arXiv subjects

Ayush Bhandari

Publications and source records attributed to Ayush Bhandari.

At least 19 recordsLinked to original sources

arXiv2026

Asynchronous Multi-Channel USF: Modified CRT for Modulo Unfolding

The Unlimited Sampling Framework (USF) overcomes the traditional trade-off between dynamic range and digital resolution, achieving performance unattainable with standard ADCs. Its multi-channel extension (MC-USF) enables reconstruction from multiple folded measurements at critical sampling rates. Existing MC-USF methods typically rely on Chinese Remainder Theorem (CRT)-based unfolding, which requires strict channel-level sampling synchronization and is therefore vulnerable to timing mismatch, jitter, and drift. This paper introduces an asynchronous MC-USF architecture that eliminates the need for synchronization. By viewing spatial-temporal signal lifting as inducing smoothness over a graph of sensing channels, we develop a reconstruction strategy robust to temporal misalignment. Numerical experiments validate the approach, demonstrating accurate recovery and enabling more practical multi-channel USF implementations.

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arXiv2025

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

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.

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arXiv2025

Unlocking Off-the-Grid Sparse Recovery with Unlimited Sensing: Simultaneous Super-Resolution in Time and Amplitude

The recovery of Dirac impulses, or spikes, from filtered measurements is a classical problem in signal processing. As the spikes lie in the continuous domain while measurements are discrete, this task is known as super-resolution or off-the-grid sparse recovery. Despite significant theoretical and algorithmic advances over the past decade, these developments often overlook critical challenges at the analog-digital interface. In particular, when spikes exhibit strong-weak amplitude disparity, conventional digital acquisition may result in clipping of strong components or loss of weak ones beneath the quantization noise floor. This motivates a broader perspective: super-resolution must simultaneously resolve both amplitude and temporal structure. Under a fixed bit budget, such information loss is unavoidable. In contrast, the emerging theory and practice of the Unlimited Sensing Framework (USF) demonstrate that these fundamental limitations can be overcome. Building on this foundation, we demonstrate that modulo encoding within USF enables digital super-resolution by enhancing measurement precision, thereby unlocking temporal super-resolution beyond conventional limits. We develop new theoretical results that extend to non-bandlimited kernels commonly encountered in practice and introduce a robust algorithm for off-the-grid sparse recovery. To demonstrate practical impact, we instantiate our framework in the context of time-of-flight imaging. Both numerical simulations and hardware experiments validate the effectiveness of our approach under low-bit quantization, enabling super-resolution in amplitude and time.

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arXiv2025

1-Bit Unlimited Sampling Beyond Fourier Domain: Low-Resolution Sampling of Quantization Noise

Analog-to-digital converters (ADCs) play a critical role in digital signal acquisition across various applications, but their performance is inherently constrained by sampling rates and bit budgets. This bit budget imposes a trade-off between dynamic range (DR) and digital resolution, with ADC energy consumption scaling linearly with sampling rate and exponentially with bit depth. To bypass this, numerous approaches, including oversampling with low-resolution ADCs, have been explored. A prominent example is 1-Bit ADCs with Sigma-Delta Quantization (SDQ), a widely used consumer-grade solution. However, SDQs suffer from overloading or saturation issues, limiting their ability to handle inputs with arbitrary DR. The Unlimited Sensing Framework (USF) addresses this challenge by injecting modulo non-linearity in hardware, resulting in a new digital sensing technology. In this paper, we introduce a novel 1-Bit sampling architecture that extends both conventional 1-Bit SDQ and USF. Our contributions are twofold: (1) We generalize the concept of noise shaping beyond the Fourier domain, allowing the inclusion of non-bandlimited signals in the Fourier domain but bandlimited in alternative transform domains. (2) Building on this generalization, we develop a new transform-domain recovery method for 1-Bit USF. When applied to the Fourier domain, our method demonstrates superior performance compared to existing time-domain techniques, offering reduced oversampling requirements and improved robustness. Extensive numerical experiments validate our findings, laying the groundwork for a broader generalization of 1-Bit sampling systems.

