Improper Signaling for Symbol Error Rate Minimization in <inline-formula> <tex-math notation="TeX">$K$</tex-math></inline-formula>-User Interference Channel

The rate maximization for the K-user interference channels (ICs) has been investigated extensively in the literature. However, the practical problem of minimizing the error probability with given signal modulations and/or data rates of the users is less studied. In this paper, by utilizing additional degrees of freedom from the improper signaling (versus the conventional proper signaling) , we seek to optimize the precoding matrices for the K-user single-input single-output (SISO) ICs to minimize pair-wise error probability (PEP) and symbol error rate (SER) with two proposed algorithms, respectively. Compared with conventional proper signaling and other state-of-the-art improper signaling designs, our proposed improper signaling schemes achieve notable error rate improvement in SISO-ICs under both the additive white Gaussian noise (AWGN) and cellular system setups with or without channel coding. Our study provides another viewpoint for optimizing transmissions in ICs and further justifies the practical benefit of improper signaling in interference-limited communication systems.