Weighted harmonic mean SINR maximization for the MIMO downlink

Leakage-based methods which are based on the harmonic mean signal-to-interference ratio (SIR) maximization deliver a good tradeoff between the sum rate and bit-error rate (BER). In this paper, we present the joint design of linear transmit and receive beamformers that maximize the weighted harmonic mean signal-to-interference-and-noise ratio (SINR) for the downlink of the multiuser MIMO channel. By exploiting the uplink-downlink SINR duality, the non-convex optimization problem is transformed into a series of simpler problems which can be solved by geometric programming. When the minimum mean square error (MMSE) receive beamformers are employed, it is shown that the harmonic mean SINR maximization becomes a close approximation to the sum MSE minimization problem in the high SINR region. The simulations show that the proposed scheme outperforms other leakage-based schemes in terms of harmonic mean SINR, sum MSE, BER and sum rate.