Design and Analysis of Amplitude-Phase-Form Detection in Residual Phase Noise.

High-order modulations are widely used in wireless communications. And the existence of phase noise, especially in mm-wave or THz high-frequency systems, will greatly impair the transmission reliability. Most existing works still use the minimum Euclidean distance (MED) rule for performance analysis, which is actually a mismatched Gaussian receiver in phase noise. This paper thus proposes approximately optimum amplitude-phase-form detection schemes and analyzes the error performance in the presence of both additive Gaussian white noise (AWGN) and residual phase noise (RPN) due to imperfect carrier phase estimation. Based on the matched maximum-likelihood (ML) receiver proposed in our earlier work, the joint amplitude and phase detection criteria in polar coordinates are given thoroughly. Then a suboptimal annular-sector (AS) detector is obtained, which corresponds to the separate amplitude and phase detection. This AS detector has low complexity to implement and does not depend on the specific channel information. And the optimal ML decision boundaries are explicitly shown, which tend to be circular as the signal-to-noise ratio (SNR) or RPN variance increases. Star-8QAM and Rect-8QAM are used here to illustrate the error performance by both theoretically derivation and detailed simulations. It is shown that the AS detector performs much better than the MED detector for high SNR or strong phase noise. Moreover, Star-8QAM with optimized ring ratio outperforms Rect-8QAM with optimized power ratio for a large range of RPN variances.