An OFDM based on Analytic Discrete Cosine HarmonicWavelet Transform (ADCHWT_OFDM) has been proposed in this paper. Analytic DCHWT has been realized by applying DCHWT to the original signal and to its Hilbert transform. ADCHWT has been found to be computationally efficient and very effective in improving Bit Error Rate (BER) and Peak to Average Power Ratio (PAPR) performance. Improvement compared to that of Haar-WT OFDM and DFT OFDM is achieved without employing Cyclic Prefix BER is 0.002 for ADCHWT OFDM compared to Haar WT, DFT OFDM which have BER of 0.06 and 0.4, respectively, at 15 dB SNR. PAPR is also reduced by 3 dB compared to DFT OFDM and 0.3 dB reduction compared to Haar WT OFDM.