Joint estimation of channel phase and oscillator phase noise in multi-satellite, multi-ground-based phased array networks

Abstract We study joint estimation of channel phase and oscillator phase noise (PN) for multi-satellite downlinks to geographically separated ground-based phased arrays (GAs) with unequal propagation latencies, where per-GA observations are jointly processed at a central processor. Each satellite transmits a pseudorandom noise (PRN) pilot; finite code length, code cross-correlation, PN diffusion from the satellite local oscillator (LO), and multi-satellite interference add disturbance beyond thermal noise, summarized by a disturbance-aware signal-to-disturbance-plus-noise ratio (SDNR). Since the observed phase is a composite phase including channel phase and LO phase noise, the per-satellite phases observed across GAs are correlated, so we select one reference GA per satellite and model the remaining links as relative phases with latency-dependent process noise terms. We propose reference-selection metrics based on latency, SDNR, and a mean squared error (MSE) criterion combining SDNR, latency, and cross-GA correlation. From this model, we develop a linearized single-quadrature Kalman filter (L1Q KF) and a moment-matched two-quadrature extended Kalman filter (MM2Q EKF) for robustness under large phase uncertainty. Simulations show that the MSE-based metric and MM2Q yield more stable tracking and lower phase error, especially at low SDNR and large latency spreads; moreover, both filters scale cubically with the number of GAs.