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Generalized mutual information (GMI) has become a key metric for bit-interleaved coded modulation (BICM) system design and performance analysis. As residual phase noise (RPN) normally exists after imperfect phase estimation, the mostly used mismatched Gaussian receiver is suboptimal for GMI analysis in phase noise. This letter thus analyzes the GMI of BICM systems using 8-ary quadrature-amplitude-modulations (QAM) in the presence of both RPN and additive white Gaussian noise (AWGN). We will use the maximum-likelihood receiver derived in our earlier work to calculate the GMI of Star-8QAM, Circular-8QAM, Rect-8QAM and 8PSK. The explicit symbol and bit loglikelihood ratios are specifically expressed in amplitude-phase form with RPN considered. Numerical results are given in details to show the GMI comparison in phase noise and the GMI loss compared to the pure AWGN case. It is shown that Star-8QAM is much more tolerant to large RPN. Moreover, the ratio parameters of Rect-8QAM and Star-8QAM are optimized to maximize the GMI as the RPN variance increases. We also optimize the bit mapping for non-Gray 8QAM.

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We address here the issue of jointly estimating the angle parameters of a single sinusoid with Wiener carrier phase noise and observed in additive, white, Gaussian noise (AWGN). We develop the theoretical foundation for time-domain, phase-based, joint maximum likelihood (ML) estimation of the unknown carrier frequency and the initial carrier phase, with simultaneous maximum a posteriori probability (MAP) estimation of the time-varying carrier phase noise. The derivation is based on the amplitude and phase-form of the noisy received signal model together with the use of the best, linearized, additive observation phase noise model due to AWGN. Our newly derived estimators are closed-form expressions, consisting of both the phase and the magnitude of all the received signal samples. More importantly, they all have a low-complexity, sample-by-sample iterative processing structure, which can be implemented iteratively in real-time. As a basis for comparison, the Cramer-Rao lower bound (CRLB) for the ML estimators and the Bayesian CRLB (BCRLB) for the MAP estimator are derived in the presence of carrier phase noise, and the results simply depend on the signal-to-noise ratio (SNR), the observation length and the phase noise variance. It is theoretically shown that the estimates obtained are unbiased, and the mean-square error (MSE) of the estimators attain the CRLB/BCRLB at high SNR. The MSE performance as a function of the SNR, the observation length and the phase noise variance is verified using Monte Carlo simulation, which shows a remarkable improvement in estimation accuracy in large phase noise.

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