In this paper, we study the joint power and rate adaptation in a cognitive radio network (CRN) using the rate-distance nature as the central criterion. The rate-distance nature describes the relationship between transmission rate and signal strength and can further enhance the spectrum efficiency. A general channel model considering composite effects such as distance-dependent pathloss, large-scale shadowing, and small-scale fading is considered. Through emitting a pseudo-carrier, the cognitive radio (CR) transmit-receive (T-R) pair determines the maximal allowable transmission power and thus transmission rate for maximizing the sum-rate of the CRN with guaranteed bit error rate (BER) and outage probability of signal-to-interference ratio (SIR). The proposed algorithm is suitable for real-time adaptation and a maximal sum-rate of the CRN is achieved.