This paper examines the problem of carrier phase recovery in turbo-coded systems. We introduce a new concept of "a priori probability aided phase estimation", where the extrinsic information (log-likelihood ratio) obtained from turbo decoder is used to aid an iterative phase estimation process, which is based on a maximum-likelihood strategy. The phase estimator operates jointly with the turbo decoding rather than separately prior to the decoder as in traditional approaches. This technique provides reliable phase estimation with variance of estimation errors approaching the Cramer-Rao bound at very low signal-to-noise ratio and allows robust decoding with a wide range of phase errors. This paper addresses its application in turbo-coded binary phase-shift keying and quaternary phase-shift keying systems over the additive white Gaussian noise channel. The bit-error-rate performance is investigated and shows that the performance of this technique is very close to the optimally synchronised system and significantly outperforms the traditional non-data-aided method without using additional pilot symbols
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