A posteriori probability detection of pulse position modulated signals under imperfect channel estimation

In this paper, we consider two sets of pulse position modulated (M-PPM) signals related by M estimation error signals. The first signal set is transmitted on a Gaussian channel and is unknown to the receiver. The second signal set is used in the receiver filter bank in order to generate likelihoods for coherent a posteriori probability (APP) detection. The error model is defined by a Toplitz matrix and a normalization coefficient. We compute the information rate under such channel estimation errors and we show how the APP detection mismatch can be corrected via the expectation-maximization algorithm.