Robust Precoding for HF Skywave Massive MIMO

In this paper, we investigate the robust precoding with imperfect channel state information (CSI) for high frequency (HF) skywave massive multiple-input multiple-output (MIMO) communications. Starting with a sparse beam based a posteriori channel model for the available imperfect CSI at the base station (BS), we prove that the robust precoder for ergodic sum-rate maximization can be designed by optimizing the beam domain robust precoder (BDRP) without any loss of optimality. Furthermore, the asymptotic optimal precoder is beam structured for a sufficiently large number of antennas at the BS, involving a low-dimensional BDRP. As a result, the beam structured robust precoding is asymptotic optimal and can be efficiently implemented based on chirp z-transform. We then derive an iterative algorithm to design the BDRP using majorization-minimization (MM). Furthermore, we develop a low-complexity BDRP design with an ergodic sum-rate upper bound, simplifying the MM based design algorithm. Based on our simulation results, the proposed beam structured robust precoding can achieve a near-optimal performance with significantly reduced complexity in various scenarios.