Sequence detection for MPSK/MQAM with adaptive phase tracking

In [P.Y. Kam, P. Sinha, A Viterbi-type algorithm for efficient estimation of MPSK sequences over the Gaussian channel with unknown carrier phase, IEEE Trans. Commun. COM-43 (1995) 2429–2433], we developed a Viterbi algorithm for efficient detection of MM-ary phase-shift keyed (MPSK) sequences received over the additive, white, Gaussian noise (AWGN) channel with an unknown carrier phase. By assuming the carrier phase is constant over some LL symbol intervals and using the sequence detection metric in [P.Y. Kam, Maximum-likelihood digital data sequence estimation over the Gaussian channel with unknown carrier phase, IEEE Trans. Commun. COM-35 (1987) 764–767] as the decoding metric, it approaches the performance of coherent detection, provided the observation interval LL for forming the decoding metric is sufficiently long. However, this observation interval LL is fixed, and chosen based on prior knowledge of the carrier phase characteristics. Thus, the metric is nonadaptive, and cannot be optimized when a priori   statistical knowledge of the carrier phase is not available. The work here renders it adaptive by developing a recursive metric that is adapted on-line based on the received signals, without prior knowledge of the carrier phase characteristics. We first derive a metric for the maximum likelihood sequence detector for a general MM-ary quadrature amplitude modulation (MQAM) sequence received in the presence of AWGN and an unknown, slowly- and randomly-varying carrier phase. To reduce the receiver complexity, a practical, suboptimal metric is obtained. A recursive form of the metric using adaptive reference estimation as in [P.Y. Kam, K.H. Chua, X. Yu, Adaptive symbol-by-symbol reception of MPSK on the Gaussian channel with unknown carrier phase characteristics, IEEE Trans. Commun. COM-46 (1998) 1275–1279], is proposed. Comparison between the proposed adaptive, recursive metric and those in the literature is provided. Simulation results using a random-walk carrier phase model show the superior performance of the adaptive sequence detector over the original nonadaptive sequence detector of [P.Y. Kam, P. Sinha, A Viterbi-type algorithm for efficient estimation of MPSK sequences over the Gaussian channel with unknown carrier phase, IEEE Trans. Commun., COM-43 (1995) 2429–2433].