Cognitive radios are slated to be the next generation of smart transceivers that can dynamically sense and respond to its immediate radio frequency (RF) environment. It is highly likely that the RF environment will vary with time as various interferers come and go out of the range of the target receiver. This leads to the interference at the receiver being impulsive in nature, which if not properly handled can cause irrecoverable damage to the transmitted data. The traditional cognitive radio would, in such a scenario, decide against transmitting when a harmful interferer is present in the vicinity. In this work, we investigate methods to mitigate the effects of such interference through intelligent signal processing at the receiver such that throughput can be greatly enhanced. We introduce receiver structures for the more practical scenario of temporally correlated interference and quantify the achievable gains when simple yet effective interference suppression methods are applied at the receiver.