Optimal Sub-Nyquist Nonuniform Sampling and Reconstruction for Multiband Signals

摘要

We study the problem of optimal sub-Nyquist sampling for perfect reconstruction of multiband signals. The signals are assumed to have a known spectral support F that does not tile under translation. Such signals admit perfect reconstruction from periodic nonuniform sampling at rates approaching Landau's lower bound equal to the measure of F. For signals with sparse F, this rate can be much smaller than the Nyquist rate. Unfortunately, the reduced sampling rates afforded by this scheme can be accompanied by increased error sensitivity. In a recent study, we derived bounds on the error due to mismodeling and sample additive noise. Adopting these bounds as performance measures, we consider the problems of optimizing the reconstruction sections of the system, choosing the optimal base sampling rate, and designing the nonuniform sampling pattern. We find that optimizing these parameters can improve system performance significantly. Furthermore, uniform sampling is optimal for signals with F that tiles under translation. For signals with nontiling F, which are not amenable to efficient uniform sampling, the results reveal increased error sensitivities with sub-Nyquist sampling. However, these can be controlled by optimal design, demonstrating the potential for practical multifold reductions in sampling rate.