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arXiv2025

USF Spectral Estimation: Prevalence of Gaussian Cramér-Rao Bounds Despite Modulo Folding

Spectral Estimation (SpecEst) is a core area of signal processing with a history spanning two centuries and applications across various fields. With the advent of digital acquisition, SpecEst algorithms have been widely applied to tasks like frequency super-resolution. However, conventional digital acquisition imposes a trade-off: for a fixed bit budget, one can optimize either signal dynamic range or digital resolution (noise floor), but not both simultaneously. The Unlimited Sensing Framework (USF) overcomes this limitation using modulo non-linearity in analog hardware, enabling a novel approach to SpecEst (USF-SpecEst). However, USF-SpecEst requires new theoretical and algorithmic developments to handle folded samples effectively. In this paper, we derive the Cramér-Rao Bounds (CRBs) for SpecEst with noisy modulo-folded samples and reveal a surprising result: the CRBs for USF-SpecEst are scaled versions of the Gaussian CRBs for conventional samples. Numerical experiments validate these bounds, providing a benchmark for USF-SpecEst and facilitating its practical deployment.

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arXiv2024

Full-Duplex Beyond Self-Interference: The Unlimited Sensing Way

The success of full-stack full-duplex communication systems depends on how effectively one can achieve digital self-interference cancellation (SIC). Towards this end, in this paper, we consider unlimited sensing framework (USF) enabled full-duplex system. We show that by injecting folding non-linearities in the sensing pipeline, one can not only suppress self-interference but also recover the signal of interest (SoI). This approach leads to novel design of the receiver architecture that is complemented by a modulo-domain channel estimation method. We then demonstrate the advantages of modulo ADC by analyzing the relationship between quantization noise, quantization bits, and dynamic range. Numerical experiments show that the USF enabled receiver structure can achieve up to 40 dB digital SIC by using as few as 4-bits per sample. Our method outperforms the previous approach based on adaptive filters when it comes to SoI reconstruction, detection, and digital SIC performance.

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arXiv2024

Blind Time-of-Flight Imaging: Sparse Deconvolution on the Continuum with Unknown Kernels

In recent years, computational Time-of-Flight (ToF) imaging has emerged as an exciting and a novel imaging modality that offers new and powerful interpretations of natural scenes, with applications extending to 3D, light-in-flight, and non-line-of-sight imaging. Mathematically, ToF imaging relies on algorithmic super-resolution, as the back-scattered sparse light echoes lie on a finer time resolution than what digital devices can capture. Traditional methods necessitate knowledge of the emitted light pulses or kernels and employ sparse deconvolution to recover scenes. Unlike previous approaches, this paper introduces a novel, blind ToF imaging technique that does not require kernel calibration and recovers sparse spikes on a continuum, rather than a discrete grid. By studying the shared characteristics of various ToF modalities, we capitalize on the fact that most physical pulses approximately satisfy the Strang-Fix conditions from approximation theory. This leads to a new mathematical formulation for sparse super-resolution. Our recovery approach uses an optimization method that is pivoted on an alternating minimization strategy. We benchmark our blind ToF method against traditional kernel calibration methods, which serve as the baseline. Extensive hardware experiments across different ToF modalities demonstrate the algorithmic advantages, flexibility and empirical robustness of our approach. We show that our work facilitates super-resolution in scenarios where distinguishing between closely spaced objects is challenging, while maintaining performance comparable to known kernel situations. Examples of light-in-flight imaging and light-sweep videos highlight the practical benefits of our blind super-resolution method in enhancing the understanding of natural scenes.

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arXiv2024

Unleashing Dynamic Range and Resolution in Unlimited Sensing Framework via Novel Hardware

Conventional digitization based on the Shannon-Nyquist method, implemented via analog-to-digital converters (ADCs), faces fundamental limitations. High-dynamic-range (HDR) signals often get clipped or saturated in practice. Given a fixed bit budget, one must choose between minimizing quantization noise or accommodating HDR inputs. The Unlimited Sensing Framework (USF) eliminates saturation by incorporating nonlinear folding in analog hardware, resulting in modulo signals. Quantizing or digitizing modulo signals enables low quantization noise as the modulo representation maps HDR signals into low-dynamic-range (LDR) samples. In the context of USF, the core innovation of this paper is a novel, low-cost, integrator-based efficient modulo ADC hardware implementation that imposes no restrictions on folding rates, enabling significantly HDR capture. The feasibility of this design is demonstrated by hardware experiments showcasing clear advantages across different quantitative performance metrics. These include capturing HDR signals with a 60-fold increase in dynamic range, achieving up to 5 Effective Number of Bits (ENOBs), and improving Signal-to-Noise and Distortion (SINAD) by 30 dB.

