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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
aaquibnawazrvce@gmail.com
(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
Proceedings of National Conference on Networking, Embedded and Wireless Systems, NEWS-2010,
BMSCE
113
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
Proceedings of National Conference on Networking, Embedded and Wireless Systems, NEWS-2010,
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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
Proceedings of National Conference on Networking, Embedded and Wireless Systems, NEWS-2010,
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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.
Figure 8: Detection of Direction of Maximum
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).
Figure 9: Detection of Direction of Maximum
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
Proceedings of National Conference on Networking, Embedded and Wireless Systems, NEWS-2010,
BMSCE
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
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Steenaart,“Effect of Delay on the Performance of
the Leaky LMS Adaptive Algorithm”, IEEE
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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
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[4]Márcio H. Costa and José C.M. Bermudez, “A
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[7] R. M. Shubair and A. Al-Merri Convergence
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