Improper Signaling for Symbol Error Rate Minimization in K-User Interference Channel

The rate maximization for the $K$-user interference channels (ICs) has been investigated extensively in the literature. However, the dual problem of minimizing the error probability with given signal modulations and/or data rates of the users is less exploited. In this paper, by utilizing the additional degrees of freedom attained from the improper signaling (versus the conventional proper signaling), we optimize the precoding matrices for the $K$-user single-input single-output (SISO) ICs to achieve minimal pair-wise error probability (PEP) and symbol error rate (SER) with two proposed algorithms, respectively. Compared to conventional proper signaling as well as other state-of-the-art improper signaling designs, our proposed improper signaling schemes achieve notable SER improvement in SISO-ICs under both additive white Gaussian noise (AWGN) channel and cellular system setups. Our study provides another viewpoint for optimizing transmissions in ICs and further justifies the practical benefit of improper signaling in interference-limited communication systems.