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Deconvolution and preequalization with best delay LS inverse filters

A new method for finding the best delay for the design of least-squares (1,S) inverse filters is introduced. It is shown that there is a considerable difference between the LS errors of a best delay filter and an arbitrary LS inverse filter. Proposed method is an effective and computationally efficient approach for the design of LS optimum filters. Deconvolution problem is considered and the MSE performances of pseudoinverse, preequalization and LS inverse filtering are investigated. In this respect, the theoretical bounds are found for better MSE performance for each method. The sufficient conditions presented in this context are easy to check which gives the flexibility to pick the most suitable method for a deconvolution application. The practical performances of the three approaches are also identified by considering fixed transmit signal power. It is shown that preequalization, LS inverse filtering and pseudoinverse are ordered with respect to their MSE performances from best to worst, respectively, in practical channel and noise conditions.