ADAPTIVE BEAMFORMING USING
NEURAL NETWORK
Ebrahim Karami 1, 2 , Jahangir Dadkhah Chimeh 1 , Mohsen Khansari 1
1
2
Iran Telecommunication Research Center, P. O. Box 14155-3961, Tehran, Iran
Department of Electrical and Computer Engineering, Faculty of Engineering, University of Tehran, Campus No. 2,
North Kargar Ave., Tehran 14399, Iran, Tel: +98 21 8008485, Fax: +98 21 633029
Abstract - The central theme of this paper is to demonstrate how a neural network can be incorporated into
an antenna array for adaptive beamforming. Specifically, the problem considered involves a single desired
signal arriving at the array simultaneously with an unwanted interfering signal of the same carrier frequency
but different direction. The neural network adopted herein has a feedforward multilayer architecture. A new
array performance measure in terms of directive gain is introduced. Excellent simulation results are obtained
for a uniform linear array of three elements placed half wavelength apart.
Keywords: Beamforming, Adaptive antennas, Artificial neural network, Interference, Capacity, Wireless
communication, training.
A.
INTRODUCTION
This paper presents a viable scheme for combining a multilayer feedforward neural network with a linear
phased array to effectively steer the beampattern of the array adaptively. Most of the beamforming
techniques are based on the sum-and-delay principle and its variants. The current concentration on
adaptive algorithms includes the constrained optimization methods (such as the minimum variance and
the linear predictive techniques), the eigenanalysis methods (which are based on Fourier analysis), and
the dynamic adaptive methods (such as the LMS algorithm, Frost's algorithm, and the matrix update
algorithms) [1,2]. An adaptive array consists of a set of strategically placed array elements (sensors or
transducers) capable of controlling its own sensing characteristics by adjusting the gains and phases or
delays of its elements. In this paper, the array elements refer to antenna elements which are deployed to
measure propagating electromagnetic signals. Adaptive arrays play an important role in radar and
communication systems which are inherently subject to interference and jamming.
The other principal component of the proposed scheme involves a neural network. A neural network is a
distributed signal processor consisting of interconnected computing units. It processes information using
parallel operations and displays capability of organizing and updating information. In short, the term
'neural networks' embodies information processing systems using a combination of nonlinear adaptive
networks, and parallel processing technologies. The technique proposed in this paper may represent an
attractive alternative to the current adaptive methods.
II. NEURAL NETWORK BASED ADAPTIVE ARRAY
The structure of the neural network based adaptive array is shown in Figure 1. The characteristics
and operations of the key components are presented in the following.
A. Linear Phased Array
Sum-and-Delay Principle: The underlying idea of sum-and-delay beamforming is quite simple:
when an electromagnetic signal impinges upon the aperture of the antenna array, the element
outputs, added together with appropriate amounts of delays, reinforce signals with respect to
noise or signals arriving at different directions. The delays required depend on the physical
spacing between the elements in the array. The geometrical arrangement of elements and weights
associated with each element are crucial factors in defining the array's characteristics.
Wavenumber-Frequency Response: For simplicity, this paper considers the case of a linear array
of N elements placed along the x axis in the z = 0 plane at positions { rn  x̂nd } with weights
{ wn } , n  0,, N  1 . The present discussion focuses on array processing for narrowband
signals. In view of the fact that a superposition of plane waves expresses an arbitrary wavefield,
the frequency response of the array is found by letting the test wavefield be the monochromatic
plane wave exp[ j( t  k  r )] . For this important special case, the output of the array is given by
N 1
 w exp[  j( 
z( t )  exp( jt )
n
n
 k  rn )]
(1)
n 0
where  denotes the temporal frequency of the wavefield, and k the propagation vector. The
delays {  n } are set by
 n    rn / c  a  rn
(2)
where  is the assumed direction of propagation, and c the speed of light in free space. Now the
array's response to the plane wave excitation can be expressed as
(3)
z( t )  exp( jt )W ( a  k )
where W ( a  k ) is referred to as the wavenumber-frequency response which summarizes the
effect of delays and weights on the array's spatiotemporal filtering properties. It also forms the
basis for the angle of arrival detection. Further, the array pattern is specified by
N 1
W( k ) 
 w exp( jk  r
n
n)
(4)
n 0
Quadrature Representation: It is useful to represent a bandpass signal in terms of its in-phase
and quadrature components which are at baseband. In the present work, the output of an array
element is first applied to a quadrature hybrid, a three-port device, to produce two equalamplitude output signals whose carriers are in time quadrature. For the purpose of computer
simulation, the quadrature component is actually obtained via the Hilbert transform of the inphase component. This also suggests that there will be two input neurons for every array element.
