Optimum analog receive filters for detection and inference under a sampling rate constraint

The problem of optimum analog receive filtering for digital signal detection and parameter estimation is considered. Here the case of a signal source with bandwidth B_t and a receiver with fixed sampling rate f_s is discussed under the assumption that 2B_t > f_s. We investigate the impact of adjusting the receive bandwidth B_r of the analog pre-filter, which is applied prior to the sampler, with respect to the deflection coefficient or the Fisher information measure. This reveals that the design rule 2B_r <; f_s, known as the sampling theorem, does not necessarily lead to optimum system performance. Studying the two analytical information measures under a fix sampling rate f_s and an arbitrary choice of B_r, we provide an example where receive setups with 2B_r > f_s achieve higher detection and parameter estimation performance.