The error in the optimum gain of an antenna array arising from errors in the measured noise covariance matrix

The optimal processing of a signal by an antenna array requires that the noise covariance matrix be known. In the measurement process which determines this matrix, an error is incurred. When the ideal Wiener shading vector is chosen, so as to optimize the array gain, the choice depends upon the measured noise covariance matrix. Thus, the noise covariance matrix measurement error results in an error in the achieved optimal gain. The primary purpose of this paper is to estimate this gain error. It is shown that, for an error of order ∈ in the noise covariance matrix, an error of order ∈ 2 is produced in the achieved optimal gain. The estimates obtained depend upon the norms of the noise covariance matrix and its inverse, which in turn depend upon the character and spatial distribution of the noise field. The effects of these latter considerations will be analyzed in a subsequent paper.