
Algorithm 
Number of Array Elements 
Look Direction 
Jammer Directions 
SSLMS 
8 
300 
[100,200,700] 
Figure (9): DSP kit Output for real array weights calculation using SSLMS Algorithm
Figure(9)gives the real part of array weights calculated on DSP kit. w(i) indicates array weight, i is the index corresponding to antenna element.
Figure (10): DSP kit Output for imaginary array weights calculation using SSLMS Algorithm
Figure (10) gives the imaginary part of array weights calculated on DSP kit.

COMPARISON OF SIMULATION AND IMPLEMENTATION RESULTS
Figure (11): Comparison of MATLAB and DSP kit Result for SSLMS
Figure(11) provides the comparison of weigth vector obtained using MATLAB and DSP kit. Both the weigth vectors almost Converges.

CONCLUSION
LMS algorithm is modified to obtain sign algorithms of beamforming by applying the sgn operator to error, data and both.
It is shown that sign algorithms have reduced Error Vector Magnitude, complexity and execution speed as compared to conventional LMS algorithm. Simulation curves also reveal that the phase transients of LMS are higher as compared to Sign algorithms. Performance of SDLMS is simulated by varying step size.
REFERENCES

Z. Zhang, M. F. Iskander, Z. Yun, and A. Host Madsen, Hybrid smart antenna system using directional elements performance analysis in flat Rayleigh fading, IEEE Trans. Antennas Propag., vol. 51, no. 10, pp. 29262935, Oct. 2003.

M. Rezk,W. Kim, Z. Yun, and M. F. Iskander, Performance comparison of a novel hybrid smart antenna system versus the fully adaptive and switched beam antenna arrays, IEEE Antennas Wireless Propag. Lett., vol. 4, pp. 285 288, 2005.

L. C. Godara, Applications of antenna arrays to mobile communications, part II: beamforming and directionofarrival considerations, Proc. IEEE, vol. 85, no. 8, pp. 11951245, Aug. 1997.

Guancheng Lin, Yaan Li, and Beili Jin, Research on Support Vector Machines Framework for Uniform Arrays Beamforming, IEEE International Conference on Intelligent Computation Technology and Automation, 2010.

O. Tanrikulu and A. G. Constantinides, Least mean kurtosis: A novel higherorder statistics based adaptive filtering algorithm Electron.letter., vol. 30, no. 3, pp. 189190, Feb. 1994.

T. Aboulnasr and K. Mayyas, A robust variable stepsize LMStype algorithm: Analysis and simulations, IEEE Trans. Signal Process., vol. 45, no. 3, pp. 631639, Mar. 1997.

D. I. Pazaitis and A. G. Constantinides, A novel kurtosis driven variable stepsize adaptive algorithm, IEEE Trans. Signal Process., vol. 47, no. 3, pp. 864872, Mar. 1999.

Arslan, H. and H. Mahmoud, "Error vector magnitude to SNR conversion for nondataaided receivers", IEEE Trans. on Wireless Communications, vol. 8(5), pp. 2694 2704, 2009.

Nascimento, V.H., "Improving the initial convergence of adaptive filters: variablelength LMS algorithms", 14th International Conference on Digital Signal Processing, Santorini, Greece, pp. 667670, July 2002.

Zhao, S., Z. Man, and S. Khoo, "A Fast Variable StepSize LMS Algorithm with System
Identification", 2ndIEEE Conference on Industrial Electronics and Applications, Harbin, China, pp. 23402345, May2007.
BIODATA OF AUTHORS

IFFATH FAWAD
Assistant Professor, Dept. of lectronics &Communication Islamiah Institute of Technology, Bangalore
Her areas of interest include Digital Signal Processing, Antenna Theory and Design, Microwave and Radar, Multirate Filter Banks, Statistical Signal Processing, Satellite Communication and Network Protocol Design.

AAQUIB NAWAZ.S
Software Engineer, ACI Pvt Limited Bangalore
He completed his M.Tech in 2010 from RV College of Engineering and presently working as a software engineer. His areas of interest include Smart Antennas, Web Mining, Enterprise Applications, FrameworksStruts and Design Patterns.

SYED YOUNUS
Dept. of Telecommunication, RVCE, Bangalore
His areas of interest are Adaptive Beamforming, Network Protocol Design, Multirate Filter Banks, Wireless communication and Antenna Theory & Design.