Code-Aided CFOs and CPOs Estimation in Cooperative Satellite Communication

Low Earth Orbit (LEO) satellites have recently emerged as promising candidates for secure Internet of Remote Things (IoRT). However, in scenarios involving miniaturized terminals, limited transmission power and long distances often lead to diminished Signal-to-Noise Ratio (SNR) at satellite receivers, resulting in degraded communication quality. To address this challenge, the implementation of cooperative satellite systems has been proposed, where signals from multiple satellites are combined to improve SNR. Achieving optimal gain necessitates precise synchronization of carrier frequency and phase across all received signals, particularly challenging under low SNR conditions, and in short burst transmissions without training sequences. We propose an iterative code-aided estimation algorithm for joint estimation of Carrier Frequency Offset (CFO) and Carrier Phase Offset (CPO), employing Iterative Cross Entropy (ICE) and Cooperative Taylor Expansion of Objective Function (CTEOF). Simulation results show that our algorithm achieves accurate estimation within the normalized frequency range that exceeds existing algorithms and phase interval (-pi, +pi]. Moreover, the algorithm demonstrates the ability to approach the Bit Error Rate (BER) performance bounds with deviations of 0.3 dB and 0.4 dB in dual-satellite and quad-satellite collaboration scenarios, respectively.