Analysis of Rake reception with multiple symbol weight estimation for antipodal signaling

In Rake receiver for coherent binary antipodal signaling with weight estimation by matched filtering using the reference signal along with the decision of the previous M symbol intervals, and predetection maximal-ratio combining (MRC), the estimation errors are not independent of the additive noise, and do not fit into the Gaussian weighting error model for MRC. Here we analyze the error performance of the receiver by: (1) obtaining the conditional symbol error probability (SEP), conditioned on past decisions, from the characteristic function of the decision variable, (2) getting the unconditional SEP using a Markov model of the decision process.