On the utility of frequency reuse in cognitive radio channels

We consider the generalized cognitive radio channel where the secondary user is allowed to reuse the frequency during the active periods of the primary user, as long as the primary rate remains the same. In this setting, the optimal power allocation policy with a single antenna secondary transmitter (and receiver) is explored. Interestingly, we show that the offered gain resulting from the frequency reuse during the active periods of the spectrum disappears in both the low and high signal-to-noise ratio (SNR) regimes. This drawback, however, is shown to disappear with multi-antenna nodes by using simple zero-forcing strategies at both ends of the secondary channel.