Estimation of Communications Channels Using Discrete Wavelet Transform-Based Deconvolution

In this paper a technique for the deconvolution of signals in the wavelet-domain is presented. It makes use of the Discrete Wavelet Transform (DWT) implemented with filter banks, and is based on expressing the convolution of two signals using the Forward Merge Approach for DWT-based convolution. The DWT-based deconvolution technique is then applied to the problem of pilot-based channel estimation, which can be used in the design of wavelet-based agile radio systems. \par DWT-based deconvolution is first described analytically and is then implemented in MATLAB to validate the theory and evaluate its performance. Monte Carlo simulations of DWT-based deconvolution of transmitted signals from received signals, both known a priori, are performed to estimate channel impulse responses. Transmitted signals are corrupted by Additive White Gaussian Noise (AWGN) resulting in E_b/N_0 ratios ranging from 0 dB to 30 dB. Fast-fading channels with Gaussian and "hilly area" Power Delay Profiles (PDPs) are used, along with four different wavelets for the DWTs. The results of the simulations show that DWT-based deconvolution is a viable technique and its performance in some cases is comparable to direct discrete time-domain deconvolution.