Bayesian feedback detection for adaptive transmission systems

The paper considers adaptive transmission systems with imperfect feedback channels. It is shown that if the average SNR for the forward channel is known to the transmitter, the feedback detection can be modeled as a classical multiple hypotheses testing problem. Though maximum a posteriori detection is optimal compared to maximum likelihood (in the sense of minimum probability of error) from a feedback communication link viewpoint, the overall effect on adaptive system performance shows that ML detection could be better in the high SNR range. The MAP scheme is generalized to Bayesian detection by defining a cost function matrix, which assigns (unequal) weights to the feedback decision error probabilities. The result is close to ideal bit error rate (BER) performance with only a small drop in spectral efficiency.