B. Signal Detection
Pilot Signals: In many practical applications the cost is high if the array is t operate adaptively
on a real-time basis. The communication scheme proposed there involves the use of a coded pilot
signal to establish the communication link, preceding the actual message signal. Such approach
is viable because the neural network can be trained offline for weight adaptation based on
minimal information. In fact, the neural network can be trained to provide a given steered
response using only sinusoidal signals. It is therefore sufficient to consider coded time-harmonic
plane waves as pilot signals.
Propagation Direction: By fixing propagation parameters of a wavefield, the wavenumberfrequency response W ( a  k ) becomes the steered response. This means space can be scanned
by systematically varying the delays and possibly the weight sequence of the array to detect the
propagation direction of a given wavefield. The angle-of-arrival detector in Figure 1 implements
a direction-finding scheme based on W ( a  k ) . As an illustration, Figure 2 shows the output of
the detector with three plane waves impinging upon a linear uniform 10-element array with
incidence angles -50, 30, and 45. The angular resolution is found to be 7.
Desired Signals And Interference Signals: Various encoding techniques can be applied to the
pilot signals for identification against interference signals. In the presentation, the case
considered involved a desired signal arriving at the array simultaneously with an unwanted
interfering signal of the same carrier frequency but different direction. For the purposes of
computer simulation, the desired signal is modulated as a direct-sequence spread-spectrum
signal. The signal detector includes a correlator which is equipped with an appropriate
pseudonoise generator. The correlator server to "despread" and recover the desired signal to yield
a high correlation output. On the contrary, the interfering signal, in all likelihood, will be
randomly disrupted by the pseudonoise generator to result in a low correlation output. These
distinct outputs are the exploited to construct exemplary signals for training the neural network.
C. Training Signals Generation
Two pairs of sinusoidal signals are synthesized for the training of the neural network. The
first pair has the form
N 1
sv ( t ) 
{sin  [ t  ( n 1) ]  cos [ t  ( n 1) ]}
v
v
(5)
n 1
When v  d , sd ( t ) corresponds the desired signal,  d  d sin  d / c is the delay between two
adjacent elements separated by d meters, and  d is the angle of arrival of the desired signal.
Similarly, the case v  i corresponds to the interference signal. The second signal pair { sdo , sio }
are defined as
s o ( t )  B~
s (t )
(6)
s o ( t )  A~
s (t )
i
d
d
i
where ~
sv ( t ) is sv ( t ) normalized to unity amplitude, and the parameters A and B are so chosen
that the directive gain in the direction of the desired signal has a gain of G decibels (dB) over that
in the direction of the interference signal. It is worth pointing out that this performance criterion
is fundamentally different from the least-mean-square (LMS) criterion [3] or the maximum
signal-to-interference-plus-noise ratio (SINR) criterion [4] that are commonly used as
performance measures for adaptive arrays.
The error signals that are pertinent to the implementation of the back-propagation
learning algorithm (to be discussed in the following section) are defined as follows
ed ( t )  sdo ( t )  yd ( t ) ,
ei ( t )  sio ( t )  yi ( t )
(7)
where yv ( t ) denotes the neural network output when the input signal is sv ( t ) . The critical
squared-error function is defined by
E
 E   [ e ( t )  e ( t )]
2
d
t
t
2
i
(8)
t
It should be pointed out that the input signals, sd ( t ) and si ( t ) , are applied sequentially during
training.
D. Multilayer Feedforward Neural Network
A neural network is a parallel, distributed signal processor consisting of interconnected
computing elements called neurons [5]. It is generally agreed that a neural network resembles the
human brain in two respects: (a) it acquires knowledge through a learning process. (b) The
synaptic weights associated with the interconnections between neurons are used to code prior
information as well as information acquired through observations (measurements) by means of
sensors designed to probe the environment in which the neural network operates.
