  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. 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 Decoding-Forwarding-Dirty Paper Coding strategy (especially in the
high SNR regime).
