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We consider a primary and a cognitive user transmitting over a wireless fading interference channel. A discrete rate link adaptation scheme is proposed to maximize the average spectral efficiency of the cognitive radio, while a minimum average spectral efficiency for the primary user is provisioned. The discrete rate scheme for interfering transmission is devised based on two sets of modulation and coding pairs for the primary and cognitive links. The primary transmitter adapts its rate (modulation and coding) solely based on signal to interference plus noise ratio of its link; however, the cognitive transmitter influences the primary link rate by imposing a proper SINR. The adaptive modulation and coding mode selection and power control at the cognitive transmitter are optimized based on SINR of both links. The problem is then cast as a nonlinear discrete optimization problem for which a fast and efficient suboptimum solution is presented. We also present a scheme with rate adaptive and constant power cognitive radio. An important characteristic of the proposed schemes is that no computation overhead is imposed on primary radio due to cognitive radio activity. Numerical results and comparison with the interweave approach to cognitive radio demonstrate the efficiency of the proposed solutions.