SMART ANTENNAS – PERFORMANCE ANALYSIS OF

BEAMFORMING ALGORITHMS

N.Karthik*, B.Bhuvaneswari, K.Malathi, R.Rajesh Kumar, M.Gulam Nabi Alsath, A.Henridass

Department of ECE, CEG Campus, Anna University, Chennai – 600025, India.

E-mail: karthik.rnatarajan@gmail.com

Abstract-There has been a growing demand for

mobile communications and for the more efficient

use of the radio spectrum, smart antenna systems

are used. There are a number of techniques

available for estimating the direction of arrival of

the signals. This paper presents the analysis,

simulation and performance of adaptive

beamforming algorithms on a five element

microstrip patch array which is used as a smart

antenna for wireless mobile communications.

Here, the performance comparison of the different

beamforming algorithms namely, LMS, NLMS,

Griffiths LMS and RLS algorithms is done. The

array factors obtained in MATLAB and standard

EM simulation software are compared and the

performance of the different adaptive beam-

forming algorithms is analyzed.

Keywords: LMS, NLMS, Beam-forming,

Direction of arrival, smart antennas, antenna

array, RLS.

I. INTRODUCTION

There has been a steady increase in the

development of broadband wireless access

technologies for wireless Internet services. This

is due to the increase in the number of users and

new high bit rate data services. The rise in traffic

will lead to insufficient capacity in the networks

which will be a problem for service providers.

Co-channel interference is a major limitation in

capacity caused by the increasing number of

users. Also, Internet usage in mobile has resulted

in increase in airtime usage thus saturating the

system’s capacity. Wireless carriers have begun

to explore new ways to maximize spectral

efficiency of their networks and improve their

return on investment. The development of smart

antennas for wireless communications has

emerged as one of the leading technologies for

achieving high efficiency networks that

maximize capacity and improve quality and

coverage. Smart antennas can increase the

system capacity by dynamically turning out

interference while focusing on intended user [1].

Smart antennas can provide higher system

capacities, increase signal to noise ratio, reduce

multipath and co-channel interference. Based on

the time delays due to the impinging signals

onto the antenna elements, the digital signal

processor computes the direction-of-arrival

(DOA) of the signal of interest (SOI), and then it

adjusts the excitations (gains and phases of the

signals) to produce a radiation pattern that

focuses on the SOI while tuning out any

interferers or signals-not-of-interest (SNOI). The

base station listens to the signals sent by the

cellular telephones.

Fig.1 Smart Antenna system.

A digital signal processor located at the

base station works in conjunction with the

antenna array and is responsible for adjusting

various system parameters to filter out any

interferers or signals-not-of-interest (SNOI)

while enhancing desired communication or

signals-of-interest (SOI). Thus, the system forms

the radiation pattern in an adaptive manner,

responding dynamically to the signal

environment and its alterations.

Two major configurations of smart antennas:

1. Switched Beam: A finite number of

fixed, predefined patterns or combining

strategies.

2. Adaptive Array: A theoretically infinite

number of patterns that are adjusted in

real time according to the spatial

changes of SOIs and SNOIs.

In Switched Beam approach, the

antennas form multiple fixed beams with

heightened sensitivity in particular directions.

Such an antenna system detects signal strength,

chooses from one of the several predetermined

fixed beams, and switches from one beam to

another as the cellular phone moves throughout

the sector.

In Adaptive Array approach, the antenna

adjusts to the RF environment as it changes.

Hence, the adaptive antenna technology can

dynamically alter the signal patterns to optimize

the performance of the wireless system. Hence,

it provides more degrees of freedom since they

have the ability to adapt in real time the

radiation pattern to the RF signal environment

[2].

The accurate estimation of direction of

arrival of all signals transmitted to the adaptive

array antenna contributes to the maximization of

its performance with respect to recovering the

signal of interest and suppressing any present

interfering signals. Data from an array of sensors

are collected, and the objective is to locate point

sources assumed to be radiating energy that is

detectable by the sensors. DOA estimation

algorithms can be categorized into two groups;

the conventional algorithms and the subspace

algorithms. Suitable DOA estimation algorithms

can be used [4].

