Compressive Power Spectrum Sensing via Multi-channel Collaborative Modulo Undersampling

Due to the limited power consumption and dynamic range of analog-to-digital converters (ADCs), the combination of modulo sampling and sub-Nyquist sampling—referred to as modulo undersampling—offers a more competitive strategy than using either method alone for wide-sense stationary (WSS) signals with a high dynamic range (HDR). However, few studies have explored this direction. This paper proposes a modulo undersampling method for the efficient acquisition and analysis of WSS signals with HDR. In terms of sampling architecture, the proposed method is based on multi-channel collaborative modulo undersampling, where each channel performs purposefully delayed low-rate modulo sampling using two collaborative self-reset ADCs with different thresholds. In terms of recovery algorithm, we use a lightweight algorithmic variant of the Chinese remainder theorem to reconstruct unfolded signal samples and then estimate the consecutive covariance. In addition, we present the error behavior of the proposed method and derive the optimal sampling pattern to minimize the compression ratio. The proposed method addresses the amplitude folding issue in time-domain arising from modulo sampling and spectrum folding issue in frequency-domain due to sub-Nyquist sampling. Compared with existing methods, the proposed method can operate at a substantially lower sampling rate while maintaining low computational complexity.