Abstract: Improper Gaussian signaling is a well-known technique that has been shown to improve performance in different multi-user scenarios. In this paper, we analyze the benefit of improper signaling in underlay cognitive radio when users are equipped with multiple antennas. Specifically, we assume that the primary user is protected by the so-called interference temperature constraint, which guarantees a prescribed rate requirement. In this setting, we study how the maximum tolerable interference power changes when the interference is additionally constrained to be maximally improper (strictly noncircular, or rectilinear). We observe that the correlation structure of a maximally improper interference is an additional degree of freedom that can be exploited to improve the SU performance. Because of that, we propose two different protection strategies for the PU where this structure is either constrained or unconstrained, and derive the interference temperature threshold for both cases. We then focus on the secondary user and provide designs of the transmission parameters under the proposed protection strategies.

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