Analysis of Wavelet Modulation in Frequency-Selective Fading

We consider an antipodal signaling system using wavelet modulation (WM) with scale diversity over a frequency-selective fading channel. The channel introduces a random gain for each scale. These scale gains are estimated by sending a block of pilot symbols before the data. Coherent demodulation is carried out along with maximal-ratio combining using the estimated scale gains. From the characteristic function of the resulting decision variable, we analyze the bit error performance. For the case of large signal-to-noise ratio (SNR), we obtain a closed-form expression for the bit error probability (BEP). It is seen that BEP decreases with increase in the number of pilot symbols. We also find a significant improvement in BEP with increase in the number of scales for a fixed pilot length. It is also found that, when compared with frequency diversity, WM can perform better over a certain range of SNR, with the range decreasing with increase in the number of scales.