Widely linear MMSE transceiver for real-valued sequences over MIMO channel

Joint design of the precoder and the decoder (say, transceiver) for multiple-input/multiple-output (MIMO) channels is considered and, in particular, the already existing procedure for the design of the linear transceiver according to the minimum-mean-square-error (MMSE) criterion is extended to the more general case where the transceiver resorts to widely linear (WL) processing rather than to linear one. WL filters linearly and independently process both the real and the imaginary parts of the input signals, and they are usually employed in order to trade-off a limited increase in the computational complexity with performance gains when the input signals are circularly variant. For this reason, we propose to resort to WL processing in the synthesis of the MIMO transceiver when real-valued data streams have to be transmitted. The performance analysis shows significant performance advantages of the proposed WL-MMSE MIMO transceiver with respect to the linear one.