INTRODUCTION
In the past decade, a great effort has been made to build the future generation
mobile communication systems. It is expected to provide highspeed and highquality
information services. Adaptive beamforming has numerous applications in array
signal processing, radar, sonar, astronomy, medical imaging and wireless communications
(Xie et al., 2008; Chen et
al., 2007; Yang et al., 2006; Krolik,
1996; Godara, 1997; Rapapport, 1998;
Gorodetskaya et al., 1999). A beamformer in smart
antenna systems employing multiple antennas promise 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 whilst placing
nulls at interferer locations (Zhang et al., 2003;
Rezk et al., 2005). Beamforming is a key technology
in smart antenna systems so that many different adaptive beamforming algorithms
have been the subject of active research (Agee, 1989;
Krim and Viberg, 1996; Liberti and Rappaport,
1999; Chen et al., 2005).
The employment of the spacedivision multipleaccess technique has been motivated
by the everincreasing demand on mobile communication capacity (Xie
et al., 2008). The smart antenna array is capable of separating signals
transmitted on the same carrier frequency, provided that they are separated
in the spatial domain. When there are reference signals, the nonblind algorithm
is desirable. Among these algorithms, temporal updating algorithms such as Least
Mean Square (LMS) and Recursive LeastSquares (RLS) which determine the optimum
weight vectors sample by sample in time domain (Chen et
al., 2005) take a long time to converge. This situation becomes worse
if channel situation varies rapidly in time domain, where in such time variance,
weight vectors updating becomes more complicated. To overcome this problem,
block adaptation approach such as Sample Matrix Inversion (SMI) is employed.
However, due to its discontinuity in updating the weight vectors, adaptive block
approach is unsuitable for continuous transmission. A new beamforming algorithm
that will be easy to implement with less complexity and having faster convergence
speed and accurate tracking capability is extremely crucial and a challenging
issue to explore. The individual good aspects of both block adaptive and sample
by sample technique that employed by Mohammad and Zainol
(2006) is utitilized to address the issue of tracking ability in this study.
SYSTEM MODEL AND MINLMS ADAPTIVE BEAMFORMING ALGORITHM
Consider an antenna array with kth antenna element. It is assumed that
the base station is equipped with an antenna array to receive and transmit
signals from and to mobiles. No antenna arrays are assumed for mobiles.
Since, the antenna elements are uniformly distributed across the antenna
array, the propagation delay along with any two consecutive elements is
the same and therefore, the complex envelope representation of the received
signal at the kth antenna element can be expressed as:
where, λ is the wavelength of the carrier frequency. The received signal is
expressed in terms of vector notation. The lower and upper case boldface within
the equation represents vector and matrix quantities, respectively. Thus the
received signal is identified as (Litva and Lo, 1996):
where, T represents transpose. Let a(θ) define a vector which yields:
The complex envelope representation of the received signal in the array
is thus given by:
The vector a(θ) is the steering vector.
Assuming multiple users transmitting at the same time, antenna elements
are isotropic and the channel is considered to be an Additive White Gaussian
Noise (AWGN). The complex envelope representation of the received signal
can be expressed as follows:
where, q is the number of users, θ_{k} is the direction
of arrival for the kth user, s_{k}(t) is the transmitted signal
for the kth user, n(t) denotes the M×1 vector of the noise at the array
element and
where, a(θ_{k}) is the corresponding array response vector
of each of the signals. In matrix notation, Eq. 5 becomes:
Where:
In Eq. 8, A(θ) is the matrix containing
the steering vectors and
where, s(t) is the input signal. The proposed beamforming algorithm is
utilized to determine the input signal s(t) from the received signal vector
x(t).
The adaptive beamforming algorithm MINLMS (Mohammad and
Zainol, 2006) is employed in this study to calculate final weights vectors
according to the Eq. 10 as follows:
where, w(n) denotes the estimate of the weight vector at the nth iteration
and e(n) is the mean square error, μ is a small positive constant,
called the step size whose value is between 0 and 1 and the next estimation
of the weight vector for the (n+1)th iteration is w(n+1).
In this algorithm, the initial weight vector is obtained by matrix inversion
through SMI algorithm, only for the first few samples or for a small block
of incoming data instead of arbitrary value before calculating the final
weight vector. The final weight vector is updated by using the LMS algorithm.
RESULTS AND DISCUSSION
The performance of the MINLMS algorithm is evaluated through simulation
study by using MATLABĀ®6.5. The adaptive algorithm must be able to
track the desired signal source because of the mobility of user terminal
in the dynamical environment. In this study the tracking capability of
the MINLMS algorithm is investigated. For the sake of simplicity the
radio channel is assumed to be multipath free and nondispersive with
Additive White Gaussian Noise (AWGN). A simple uniform linear array antenna
with half wavelength spacing between the elements is considered. Data
sequences are generated using Binary Phase Shift Keying (BPSK) modulation.
All DOAs of the signals are uniformly distributed from 30 and 180°.
The array antenna receives 8 users signals with different DOAs of 30,
50, 70, 90, 110, 130, 150 and 170°, respectively. In the simulation,
an 8 element simple uniform linear array antenna with half wavelength
spacing between the elements is assumed to be located at the base station
to perform spatial filtering. The SNR is set at 20 dB and the number of
data bit length is 500. The main source of the AWGN is the receiver frontend
noise and the noise from the receiver frontend appears to be coming from
the all azimuthal directions.
Figure 1 shows the BER performance of the MINLMS algorithm
with SNR variation when the number of antenna element changes. In the
simulation, the angle of arrival of the desired user and the interferer
are at 30 and 60°, respectively. The improvement in BER performances
is proportional to the number of antenna elements employed in the antenna
array. From the Fig. 1, the BER performance can be clearly
seen that the BER decreases with the increase of the number of antenna
elements. For instance in the AWGN channel, at SNR = 2 dB with antenna
element 2, BER is 0.1183 while for the number of antenna element 4, 6,
8 and 10, the corresponding values of BER are 0.0521, 0.0039, 0.0164,
0.0039 and 0.0016. On the other hand, the SNR value decreases with the
number of antenna elements increases.
Figure 2 and 3 show the beampattern
of first 4 user and last 4 user generated by using the MINLMS algorithm
in the well separated changing environment, respectively.
In Fig. 2 and 3, it can be seen that most
of the signals can be extracted by nulling out all other interference except
for the signals with DOAs near the endfire of the array. As shown in both Fig.
2 and 3, the nulls are not constructed perfectly, but
the interference suppression is almost less than 25 dB in the most cases except
endfire due to the existence of noise. For the signals with DOAs near the endfire
of the array (e.g., signals of user 1 and user 8), two or more signals may be
fallen into one main beam depending on the angle separation of the signals since
the beamwidth of the beam near the endfire is wider than that of the beam steered
to other direction.
In such a case, although the interference is not completely rejected
due to the wide beamwidth of the main beam directed to the endfire, most
of the interference coming from other directions is rejected; therefore,
the overall interference level is reduced.

