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This paper considers the generalized cognitive radio channel where thesecondary user is allowed to reuse the frequency during both the idle andactive periods of the primary user, as long as the primary rate remains thesame. In this setting, the optimal power allocation policy with single-inputsingle-output (SISO) primary and secondary channels is explored. Interestingly,the offered gain resulting from the frequency reuse during the active periodsof the spectrum is shown to disappear in both the low and high signal-to-noiseratio (SNR) regimes. We then argue that this drawback in the high SNR regioncan be avoided by equipping both the primary and secondary transmitters withmultiple antennas. Finally, the scenario consisting of SISO primary andmulti-input multi-output (MIMO) secondary channels is investigated. Here, asimple Zero-Forcing approach is shown to significantly outperform thecelebrated Decoding-Forwarding-Dirty Paper Coding strategy (especially in thehigh SNR regime).

On Power Control and Frequency Reuse in the Two User Cognitive Channel