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Unlimited Sampling of Multiband Signals: Single-Channel Acquisition and Recovery

Gal Shtendel, Ayush Bhandari

TL;DR

This work tackles recovery of multiband signals from modulo-folded samples within the Unlimited Sensing Framework (USF), enabling single-channel, sub-Nyquist acquisition. It introduces a carrier-aware filter and a multiband unfolding algorithm that leverage spectral structure to separate folded residuals and recover the original signal under rate constraints such as $T_S <= 1/(2^P OmegaB e)$. Key contributions include theoretical recovery guarantees for bandpass and multiband cases, plus hardware validation showing up to $13×$ dynamic-range improvement with 7-bit quantization and $2.7e-3$ MSE. These results advance USF for HDR/HDRes multiband sampling and motivate future work on multi-channel extensions and physical implementations of the M-ADC.

Abstract

In this paper, we address the problem of reconstructing multiband signals from modulo-folded, pointwise samples within the Unlimited Sensing Framework (USF). Focusing on a low-complexity, single-channel acquisition setup, we establish recovery guarantees demonstrating that sub-Nyquist sampling is achievable under the USF paradigm. In doing so, we also tighten the previous sampling theorem for bandpass signals. Our recovery algorithm demonstrates up to a 13x dynamic range improvement in hardware experiments with up to 6 spectral bands. These results enable practical high-dynamic-range multiband acquisition in scenarios previously limited by dynamic range and excessive oversampling.

Unlimited Sampling of Multiband Signals: Single-Channel Acquisition and Recovery

TL;DR

This work tackles recovery of multiband signals from modulo-folded samples within the Unlimited Sensing Framework (USF), enabling single-channel, sub-Nyquist acquisition. It introduces a carrier-aware filter and a multiband unfolding algorithm that leverage spectral structure to separate folded residuals and recover the original signal under rate constraints such as . Key contributions include theoretical recovery guarantees for bandpass and multiband cases, plus hardware validation showing up to dynamic-range improvement with 7-bit quantization and MSE. These results advance USF for HDR/HDRes multiband sampling and motivate future work on multi-channel extensions and physical implementations of the M-ADC.

Abstract

In this paper, we address the problem of reconstructing multiband signals from modulo-folded, pointwise samples within the Unlimited Sensing Framework (USF). Focusing on a low-complexity, single-channel acquisition setup, we establish recovery guarantees demonstrating that sub-Nyquist sampling is achievable under the USF paradigm. In doing so, we also tighten the previous sampling theorem for bandpass signals. Our recovery algorithm demonstrates up to a 13x dynamic range improvement in hardware experiments with up to 6 spectral bands. These results enable practical high-dynamic-range multiband acquisition in scenarios previously limited by dynamic range and excessive oversampling.

Paper Structure

This paper contains 7 sections, 2 theorems, 25 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Towards Recovery
  3. The Proposed Filter
  4. Recovery Algorithm
  5. Experimental Validation
  6. Conclusions
  7. Supplementary Material

Key Result

Lemma 1

Let $x$ be defined in eq:MBsig with frequencies $\Omega_{\mathsf{C}} \stackrel{\rm{def}}{=} \left\lbrace \omega_{p} \right\rbrace_{p=0}^{P-1}$, $\# \Omega_{\mathsf{C}} =P$. Let $x\left[ k \right]=x(t)|_{t=k T_\mathsf{S}}$. Define and $\Psi_{\Omega_{\mathsf{C}}}^{N} \stackrel{\rm{def}}{=} \Psi_{\Omega_{\mathsf{C}}} \ast \Psi_{\Omega_{\mathsf{C}}}^{N-1}$. Let ${||\varphi||}_\infty \stackrel{\rm{def

Figures (5)

  • Figure 1: The spectrum of a multiband signal $x(t)$ (orange), and its corresponding modulo folded signal $\mathscr{M}_\lambda ({x(t)} )$ (blue), which is not bandlimited.
  • Figure 2: Flowchart of the proposed recovery algorithm.
  • Figure 3: Achievable (white) and unachievable (red) sampling rates under the Unlimited Sensing Framework as a function of the maximal frequency $f_{\mathsf{U}}$. They differ from the conventional result Vaughan:1991:J only by a lower bound, while allowing high dynamic range recovery.
  • Figure 4: Reconstruction of a multiband signal. Left: Numerical experiment where the multiband spectrum approaches the first Nyquist zone, demonstrating an "alias-free" Lin:1998:J but undersampled scenario. Right: Reconstruction from $7$-bit quantized samples acquired via hardware. The dynamic range improvement is $13.7\times$, and the reconstruction MSE is $2.7\times 10^{-3}$. As shown, recovery using US--Alg fails for the given $T_\mathsf{S}$.
  • Figure 5: Reconstruction performance under additive white Gaussian noise. The proposed algorithm maintains stable recovery down to $20 \ \mathrm{dB}$.

Theorems & Definitions (4)

  • Lemma 1
  • proof
  • Theorem 1: Multiband Unfolding from Uniform Samples
  • proof