Last years, Wavelet Packet Modulation (WPM) or Wavelet Packet Transform based Orthogonal Frequency Division Multiplexing (WPT-OFDM) have been introduced to wired and wireless communication fields as efficient Multicarrier Modulation (MCM) techniques. The wavelets have interesting features such as flexibility, compatibility and localization in both time and frequency domains with no need to use rectangular window function. As a result, the transmitted signal is naturally less sensitive to inter-symbol and inter-carrier interferences (ISI and ICI). Also, it is possible to implement OFDM modulation without adding cyclic prefix (CP) and it is enough only to use time domain or overlap frequency domain equalization (TEQ or overlap FEQ) in order to shorten the effective channel impulse response length with the purpose of avoiding the ISI and decreasing the ICI. In this paper, we compare BER performance for FFT-OFDM and WPT-OFDM in the presence of two types of channels defined by ETSI (i.e. Rayleigh P1 and Rician F1 channels). In our simulation Haar, Daubechies6, Symlet5 and Coiflet5 wavelets and overlap frequency domain equalization (overlap FEQ) are used for WPT-OFDM in contrast with FFT-OFDM which uses FEQ equalization. Simulation results show that the performance of OFDM will be improved by using WPT transform and due to no need of CP, the power/bandwidth efficiency of OFDM modulation will be improved as well.