  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.
