Analysis of Performance Degradation using Convex Optimization for a Mismatched Receiver

Consider a binary baseband vector-valued communication channel modeled by a zero-mean CGN vector N with a non-singular covariance matrix . 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 s to a threshold determined by PFA. However, the suboptimum mismatched receiver assumes a WGN with a statistic given by xs, with its sub D P satisfying -1 1 Q Q ( ) sub T opt D FA D P P P s s , which is equal to 4 1 T T s s s s s , and is satisfied by Schwarz Inequality. For a given , the solution for finding the maximum degraded (i.e., smallest) sub D P is equivalent to finding the signal vector s that attains the maxium of 1 T T s s s s , 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. Index Terms Digital communication system performance degradation, mismatched receiver, margin loss, convex optimization, KKT condition.