TABLE OF CONTENTS In Chapter 5, several adaptive beamforming criteria were discussed and a general form for the optimum array weight vector was derived that would require large amounts of computational load. Hence, it is necessary to find techniques that can find this optimum solution in real time, adapting to the time variant channel while keeping the computational load to a reasonable level. A classification of such adaptive array algorithms is shown in Figure 6.1. A brief description of these algorithms can be found in [1]. In the remainder of this chapter we will describe some of these algorithms in detail and investigate issues related to their performance.
As we can see from Figure 6.1, the least mean square (LMS) algorithm belongs to the trained algorithms category in which a reference signal is used to update the weights at each iteration as follows
where ? w is the gradient of the MSE, which is the mean square error between the reference signal r(n) and the array output given by
In the LMS algorithm, we are searching for the optimal weight that would make the array output either equal or as close as possible to the reference signal, which is the weight that minimizes the MSE. Since the MSE has a quadratic form, moving the weights in the negative direction of the gradient of the MSE should lead us to the...
