This paper addresses the problem of power allocation of the downlink in cognitive radio networks (CRNs). In a CRN the channel availability for the secondary users (SUs) is a random process determined by primary user (PU) behavior. In an overlay CRN where the PU has the priority and CRN may use only the idle channels, CRN loses the symbols that are being transmitted during that time slot when the PU takes the channel and if the error correction code cannot handle the length of symbol loss. Further, in the next time slot, the CRN has to select again a free channel to continue the communication or in the event that all channels are occupied by PUs and other SUs it enters an indefinite waiting process. Thus it is intuitive that the time averaged data rate of the CRN does not only depend on the channel characteristics (governed by Shannon's law) but also on the channels PU activity level. CRNs, with the spectrum sensing capabilities inherent to them, have the ability to characterize those activity statistics. In this paper, we propose two schemes named ENPA (equivalent noise of PU activity) and EBPA (effective bandwidth of PU activity), which take into account the PU activity in CRN downlink power allocation. These schemes are shown to achieve higher average rates than the water-filling algorithm which is optimal for a linear filter channel