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Consider a binary baseband vector-valued communication channel modeled by a zero-mean CGN vector N with a non-singular covariance matrix. Â¿ 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 xT Â¿-1s to a threshold Â¿ determined by PFA. However, in a mismatched system, the sub-optimum receiver assumes a WGN vector using the statistic xTs, such that the PD sub Â¿ Q(Q-1(PFA)-Â¿(sTÂ¿-1s)) = PD opt, which is equivalent to ||s||4 Â¿ (sT Â¿s)(sTÂ¿-1s), which is satisfied by Schwarz Inequality. For a given Â¿, the solution for the smallest (worst) PD sub is equivalent to finding the signal vector s that attains the largest value of (sT Â¿s)(sTÂ¿-1s), which can be obtained using convex optimization method based on the Karush-Kuhn-Tucker condition. Various explicit examples are given.