  We consider the interference-mitigation based cognitive radio where the
primary and secondary users can coexist at the same time and frequency bands,
under the constraint that the rate of the primary user (PU) must remain the
same with a single-user decoder. To meet such a coexistence constraint, the
relaying from the secondary user (SU) can help the PU's transmission under the
interference from the SU. However, the relayed signal in the known dirty paper
coding (DPC) based scheme is interfered by the SU's signal, and is not "clean".
In this paper, under the half-duplex constraints, we propose two new
transmission schemes aided by the clean relaying from the SU's transmitter and
receiver without interference from the SU. We name them as the clean
transmitter relaying (CT) and clean transmitter-receiver relaying (CTR) aided
cognitive radio, respectively. The rate and multiplexing gain performances of
CT and CTR in fading channels with various availabilities of the channel state
information at the transmitters (CSIT) are studied. Our CT generalizes the
celebrated DPC based scheme proposed previously. With full CSIT, the
multiplexing gain of the CTR is proved to be better (or no less) than that of
the previous DPC based schemes. This is because the silent period for decoding
the PU's messages for the DPC may not be necessary in the CTR. With only the
statistics of CSIT, we further prove that the CTR outperforms the rate
performance of the previous scheme in fast Rayleigh fading channels. The
numerical examples also show that in a large class of channels, the proposed CT
and CTR provide significant rate gains over the previous scheme with small
complexity penalties.
