The Major Setback of a Multi-Carrier Modulation (MCM) is Synchronization Errors, which includes time, frequency and phase offset. Especially, Wavelet based MCM catches the eyes of researchers due to its flexibilities which are seen as one of the strong contender for Cognitive Radios. Synchronization errors are mainly due to mobility between nodes and sub-optimal local oscillators and it is necessary to learn the behavior of wavelets under these channel fading conditions. In this paper, we present the joint effects of Wavelet-based Cognitive Radio OFDM (CR-WOFDM) systems under Synchronization Error in terms of based bit error rate (BER). BER Outputs of WOFDM is compared with FFT based OFDM with Cyclic Prefix (CP-OFDM) systems in a doubly-selective channel by designing a communication system for computer simulation. Several well-known wavelets are chosen and analyzed, including Daubechies (db), Symlets (sym), Coiflets (coif), Fejér-Korovkin (fk) filters, and biorthogonal (bior) wavelets. First, we show the behavior of wavelets in terms of BER by considering different doubly selective channel Power Delay Profile (PDP) like, AWGN, FLAT, Pedestrian and Vehicular and channel Doppler models like, Uniform and JAKES. Finally, we calculate and plot Signal-to-Interference Ratio (SIR) of WOFDM with Time and Frequency Offset and compared the results with FFT based CP-OFDM.