From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals

TL;DR

This paper introduces a practical sub-Nyquist sampling system for blind multiband signals, enabling efficient hardware implementation and low-complexity digital processing, with proven perfect recovery under certain conditions.

Contribution

Proposes the modulated wideband converter system for blind sub-Nyquist sampling, combining hardware efficiency with robust digital reconstruction capabilities.

Findings

Robustness to noise and mismodeling demonstrated through simulations

Potential hardware simplifications for wideband analog-to-digital conversion

Real-time performance for signals with time-varying spectral support

Abstract

Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. Our primary design goals are efficient hardware implementation and low computational load on the supporting digital processing. We propose a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. The product is then lowpass filtered and sampled uniformly at a low rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions. We also develop a digital architecture, which allows either reconstruction of the analog input, or processing of any band of interest at a low rate, that is, without interpolating to the high Nyquist rate. Numerical simulations demonstrate many engineering aspects: robustness to noise and mismodeling, potential hardware simplifications, realtime performance for signals with time-varying support and stability to quantization effects. We compare our system with two previous approaches: periodic nonuniform sampling, which is bandwidth limited by existing hardware devices, and the random demodulator, which is restricted to discrete multitone signals and has a high computational load. In the broader context of Nyquist sampling, our scheme has the potential to break through the bandwidth barrier of state-of-the-art analog conversion technologies such as interleaved converters.