  A Dirty Paper Coding (DPC) based transmission scheme for the Gaussian
multiple-input multiple-output (MIMO) cognitive radio channel (CRC) is studied
when there is imperfect and perfect channel knowledge at the transmitters
(CSIT) and the receivers, respectively. In particular, the problem of
optimizing the sum-rate of the MIMO CRC over the transmit covariance matrices
is dealt with. Such an optimization, under the DPC-based transmission strategy,
needs to be performed jointly with an optimization over the inflation factor.
To this end, first the problem of determination of inflation factor over the
MIMO channel $Y=H_1 X + H_2 S + Z$ with imperfect CSIT is investigated. For
this problem, two iterative algorithms, which generalize the corresponding
algorithms proposed for the channel $Y=H(X+S)+Z$, are developed. Later, the
necessary conditions for maximizing the sum-rate of the MIMO CRC over the
transmit covariances for a given choice of inflation factor are derived. Using
these necessary conditions and the algorithms for the determination of the
inflation factor, an iterative, numerical algorithm for the joint optimization
is proposed. Some interesting observations are made from the numerical results
obtained from the algorithm. Furthermore, the high-SNR sum-rate scaling factor
achievable over the CRC with imperfect CSIT is obtained.
