Reduced Complexity Sign Beamforming Algorithms for Mobile Communication Systems

DOI : 10.17577/IJERTV1IS8346

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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 Tele-communication, 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 (SE-LMS), Sign Data LMS (SD-LMS), Sign Sign LMS (SS-LMS)

algorithms were simulated for various look directions and jammer configurations and their MSE characteristics and phase transients are compared. Performance of SD-LMS algorithm is studied by varying the step size. SS-Beamforming algorithm is also implemented on DSP kit TMS320C6713 and compared with simulation result.

KeywordsAdaptive array beamforming, LMS algorithm, sign algorithms, MSE


    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 Switched-beam approach a set of weight vectors are pre-calculated 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 SE-LMS, SD-LMS and SS-LMS algorithms.


Figure1: Uniform Linear Array

A uniform linear array is as shown in Figure(1), which consists of L equi-spaced omni- directional sensors with inter-element spacing of .


It receives M narrowband interference signals, one The array weight coefficients of LMS are

desired signal


and noise signal

n(n) .The

modified by applying sign operator to error e(n)

received data vector x(n) is given by


given by

x(n) a(0 )s(n) a(i ) i(n) n(n)



w(n 1) w(n) x(n) sgn(e(n))

Where, sgn(e(n)) is given by


Where, a(0 ) is the desired steering vector

1 e(n) 0


a(i ) is the steering vector for the ith

sgn(e(n)) 0 e(n) 0

1 e(n) 0


interference signal [3].

If w(n) is the complex weight then the

The SE-LMS algorithm is also known as

output of a linear beamformer is

y(n) w(n)T x (n)


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).



    are usually estimated through the

    This is similar to SE-LMS, instead of using

    minimization of error e(n) given by

    e(n) s(n) y(n)


    the sgn operator for error, the computational requirement of the LMS algorithm may be simplified by applying sgn operator to the data as


    w(n 1) w(n) sgn(x(n)) e(n)

    Where, sgn(x(n)) is sign of data vector given by


    The LMS algorithm is the most widely used adaptive beamforming algorithm, being employed in





    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 SD-LMS algorithm is that it sometimes alters the direction of weight vectors.


    w(n 1)

    w(n) e(n) x* (n)


    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))




    3tr( Rxx )



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


      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 SE-LMS.

      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

      1. Mutual Coupling effects are zero between antenna elements

      2. Distance between antenna elements is


        an optimum value to avoid grating lobes

      3. Look Direction and jammer directions have been determined aprior.

      4. The propagation environment is stationary.

      5. 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 SE-LMS

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 SE-LMS 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 SD-LMS 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 SD-LMS algorithm is able to orm the main beam in the look direction of 300 and nulls are diminishing in the direction of interferers. Hence SD-LMS has an advantage of completely blocking the jammer directions.

Case (d) Beamforming Result for SS-LMS

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 SS-LMS 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 SD-LMS 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


1 S ( j) S ( j) 2




r t


j 1


Where, K is the number of observations


Sr ( j)

is the normalized jth output of the

beamformer and

St ( j)

is the jth transmit signal. P

Figure(7): MSE of SD-LMS algorithm

The performance of SD-LMS 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











From the MATLAB simulation results of Table(1) it is clear that the EVM of SD-LMS 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


Number of Additions

Number of Multiplications


N (L+1)











From the Table(2) SE-LMS requires least number of multiplications and additions followed by SS-LMS where as conventional LMS requires large amount of multiplications.

Table(3): Execution Speed of Beamforming

Beamforming algorithm

Execution Time in seconds


0. 8541







From the Table (3) it is clear that SE-LMS takes least amount of execution time followed by SD-LMS as compared to conventional LMS.


In this section graphs for real and imaginary phase shifts obtained using DSP kit for SS-LMS algorithm are presented.

Table (4): Input to SS-LMS Beamformer


Number of Array Elements

Look Direction

Jammer Directions





Figure (9): DSP kit Output for real array weights calculation using SS-LMS 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 SS-LMS Algorithm

Figure (10) gives the imaginary part of array weights calculated on DSP kit.


    Figure (11): Comparison of MATLAB and DSP kit Result for SS-LMS

    Figure(11) provides the comparison of weigth vector obtained using MATLAB and DSP kit. Both the weigth vectors almost Converges.


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 SD-LMS is simulated by varying step size.


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    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.


    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, Frameworks-Struts and Design Patterns.


Dept. of Telecommunication, RVCE, Bangalore

His areas of interest are Adaptive Beamforming, Network Protocol Design, Multirate Filter Banks, Wireless communication and Antenna Theory & Design.

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