Genie-aided Optimal Sequence Detection Under Mismatch
Tor Aulin · International Symposium on Information Theory and its Applications · 1994
The detection performance of a Maximum Likelihood Sequence Detector (MLSD) is studied and especially its asymptotic behaviour. The channel is considered to be additive, white and Gaussian. By using properly designed upper and lower bounds on the first error event probability, Forney has shown that this is determined by the two distinct paths through the trellis whose signals are as close to each other in signal space as possible (the Euclidean distance between them is minimal). In this paper an attempt is made to extend Forney's result to the case where sequence detection using the Viterbi Algorithm (VA) is performed under mismatch. By mismatch is here meant that a sufficient statistic needed to perform MLSD is not available. These quantities are instead observed in some other signal space, not entirely coinciding with the signal space associated with the transmitter. The concept of a good genie is utilized and it is demonstrated that the problem to determine the asymptotic behaviour of the mismatched detector is far from trivial. It is shown how easy it is to be tempted to draw hasty conclusions which might not be correct.