As wireless applications are ever increasing, because of spectrum scarcity it is not possible to assign spectrum to each application statistically. Federal Communications Commission (FCC) measurements reveal extensive portions of allocated spectrum in different time and frequencies are not used sufficiently. Thus licensed spectrum is not utilized optimally. In order to deal with these two problems, the concept of dynamic spectrum access (DSA) has been proposed. Cognitive radios offer wireless transceivers enabling DSA. In dynamic spectrum access the secondary user decides on whether or not a particular licensed frequency band is currently used and transmits data in the band if it is not being used by primary user. While secondary user is renting the band, it must insure that performance of primary user as well as secondary user is not affected. Therefore, coexistence of the primary and the secondary users is an important criterion that makes DSA a feasible solution for efficient spectrum usage. This dissertation investigates physical layer techniques to enhance a cognitive radio performance. Orthogonal frequency division multiplexing (OFDM) has proven to be the prime candidate for cognitive radio systems as it divides spectrum into many subcarriers. Using OFDM, it is possible to partition broad sections of spectrum into a lot of channels and assign each channel to a distinct user. This thesis investigates an important problem concerning the coexistence of the primary and the secondary users. The problem is that the interference level imposed on primary user by neighboring secondary user must be kept within a determined (limited) range. As OFDM uses sinc-type pulses in representing the symbols transmitted over all the subcarriers during one time instant, the large sidelobes that occur can potentially interfere with the signal transmissions of the adjacent primary systems or with the transmissions of other secondary users. These high-level sidelobes can also cause inter-carrier interference (ICI). Thus, the fundamental goal of this thesis is to develop a technique which suppresses the interference caused by the secondary user while not significantly having influence on the system performance of the secondary user. High spectral efficiency of MSK provides great reduction in out of band radiation and the same idea is used to decrease inter carrier interference and consequently out of band interference to primary user in OFDM based cognitive radio systems. This thesis uses OFDM-MSK for this objective. OFDM-MSK is presented in order to reduce system sensitiv Key Words cognitive radio systems, OFDM, sidelobe level, out of band interference, ICI.