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Coexistence of one or more cognitive radios with a primary radio where the cognitive radios transmit in a spectrum allocated to the primary radio has been investigated in this paper. We consider two distinct scenarios: one in which the cognitive radios give higher priority to one of the cognitive radios and a second in which all the cognitive radios compete to get maximum possible data rates for themselves. In first scenario, the cognitive radio with higher priority gets a choice to decide how much of available resources it wants to use, and rest of the cognitive radios scavenge the left-over resources. We propose power allocation strategies to be used by the radios under both scenarios. We show that proposed power allocation strategy to be used in the first and cooperative scenario leads to overall system capacity improvement. We also prove convergence of power allocation algorithm proposed for the second and greedy scenario. In both cases the cognitive radios ensure that sum of interference caused by them in the spectrum remains below interference threshold.