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arXiv2024

Sub-Nyquist USF Spectral Estimation: $K$ Frequencies with $6K + 4$ Modulo Samples

Digital acquisition of high bandwidth signals is particularly challenging when Nyquist rate sampling is impractical. This has led to extensive research in sub-Nyquist sampling methods, primarily for spectral and sinusoidal frequency estimation. However, these methods struggle with high-dynamic-range (HDR) signals that can saturate analog-to-digital converters (ADCs). Addressing this, we introduce a novel sub-Nyquist spectral estimation method, driven by the Unlimited Sensing Framework (USF), utilizing a multi-channel system. The sub-Nyquist USF method aliases samples in both amplitude and frequency domains, rendering the inverse problem particularly challenging. Towards this goal, our exact recovery theorem establishes that $K$ sinusoids of arbitrary amplitudes and frequencies can be recovered from $6K + 4$ modulo samples, remarkably, independent of the sampling rate or folding threshold. In the true spirit of sub-Nyquist sampling, via modulo ADC hardware experiments, we demonstrate successful spectrum estimation of HDR signals in the kHz range using Hz range sampling rates (0.078\% Nyquist rate). Our experiments also reveal up to a 33-fold improvement in frequency estimation accuracy using one less bit compared to conventional ADCs. These findings open new avenues in spectral estimation applications, e.g., radars, direction-of-arrival (DoA) estimation, and cognitive radio, showcasing the potential of USF.

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arXiv2024

Sparse Sampling in Fractional Fourier Domain: Recovery Guarantees and Cramér-Rao Bounds

Sampling theory in fractional Fourier Transform (FrFT) domain has been studied extensively in the last decades. This interest stems from the ability of the FrFT to generalize the traditional Fourier Transform, broadening the traditional concept of bandwidth and accommodating a wider range of functions that may not be bandlimited in the Fourier sense. Beyond bandlimited functions, sampling and recovery of sparse signals has also been studied in the FrFT domain. Existing methods for sparse recovery typically operate in the transform domain, capitalizing on the spectral features of spikes in the FrFT domain. Our paper contributes two new theoretical advancements in this area. First, we introduce a novel time-domain sparse recovery method that avoids the typical bottlenecks of transform domain methods, such as spectral leakage. This method is backed by a sparse sampling theorem applicable to arbitrary FrFT-bandlimited kernels and is validated through a hardware experiment. Second, we present Cramér-Rao Bounds for the sparse sampling problem, addressing a gap in existing literature.

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arXiv2024

Fourier-Domain Inversion for the Modulo Radon Transform

Inspired by the multiple-exposure fusion approach in computational photography, recently, several practitioners have explored the idea of high dynamic range (HDR) X-ray imaging and tomography. While establishing promising results, these approaches inherit the limitations of multiple-exposure fusion strategy. To overcome these disadvantages, the modulo Radon transform (MRT) has been proposed. The MRT is based on a co-design of hardware and algorithms. In the hardware step, Radon transform projections are folded using modulo non-linearities. Thereon, recovery is performed by algorithmically inverting the folding, thus enabling a single-shot, HDR approach to tomography. The first steps in this topic established rigorous mathematical treatment to the problem of reconstruction from folded projections. This paper takes a step forward by proposing a new, Fourier domain recovery algorithm that is backed by mathematical guarantees. The advantages include recovery at lower sampling rates while being agnostic to modulo threshold, lower computational complexity and empirical robustness to system noise. Beyond numerical simulations, we use prototype modulo ADC based hardware experiments to validate our claims. In particular, we report image recovery based on hardware measurements up to 10 times larger than the sensor's dynamic range while benefiting with lower quantization noise ($\sim$12 dB).

