Channel state information (CSI) is essential for efficient power and spectrum allocation policies. In cognitive radio (CR) channels, although perfect CSI of the direct link (between the secondary transmitter and the secondary receiver) is a reasonable assumption at the secondary transmitter (ST), however, perfect knowledge of its interfering links to the primary receivers (PRs) is not. Power allocation and scheduling algorithms are often based on perfect global CSI at the secondary transmitter (ST). In this paper, we analyze the impact of channel estimation errors on both the secondary and primary users. On the one hand, the robustness of water-filling type of algorithms allowing the secondary user (SU) to minimize its power consumption under QoS and CR interference power constraints to channel estimation errors in the SU interfering links is analyzed. On the other hand, the impact of these estimation errors on the PU interference constraints is also analyzed. To this aim, we consider the worst case with respect to these estimation errors. Our analysis shows that the water-filling algorithm provides robustness in terms of power consumption and scheduling of the SU given the realistic estimation error models especially when the SU is overestimating the interfering power gains. We also provide possible solutions to ensure that the created interference is below the tolerated thresholds.