Abstract

In adaptive array processors, a performance measure, such as mean-square error or signal-to-noise ratio, converges to the optimum Wiener solution after starting from an initial setting. The choice of adaptive algorithms to solve the Wiener-filtering problem is mainly guided by the desired processing time. An optical realization for direct calculation of the Wiener solution was discussed by Welstead.¹ In this approach, the covariance matrix and vector for a Wiener filter are computed at high speed on acousto-optic processors. The resulting linear system of equations is solved on an iterative optical processor. The matrix and vector data are recomputed in every iteration. This introduces variations in their values owing to optical errors and noise. A nonstationary steepest-descent algorithm is a simple method that can be used for the optical calculation, and such an algorithm slowly converges to the Wiener solution.¹ It has been shown that the size of the error in the solution introduced by perturbations in the sequence is governed by the condition number of the sequence; this is similar to the case of a single fixed system of linear equations.¹

© 1990 Optical Society of America