Cognitive radio (CR) systems aim for more efficient spectrum utilization by having so called secondary users (SUs) transmit on a frequency band reserved for licensed primary users (PUs). The secondary transmissions are allowed provided that no harmful interference will be caused to the PUs. SU terminals with multiple antennas can employ transmit power control with transmit precoding in order to control the interference levels. In most of the existing works, perfect channel state information (CSI) is assumed to be available for the SUs. However, in practical systems where perfect CSI is not available, the SUs are not able to guarantee that the interference constraints are sufficiently satisfied. In this paper, we investigate the problem of spectrum sharing for multiantenna CR systems using estimated CSI. Due to the random nature of the estimation error, we set a probabilistic interference constraint and, in order to satisfy it, provide a density function for the interference power. In addition, we present a power control framework for the SU to meet the probabilistic interference constraint.