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Proceedings of National Conference on Networking, Embedded and Wireless Systems, NEWS-2010, BMSCE

111

BLIND BEAMSTEERING AND DIRECTIONAL BEAMFORMING USING

LEAKY LMS FOR MOBILE APPLICATIONS

(1)H.V.Kumaraswamy

(2) Aaquib Nawaz.S

[email protected]

(1)Assistant Professor, Dept of Telecommunication, R.V.C.E, Bangalore (2)

Mtech 4th

semester, Digital Communication, R.V.C.E, Bangalore

Abstract: Wireless networks face ever-

changing demands on their spectrum and

infrastructure resources. Increased minutes of

use, capacity-intensive data applications, and the

steady growth of worldwide wireless subscribers

mean carriers will have to find effective ways to

accommodate increased wireless traffic in their

networks.

Beam steering has emerged as one of the

leading innovations for achieving highly efficient

networks that maximize capacity and improve

quality and coverage.

This paper presents a way in which a

Linear array of sensors is used to steer the beam

from -90 0to 90

0 and finally form the beam in the

direction of maximum power. The Beam steering

unit is integrated into four main blocks. The first

block is Angle Of Arrival estimation which uses a

array of sensors to detect direction of arrival of

signals by computing Array Correction Matrix

and corresponding power spectrum for different

directions .The AOA algorithms namely Linear

Prediction Method (LPM) and Maximum

Likelihood Method(MLM) are used in AOA block.

The second block is used to determine direction of

maximum power. The third block is used to steer

the beam from -900 to 90

0 by applying complex

phase shifts to individual array elements .The

phase shifts to different array elements are

computed by using adaptive algorithm namely

Leaky Least Mean Square (LLMS) The fourth

block uses the beamforming algorithms to form

the beam in the look direction.

This paper discusses the Beam steering

using LLMS-LPM and LLMS-MLM. The

Beamsteering algorithms are simulated in

MATLAB. The LLMS beamforming algorithm is

implemented on Texas Instrument Digital Signal

Processor TMS320C6713.

Keywords: Steering Vector, Mean Square

Error, Eigen Values and Eigen Vectors.

1. Introduction A smart antenna is an array of

antenna elements associated with a digital

signal processor. The system utilizes

multiple antenna elements combined with

a signal processing capability to optimize

its radiation and reception patterns

automatically in response to the signal

environment. Smart antennas have the

property of spatial filtering, which leads

to an effective spectrum utilization in

mobile communication system.

2. ULA Signal Model

Consider a Uniform Linear Array

with spacing ‘d’ between antenna array

sensors which consist of ‘L’ antenna

elements and ‘M’ signals are impinging

on the array from different direction’s as

shown in figure1. Let S(t) be the complex

baseband signal.

Figure 1: Array signal model

The received data vector x(n) is given by

equation(1)

)()()()()()(1

0 nnaninSanx m

M

m

m ++= ∑=

θθ (1)

Proceedings of National Conference on Networking, Embedded and Wireless Systems, NEWS-2010,

BMSCE

112

where is )(nn a noise vector modeled as

temporally white and zero-mean complex

Gaussian process, )( 0θa is the look

steering vector and )( ma θ is the steering

vector for mth

jamming direction . The

steering vector for the ith

direction is

defined as in (2)

[ ]TLdjdj

iii eea

θπθπθ sin)1(2sin21)(

−= ��

(2)

3. Angle of Arrival (AOA) Algorithms

The Angle Of Arrival algorithms

will take number of array sensors,

number of signal sources, source

amplitude and source direction as input

and produce peaks for the corresponding

source directions as an output. The AOA

algorithms discussed here are Linear

Prediction Method (LPM) and Maximum

Likelihood Method (MLM).

3.1 Linear Prediction Method (LPM)

In LPM method the output of one

sensor is estimated using linear

combinations of the remaining sensor

outputs and minimizes the error between

the estimate and the actual output i.e.

mean square prediction error. Thus by

minimizing the mean output power it

obtains the weights of the array subject to

the constraint that the weight on the

selected sensor is unity. The Power

spectrum for Linear Prediction Method is

given by equation (3)

)(

1

θVALINV

H

m

LPMARU

P =

(3)

H

mU is the unit norm vector. There is no

criterion for proper choice of this

element. The choice of this element,

however, affects the resolution capability

and the bias in the estimate, and these

effects are dependent upon the SNR and

separation of the directional sources.

