Single-user multiple-input / multiple-output (SU-MIMO) communication systems have been successfully used over the years and have provided a significant increase on a wireless links capacity by enabling the transmission of multiple data streams. Assuming channel knowledge at the transmitter, the maximization of the mutual information of a MIMO link is achieved by finding the optimal power allocation under a given sum-power constraint, which is in turn obtained by the water-filling (WF) algorithm. However, in spectrum sharing setups, such as Licensed Shared Access (LSA), where a primary link (PL) and a secondary link (SL) coexist, the power transmitted by the SL transmitter may induce harmful interference to the PL receiver. While such co-existing links have been considered extensively in various spectrum sharing setups, the mutual information of the SL under a constraint on the interference it may cause to the PL receiver has, quite astonishingly, not been evaluated so far. In this paper, we solve this problem, find its unique optimal solution and provide the power allocation policy and corresponding precoding solution that achieves the optimal capacity under the imposed constraint. The performance of the optimal solution and the penalty due to the interference constraint are evaluated over some indicative Rayleigh fading channel conditions and interference thresholds. We believe that the obtained results are of general nature and that they may apply, beyond spectrum sharing, to a variety of applications that admit a similar setup.
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