This paper proposes a novel approach to phase-noise compensation. The basic idea is to approximate the phase-noise statistics by a finite number of realizations, i.e., a phase-noise codebook. The receiver then uses an augmented received signal model, where the codebook index is estimated along with other parameters. The realization of the basic idea depends on the details of the air interface, the phase-noise statistics, the propagation scenario and the computational constraints. In this paper, we will focus on a MQAM-OFDM system with pilot sub-carriers within each OFDM symbol. The channel is frequency selective, fading and unknown. A decision-feedback method is employed to further enhance performance of the system. Simulation results are shown for uncoded and coded systems to illustrate the performance of the algorithm, which is also compared with previously employed methods. Our simulations show that for a 16-QAM coded OFDM system over a frequency selective Rayleigh fading channel affected by phase noise with root-mean-square (RMS) of 14.4 degrees per OFDM symbol, the proposed algorithm is 1.5dB from the ideal phase-noise free case at a BER of $10^{-4}$. The performance of the best reference scheme is 2.5dB from the ideal case at BER of $10^{-4}$. The proposed scheme is also computationally attractive.Comment: Accepted for publication in IEEE Transactions on Communications, 201

This paper considers the three-parameter-fit sine wave model. Under a Gaussian noise assumption, it is known that the three-parameter fit given in IEEE Standards 1057 and 1241 coincides with the method of maximum likelihood (ML), which is known for its favorable properties in large samples. Under coherent sampling assumption, the Cramér-Rao Bound of an unbiased estimator (UE) of the signal-to-noise ratio (SNR) is derived followed by an exact finite-sample analysis of the ML estimator of SNR derived from the three-parameter fit, revealing its nonsymmetric F-distribution. Exact expressions for the bias, variance, and the mean squared error (MSE) of the ML estimator are then derived, revealing that the ML estimator in finite samples is far from optimal in terms of precision and accuracy. With the ML estimator as a starting point, several alternative estimators are derived, which outperform the method of ML. In particular, a UE is derived, with lower variance compared with the ML for small sample size. In addition, estimators are derived based on constrained minimization of the MSE. The theoretical findings are illustrated by simulations, showing an excellent agreement between theory and practice. Simulations using quantized data are also used to show the performance of the derived estimators mimicking an analog-to-digital converter (ADC) testing scenario. Furthermore, the derived estimators are applied to coherently and noncoherently sampled measurement data from a 12-bit ADC and, for small number of samples, all are shown to outperform the original estimate, showing the practical relevance of the theoretical findings.Index Terms-Cramér-Rao bound (CRB), maximumlikelihood (ML) estimation, signal-to-noise ratio (SNR), sine-fit, unbiased estimator (UE).

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Abstract-In this paper, theoretical properties of a maximumlikelihood (ML) estimator of signal-to-noise ratio (SNR) is discussed. The three-paremter sine fit algorithm is employed on a finite and coherently sampled measurement set corrupted by additive white Gaussian noise. Under the Gaussian noise model, the least squares solution provided by the three-parameter sine fit is also ML estimator. Exact distribution and finite sample properties of the SNR estimate are derived. Moreover, an explicit expression for the mean squared error (MSE) of the estimator is given. Simulation results are shown to verify the underlying theoretical results.