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

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2 Author(s)
Yao, K. ; Electr. Eng. Dept., UCLA, Los Angeles, CA, USA ; Lorenzelli, F.

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 xT ¿-1s to a threshold ¿ 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 ¿ Q(Q-1(PFA)-¿(sT¿-1s)) = PD opt, which is equivalent to ||s||4 ¿ (sT ¿s)(sT¿-1s), which is satisfied by Schwarz Inequality. For a given ¿, the solution for the smallest (worst) PD sub is equivalent to finding the signal vector s that attains the largest value of (sT ¿s)(sT¿-1s), which can be obtained using convex optimization method based on the Karush-Kuhn-Tucker condition. Various explicit examples are given.

Published in:

Communications and Mobile Computing (CMC), 2010 International Conference on  (Volume:2 )

Date of Conference:

12-14 April 2010