TABLE OF CONTENTS The gradient approach to solving the control problem posed by adaptive array weight adjustment is very popular since it is a relatively simple and generally well understood method that permits the solution of a large class of problems. The selected performance measure and the parameters to be adjusted (which are usually, but not always, complex weights) determine the nature of the performance surface over which the adaptive processor must operate. The performance surface is determined by the nature of 
, where 
is the performance measure of concern and w is the complex weight vector whose components it is desired to adjust. When the selected performance measure is a quadratic function of the weight settings, then the performance measure can be visualized as a bowl-shaped surface, so the adaptive processor has the task of continually seeking the "bottom of the bowl." In this case optimization of the performance measure can be accomplished by "hill climbing" methods of which the various gradient methods are representative. In the event that the performance surface is irregular, having several relative optima or saddle points, then the transient response of the gradient-based hill climbing procedures may suffer in comparison with other methods. The various gradient-based algorithms to be considered here include the following:
Least mean square (LMS).
Differential steepest descent (DSD).
Accelerated gradient (AG).
Variations of the above algorithms can easily be derived by introducing constraints into the adjustment rule, and one section develops the procedure for deriving such variations. Finally, changes in...