INVR is the inverse of Array correlation

matrix as in (4)

IASAR H σ+= (4)

A is the steering vector ( )HsstrS =

is the matrix comprising square amplitude

of sources along the diagonal and σ denotes variance of white noise.

)(θVALA is same as steering vector for an

angle θ .

The linear prediction methods

perform well in a moderately low SNR

environment and are a good compromise

in situations where sources are of

approximately equal strength and are

nearly Coherent.

3.2 Maximum Likelihood Method

The maximum likelihood method

(MLM) of spectrum estimation finds the

maximum likelihood (ML) estimate of

the power arriving from a point source in

direction θ assuming that all other sources

are interference. This method uses the

array weights obtained by minimizing the

mean output power subject to a unity

constraint in the look direction. The

expression for the power spectrum PMV(θ)

is given by (5)

)()(

1

θθ vINV

H

v

MVARA

P =

(5)

Where AV(θ) is 1xL Steering

vector for a given angle θ, RINV is

inverse of Array correlation matrix and

AV(θ)H is a vector obtained from

hermitian transpose of Steering vector

AV(θ).

The ML method gives a superior

performance compared to other methods,

particularly when the SNR is small, the


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number of samples are small, or the

sources are correlated, and thus is of

practical interest. For a single source, the

estimates obtained by this method are

asymptotically unbiased, i.e the expected

values of the estimates are equal to their

true values. In that sense, it may be used

as a standard to compare the performance

of other methods. The method normally

assumes that the number of sources M is

known.

4. Beamforming

Adaptive Beamformer consists

multiple antennas, complex phase

shifters(weights) , the function of which

is to amplify (or attenuate) and delay the

signals from each antenna element and a

summer to add all of the processed

signals, in order to tune out the signals

not of interest, while enhancing the signal

of interest. Hence, beam forming is

sometimes referred to as spatial filtering,

since some incoming signals from certain

spatial directions are filtered out, while

others are amplified.

4.1 Leaky LMS (LLMS) Beamformer

This is the variation of LMS

algorithm. In this case to the

autocorrelation matrix noise is added by

using Leaky factor. The autocorrelation

matrix xxR used in LMS algorithm in

some cases has zero Eigen values. This

causes LMS algorithm to have un-

damped and un-driven modes. Since it is

possible for these un- damped modes to

become unstable. It is important to

stabilize the LMS by forcing these modes

to zero. One way to accomplish this is to

introduce leakage coefficient γ which is

in the range0<γ <1 into auto correlation

matrix, step size calculation and weight

vector equation. The weight update

equation of LLMS is given by (6)

[ ] |)()()(1)1( *nxnenWnW µµγ +−=+ (6)

The step size is computed by using (7)

γλµ

+=

max

2

(7)

Where maxλ is the maximum

Eigen value obtained from Eigen value

decomposition of correlation matrix as

in(8)

[ ] IXXERH

xx γ+= (8)

Specifically, if s(n) denotes the

sequence of reference or training symbols

known a priori at the receiver at time n,

an error signal is formed as

)()()( nynsne −= .This error signal e is

used by the Beamformer to adaptively

adjust the complex weights vector w so

that the mean squared error (MSE) is

minimized.

5. BEAMSTEERING

This is similar to Beamforming

but here complex phase shifts are applied

to individual array elements vary for

every second to steer the beam along

varying directions. The Beam steering

matrix as in (9) depends upon the steering

angle and directional range and it

columns consist of phase shifts applied to

array elements obtained from beam

forming algorithms.

[ ])(.................).........()( 21 lphase WWWW θθθ=(9)

Where )( iW θ is the Weight update vector

corresponding to direction iθ obtained

from beam forming algorithm LLMS.

Figure (2) gives details for the

implementation of Beamsteering using


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Beamsteering Unit

LLMS-LPM and LLMS-MLM. In the

Beamsteering unit initially the look

direction is assumed to be -900 beam is

formed for an angle of -900.The Direction

is incremented and beam is steered from

various angles over -900 to 90

0 and finally

beam is formed in the direction of

maximum power.

Figure2: Implementation of Beamsteering

6. RESULTS:

In this section MATLAB results

for Beamsteering algorithms are

presented for LLMS-LPM and LLMS-

MLM.

6.1 Beamsteering using LLMS-LPM

L=Number of array elements=20.

