Estimation and equalization of communications channels using wavelet transforms

This dissertation features the development of signal processing strategies for the estimation of channel impulse responses and the equalization of the effects of channels on communications signals propagating through them using the Discrete Wavelet Transform (DWT). The two strategies are developed as part of a wavelet-based signal processing platform, which can be used to enable reconfigurable radio transceivers.;The approach taken is to recast standard discrete time-domain signal processing procedures into a DWT-based framework. To facilitate this, three equivalent techniques of DWT-based convolution that use both subband coding as well as polyphase filter implementations are devised.;A DWT-based deconvolution procedure is derived analytically and is applied to perform estimation of several time-invariant multipath communications channels. Conditions of slow and fast fading are considered, and faded test signals are corrupted by Additive White Gaussian Noise (AWGN) that results in ratios of bit-energy-to-noise-power-density, Eb/N 0, in the range of 0 to 30 dB. Monte Carlo simulations of the estimation of the channel impulse responses yield Mean-Square Error (MSE) results with excellent agreement for coarse levels of DWT resolution when compared with standard discrete time-domain deconvolution.;Using DWT-based convolution the linear equalization techniques of Zero Forcing Equalization (ZFE) and Minimum Mean-Squared Error (MMSE) equalization, are formulated and implemented in the wavelet-domain. Monte Carlo simulations of the equalization of a fast fading channel with Eb/N 0 in the range 0 dB to 60 dB show that the performance of both linear equalizers in the time- and wavelet-domains is essentially identical.;Allied with the primary objective of the dissertation, both DWT-based channel estimation and equalization are included in communications systems. In Monte Carlo simulations of these systems, signals that are digitally modulated using Binary Amplitude Shift Keying (BASK), Binary Frequency Shift Keying (BFSK) and 16-Quadrature Amplitude Modulation (16-QAM) schemes are propagated through a fast fading channel. The faded signals are corrupted by AWGN resulting in Eb/N0 in the range 0 dB to 20 dB. The performance of these hybrid time- and DWT-based communications systems is evaluated with Symbol Error Rate (SER) curves showing no decrease in performance when compared with discrete time-domain system methods.