Evaluation of System Performance Degradation of a Mismatched CGN Channel Using Convex Optimization Method

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 P_D for a fixed P_FA. Under H₀, the observed vector is given by x = n, while under H₁, x = s + n. The optimum receiver compares the statistic x^T ¿^-1s to a threshold ¿ determined by P_FA. However, in a mismatched system, the sub-optimum receiver assumes a WGN vector using the statistic x^Ts, such that the P_D ^sub ¿ Q(Q^-1(P_FA)-¿(s^T¿^-1s)) = P_D ^opt, which is equivalent to ||s||⁴ ¿ (s^T ¿s)(s^T¿^-1s), which is satisfied by Schwarz Inequality. For a given ¿, the solution for the smallest (worst) P_D ^sub is equivalent to finding the signal vector s that attains the largest value of (s^T ¿s)(s^T¿^-1s), which can be obtained using convex optimization method based on the Karush-Kuhn-Tucker condition. Various explicit examples are given.