Innovation-Domain Decision-Directed Phase Tracking for Wiener Phase Noise in Fast Rayleigh Fading

Ura Klongklaew, Nithiroth Pornsuwancharoen, Phichai Youplao

This letter proposes an innovation-domain decision-directed phase tracking (ID-DDPT) architecture for coherent detection over Rayleigh fading channels with temporally correlated phase evolution and Wiener phase noise. By reformulating phase tracking into the innovation domain, replacing the unbounded cumulative phase with its stationary increments, the proposed method converts a non-stationary estimation problem into a stable low-complexity filtering problem. A closed-form expression for the steady-state residual phase error variance is derived under the locked-regime assumption, along with an analytical optimal smoothing factor. Modeling the residual phase distortion as an effective signal-to-noise ratio (SNR) attenuation yields a tractable bit error rate (BER) approximation for BPSK over Rayleigh fading. A first-order error-propagation analysis further characterizes the impact of decision errors and provides insight into the onset of cycle slips. Simulation results demonstrate that ID-DDPT outperforms DBPSK and a complexity-equivalent scalar Kalman tracker (SKT), achieving near-coherent performance with $\mathcal{O}(1)$ per-symbol complexity and minimal pilot overhead.