Considered in this paper is a multilayer feedforward neural network based on the
Perceptron networks originally developed by Rosenblatt [6]. A nonlinear model of a neuron and
a three-layer network (two hidden layers and one output layer) are shown in Figure 3. The
characteristic equation for all neurons is identical. The output signals for the kth neuron in the
mth layer is defined by
p
ykm ( t )   [ ukm ( t )] ,
u km ( t ) 
w ( t )y
m
kj
m 1
m
j ( t )  Tk
(9)
j 1
m
where t is the discrete time index, wkj
is the connection weight of the jth input from the previous
layer to the kth neuron in the mth layer, Tkm  wkm0 ( t ) is the weighted bias applied to the neuron,
and  (  ) is the nonlinear activation function.
The process of learning a given task by the neural network is the weight adaptation. The learning
law applied here for weight adaptation is the error back-propagation algorithm implemented as a
batch learning process [7,8]. For an M-layer network, the synaptic weight, w m
ji ( t ) , linking
neuron i of layer ( m  l ) to neuron j of layer m, l  m  M , is updated according to
m
m
wm
ji ( t 1 )  w ji ( t )  w ji ( t ) ,
m
m 1
wm
(t ),
ji ( t )   j ( t ) yi
m
j (t )  
(10)
Et
u m
j
where 0    1 is the learning rate, and  m
j ( t ) is the local error gradient. For the output layer
( m  M ) , the local error gradient has the form
M
 M
 M
(11)
M
j ( t )  [ d j ( t )  y j ( t )] [ u j ( t )]  e j ( t ) [ u j ( t )]
where d ( t ) is the desired output signal of neuron j in the output layer, and (  ) denotes the
j
derivative of the sigmoid function with respect to its argument. For hidden layer m
( l  m  M  1 ) , the local error gradient is given by
N m1
 m
m
j ( t )   [ u j ( t )]

m 1
m 1
( t )wkj
(t )
k
(12)
k 1
To improve the back-propagation learning algorithm, a momentum term is added to
smooth the weight changes
m
m 1
wm
( t )  wm
ji ( t )   j ( t ) yi
ji ( t  1 )
(13)
where 0    1 is the momentum factor. The overall weight adjustment for the batch learning
algorithm is given by
w m
ji 
 w ( t )
m
ji
(14)
t
The present application utilizes a total of 60 signal sample values (patterns) for each iteration.
III. COMPUTER SIMULATION AND RESULTS
The computer simulation program is written in BASIC and runs on and IBM-compatible 386based or higher personal computer. The simulation results presented here were obtained for the
following array configuration: N  3,d  rn  rn 1   / 2 where  is the wavelength. After
extensive simulation runs, the following neural network architecture is recommended: (1) An
input layer with 6 neurons. (2) Two hidden layers with 8 neurons each. (3) A single neuron in the
output layer with linear activation function. The appropriate parameter values for network
training were found by experimenting that   0.001 , and   0.01. The data for two simulation
runs are summarized in the following. n both case, the desired and interference signals have
equal strength, and the overall signal-to-interference gain factor G was set to 40dB.
Simulation #1
Incident angles
Desired signal sd ( t ) : -40
Pre-training directive gain sd ( t ) : -3.43 (dB)
Post-training directive gain sd ( t ) : 0 (dB)
Interference signal si ( t ) : 0
si ( t ) : -7.49 (dB)
si ( t ) : -39.44 (dB)
Interference
Target
0
Array Pattern (dB)
-10
-20
-30
-40
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
20
30
40
50
60
70
80
90
Incident Angle (Deg)
pre-training
post-training
Simulation #2
Incident angles
Desired signal sd ( t ) : +10 Interference signal si ( t ) : +7
Pre-training directive gain sd ( t ) : -2.08 (dB)
si ( t ) : -3.27 (dB)
Post-training directive gain sd ( t ) : -2.97 (dB) si ( t ) : -37.60 (dB)
IV. CONCLUSION
Overall, this neural-network based array demonstrates a high level of adaptive beamforming
with good angular resolution. The proposed adaptation scheme relies only on the direction and
some minimal modulation information of the pilot signal, but not on the actual message signal.
This essentially reduces the burden of generating the reference signal. Most significantly, the
directivity gain on the desired signal versus that on the interference signal can be arbitrarily set
by properly choosing the scaling factors A and B, thereby resulting in a fundamentally different
performance measure compared to the LMS and SINR criteria.
Target
Interference
0
Array Pattern (dB)
-10
-20
-30
-40
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
20
30
40
50
60
70
80
90
Incident Angle (Deg)
pre-training
post-training
The pre-training and post-training array patterns for both cases are shown in Figure 4.
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