2. 3.2. Smart Antenna Composition
Smart Antenna mainly consists four parts: the antenna
array, analog-to-digital conversion, digital beam-forming
and adaptive network processor. Smart antenna structure
is shown in figure 1:
Figure 1.Smart antenna structure diagram
(1) Antenna Array
The number of antenna array and antenna array
configuration has a direct impact on the performance of
smart antenna. Usually located array number for M, in the
mobile communications M = 8 or M = 16, etc.
(2) Analog-to-Digital Converter
Consider the base station terminal smart antenna, in
the uplink antennas convert the received analog signal
into a digital signal.
(3) Beam-forming Network
The main functions of beam-forming network reflects
that antenna beam in a certain range based on the user's
needs and the dissemination of the antenna transform
environment through the adaptive digital signal
processors adaptive adjust the weights of the
coefficient 1w 、 2w 、…、 Mw ,in order to adjust to the
appropriate beam-forming network. Or it according to
certain criteria from a pre-set weight coefficient list,
selects a group of the best value to get the best direction
of the main beam[2]
.
(4) Adaptive signal processing
The intelligence of the smart antenna is embodied in
adaptive signal processing. It is the core of adaptive
algorithm, dynamically adjust the optimal weighted
factor.
4. Adaptive Beam forming Algorithms
In smart antenna technology, according to the needs of
different users it needs to identify different weights in
order to achieve the tracking of users. These algorithms to
determine weight value are collectively referred to as
intelligent adaptive algorithm, which is the core of smart
antenna technology.
Beam forming algorithm determines the antenna array
of transient response rates and the realization of the
circuit of the complexity, so the choice of what kind of
algorithm for intelligent control of the beam is very
important.
The essence of smart antenna is a spatial filter, while
the filter's function is to rely on the adaptive algorithm to
complete.
4.1. Least Mean Square Algorithm (LMS)
LMS is a most widely used adaptive optimization
algorithm. It is based on the steepest descent algorithm,
through recursion to update the weight vector, and
reaches its apex of error performance (that is, the optimal
value). LMS algorithm includes beam forming and
adaptive weight control in two parts(as shown in figure 2).
Figure 2.Beam forming schematic diagram
Adaptive algorithm includes two steps:
(1) According to the array signal and the current weight
calculate the difference of the output value of the beam
former and desired signal.
Assuming the signal the array antenna received can be
expressed as[3]
:
1 2( ) [ ( ), ( ),..., ( )]H
Mx n x n x n x n=
(1)
The weighted coefficient received is:
1 2[ , ,... ]H
Mw w w w=
(2)
The output of the beam former can be written as follows:
( ) ( ) ( )H
y n w n x n= (3)
The error of the beam former, this is the difference
between the desired signal and the output signal:
( ) ( ) ( )e n s n y n= − (4)
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3. (2) According to the calculated difference automatically
adjust the weighting of the beam former:
( 1) ( ) 2 ( ) ( )w n w n e n x nμ+ = + (5)
Among them, μis step factor, the value of μe(n)x(n)
impact on the LMS algorithm performance, value is too
small that will lead to algorithm convergent slowly, value
is too large that will lead to algorithm instability, and
even divergent[4]
.
4.2. Recursive Least Squares (RLS)
Recursive least squares (RLS) algorithm is strictly
based on least square criterion, Its main advantage is that
convergence rate is fast, the main disadvantage is that
each iteration needs a large amount of computing.
Specific iterative steps of the algorithm are as follow:
(1) Initialize covariance matrix P [n] and w [n], the
initialization of P [n] should be pay attention to ensure
that it is a non-singular matrix, and set w [n] is 0 matrix.
( 0 ) ( 0 ) 0W X= = (6)
1
(0)P I
δ
=
(7)
(2) After algorithm into the data processing stage,
calculate iterative gain K [n] and the absolute error e(n),
then by iterative gain and error calculate the estimated
value of weights w [n]. Finally modify P[n].
( ) ( ) ( ) ( 1)T
e n y n x n w n= − − (8)
( 1 ) ( )
( )
( ) ( 1 ) ( )T
P n x n
k n
x n P n x nλ
−
=
+ −
(9)
1
( ) [ ( 1) ( ) ( ) ( 1)]T
P n P n k n x n P n
λ
= − − − (10)
(3) The algorithm enters into the treatment of the next
data sample u (n), so repeat the iteration final get the best
weight values.
( ) ( 1) ( ) ( )w n w n k n e n= − + (11)
5. The smart antenna of software
simulation
Write a M document in the MATLAB environment,
we design and simulate the application of smart antenna
adaptive beam forming algorithm in interference
suppression, And compare the algorithms performance
under different situations, verify the feasibility of
algorithm.