II. FIVE ELEMENT MICROSTRIP PATCH

ANTENNA

A five element microstrip patch antenna

array designed for a frequency of 5.2 GHz is

depicted in Fig.2 and S-parameter (Reflection

coefficient) for the same is shown in Fig.3. The

specifications for the designed array is as

follows,

Substrate used : FR-4 with εr = 4.3

Substrate height: 1.6mm

Type of feed: Co-axial

Dimension of single patch: 13.35x17.72 mm2

Number of array elements: 5

Spacing between elements: λ/2

Fig. 2 Design of five element microstrip patch Antenna Array

Fig. 3 S-Parameter (Reflection Coefficient)

characteristics (f0 = 5.2 GHz)

III. ADAPTIVE BEAMFORMING

ALGORITHMS

The process of combining the signals

from different antenna elements is known as

beamforming. Beamforming is generally

accomplished by phasing the feed to each

element of an array so that signals received or

transmitted from all elements will be in phase in

a particular direction.

Adaptive Beamforming is a technique in

which an array of antennas is exploited to

achieve maximum reception in a specified

direction by estimating the signal arrival from a

desired direction (in the presence of noise) while

signals of the same frequency from other

directions are rejected. This is achieved by

varying the weights of each of the sensors

(antennas) used in the array. Though the signals

emanating from different transmitters occupy the

same frequency channel, they still arrive from

different directions. This spatial separation is

exploited to separate the desired signal from the

interfering signals. The optimum weights are

iteratively computed using complex algorithms

based upon different criteria.

In this paper, LMS algorithm, NLMS

algorithm, Griffiths LMS, RLS algorithms are

simulated in MATLAB. The tap weights

obtained are fed as inputs to the simulated

antenna array. The array factors obtained in

MATLAB and standard EM simulation software

are compared. The performance of the different

adaptive beam-forming algorithms is analyzed.

The simulation parameters used to simulate the

smart antenna system are

Angle of arrival of intended user = 40 о

Angle of arrival of unintended user = -20о

A. Least Mean Square algorithm (LMS)

The least mean square (LMS) algorithm

belongs to the trained algorithms category in

which a reference signal is used to update the

weights at each iteration. Here, we are searching

for the optimal weight that would make the array

output either equal or as close as possible to the

reference signal. The error signal e (n) is fed into

the weight updating algorithm. The criterion for

determining the weights is based on minimizing

the mean squared error (MSE) between beam-

former output and reference signal [3].

Let d (n) be the reference signal, x(n)

be the input signal and w(n) be the filter

weights. The filter coefficients that minimize the

mean squared error are found by solving the

Wiener-Hopf equation

Wopt = Rxx-1

ρ (1)

Where Wopt is the optimum filter

weights, Rxx is the autocorrelation matrix of the

input signal and ρ is the cross correlation

between the input and the output signal. Since

the MSE has a quadratic form, moving the

weights in the negative direction of the gradient

of the MSE should lead us to the minimum of

the error surface.

LMS algorithm is based on a traditional

optimization technique called the method of

steepest descent. A model of LMS Beamformer

is shown in Fig.4.

The output of the array is, y (n) = w

H(n) x(n) (2)

Error: e (n) = d (n) - y (n) (3) Weight: w (n+1) = w (n) + x (n) e*(n) (4)

Simulation

d (n) = cos (2*pi*f*t);

Normalized distance of separation of antenna

elements = 0.5

No. of antenna elements = 5

Fig. 4 LMS Beamformer.

The constant , also called the step size,

determines how close the weights approach the

optimum value after each iteration and it

controls the convergence speed of the algorithm.

The larger the value of , the faster the

convergence but lowers the stability around the

minimum value. The smaller the value of , the

slower the convergence but higher the stability

around the optimum value. Typical values for

the step size are 0 < < 2/λmax where λmax is the

largest eigen value of correlation matrix R. A

comparison of the array factor for LMS

algorithm obtained in MATLAB and standard

simulation software is shown in Fig.5.

Directivity of LMS algorithm obtained in EM

simulation software is shown in Fig.6.

