Data-Aided and Non-Data-Aided Maximum Likelihood SNR Estimators for CPM


Information-aided (DA) and non-data-aided (NDA) most chance (ML) estimators for the SNR of CPM in the presence of phase and frequency offset are derived and analyzed. Cramér-Rao bounds for each are obtained and compared to the simulated performance of these estimators for a full response example, CPSFK and a partial response example, GMSK. Analysis and simulations show that the performance of the DA ML estimator suffers from an unremovable bias caused by uncompensated frequency offset thanks to frequency offset estimation errors. As a consequence, the estimator error variance of the DA ML estimator is not in a position to attain its lower certain. In distinction, the estimator error variance of the NDA ML estimator is capable of achieving its lower certain (although the lower certain for NDA ML estimator is over the lower bound for the DA ML estimator). This is as a result of the NDA ML estimator is not burdened with the requirement of hoping on estimates of nuisance parameters. The NDA estimator only achieves its lower sure when the observation length or true SNR are sufficiently massive.

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