Abstract - 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 s to a threshold Ȗ determined by PFA. However,  the sub¬optimum mismatched receiver assumes a WGN with a statistic Psub dD

equal to
T
given by x s,
 -1
 T
QQ( PFA ) _ s
4
s
d T ȁss T
_s __
Schwarz Inequality.  For a
finding the maximum degraded (i.e., smallest) P is
D
equivalent to finding the signal vector s that attains the
TT _1
maxium of _s ȁss ȁ 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. 
 

Cite: Kung Yao and Flavio Lorenzelli, "Analysis of Performance Degradation using Convex Optimization for a Mismatched Receiver ," Journal of Communications, vol. 5, no.6, pp.483-492, 2010. Doi: 10.4304/jcm.5.6.483-492