Joint Design of Transceivers for Multiple-Access Channels using MMSE Decision Feedback Detection

We consider the joint design of transceivers for a multiple-access multi-input–multi-output (MIMO) system communicating over intersymbol interference (ISI) channels. The system we consider is equipped with the minimum mean-square error (MMSE) decision-feedback (DF) detector. Here, we explore a novel perspective of designing a transceiver that minimizes the arithmetic mean-square error (MSE) of MMSE-DF detection and satisfies a fixed-sum Gaussian mutual information constraint. For this optimization problem, a direct explicit solution is obtained. We show that the optimal solution is achieved if and only if uniform user mutual information and uniform symbol mutual information are both achieved. Uniform user mutual information is attained by successively solving a series of problems of minimizing individual user transmission power under fixed mutual information, whereas uniform symbol mutual information is maintained by applying the equal-diagonal QRS decomposition. We also show that, in addition to minimizing the arithmetic MSE of MMSE-DF detection, such uniform mutual information distribution has also other desirable properties: 1) The optimal detection order in terms of signal-to-interference-noise ratios (SINRs) for both the users and the symbols is the natural transmission order of the system; and 2) when the sum Gaussian mutual information is large, the performance of the optimum transceiver using the MMSE-DF receiver asymptotically approaches that of the maximum-likelihood (ML) receiver.