Minimum mean‐square error transceiver optimisation for downlink multiuser multiple‐input‐multiple‐output network with multiple linear transmit covariance constraints

The authors propose two algorithms to solve sum mean‐square error (MSE) minimisation and mixed quality of service (QoS) requirement problems for a multiuser multiple‐input‐multiple‐output system with multiple linear transmit covariance constraints. These original problems in the downlink are complicated because of the coupled structure of the transmitter filters. To overcome this issue, MSE duality proposed in the literature is extended at different levels for a general linear transmit covariance constraint. Exploiting the general sum‐MSE duality and subgradient method, the sum‐MSE minimisation algorithm is proposed first for multiple linear transmit covariance constraints. Secondly, a novel algorithm is proposed to solve mixed QoS requirement problem, where multiple linear transmit covariance constraints are incorporated in the design of the receiver filters in the equivalent multiple access channel. This algorithm is developed based on stream‐wise MSE duality and alternating optimisation framework. Simulation results have been provided to validate the convergence of the proposed algorithms. In addition, the proposed sum‐MSE minimisation algorithm with per‐antenna power constraints outperforms the existing algorithm in terms of achieved sum‐MSE and power consumption at each transmit antenna.