Optimal digital filter design for dispersed signal equalization

Any signal a satellite receives from Earth has traveled through the ionosphere. Transmission through the ionosphere results in a frequency dependent time-delay of the signal frequency components. This effect of the medium on the signal is termed dispersion, and it increases the difficulty of pulse detection. A system capable of compensating for the dispersion would be desirable, as pulsed signals would be more readily detected after compression. In this thesis, we investigate the derivation of a digital filter to compensate for the dispersion caused by the ionosphere. A transfer function model for the analysis of the ionosphere as a system is introduced. Based on the signal model, a matched filter response is derived. The problem is formulated as a group delay compensation effort. The Abel-Smith algorithm is employed for the synthesis of a cascaded allpass filter bank with desired group delay characteristics. Extending this work, an optimized allpass filter is then derived using a pole location approach. A mean-square error metric shows that the optimized filter can reproduce, and even improve upon, the results of the Abel-Smith design with a significantly lower order filter. When compared against digital filters produced with the least p-th minimax algorithm, we find that the new method exhibits significantly lower error in the band of interest, as well as lower mean squared error overall. The result is a simple optimized equalization filter that is stable, robust against cascading difficulties, and applicable to arbitrary waveforms. This filter is the cornerstone to a new all-digital electromagnetic pulse detection system