Fig. 5 Normalized Array Factor of LMS Algorithm in

MATLAB and EM Simulation software.

Fig. 6 Directivity of LMS Algorithm in dB in

EM simulation software.

B. Normalized Least Mean Square Algorithm

(NLMS)

One of the difficulties in the design of

the LMS adaptive filter is the selection of the

step size. Since Rxx is generally unknown,

finding the value of is difficult [6]. The

difficulty is overcome by replacing the value of

step size with a parameter β where β is the

normalized step size with 0 < β < 2.

n) = β / ||x (n) ||2 (5)

X (n)

Dir

ecti

vit

y (

dB

) Update

y(n

)

y(n)

- e(n) w (n+1) = w (n) +

x (n) e*(n)

Adaptive Complex

Weight w (n)

d(n)

0

+

Arr

ay F

acto

r

Theta/Degree

Replacing in the weight vector update

equation with n) leads to Normalized LMS

algorithm (NLMS) which is given by

w (n+1) = w (n) + β x(n) e*(n)/ ||x(n)||2

(6)

Simulation

d (n) = cos (2*pi*f*t);

Normalized distance of separation of antenna

elements = 0.5

No. of antenna elements = 5.

A comparison of the array factor for

NLMS algorithm obtained in MATLAB and

standard simulation software is shown in Fig.7.

Directivity of NLMS algorithm obtained in EM

simulation software is shown in Fig.8.

Fig. 7 Normalized Array Factor of NLMS Algorithm

in MATLAB and EM Simulation software.

Fig. 8 Directivity of NLMS Algorithm in dB in

EM simulation software.

C. Griffiths Least Mean Square Algorithm

(Griffiths LMS)

A DOA based LMS algorithm is due to

Griffiths, and is referred to as the modified LMS

algorithm, the Griffiths algorithm, or the steered

direction algorithm. Here, the direction to which

the beam is to be steered will be the input to the

algorithm. The LMS algorithm which needs the

reference signal is modified to use the direction

instead of the reference signal.

The weights can be updated as,

w(k) = w(k-1) + α(k) (σs2Vs-X(k)Yp

*(k) ) (7)

where,

w(k) - Weights w(k-1) - Previous weights α(k) - a constant σs - Signal Power X(k) - input samples

Y(k) - Output of the array

Vs - Steering Vector of

Signal Direction

Simulation

d (n) = cos (2*pi*f*t);

Vs = exp (j*2*pi*d*sin(thetaS))

Normalized distance of separation of

antenna elements = 0.5

No. of antenna elements = 5

Fig. 9 Normalized Array Factor of Griffiths LMS

Algorithm in MATLAB and EM Simulation software

Arr

ay F

acto

r

Theta/Degree

Dir

ecti

vit

y (

dB

)

Arr

ay F

acto

r

Theta/Degree

Fig. 10 Directivity of Griffiths LMS Algorithm in dB

in EM simulation software.

A comparison of the array factor for

Griffiths LMS algorithm obtained in MATLAB

and standard simulation software is shown in

Fig.9. Directivity of Griffiths LMS algorithm

obtained in EM simulation software is shown in

Fig.10.

D. Recursive Least Squares Algorithm (RLS)

One of the drawbacks of the LMS

algorithm is its slow convergence speed under

certain conditions, for example when the Eigen

value spread of R is large. This leads to the

development of the Recursive Least Squares

(RLS) algorithm, which replaces the step size

with the inverse of R. The RLS adaptive

algorithm approximates the Wiener solution

directly using the method of least squares to

adjust the weight vector, without imposing the

additional burden of approximating an

optimization procedure. In the method of least

squares, the weight vector w(k) is chosen so as

to minimize a cost function that consists of the

sum of error squares over a time window, i.e.,

the least-square (LS) solution is minimized

recursively . In the method of steepest-descent,

on the other hand, the weight vector is chosen to

minimize the ensemble average of the error

squares [5].

