Analysis of Performance Degradation using Convex Optimization for a Mismatched Receiver

Abstract

Consider a binary baseband vector-valued communication channel modeled by a zero-mean CGN vector N with a non-singular covariance matrix Λ. We study the maximum loss of system performance using the metric of a decrease of PD for a fixed PFA. Under H0, the observed vector is given by x = n, while under H1, x = s + n. The optimum receiver compares the statistic x^TΛ^-1s to a threshold γ determined by PFA. However, the suboptimum mismatched receiver assumes a WGN with a statistic given by x^Ts, with its P^sub_D satisfying P^subD ≤ Q(Q^-1 (P_FA) – SQRT(S^TΛ^-1s))=P^opt_D, which is equal to ||s||⁴≤(s^TΛs)(s^TΛ^-1s) , and is satisfied by Schwarz Inequality. For a given Λ, the solution for finding the maximum degraded (i.e., smallest) P^sub_D is equivalent to finding the signal vector s that attains the maxium of (s^TΛs)(s^TΛ^-1s), which uses the convex optimization method based on the Karush-Kuhn-Tucker conditions. The mismatched system performance degradation is formulated as a margin loss in SNR(dB) useful for robust communication system engineering analysis and design. Some explicit examples illustrating the margin loss are given.