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

Consider a Rake receiver for coherent binary antipodal signaling with: 1) a delayed received signal configuration; 2) weight estimation by matched filtering using the reference signal along with the decisions of the previous M symbol intervals; and 3) predetection maximal-ratio combining (MRC). The weight estimation errors here 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 obtaining the conditional symbol error probability, conditioned on past decisions, from the characteristic function of the decision variable, and getting the unconditional error probability (UEP) for a block of M consecutive symbols using a Markov model of the decision process. The channel is Rayleigh fading with independent and identically distributed branch gains. Results show that the error performance of the Gaussian distributed weighting error model is a bound for that of multiple symbol weight estimation by matched filtering, and the steady state UEP decreases with increase of M, but the amount of decrease reduces as M increases.