In this thesis, we develop an subcarrier transmission suboptimal power allocation algorithm
and an underlay subcarrier transmission optimal power allocation algorithm for the orthogonal frequency division multiplexing (OFDM)-based cognitive radio (CR) systems with different statistical interference constraints imposed by different primary users (PUs). Given the fact that the interference constraints are met in a statistical manner, the CR transmitter does not require the instantaneous channel quality feed-back from the PU receivers. First an alternative subcarrier transmission suboptimal algorithm with reduced complexity has been proposed and the performance has been investigated. Presented numerical results show that with our proposed suboptimal power allocation algorithm CR user can achieve 10 percent higher transmission capacity for given statistical interference constraints and a given power budget compared to the traditional suboptimal power allocation algorithms, uniform and water-filling power allocation algorithms. The proposed suboptimal algorithm outperforms traditional suboptimal algorithm, water-filling algorithm and uniform power loading algorithm. Second,We introduce an underlay subcarrier transmission optimal power allocation algorithms which allows the secondary users use the bandwidth used by Pus. And at the same time we consider the individual peak power constraint as the forth constraint added to the objective function which is the transmission capacity rate of the secondary users.Third, we propose suboptimal algorithm using GWF which has less complexity level than traditional water-filling algorithm instead of conventional water-filling algorithm in calculating the assigned power while considering the satisfaction of the total power constraint. The proposed suboptimal algorithm gives an option of using a low complexity power allocation algorithm where complexity is an issue.