Joint MMSE precoder and decoder design for downlink multiuser MIMO systems with arbitrary transmit power constraints

A novel unified approach to deal with arbitrary transmitted power constraints for designing jointly the MMSE precoders and decoders in downlink multiuser MIMO systems is developed. This work is an extension of the iterative approach developed in [1] for the total power constraint. An explicit expression relating Lagrange multipliers with the per-user constraint can be obtained using the proposed approach to mitigate the time consuming root searching for the Lagrange multipliers in [1]. Moreover, the explicit expression allows the MMSE solution subject to arbitrary transmit power constraints. In this paper, total, per-user, per-antenna, and peak power constraints are formulated in under the same format and solved using the proposed approach. It is shown in some two-user numerical examples that the raw BER performance obtained from the practical per-antenna power constraint is similar to those of the per-user and total power constraints and is 1–1.5 dB better than that of the peak power constraint.