Minimum Rate Sampling and Spectrum Blind Reconstruction in Random Equivalent Sampling

摘要

The random equivalent sampling (RES) is a well-known sampling technique thatcan be used to capture a high-speed repetitive waveform with low sampling rate.In this paper, the feasibility of spectrum-blind multiband signalreconstruction for data sampled from RES is investigated. We propose a RESsampling pattern and its corresponding mathematical model that guaranteeswell-conditioned reconstruction of multiband signal with unknown spectralsupport. We give the minimum number of RES acquisitions that hold overwhelmingprobability to successfully reconstruct original signal. We demonstrate thatfor signal with specific spectral occupation, the number of RES acquisitionsand the minimum sampling rate could be approached. The signal reconstruction isstudied in the framework of compressive sampling (CS) theory. Theeigen-decomposition and minimum description length (MDL) criteria are adoptedto adaptively estimate the dimension of signal, and the number of unknowns ofreconstruction problem is reduced. Experimental results are reported toindicate that, for a spectrum-blind sparse multiband signal, the proposedreconstruction algorithm for RES is feasible and robust.