18-09-2012, 03:15 PM
Adaptive Beam forming of Smart Antenna using Conjugate Gradient Method
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ABSTRACT:
This Paper focused on adaptive conjugate gradient method (CGM) algorithm and the same is compared with one of the fastest adaptive algorithm named recursive least squares (RLS) algorithm. This algorithms has improved the computation complexity and better convergence. MATLAB simulation showed that conjugate gradient algorithm has better output signal resolution.
INTRODUCTION
A smart antenna usually involves spatial processing and adaptive filtering techniques. The field of application is very large, ranging from signal to noise improvement to the user capacity enlargement of the mobile network. A typical application will involve an adaptive algorithm to create a beam to track a user or to eliminate noise sources and therefore the smart antenna is also referred to as adaptive array or adaptive beam former. This chapter discusses two algorithms, the Least Mean Square algorithm and the Constant Modulus algorithm.
Smart antenna basics
The smart antenna is basically a set of receiving antennas in a certain topology.
The received signals are multiplied with a factor, adjusting phase and amplitude.
Summing up the weighted signals, results in the Output signal. The concept of a transmitting smart antenna is rather the same, by splitting up the signal between multiple antennas and then multiplying these signals with a factor, which adjusts the phase and amplitude. Figure 1 represents the concept of the smart antenna. The signals and weight factors are complex.
Adaptive beam forming
Adaptive beam forming can be done in many ways. Many algorithms exist for many applications varying in complexity. Most of the algorithms are concerned with the maximization of the signal to noise ratio. A generic adaptive beam former is shown in Figure 3. The weight vector w is calculated using the statistics of signal x (t) arriving from the antenna array. An adaptive processor will minimize the error e between a desired signal d(t) and the array output y(t).
Some adaptive algorithms that suitable in mobile communication with their implementation issues then were briefly discussed. This includes LMS algorithm, SMI technique, RLS algorithm touching on the pro and cons of each of them. Other algorithms that proposed to overcome shortcomings or improve the performance of the three basic algorithms such as conjugate gradient method, eigenanlysis algorithm, rotational invariance method, linear least square error (LSSE) algorithm, and Hopfield neural network with respective references are listed.
CONJUGATE GRADIENT METHOD
The Conjugate Gradient method is an effective method for symmetric positive definite systems. The method proceeds by generating vector sequences of iterates, residuals corresponding to the iterates, and search directions used in updating the iterates and residuals.