Résumé: We maximize the performance of multiple-input multiple-output (MIMO) multiple access channels (MAC) and broadcast channels (BC) under individual and sum power constraints.We observe that the performance metrics sum capacity and sum mean-square error (MSE) belong to a general class of functions which are the trace of a matrix-monotone function. The sum capacity if successive interference cancellation (SIC) is applied in the uplink or if Costa Precoding is applied in the downlink, or the normalised sum MSE if a multiuser minimum mean-square error (MMSE) receiver is applied at the base, belong to that class of performance functions.We use L¨owner’s representation of matrix monotone functions in order to characterise the optimum transmission strategies. Using the Karush-Kuhn-Tucker optimality conditions, we show that the mutual covariance matrix optimisation can be decomposed into power allocation and covariance matrix optimisation under individual power constraints. The covariance matrix optimisation under individual power constraints in turn can be decomposed into a kind of modified single-user covariance matrix optimisation treating the other users as noise. The concrete structure of the single-user program depends on the performance metric used. The proposed algorithms efficiently solve the multi-user MIMO performance optimisation problem. These results generalise the results regarding the performance capacity optimisation recently reported for sum capacity optimisation and the results regarding the sum MSE optimisation. The optimal transmit strategy deconstructs into two independent parts: the coding and the signal processing part. The second part is adapted to the channel and performs multi-user power control and transmit covariance matrix optimisation.

Langue: Anglais