It has been shown that improper Gaussian signaling (IGS) can improve the performance of wireless interference-limited systems when perfect channel-state information (CSI) is available. In this paper, we investigate the robustness of IGS against imperfect CSI on the transmitter side in a two-user single-input single-output (SISO) interference channel (IC) as well as in a SISO Z-IC, when interference is treated as noise. We assume that the true channel coefficients belong to a known region around the channel estimates, which we call the uncertainty region. Following a worst-case robustness approach, we study the rate-region boundary of the IC for the worst channel in the uncertainty region. For the two-user IC, we derive a robust design in closed form, which is independent of the phase of the channels by allowing only one of the users to transmit IGS. For the Z-IC, we provide a closed-form design for the transmission parameters by considering an enlarged uncertainty region and allowing both users to employ IGS. In both cases, the IGS-based designs are ensured to perform no worse than proper Gaussian signaling. Furthermore, we show, through numerical examples, that the proposed robust designs significantly outperform non-robust solutions. Index Terms-Achievable rate region, improper Gaussian signaling, imperfect CSI, two-user interference channel, worst-case robustness. 1 The two-user X-IC is a generalization of the two-user IC where there is an independent message from each transmitter to each receiver [20] . 2 Z-IC is a special case of the two-user IC, in which only one of the users interferes with the other user. 0090-6778
A robust IGS design for the 2-user IC with imperfect channel state information (CSI) was proposed in REF .
Robust Improper Signaling for Two-User SISO Interference Channels
IEEE Transactions on Communications
IEEE Transactions on Communications
Computer Science Engineering