Downlink Transmitter Design With Statistical CSI for HF Skywave Massive MIMO

In this article, we investigate the downlink (DL) transmitter design for high frequency (HF) skywave massive multiple-input multiple-output (MIMO) communications with only statistical channel state information (CSI) available at the base station (BS). Motivated by the spatial sparsity of HF skywave massive MIMO channels, we first prove that the ergodic sum-rate maximization problem can be solved in the beam domain without any loss of optimality. We prove that the beam domain transmission only involving power allocation for the beams that each user terminal (UT) occupies is asymptotic optimal if there are a sufficiently large number of antennas at the BS. Then, we derive an iterative beam domain power allocation algorithm using majorization-minimization (MM). Furthermore, we investigate a low-complexity DL transmitter design with ergodic sum-rate upper bound. We show that the beam domain design is still optimal and the asymptotic optimal solution can also be obtained by the beam domain power allocation. Specifically, we prove that the power allocation for different UTs should be performed in non-overlapped beams and simplify the MM based iterative power allocation algorithm. Simulation results confirm the effectiveness of proposed DL transmitter designs for HF skywave massive MIMO systems.