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arXiv2023

Unlimited Sampling of Bandpass Signals: Computational Demodulation via Undersampling

Bandpass signals are an important sub-class of bandlimited signals that naturally arise in a number of application areas but their high-frequency content poses an acquisition challenge. Consequently, "Bandpass Sampling Theory" has been investigated and applied in the literature. In this paper, we consider the problem of modulo sampling of bandpass signals with the main goal of sampling and recovery of high dynamic range inputs. Our work is inspired by the Unlimited Sensing Framework (USF). In the USF, the modulo operation folds high dynamic range inputs into low dynamic range, modulo samples. This fundamentally avoids signal clipping. Given that the output of the modulo nonlinearity is non-bandlimited, bandpass sampling conditions never hold true. Yet, we show that bandpass signals can be recovered from a modulo representation despite the inevitable aliasing. Our main contribution includes proof of sampling theorems for recovery of bandpass signals from an undersampled representation, reaching sub-Nyquist sampling rates. On the recovery front, by considering both time-and frequency-domain perspectives, we provide a holistic view of the modulo bandpass sampling problem. On the hardware front, we include ideal, non-ideal and generalized modulo folding architectures that arise in the hardware implementation of modulo analog-to-digital converters. Numerical simulations corroborate our theoretical results. Bridging the theory-practice gap, we validate our results using hardware experiments, thus demonstrating the practical effectiveness of our methods.

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arXiv2023

Unlimited Sampling Radar: a Real-Time End-to-End Demonstrator

In this paper, the trade-off between the quantization noise and the dynamic range of ADCs used to acquire radar signals is revisited using the Unlimited Sensing Framework (USF) in a practical setting. Trade-offs between saturation and resolution arise in many applications, like radar, where sensors acquire signals which exhibit a high degree of variability in amplitude. To solve this issue, we propose the use of the co-design approach of the USF which acquires folded version of the signal of interest and leverages its structure to reconstruct it after its acquisition. We demonstrate that this method outperforms other standard acquisition methods for Doppler radars. Taking our theory all the way to practice, we develop a prototype USF-enabled Doppler Radar and show the clear benefits of our method. In each experiment, we show that using the USF increases sensitivity compared to a classic acquisition approach.

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arXiv2022

$λ$-MIMO: Massive MIMO via Modulo Sampling

Massive multiple-input multiple-output (M-MIMO) architecture is the workhorse of modern communication systems. Currently, two fundamental bottlenecks, namely, power consumption and receiver saturation, limit the full potential achievement of this technology. These bottlenecks are intricately linked with the analog-to-digital converter (ADC) used in each radio frequency (RF) chain. The power consumption in MIMO systems grows exponentially with the ADC's bit budget while ADC saturation causes permanent loss of information. This motivates the need for a solution that can simultaneously tackle the above-mentioned bottlenecks while offering advantages over existing alternatives such as low-resolution ADCs. Taking a radically different approach to this problem, we propose $λ$-MIMO architecture which uses modulo ADCs ($M_λ$-ADC) instead of a conventional ADC. Our work is inspired by the Unlimited Sampling Framework. $M_λ$-ADC in the RF chain folds high dynamic range signals into low dynamic range modulo samples, thus alleviating the ADC saturation problem. At the same time, digitization of modulo signal results in high resolution quantization. In the novel $λ$-MIMO context, we discuss baseband signal reconstruction, detection and uplink achievable sum-rate performance. The key takeaways of our work include, (a) leveraging higher signal-to-quantization noise ratio (SQNR), (b) detection and average uplink sum-rate performances comparable to a conventional, infinite-resolution ADC when using a $1$-$2$ bit $M_λ$-ADC. This enables higher order modulation schemes e.g. $1024$ QAM that seemed previously impossible, (c) superior trade-off between energy efficiency and bit budget, thus resulting in higher power efficiency. Numerical simulations and modulo ADC based hardware experiments corroborate our theory and reinforce the clear benefits of $λ$-MIMO approach.

