Analysis of the Principal Component Combining with Weight Estimation for DPSK Signals

We analyze the principal component combining with differential detection (PCC-DD) with weight estimation for the demodulation of DPSK signals in diversity systems. The estimated weight vector is considered to be the principal component of the exponentially weighted sample correlation matrix of the signals at diversity channel outputs. We arrive at closed form expressions for the approximate bit error rate (BER) for the scenario where channel gains are fixed, and the approximate average BER for the scenario where channel gains are independent identically Rayleigh distributed. The analysis provides accurate BER approximation, and is justified by the results from computer simulations. We also arrive at a rule of thumb about the value of the forgetting factor of the exponentially weighted sample correlation matrix should be selected for PCC-DD to yield good performance under time varying Rayleigh fading channels