How to understand linear minimum mean-square-error transceiver design for multiple-input-multiple-output systems from quadratic matrix programming

In this study, a unified linear minimum mean-square-error (LMMSE) transceiver design framework is investigated, which is suitable for a wide range of wireless systems. The unified design is based on an elegant and powerful mathematical programming technology termed as quadratic matrix programming (QMP). Based on QMP it can be observed that for different wireless systems, there are certain common characteristics which can be exploited to design LMMSE transceivers, for example, the quadratic forms. It is also discovered that evolving from a point-to-point multiple-input-multiple-output (MIMO) system to various advanced wireless systems such as multi-cell coordinated systems, multi-user MIMO systems, MIMO cognitive radio systems, amplify-and-forward MIMO relaying systems and so on, the quadratic nature is always kept and the LMMSE transceiver designs can always be carried out via iteratively solving a number of QMP problems. A comprehensive framework on how to solve QMP problems is also given. The work presented in this study is likely to be the first shot for the transceiver design for the future ever-changing wireless systems.