Vector precoding based on Geometric Mean Decomposition for MIMO transmission system

The Geometric Mean Decomposition (GMD) for MIMO channel matrix can obtain identical subbchannel gains, which is a useful property to improve performance gains of precoding. In this paper, we combine the vector precoding with GMD for channel matrix to design the transceiver for MIMO transmission system. Under the proposed transceiver structure, the minimum square error (MSE) of receive symbols are obtained. To minimize the MSE, two schemes in terms of perturbation vector are proposed. In the first scheme, the perturbation vector has only continuous values, thus it is regarded as interference for MSE. In the second scheme, the perturbation vector is generalized to have both continuous and discrete values, so it is partially dealt with as interference after modulo operation. In these two schemes, the optimum perturbation vectors are presented in MMSE criterion respectively.