Robust Precoding for HF Skywave Massive MIMO With Slepian Transform

In this paper, we address robust precoding in high-frequency (HF) skywave massive multiple-input multiple-output (MIMO) systems with imperfect channel state information (CSI). We first employ a sparse beam based a posteriori channel model and demonstrate that robust precoding can be efficiently solved in the Slepian transform domain with a large number of base station (BS) antennas. Next, we introduce two Slepian transform based robust precoding methods, including a joint approach that leverages inverse fast Fourier transform (IFFT) for reduced complexity with a large number of user terminals (UTs). We then establish a local optimum for the Slepian transform domain robust precoder (STRP) design using the majorization minimization (MM) algorithm, taking advantages of HF skywave massive MIMO channel sparsity and Slepian sequence properties. Further, two distinct designs are presented: separate STRP (SSTRP) and joint STRP (JSTRP). Simulation results confirm the effectiveness of proposed robust precoders, showcasing their excellent ergodic sum-rate performance and low complexity.