Communication system designers need to formulate an accurate and thoroughly reproducible error model for wireless mobile channels in order to assess the quality of communication with different modulation schemes. The task is relatively easy when an ideal situation is assumed, and is covered exhaustively in standard text books. However, the random time-varying nature of radio propagation renders estimation of different channel state information (CSI) very difficult and when these non-idealities (e.g. imperfect phase/frequency/timing information) are considered, the formulation complexity increases manifold. In this paper, we have set our attention on phase shift keying (PSK), which suffers mostly from phase synchronization error when proper CSI is not available at the receiver. The article surveys various error modelling methods for a PSK system operating over a slow flat Nakagami- m distributed wireless fading channel perturbed with additive white Gaussian noise (AWGN) in the presence of phase error. The phase distortions are considered to be random, unbiased, i.e. having zero mean, and may be represented by either Gaussian or Tikhonov distribution. We also provide a novel approach to classify these schemes that are surveyed, and summarize the major contributions of related works. Further, we identify the method that requires lesser mathematical operations and thus proves to be less complex, more stable and accurate than others. Apart from this, simple alternative approaches for calculating analytical bit error rate (BER) through Hermite's method of integration for Gaussian distributed phase error and through moment generating function (MGF) for Tikhonov distributed phase error have been proposed. Both of these methods have wider applicability, are able to furnish reproducible results, and show significant improvement in accuracy regarding theoretical BER calculation as seen from the graphical comparisons. Extensive Monte Carlo simulations were performed to validate the theoretical results. © 2010 Elsevier B.V.
Chandra, A., Patra, A., & Bose, C. (2011, March). Performance analysis of PSK systems with phase error in fading channels: A survey. Physical Communication. https://doi.org/10.1016/j.phycom.2010.12.001