RAKE Receiver for Channels with a Sparse Impulse Response

We derive the optimal receiver for RAKE diversity combining on channels with a sparse impulse response. The receiver is based on the Bayesian philosophy and thus it requires the knowledge of certain a priori parameters. However, we also derive an empirical Bayesian version of our receiver, which does not require any a priori knowledge, nor the choice of any user parameters. We show that both versions of our detector can outperform a classical training-based maximum-ratio-combining detector.