In this paper, we propose a generalized model for underlay based cognitive radio (CR) that is based on the information theoretic interference channel model. Utilizing the achievable rate region for the two user interference channel proposed by Han and Kobayashi, we establish achievable rates for the unlicensed or the Secondary User (SU) that depends upon a given target rate for the licensed or the Primary User. Hence, the transmission of the SU is rate limited due to the PU achievable rate. Unlike the traditional approach for underlay, our results bring out the impact of SU transmission on the set of achievable rates for the PU and also of the effect of PU target rate (which may be called its QoS) on the set of achievable rate for the SU.