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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 Single-Output (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. The authors then argue that this drawback in the high SNR region can be avoided by equipping both the primary and secondary transmitters with multiple antennas.
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