A novel method to improve the performance of the frequency band is cognitive radio that was introduced in 1999. Due to a lot of advantages of the OFDM, adaptive OFDM method, this technique is used in cognitive radio (CR) systems, widely. In adaptive OFDM, transmission rate and power of subcarriers are allocated based on the channel variations to improve the system performance. This paper investigates adaptive resource allocation in the CR systems that are used OFDM technique to transmit data. The aim of this paper is to maximize the achievable transmission rate for the CR system by considering the interference constraint. Although secondary users can be aware form channel information between each other, but in some wireless standards, it is impossible for secondary user to be aware from channel information between itself and a primary user. Therefore, due to practical limitation, statistical interference channel is considered in this paper. This paper introduces a novel suboptimal power allocation algorithm. Also, this paper introduces a novel bit loading algorithm. In the numerical results sections, the performance of our algorithm is compared by optimal and conventional algorithms. Numerical results indicate our algorithm has better performance than conventional algorithms while its complexity is less than optimal algorithm.