Due to the limited supply and the strict management policy of the spectrum, it is very difficult to overcome the requirements of data rates and bandwidth in communication systems. To successfully deal with this problem, the idea of random allocation of spectrum rather than fixed allocation of spectrum has come into existence which leads to the idea of cognitive radio (CR). Orthogonal frequency division multiplexing (OFDM) is a best candidate for CR. It has an ability and agility to occupy the spectral holes that are not currently in use by the licensed user and whose positions are changing randomly by simply turning on and off its subcarriers. In order to maintain the successful co-existence between the licensed and un-licensed users, the interference between them should be minimized and one such interference is due to the high sidelobes of OFDM subcarriers that should be minimized at the transmitter side of the OFDM system. Some techniques are found in literature for the suppression of the sideobes, but a need of even better techniques that suppresses the sidelobes in a better way is required. This dissertation is a contribution towards the above mentioned area. The dissertation is mainly divided into three parts. In the first part, cancellation carriers (CC) based sidelobe reduction technique is presented. A few number of CCs are inserted on either side of used OFDM spectrum, the amplitude of the main lobe of these CCs are adjusted in such a way when it is added with the OFDM spectrum it will results in the reduction of sidelobes. For the adjustment of amplitudes of the main lobe of CCs, we have proposed different heuristic algorithms, including Genetic algorithm (GA), Firefly algorithm (FFA), Differential evolution (DE) and Cuckoo search algorithm (CSA). In the second part, we have proposed Generalized sidelobe canceller (GSC) for the reduction of sidelobes. In this proposed technique the input signal is passed through the two v branches of GSC, the upper branch and the lower branch. The upper branch consist of weight vector allows the signal to pass through it and provides the necessary gain to the desired portion of the signal satisfying the constraint. The lower branch consists of blocking matrix followed by adaptive weight vector, the blocking matrix blocks the desired portion of the signal and pass the undesired portion of the signal while the adaptive weight vector adjusts the amplitudes of the undesired portion of the signal. Finally the signal from the upper branch and lower branch are then subtracted, results in the reduction of sidelobes. In the last part, for further suppression of sidelobe, we have proposed an OFDM framework that is capable of describing any out-of-band (OOB) radiation technique, irrespective of whether one or more than one techniques are applied. Based on that framework, we proposed eight different techniques that can be viewed as two step reduction techniques and are divided into two main groups: The first group, is a combination of our proposed technique GSC with the existing techniques and in the second group is a combination of our proposed techniques GSC with GA, FFA, DE and CSA based CCs. To show the effectiveness and reliability of all our proposed techniques, we have considered five different spectrums sharing environments. Simulation results show that our proposed techniques, get better suppression of sidelobes.