On power control and frequency reuse in the two user cognitive channel

This paper considers the generalized cognitive radio channel where the secondary user is allowed to reuse the frequency during both the idle and active periods of the primary user, as long as the primary rate remains the same. In this setting, the optimal power allocation policy with single-input singleoutput (SISO) primary and secondary channels is explored. Interestingly, the offered gain resulting from the frequency reuse during the active periods of the spectrum is shown to disappear in both the low and high signal-to-noise ratio (SNR) regimes. We then argue that this drawback in the high SNR region can be avoided by equipping both the primary and secondary transmitters with multiple antennas. Finally, the scenario consisting of SISO primary and multi-input multi-output (MIMO) secondary channels is investigated. Here, a simple Zero-Forcing approach is shown to significantly outperform the celebrated DecodingForwarding-Dirty Paper Coding strategy (especially in the high SNR regime).