Iterative Algorithms for Transceiver Design in MIMO Broadcast Channels with Improper Signaling

Recent research has revealed that using improper (noncircular) transmit signals can be beneficial in multiple-input multiple-output broadcast channels if highly complex nonlinear interference cancellation schemes such as dirty paper coding are avoided. However, finding the optimal improper transmit strategy in such a scenario is a nonconvex optimization problem for which no globally optimal solution is known in general. In this paper, we study whether suboptimal solution approaches that are known from linear transceiver design with proper (circularly symmetric) transmit signals can be transferred to the case with improper signals via a composite real representation. It turns out that such optimization methods may get stuck in a proper solution even if an improper strategy would be better, but an adequate initialization can prevent this behavior. The theoretical analysis is based on the recently proposed framework of block-skew-circulant matrices in complex-valued signal processing.