This paper investigates the non-data-aided (NDA) carrier frequency estimation of amplitude and phase shift keying (APSK) signals. The true Cramer-Rao bound (CRB) for NDA frequency estimation of APSK signals are derived and evaluated numerically. Characteristic and jitter variance of NDA Luise and Reggiannini (L&R) frequency estimator are analyzed. Verified by Monte Carlo simulations, the analytical results are shown to be accurate for medium-to-high signal-to-noise ratio (SNR) values. Using the proposed closed-form expression, parameters of the algorithm are optimized efficiently to minimize the jitter variance.

A low complexity log-likelihood ratio (LLR) calculation for high-order amplitude phase shift keying (APSK) signals is proposed. Using proper constellation partitioning together with a look-up table, the number of terms for the comparison of Euclidean distances can be significantly reduced. Compared with the log-sum LLR approximation, the proposed method reduces the computational complexity by more than 65% and 75% for 16-APSK and 32-APSK signals, respectively, with very small bit error rate performance degradation.