The objective of this project is to study the problem of blind deconvolution/equalization of a pulse amplitude modulated signal propagated over an unknown channel and perturbed by additive noise. Traditionally, a matched filter, based on the shape of the transmitter pulse, is used to recover the transmitted sequence. However, to avoid inter-symbol interference for channels with longer delay spread, the channel dynamics has also to be taken into account. This is most often done by applying discrete time signal processing algorithms to the received sampled signal. Recently, there has been a lot of progress in methods which estimate a finite impulse model of the combined transmitter/receiver filters and propagation channel using a certain shift structure. A sequence estimator is then implemented using the estimated model.
The main idea of this work is to use a bank of analog (continuous time) receiver filters, which is used to estimate a continuous time model of the propagation channel. By using all-pass filters as building blocks, we obtain a shift structure similar to the discrete time finite impulse response case. Hence, we can make use of the discrete time methods, mentioned above, to estimate a continuous time channel model. We then use this model to construct a sequence estimator, which can be viewed as an adaptive matched filter. The advantage of this concept is that the physical a priori information can be incorporated in the model structure, like the transmitter pulse shape. The methods can of course be implemented digitally at a higher sampling rate. Initial results are presented in Hansson and Wahlberg (1998).