In this thesis, we investigate the performance of a multi-user OFDM system under imperfect synchronization which is caused due to noise, Doppler shift and frequency selective fades in the channel. Analytical result indicates that the SNR degrades as the average power of the channel impairments such as AWGN, carrier frequency offset due to Doppler frequency and fading gain is increased.The SNR degradation leads to imperfect synchronization and hence decreases the total number of subcarriers available for allocation. Based on Monte Carlo analysis, 22% loss in the number of allocatable subcarriers is noticed under imperfect synchronization as compared to perfect synchronization. We utilize empirical modelling to characterize the available number of subcarriers as a Poisson random variable. In addition, we determine the percentage decrease in the total number of allocatable subcarriers under varying channel parameters such as AWGN, Doppler frequency and fading gain. The results indicate 19% decrease in the number of available subcarriers as average AWGN power is increased by 10dB; 44% decrease as the Doppler frequency is varied between 10Hz to 100Hz; and 56% decrease as the fading gain is varied between 0dB to -30dB. Furthermore, the evaluation of an adaptive subcarrier allocation algorithm under imperfect synchronization. Hence, radio resource allocation for multicarrier systems should consider the percentage loss in the available subcarriers under imperfcet synchronization.