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 H
₀
, the observed vector is given by x = n, while under H
₁
, x = s + n. The optimum receiver compares the statistic x
^T
¿
^-1
s to a threshold ¿ determined by P
_FA
. However, in a mismatched system, the sub-optimum receiver assumes a WGN vector using the statistic x
^T
s, such that the P
_D

^sub
¿ Q(Q
^-1
(P
_FA
)-¿(s
^T
¿
^-1
s)) = P
_D

^opt
, which is equivalent to ||s||
⁴
¿ (s
^T
¿s)(s
^T
¿
^-1
s), 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
¿
^-1
s), which can be obtained using convex optimization method based on the Karush-Kuhn-Tucker condition. Various explicit examples are given.