Broad Coverage Precoder Design for Synchronization in Satellite Massive MIMO Systems

In this paper, we investigate the massive multi-input multi-output (MIMO) transmission for the satellite communication systems equipped with a uniform rectangular array (URA) and aim to design the precoder with broad coverage radiation power pattern to improve the performance of time and frequency synchronizations. The modified Cramér-Rao vector bounds (MCRVB) are chosen as the benchmark of symbol timing offset and frequency offset estimation problem, which can be viewed as the time and frequency synchronization performance metric for the broad coverage precoder design. By considering the minimax MCRVB criterion and the per-antenna equal power constraint, the precoder design approach is formulated as the non-convex constrained minimax problem over the discrete radiation power pattern. This optimization problem is solved by the smoothing techniques combined with the manifold optimization method. To reduce the calculation complexity, the nonmonotone conjugate gradient method is applied. Simulation results show that the average and the minimum received powers in the coverage area of the proposed scheme are higher than those of the scheme based on fairness criterion. Compared with the existing omnidirectional and broad coverage schemes, the proposed scheme has the best synchronization performance among all the contrast solutions.