Joint variable factor subspace tracking and federated Kalman filtering for multi-terminal distributed cooperative communications

In recent years, distributed cooperative communications systems have demonstrated great potentials in terms of small size, lightweight, low power consumption, and low cost, allowing for the expansion of transmission range for various tasks. However, issues such as high-precision time-frequency synchronization and complex time-varying channels limit the application of distributed cooperative communications in practical communications systems. Moreover, the residual frequency offset, influenced by the accuracy of frequency offset estimation algorithms and node movement, introduces time-accumulating phase errors into each node's signal, thereby affecting signal consistency. In this paper, we propose a joint multi-terminal phase tracking and notch optimization scheme to address the limitations of time-varying phase errors in distributed nodes and mutual interference between multi-terminal signals in the multi-terminal distributed cooperative communications receiver model. In order to reduce the computational complexity, the original scheme is simplified and decoupled into the estimation of the number of terminals, distributed phase tracking, and notch optimization, where the estimation of the number of terminals is a prerequisite for multi-terminal phase tracking. Specifically, during the distributed phase tracking phase, considering the relative movement of far-field multi-terminals and distributed nodes, a federated Kalman-filter-corrected variable factor subspace tracking method is designed to address the multi-terminal phase tracking problem under low signal-to-noise ratio (SNR) conditions. Multi-terminal signal notch optimization eliminates the impact of overlapping signals on demodulation, resulting in better multi-terminal signal demodulation. Simulation results show that in multi-terminal distributed cooperative communications, the Kalman-filter-corrected variable factor subspace tracking algorithm exhibits better multi-terminal tracking capabilities compared to traditional phase tracking algorithms. More importantly, reliable phase tracking and notch optimization under low SNR conditions can effectively improve the demodulation performance of wireless distributed cooperative communications.