OFDM systems design using harmonic wavelets

Orthogonal frequency-division multiplexing (OFDM) is a popular multi-carrier technique used in many digital communication systems such as wireless fidelity (Wi-Fi), long term evolution (LTE) and power line communication systems. It can be designed using fast Fourier transform (FFT) or wavelet transform (WT). The major drawback in using WT is that it is computationally inefficient. In this study, we introduce a simple and computationally efficient WT, harmonic wavelet transform, for OFDM signal processing. The new WT uses the orthogonal basis functions of conventional FFT-OFDM except that it involves translation and dilation of the input signal; the new wavelets is referred to as harmonic wavelets (HW). When compared with pilot-assisted OFDM system in terms of reduction in the peak-to-average power ratio, the results show that HW-OFDM outperforms FFT-OFDM by 3 dB at 10−4 CCDF (complementary cumulative distribution function). Over Rayleigh fading channel with additive white Gaussian noise (AWGN), the bit error ratio of both FFT-OFDM and HW-OFDM perfectly matched, showing that the proposed HW-OFDM is better in terms of peak-to-average power ratio reduction.