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This paper studies a novel underlay MIMO cognitive radio (CR) system, wherethe instantaneous or statistical channel state information (CSI) of theinterfering channels to the primary receivers (PRs) is completely unknown tothe CR. For the single underlay receiver scenario, we assume a minimuminformation rate must be guaranteed on the CR main channel whose CSI is knownat the CR transmitter. We first show that low-rank CR interference ispreferable for improving the throughput of the PRs compared with spreading lesspower over more transmit dimensions. Based on this observation, we then proposea rank minimization CR transmission strategy assuming a minimum informationrate must be guaranteed on the CR main channel. We propose a simple solutionreferred to as frugal waterfilling (FWF) that uses the least amount of powerrequired to achieve the rate constraint with a minimum-rank transmit covariancematrix. We also present two heuristic approaches that have been used in priorwork to transform rank minimization problems into convex optimization problems.The proposed schemes are then generalized to an underlay MIMO CR downlinknetwork with multiple receivers. Finally, a theoretical analysis of theinterference temperature and leakage rate outage probabilities at the PR ispresented for Rayleigh fading channels.We demonstrate that the direct FWFsolution leads to higher PR throughput even though it has higher interference"temperature (IT) compared with the heuristic methods and classic waterfilling,which calls into question the use of IT as a metric for CR interference.

MIMO Precoding in Underlay Cognitive Radio Systems with Completely Unknown Primary CSI