Reference Phasor Based Log-Likelihood Ratios for Pilot-Symbol-Assisted BPSK Transmission of LDPC Codes over the Noncoherent Channel

We derive the log-likelihood ratio for iterative decoding of low-density parity-check codes transmitted using binary phase-shift-keying (BPSK) with pilot-symbol-assisted modulation. This is done with the aid of a reference phasor formed from the received pilot signals. We compare our metric with the existing Gaussian metric for differential BPSK transmission and also show that our metric converges to that for coherent BPSK transmission in the limit as the size of the pilot reference set becomes large. Simulation results verify our analysis and study the effects of carrier phase noise and signal-to-noise ratio mis-estimation on the performance of the metric.