Precoding for MIMO Channels in Cognitive Radio Networks with CSI Uncertainties and for MIMO Compound Capacity

Inaccurate knowledge of channel state information (CSI) limits the performance offered by multiple-input multiple-output (MIMO) communications. The design of a MIMO precoder needs to take the CSI uncertainty into consideration to mitigate its effects. This paper proposes a method to design the precoder for a secondary user in an underlay cognitive radio framework that maximizes its transmission performance, where the direct link to its receiver and the interference link to a primary user have CSI uncertainties. We model the CSI uncertainties through the Schatten norm that encompasses most commonly used norm measures such as the spectral and Frobenious norms. The proposed method solves iteratively a minimax problem by deriving the optimal solution for the worst case interference CSI uncertainty, applying the alternate-iterate technique for the worst case direct link CSI deviation, and developing a feasible direction projected subgradient technique for the precoder. Simpler solutions for the precoder are also derived under some specific norm measure of CSI uncertainty and certain requirement of transmission power. Simulations corroborate the expected performance of the proposed design.