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A Dirty Paper Coding (DPC) based transmission scheme for the Gaussianmultiple-input multiple-output (MIMO) cognitive radio channel (CRC) is studiedwhen there is imperfect and perfect channel knowledge at the transmitters(CSIT) and the receivers, respectively. In particular, the problem ofoptimizing the sum-rate of the MIMO CRC over the transmit covariance matricesis 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 theMIMO channel $Y=H_1 X + H_2 S + Z$ with imperfect CSIT is investigated. Forthis problem, two iterative algorithms, which generalize the correspondingalgorithms proposed for the channel $Y=H(X+S)+Z$, are developed. Later, thenecessary conditions for maximizing the sum-rate of the MIMO CRC over thetransmit covariances for a given choice of inflation factor are derived. Usingthese necessary conditions and the algorithms for the determination of theinflation factor, an iterative, numerical algorithm for the joint optimizationis proposed. Some interesting observations are made from the numerical resultsobtained from the algorithm. Furthermore, the high-SNR sum-rate scaling factorachievable over the CRC with imperfect CSIT is obtained.

Dirty Paper Coding for the MIMO Cognitive Radio Channel with Imperfect CSIT