M=Number of Signal Sources=4.

s= Amplitude of sources= [1 5 2 3] v

θ =Direction of sources=[100 20

0 30

0 40

0]

Figure 3: Detection of Directions using LPM

Figure (3) is the MATLAB output

shows the peaks in the direction of

sources at100 20

0 30

0 and 40

0 degrees.

Figure 4: Detection of Direction of Maximum

Power

Figure (4) shows the detection of

direction of maximum power using

selection sort.

Figure 5: Beamsteering from -90

0 to 90

0using

LLMS

Computation of Power Spectrum

for all Directions and Amplitudes

of Sources using LPM or MLM

Selection Sort for Direction of

Maximum Power

Obtain Complex Phase Shifts using

LLMS Beamformer for direction θ

Array Factor to form beam in directionθ

and increment direction θ

090≤θ

Beamforming for Direction of maximum

power


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115

Figure(5) shows beam is steered

from -900 to 90

0 by forming the beam for

every 50.

Figure 6: Beamforming using LLMS for

direction of maximum power

Figure(6) shows beam formed at

an angle 200.

6.2 Beamsteering using LLMS-MLM

L=20,M=4,s= [1 5 2 3] v

and θ =[100 20

0 30

0 40

0]

Figure 7: Detection of Directions using LPM

Figure (7) is the MATLAB output

shows the peaks in the direction of

sources at10 20 30 and 40 degrees.


Power

Figure (8) shows the detection of

direction of maximum power using

selection sort. Beamsteering and

Beamforming plots using LLMS-MLM

will be same as LLMS-LPM as in figures

(5) and (6).


Power

Figure (9) shows the complex phase

shifts computed using LLMS

Beamforming algorithm for θ = 200 to be

applied to individual element.

Figure 10: MSE Curve of LLMS

Figure (10) gives the MSE

characteristics of LLMS algorithm. The

convergence depends upon step size,

larger the step size more MSE but faster

convergence and vice versa.

Figure11: DSP Kit Output LLMS-Real


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116

Figure (11) shows the real array

weights calculated DSP kit.

Figure12: DSP Kit Output LLMS-Imag

Figure (12) gives imaginary array

weights calculated using DSP kit.

Table1: Execution Speed

Algorithm Time in seconds

LPM 3.4530

MLM 0.0950

LLMS 0.0950

Table1 gives Execution Speed of

various DOA and Beamforming

algorithms measured using timers in

MATLAB.

7. CONCLUSION

This paper provides

implementation of array beam-forming

by using LLMS and AOA using LPM and

MLM for mobile communications

systems. The paper also illustrates that

beamforming algorithms can also be used

for steering the beam over range of

directions and finally forming beam at

look direction. The execution Speed,

convergence characteristics of

beamforming algorithm and Resolution

of DOA algorithm were also presented.

REFERENCES

[1]. F. Laichi, T. Aboulnasr, and W.

Steenaart,“Effect of Delay on the Performance of

the Leaky LMS Adaptive Algorithm”, IEEE

transactions on signal processing, vol. 45, no. 3,

march 1997

[2] Lal C. Godara,“Application of Antenna Arrays

to Mobile Communications, Part II: Beam-

Forming and Direction-of-Arrival

Considerations”, Proceedings of IEEE, vol. 85,

no. 8, august 1997

[3]James Okello ,Yoshio Ztoh t Yutaka Fukui,

Zsao Nakanishi and Masaki Kobayashi,“A new

modified variable step size for the LMS

Algorithm”,1998 IEEE Proceedings of the

international symposium on circuits and systems.

Vol 5, June 1998,pp 170-173

[4]Márcio H. Costa and José C.M. Bermudez, “A

Robust Variable Step Size Algorithm for LMS

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on acoustics, speech and signal processing, Vol

3,May 2006,pp 14-19

[5]Yonggang Zhangt, Jonathon A. Chamberst,

Wenwu Wang,Paul Kendrick, and Trevor J. Cox,

“A new variable step-size LMS algorithm with

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international conference on acoustics, speech and

Signal processing.Vol 3,June 2007,pp-1349-1352

[6] R. M. Shubair and A. Al-Merri, “Robust

algorithms for direction finding [0 60 80 100 and

adaptive beamforming: performance and

optimization,”Proc. Of IEEEInt. Midwest Symp.

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[7] R. M. Shubair and A. Al-Merri Convergence

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[8] J. D. Fredrick, Y. Wang, S. Jeon, and T. Itoh,

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