Optimum spatial processing in a noisy environment for arbitrary antenna arrays subject to random errors

A procedure is presented for the maximization of the expected signal-to-noise ratio improvement factor for arbitrary antenna arrays whose excitation amplitudes and phases, as well as element positions, are subject to random errors. In its general form, the formulation imposes no restrictions on either the probability distribution or the variance of the random errors. Correlations are allowed to exist between the random variations in array parameters, and the effect of system internal noise is considered. Computed results for a linear endfire array in a typical noise environment are given, illustrating the dependence of the signal-to-noise ratio improvement factor on the system internal noise; the system bandwidth; the amplitude, phase, and position errors; and the error correlation intervals. Typical expected power pattern functions are also plotted.