Improper Signaling Versus Time-Sharing in the SISO Z-Interference Channel

It has recently been shown that improper signaling enlarges the rate region of the Gaussian single-antenna one-sided interference channel (Z-interference channel, ZIFC) under the assumptions that all input signals are Gaussian and that interference is treated as noise. It was pointed out that this result also holds if time-sharing between different operation points is allowed. However, the existing literature has considered the problem only for time-sharing under short-term average power constraints, i.e., if the average transmit powers are limited individually in each time slot. We consider the same problem under long-term average power constraints, where the transmit powers are limited only after averaging over all time slots. Interestingly, this modification changes the outcome of the study significantly: we can show that improper signaling can no longer bring any gains in this case.