Uplink/downlink duality in massive MIMO systems with hardware impairments

In this paper, we provide a new framework for the uplink/downlink duality in single-cell massive multiple-input multiple-output (MIMO) systems suffering from residual hardware impairments (HWIs) at the base station and the user terminals. Using the proposed duality, complex downlink optimization problems can be converted to equivalent dual uplink problems, which are easier to solve. As an example, we apply the proposed uplink/downlink duality to derive an HWI aware minimum mean square error (HWIA-MMSE) precoder, which minimizes the sum mean square error under a sum power constraint in a single-cell massive MIMO system with residual HWIs. Thereby, we use results from random matrix theory to derive an asymptotic expression for the downlink power allocation for large numbers of antennas, which only depends on the channel statistics and not on the individual channel realizations. Analytical results for the asymptotic achievable sum rate of the proposed HWIA-MMSE precoder for a large number of BS antennas are also provided. Our simulation and analytical results show that the proposed HWIA-MMSE precoder achieves a higher sum rate than the conventional regularized zero-forcing precoder for moderately large numbers of base station antennas.