Widely-linear precoders and decoders for MIMO channels

This paper deals with the problem of jointly designing optimum widely-linear (WL) precoders and decoders for multiple-input multiple-output (MIMO) channels, by adopting as a specific design target the minimization of the symbol mean square error and assuming that channel state information is available at both the transmitter and receiver sides. In the proposed scheme, vectors of symbols are precoded through a WL mapping, which jointly operates on the symbol block and its complex-conjugate version; additionally, a WL receiver processes both the received signal and its complex-conjugate counterpart. By using a complex-valued representation of the relevant vectors involved in the design of the WL-MIMO transceiver, we show how the optimization framework originally developed for linear precoding/decoding MIMO structures can be extended to the case where the transmitted symbols and/or the disturbance exhibit improper or noncircularity features.