Fig. 1: 
BER performance of the MINLMS algorithm with different antenna
elements 

Fig. 2: 
Beampattern corresponding first 4 user generated by MINLMS 

Fig. 3: 
Beampattern corresponding to last 4 user generated by MINLMS 

Fig. 4: 
Signal constellation of user 3 before the beamformer processing 

Fig. 5: 
Signal constellation of user 3 after the beamformer processing 
Figure 4 and 5 show the signal constellations
of user 3 before and after the beamformer processing using MINLMS algorithm,
respectively.
It can be observed in the Fig. 5 that the interference
from different DOAs is indeed rejected and the signal constellation is
reconstructed.
CONCLUSION
In this study, the tracking ability of less complex MINLMS adaptive
beamforming algorithm is presented. MINLMS combines the SMI and NLMS
algorithms by considering individual good aspects of both the sample by
sample and block adaptive algorithms. Simulation results showed that the
proposed algorithm outperforms the conventional LMS adaptive beamforming
algorithm. The proposed algorithm provided a superior performance y varying
the number of antenna element and outstanding tracking ability even when
the signal environment changes.
ACKNOWLEDGMENTS
The authors would like to thank Institute of Space Science (ANGKASA),
Universiti Kebangsaan Malaysia (UKM) and the MOSTI Secretariat, Ministry
of Science, Technology and Innovation of Malaysia, eScience fund: 010102SF0376,
for sponsoring this research.