Signal parameter estimation performance under a sampling rate constraint

Recently it has been found, that the receive filter design rule 2B_r <; f_s, known as the sampling theorem, does not necessarily lead to optimum signal parameter estimation performance. This is in particular the case if the transmit bandwidth B_t is higher than the sampling bandwidth of the receiver, i.e., 2B_t > f_s. While this result has been obtained under the assumption of ideal low-pass filters, here we extend the analysis by taking into account the possibility of optimizing the filter transfer function. We formulate the problem of finding the best unconstrained analog receive filter with respect to the asymptotic estimation performance on the basis of the Fisher information. It is shown that the problem of optimizing the filter coefficients can be decomposed into N subproblems, each reducing to a binary decision rule for the spectral filter coefficients. Based on these findings we show examples of optimized ideal filters and compare their estimation performance with classical low-pass filters. The results give insights into favorable designs of realizable filters and allow to explore the theoretic performance limits of signal processing systems with sampling rate constraints.