The corrective gradient projection method, and some adaptive algorithms for linearly constrained array processing

Abstract

The corrective gradient projection (CGP) method is described for the problem of optimizing a non-linear function (called the objective function) of multiple parameters subject to a system of linear constraint equations. This scheme, developed originally by Frost (1972) for a constrained adaptive array processing problem, is derived geometrically by modifying the gradient projection (GP) method of Rosen (1960) and is specifically designed to correct for any deviation of the parameters form the constraints at every iteration. Therefore, the CGP method can applied to those problems where large numbers of iterations are required without accumulating these deviations. The CGP method is applied to the problem of adaptive, linearly constrained array processing, that is, the problem of minimizing the expected noise power in real time while maintaining a certain frequency response to the target signal. In the adaptive CGP algorithm the input statistics are progressively updated by a simple feed-back scheme involving the instantaneous input statistics. A different (and more straightforward) approach, called the constraint elimination technique, is described for the constrained array processing problem. ...