Orthogonal Frequency Division Multiplexing (OFDM) system has been extensively studied and widely adopted in various standards, such as IEEE 802.11a/g, IEEE 802.16, HIPERLAN etc. It exhibits high spectral efficiency, and is robust against inter-carrier interference (ICI) and inter-symbol interference (ISI) caused by multipath frequency selective channel. However, OFDM is quite sensitive to phase noise (PHN) that is a random process caused by the phase fluctuation at the transmitter and receiver local oscillators. The effects of PHN on OFDM, Common Phase Error (CPE) that rotates the signal constellation and ICI among the sub-carriers. In this research, phase lock loop (PLL) frequency synthesizer is considered as the source of PHN. Most of the wireless communication standards use PLL based frequency synthesizer to generate carrier frequency because it gives high level of stability, easy control and wide range of frequency generation. The variation of PHN process is low and CPE is zero mean Gaussian random variable. The CPE is constant over one OFDM symbol whereas ICI behaves like additive noise. Moreover, recent advancement in wireless communication, such as in WiMAX, one out of three consecutive OFDM symbols are allocated for pilot while in LTE one full OFDM is devoted for channel estimation once every seven time slots. For TV nature of PHN, periodical pilot symbols are needed in each OFDM symbol at the cost of system BW. This motivation leads this research to develop a blind algorithm to estimate PHN.Therefore, in this thesis, the CPE is considered as dominant and the effect of ICI is minor compared to CPE. Several pilot based PHN estimation methods are developed in the literature. The usage of pilot symbol decreases the system bandwidth(BW) efficiency. Besides, due to the time-varying (TV) nature of PHN, the pilot sequence needs to be transmitted periodically, results further loss of system throughput. Therefore, blind PHN estimation algorithms have received considerable attention. In this thesis, a blind PHN compensation method is proposed to abate the effect of CPE in OFDM systems caused by PHN. To estimate CPE, the signal of maximum amplitude in one of the four quadrants is detected with the corresponding angle w.r.t reference axis. Then, the neighboring signal amplitudes are located by using a threshold angle. From this group of signal, average angle is estimated and this process is repeated for all quadrants. In ideal case, the angles for maximum amplitude with the reference axes are 45, 135,-45 and -135 degree. All averaged angles were compared with four ideal angles, results four CPE angles that were averaged again to estimate and compensate for CPE. An improved and bandwidth efficient new algorithm with low complexity has been developed for PHN compensation in OFDM systems. Simulations show that the proposed algorithm outperforms the conventional pilot based CPE compensation method.