TrainingBased time-delay estimation for CPM signals over time-selective fading Channels

Abstract—In this paper, we consider training-based symbol timing synchronization for continuous phase modulation over channels subject to flat, Rayleigh fading. A high signal-to-noise-ratio maximum-likelihood estimator based on a simplified channel correlation model is derived. The main objective is to reduce algorithm complexity to a single-dimensional search on the delay parameter, similar to that of the static-channel (slow fading) estimator. The asymptotic behavior of the algorithm is evaluated, and comparisons are made with the Cramer–Rao lower bound for the problem. Simulation results demonstrate highly improved performance over the conventional, static-channel delay estimator. Index Terms—Continuous phase modulation (CPM), fading channels, maximum-likelihood (ML) estimation, synchronization, timing. I