Improper Signaling versus Time-Sharing in the Two-User Gaussian Interference Channel with TIN
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So-called improper complex signals have been shown to be beneficial in the single-antenna two-user Gaussian interference channel under the assumptions that all input signals are Gaussian and that we treat interference as noise (TIN). This result has been obtained under a restriction to pure strategies without time-sharing, and it was extended to the case where the rates, but not the transmit powers, may be averaged over several transmit strategies. In this paper, we drop such restrictions and discuss the most general case of time-sharing where both the rates and the powers may be averaged. Since this information theoretic notion of time-sharing cannot be expressed by means of a convex hull of the rate region, we have to account for the possibility of time-sharing already during the optimization of the transmit strategy. By studying the properties of the resulting optimization problem using Lagrange duality, we obtain a surprising result: proper signals can be proven to be optimal if time-sharing is allowed.
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