Influence of input quantizer step sizes on the processing gain of digital beamformers

Abstract

Utilizing a formulation of output power of a digital beamformer with input quantizers of unequal input and output step sizes given previously, the optimum quantizer step sizes which yield maximum processing gain for a typical array were searched by the method of “steepest ascent” with a digital computer. For the case of two-bit /channel quantization with small input SNR (⩽ − 10 dB), the array gain surface as a function of two independent step variables exhibits a maximum which is only slightly greater than the maximum array gain achievable with uniform input quantizers. For larger input SNR, the array gain surface tends to be concave upward, and the performance of uniform quantizers can at the best be a suboptimum. The high theoretical processing gain in the limiting case of very large step sizes is attributed to a threshold effect of the input quantizers. Except for these latter conditions, the optimum uniform quantizing condition previously reported by the author represents essentially valid optimum design.