An important feature of the RLS

algorithm is that it utilizes information contained

in the input data, extending back to the time

instance the algorithm was initiated. The

resulting rate of convergence is therefore

typically an order of magnitude faster than the

simple LMS algorithm. This improvement in

performance, however, is achieved at the

expense of a large increase in computational

complexity. The RLS algorithm requires 4N2 +

4N + 2 complex multiplications per iteration,

where N is the number of weights used in the

adaptive array.

w (k+1) = w(k) + g(k)( d*(k) - x

H(k)w(k)) (8)

Where,

g(k) = Rxx-1

(k)x(k) (9)

Rxx-1

(k) = α-1

Rxx-1

(k-1)

- α-1

g(k) xH(k)

Rxx

-1(k-1) (10)

Rxx (k) = αRxx (k-1) + x (k) xH (k) (11)

Simulation

d(n) = cos(2*pi*f*t);

Vs = exp (j*2*pi*d*sin(thetaS))

Normalized distance of separation of antenna

elements = 0.5

No. of antenna elements = 5.

Fig. 11 Normalized Array Factor of RLS Algorithm

in MATLAB and EM Simulation software.

A comparison of the array factor for

RLS algorithm obtained in MATLAB and

standard simulation software is shown in Fig.11.

Directivity of RLS algorithm obtained in EM

simulation software is shown in Fig.12.

Dir

ecti

vit

y (

dB

)

Arr

ay F

acto

r

Theta/Degree

Fig.12 Directivity of RLS Algorithm in dB in EM

simulation software.

IV. COMPARISON OF ALGORITHMS

The comparison of LMS, Normalized LMS,

Griffiths LMS, RLS algorithms are done as

follows,

Table 1: Comparison of Beamforming Algorithms.

Algorithm Based on

complexity

Time taken

for 100

iterations

(ms)*

Based on

beamforming

direction

Maximum

directivity

formed at

angle

Based on

convergence

Number of

iterations to

converge

(MMSE<=0.0001)

LMS 15.625 37о 57

NLMS 15.625 37о 57

Griffiths

LMS

15.625 37о 35

RLS 31.25 40о 30

*Simulation performed in Intel® CPU T2400 @

1.83GHz processor.

V. CONCLUSION

In this paper, performance of various

beam-forming algorithms for smart antenna

system is compared. From the calculated and

simulated results, it is found that RLS algorithm

takes longer time compared to LMS and its

variants to execute a single iteration. The

maximum directivity is obtained at the intended

angle in case of RLS whereas in case of LMS

and its variants, there is a deviation in the

maximum directivity angle. In case of LMS and

its variants, convergence time is long but RLS

takes less number of iterations to converge.

Moreover, the nulls are placed exactly at the

interfering angle in the case of RLS when

compared to LMS and its variants. Thus RLS is

better compared to LMS and its variants.

REFERENCES

[1]. Constantine A. Balanis, Panayiotis I. Ioannidis,

(2007) Introduction to Smart Antennas, First

Edition, Morgan and Claypool Publishers.

[2]. Frank B. Gross, (2005) Smart Antennas for

Wireless Communications with MATLAB,

McGraw-Hill Companies, Inc.

[3]. Suchita W. Varade, K.D. Kulat, (2009)Robust

Algorithms for DOA Estimation and Adaptive

Beamforming for Smart Antenna Application,

Second International Conference on Emerging

Trends in Engineering and Technology,

ICETET-09

[4]. Richard Roy and Thomas Kailath, “ESPRIT –

Estimation of Signal Parameters Via Rotational

Invariance Techniques” - Second IEEE

Transactions on Acoustics, Speech and Signal

Processing, Vol.37, No.7, July 1989.

[5]. Lei Wang and Rodrigo C. de Lamare,

“Constrained Constant Modulus RLS-based

Blind Adaptive Beamforming Algorithm for

Smart Antennas” - Communication Research

Group, Department of Electronics, The

University of York, YO10 5DD, UK.

[6]. Rui Fa, Rodrigo C. de Lamare and Danilo

Zanatta-Filho, “Reduced-Rank STAP Algorithm

for Adaptive Radar Based on Joint Iterative

Optimization of Adaptive Filter” -

Communication Research Group, Department of

Electronics, The University of York,

YO10 5DD, UK.

Dir

ecti

vit

y (

dB

)