Sub-Nyquist Sampling for Reaching Theoretical Minimal Sampling Rate Boundary

TL;DR

This paper introduces a novel sub-Nyquist sampling system called DAWC that achieves the theoretical minimal sampling rate for wideband spectrum sensing without prior knowledge of subband locations.

Contribution

It proposes the DAWC architecture and the MSSP algorithm, enabling perfect spectrum localization and reconstruction at minimal sampling rates in blind scenarios.

Findings

DAWC achieves perfect subband localization and waveform reconstruction at the theoretical minimum rate.

MSSP algorithm exploits common support structure for exact spectrum support recovery.

Numerical simulations show superior accuracy over existing methods.

Abstract

Wideband spectrum sensing motivates sub-Nyquist sampling architectures that exploit spectral sparsity, yet in blind scenarios where subband locations are unknown, existing schemes require sampling rates at least twice the theoretical minimum. To this end, we propose a dual-frequency aliasing wideband converter (DAWC), which partitions the multiband spectrum into non-uniform frequency intervals and selectively samples only a subset of them, requiring no prior knowledge of subband locations. We demonstrate that under mild conditions on the signal and the system, DAWC achieves perfect subband localization and waveform reconstruction at the theoretical minimum rate. Moreover, we introduce an innovative side-information-aided subspace pursuit (MSSP) algorithm exploiting the common support structure inherent in the signal column submatrices for exact recovery of the spectrum support set. Based on the restricted isometry property (RIP), we provide stable recovery guarantees for MSSP in the presence of noise. Numerical simulations show that the proposed scheme achieves superior spectrum recovery accuracy compared to state-of-the-art methods.