Bounds on the performance of continuous and quantized phase-only matched filters

Abstract

The classical matched-filter definition of the signal-to-noise ratio (SNR) is used as the performance measure to present bounds for the performances of phase-only filters (POF’s), binary phase-only filters (BPOF’s), and N-ary phase-only filters (NPOF’s). Specifically, signal-dependent bounds on the SNR of the POF relative to the ideal matched spatial filter for additive white noise are developed. In addition, the tightest possible bounds on the SNR of the BPOF relative to the POF for any type of additive noise are developed. These bounds are then extended to develop the tightest possible bounds on the SNR of the NPOF relative to the POF. The extension to the generalized BPOF and the generalized NPOF is also discussed.