Preconditioning of real-time optical Wiener filters for array processing

Abstract

In adaptive array processors, a performance measure, such as mean square error or signal to noise ration, coverages to the optimum Wiener solution starting from an initial setting. The choice of adaptive algorithms to solve the Wiener filtering problem is mainly guided by the desired processing time. In an optical realization for direct calculation of the optimum weights the covariance matrix and vector for a Wiener filter are computed at a high speed on acousto-optic processors. The resulting linear system of equations can be solved on an iterative optical processor. The matrix and vector data should be recomputed in every iteration for better tracking and adaptation. This introduces variations in their values due to the time-varying jamming and interference noise and the optical errors and noise. Time variant steepest descent algorithm is a simple method that converges to the common solution. In this paper, we describe a real-time preconditioning technique for such nonstationary iterative methods. Preconditioning will progressively lower the condition number of each matrix in the sequence, thereby improving the convergence speed and accuracy of the solution. This preconditioning process involves matrix-matrix multiplications that can be performed at high speed on parallel optical processors. Results of simulations illustrate the superlinear convergence obtained from preconditioning.