A Matrix-Field Weighted Mean-Square-Error Model for MIMO Transceiver Designs

TL;DR

This paper introduces a novel matrix-field weighted MSE model for MIMO transceiver design, extending traditional weighting from vectors to matrices, and demonstrates its equivalence to sum MSE minimization and capacity maximization in AF relaying.

Contribution

A new matrix-field weighted MSE model for MIMO transceiver design is proposed, extending weighting operations to matrix fields and unifying two key optimization problems.

Findings

The model generalizes weighted MSE minimization.

Optimal solutions structure is derived.

Equivalence to sum MSE and capacity maximization problems.

Abstract

In this letter, we investigate an important and famous issue, namely weighted mean-square-error (MSE) minimization transceiver designs. In our work, for transceiver designs a novel weighted MSE model is proposed, which is defined as a linear matrix function with respect to the traditional data detection MSE matrix. The new model can be interpreted an extension of weighting operation from vector field to matrix field. Based on the proposed weighting operation a general transceiver design is proposed, which aims at minimizing an increasing matrix-monotone function of the output of the previous linear matrix function. The structure of the optimal solutions is also derived. Furthermore, two important special cases of the matrix-monotone functions are discussed in detail. It is also revealed that these two problems are exactly equivalent to the transceiver designs of sum MSE minimization and capacity maximization for dual-hop amplify-and-forward (AF) MIMO relaying systems, respectively. Finally, it is concluded that the AF relaying is undoubtedly this kind of weighting operation.