Dual optimality of the phase-only filter

A measure of the peak-to-sidelobe performance for correlation filters is defined. The phase-only filter is then shown to be optimum with respect to the peak-to-sidelobe criterion. The phase-only filter has been previously shown to give optimum signal-to-noise performance. Thus, under the assumption of a unit modulus phase device, optimum peak-to-sidelobe and signal-to-noise performance can be obtained simultaneously.