Improper Gaussian signaling for multiple-access channels in underlay cognitive radio
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This paper characterizes the achievable rate region of an unlicensed multiple-access channel (MAC) that coexists with a licensed point-to-point user, following the underlay cognitive radio paradigm. We assume that every transceiver except the secondary base station has one antenna, and that the primary user (PU) is protected by a minimum rate constraint. In contrast to the conventional assumption of proper Gaussian signaling, we allow the secondary users (SUs) to transmit improper Gaussian signals, which are correlated with their complex conjugate. In this setting, we show that a given point of the rate region boundary is attained by an improper signal if the sum of the interference channel gains (in an equivalent canonical model) is above a certain threshold. We derive an efficient algorithm to compute every point of the rate region boundary achieved by improper Gaussian signaling. The proposed algorithm exploits a single-user representation of the secondary MAC along with new results on the optimality of improper signaling in the single-user case when the PU is corrupted by improper noise.
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