Iterative LDPC-Hadamard Code-Aided Carrier Phase Synchronization at Extremely Low SNR

In this paper, we consider a method of code-aided carrier phase synchronization at extremely low signal-to-noise values based on LDPC-Hadamard code. This system comprises a low-rate LDPC-Hadamard code that is close to Shannon limit at extremely low SNR values and an EM-based carrier phase synchronizer that makes use of the posterior probabilities of the data symbols, provided by the iterative decoder. Simulations show that the proposed synchronizer can achieve a bit-error-rate (BER) performance of 10^-5 at Es/No=-10 dB, and has negligible BER performance degradation as compared to the ideally synchronized system. Through analysis and simulation, we show that our strategies are very effective at extremely low SNR values.