Quasi-Maximum-Likelihood Multiple-Symbol Differential Detection for Time-Varying Rayleigh Fading Channel

The maximum-likelihood multiple-symbol differential detector (ML-MSDD) has better bit-error-rate (BER) performance than many other detectors for differential modulation. Unfortunately, the computational complexity of ML-MSDD quickly becomes prohibitive as the observation window size grows. While low-complexity MSDD algorithms for the time-invariant Rayleigh fading channel have been considered before, there is a need for lowcomplexity MSDD algorithms for general time-varying Rayleigh fading channels. In this paper, a polynomialtime complexity approach called semi-definite relaxation (SDR) is employed to achieve differential detection with near maximum-likelihood (ML) performance. The proposed SDR quasi-maximum-likelihood (QML) multiple-symbol differential detection (SDR-QML-MSDD) is efficient in that its complexity is polynomial in the observation window size, even in the worst case, while it exhibits almost the same performance as ML-MSDD does.