CSI Impaired Precoding Optimization for Energy-Efficient MIMO Communications Under Total Power Constraint

This letter considers robust precoding for improving the energy efficiency (EE) in a multiple-input multiple-output (MIMO) channel when only imperfect or partial channel state information (CSI) is available at the transmitter. From the perspective of worst case robustness, we aim to maximize the worst case EE subject to additive or multiplicative bounded CSI uncertainties and under total power constraint. Theoretically, we prove that the robust energy-efficient precoding optimization leads to a channel-diagonalizing structure. Accordingly, the complicated matrix-valued problem is equivalently transformed into a simpler scalar optimization problem, which can be solved efficiently with a water-filling interpretation for the optimal power allocation. The obtained worst case EE was finally verified and evaluated via numerical simulations.