Optimal Transmitters for Hypothesis Testing over a Rayleigh Fading MAC

We consider the case when K sensors have strongly correlated measurements - they all observe a 0 or they all observe a 1. The two possibilities are to be tested at the output of a multiple access channel with Rayleigh fading coefficients, which are not known to the transmitter and the receiver. We study the problem of optimal transmitters for this case using the notion of generalized SNR (GSNR). Under certain symmetry and orthogonality restrictions on the transmitter, we find optimal and near-optimal transmission schemes. In particular, for low SNR, type-based multiple access is optimal, while for high SNR, the optimal strategy assigns orthogonal codewords across sensors. In between these two extremes, we identify optimal/near-optimal schemes for any fixed SNR. Simulation results for the probability of error are also given, which demonstrate the relevance of GSNR optimization.