5.1. The simulation of smart antenna Based on
the LMS adaptive beam forming algorithm
LMS algorithm flow chart is as follows:
Figure 3. LMS algorithm flow chart
Based on the above algorithm flow chart, write a M
document in the MATLAB environment, the document is
the implementation document of the LMS algorithm
smart antennas. Antenna array uses eight array elements
of uniform linear array, the distance between two array
elements is λ/2, the parameters of the document are as
follows:
M: the number of antenna array element
mu: step factor
lambda: the corresponding expressions λ
SNR: signal-to-noise ratio
INR: interference-to-noise ratio
The renewal expression of realization code in M the
document:
% initialize weight matrix and associated parameters for
LMS predictor
de =s(1, :);
mu=0.0001;
w = zeros(m, 1);
for k = 1:N
% predict next sample and error
y(k) = w'*Y(:, k);
e(k) = de(k) - y(k);
% adapt weight matrix and step size
w = w + mu * Y(:,k)*conj(e(k));
end
Calling mapping function, get the simulation results
the application of LMS adaptive beam forming algorithm
in interference suppression:
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4. Figure 4.Antenna pattern
Figure 5.Relational graph of the iterative times and error
Figure 4 is the antenna pattern, LMS algorithm can
form main beam at the direction of desired user, form
deep nulls steering at the direction of interference, reach
the effects of interference elimination. Figure 5 is the
relational graph of the iterative times and error, after a
certain number of iteration operation, LMS algorithm
reached convergence. The reference signal error is under
control within a relatively small scope.[5]
5.2. The simulation of smart antenna Based on
the RLS adaptive beam forming algorithm
RLS algorithm flow chart is as follows:
Figure 6. RLS algorithm flow chart
Based on the above algorithm flow chart, write a M
document in the MATLAB environment, the document is
the implementation document of the RLS algorithm smart
antennas. Antenna array uses eight array elements of
uniform linear array, the distance between two array
elements is λ/2, the parameters of the document are as
follow:
M: the number of antenna array element
mu: step factor
lambda: the corresponding expressions λ
SNR: signal-to-noise ratio
INR: interference-to-noise ratio
The renewal expression of realization code in M the
document:
% initialize weight matrix and associated parameters for
RLS predictor
de=s(1,:);
w = zeros(m, 1);
lambda=0.75;
delta=1e-2;
P=1/delta*eye(m);
for k = 1:N
v=P*Y(:,k);
u=1/lambda*v/(1+1/lambda*Y(:,k)'*v);
e(k)=de(k)-w'*Y(:,k);
w=w+u*conj(e(k));
P=1/lambda*(eye(m)-u*Y(:,k)')*P;
end
Calling mapping function, get the simulation results
the application of RLS adaptive beam forming algorithm
in interference suppression[6]
:
Figure 7.Antenna pattern
Figure 8.Relational graph of the iterative times and error
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5. Figure 7 is the antenna pattern, the figure can be seen
that RLS algorithm can also form main beam at the
direction of desired user, form deep nulls steering at the
direction of interference, reach the effects of interference
elimination. Figure 8is the relational graph of the iterative
times and error, after a certain number of iteration
operation, RLS algorithm reached convergence. The
reference signal error is under control within a relatively
small scope[7]
.
5.3. Comparison of two algorithm simulation
result
The simulation results show that more than LMS
algorithm and RLS algorithm in the area to cancel the
interference has very good results, to complete the task of
interference reduction.
The LMS algorithm has the advantages of a simple
algorithm and high stability. RLS algorithm the
convergence rate is faster than the LMS algorithm, and
also has a strong adaptability for non-stationary signals.
But RLS algorithm matrix iterative renewal formula has
large amount of calculation, high complexity, and is
difficult to achieve, so reducing the amount of computing
is one of the main aspects to improve algorithm.
From the simulation results of two algorithms, we can
see that LMS algorithm null steering is smaller, RLS
algorithm form nulls steering at the direction of
interference is deeper than the LMS algorithm[8]
.
6. Conclusion
Smart antenna array is the anti-interference key
technology of 3G mobile communication system. The
core of smart antenna research is the arithmetic of
beaming. In this paper, the methods proposed in the array
beam-forming antenna design and interference
suppression is very effective, have a great application
prospects and great significance to the projects guidance.
Broadband signal processing is the core of 3G
technologies, smart antennas for broadband adaptive
beam-forming algorithm is not very mature, so broadband
adaptive beam-forming algorithm for smart antenna
technology will become the focus of the study.
7. Acknowledgment
This paper is supported by Tianjin Social
Development key Foundation of China (NO.
09ZCGYSF00300) and Tianjin Key Laboratory for
Control Theory and Application in Complicated Systems,
Tianjin University of Technology, Tianjin 300191,
China.
8. References
[1]Ying He, Hong He, “The Applications and Simulation
of Adaptive Filter in Noise Canceling”, Embedded
Programming, 2008 International Conference on
Computer Science and Software Engineering (CSSE
2008).Vol.4.pp.1-4.
[2] Jian Yang, Xi Hongsheng, “RLS based blind adaptive
beamforming algorithm for antenna array in CDMA
systems”, Information Acquisition, 2005 International
Conference.
[3]Yang Song, Cao Xingbing, “The development and the
application of smart antennas in TD-SCDMA”,
Computer Knowledge and Technology, 2007,(03).
[4]Zhang Jing, “Smart Antenna Technology and its Usage
in Mobile Communication”. Information Technology
and Informatization, 2007,(02).
[5] Zhao Yu, Yuan Sicong, “Research on Beam Forming
of Smart Antennas in the TD-SCDMA System”,
Electronic Science and Technology,2008,(11).
[6] Duan Li, Xue Yongyi, “An Interference Depressing
Algorithm for Smart Antennas”.Computer Simulation,
2008,(10).
[7] Xie Xianzhong, TD-SCDMA the third generation
mobile communication systems technology and
implementation. The electronics industrial publisher,
Beijing, 2004:89-109.
[8] Zhao Hongyi, Digital Signal Processing and Its
Matlab Realization. The chemistry industrial
publisher, Beijing, 2002.
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