Analysis of RAKE reception with MRC and imperfect weight estimation for binary coherent orthogonal signaling

We consider a RAKE receiver for coherent binary orthogonal signaling employing predetection maximal-ratio combining (MRC), in which the tap weights are estimated by adding two matched filtered outputs using the two reference signals. The weight estimation errors here are not independent of the additive channel noise, and therefore do not fit into the Gaussian error model for MRC. Instead of analyzing the distribution of the weight estimation errors, we find the characteristic function of the decision variable, and from it we obtain a formula for the symbol error probability