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arXiv2022

Multi-Dimensional Unlimited Sampling and Robust Reconstruction

In this paper we introduce a new sampling and reconstruction approach for multi-dimensional analog signals. Building on top of the Unlimited Sensing Framework (USF), we present a new folded sampling operator called the multi-dimensional modulo-hysteresis that is also backwards compatible with the existing one-dimensional modulo operator. Unlike previous approaches, the proposed model is specifically tailored to multi-dimensional signals. In particular, the model uses certain redundancy in dimensions 2 and above, which is exploited for input recovery with robustness. We prove that the new operator is well-defined and its outputs have a bounded dynamic range. For the noiseless case, we derive a theoretically guaranteed input reconstruction approach. When the input is corrupted by Gaussian noise, we exploit redundancy in higher dimensions to provide a bound on the error probability and show this drops to 0 for high enough sampling rates leading to new theoretical guarantees for the noisy case. Our numerical examples corroborate the theoretical results and show that the proposed approach can handle a significantly larger amount of noise compared to USF.

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arXiv2022

Time Encoding via Unlimited Sampling: Theory, Algorithms and Hardware Validation

An alternative to conventional uniform sampling is that of time encoding, which converts continuous-time signals into streams of trigger times. This gives rise to Event-Driven Sampling (EDS) models. The data-driven nature of EDS acquisition is advantageous in terms of power consumption and time resolution and is inspired by the information representation in biological nervous systems. If an analog signal is outside a predefined dynamic range, then EDS generates a low density of trigger times, which in turn leads to recovery distortion due to aliasing. In this paper, inspired by the Unlimited Sensing Framework (USF), we propose a new EDS architecture that incorporates a modulo nonlinearity prior to acquisition that we refer to as the modulo EDS or MEDS. In MEDS, the modulo nonlinearity folds high dynamic range inputs into low dynamic range amplitudes, thus avoiding recovery distortion. In particular, we consider the asynchronous sigma-delta modulator (ASDM), previously used for low power analog-to-digital conversion. This novel MEDS based acquisition is enabled by a recent generalization of the modulo nonlinearity called modulo-hysteresis. We design a mathematically guaranteed recovery algorithm for bandlimited inputs based on a sampling rate criterion and provide reconstruction error bounds. We go beyond numerical experiments and also provide a first hardware validation of our approach, thus bridging the gap between theory and practice, while corroborating the conceptual underpinnings of our work.

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arXiv2022

Back in the US-SR: Unlimited Sampling and Sparse Super-Resolution with its Hardware Validation

The Unlimited Sensing Framework (USF) is a digital acquisition protocol that allows for sampling and reconstruction of high dynamic range signals. By acquiring modulo samples, the USF circumvents the clipping or saturation problem that is a fundamental bottleneck in conventional analog-to-digital converters (ADCs). In the context of the USF, several works have focused on bandlimited function classes and recently, a hardware validation of the modulo sampling approach has been presented. In a different direction, in this paper we focus on non-bandlimited function classes and consider the well-known super-resolution problem; we study the recovery of sparse signals (Dirac impulses) from low-pass filtered, modulo samples. Taking an end-to-end approach to USF based super-resolution, we present a novel recovery algorithm (US-SR) that leverages a doubly sparse structure of the modulo samples. We derive a sampling criterion for the US-SR method. A hardware experiment with the modulo ADC demonstrates the empirical robustness of our method in a realistic, noisy setting, thus validating its practical utility.

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arXiv2021

The Surprising Benefits of Hysteresis in Unlimited Sampling: Theory, Algorithms and Experiments

The Unlimited Sensing Framework (USF) was recently introduced to overcome the sensor saturation bottleneck in conventional digital acquisition systems. At its core, the USF allows for high-dynamic-range (HDR) signal reconstruction by converting a continuous-time signal into folded, low-dynamic-range (LDR), modulo samples. HDR reconstruction is then carried out by algorithmic unfolding of the folded samples. In hardware, however, implementing an ideal modulo folding requires careful calibration, analog design and high precision. At the interface of theory and practice, this paper explores a computational sampling strategy that relaxes strict hardware requirements by compensating them via a novel, mathematically guaranteed recovery method. Our starting point is a generalized model for USF. The generalization relies on two new parameters modeling hysteresis and folding transients} in addition to the modulo threshold. Hysteresis accounts for the mismatch between the reset threshold and the amplitude displacement at the folding time and we refer to a continuous transition period in the implementation of a reset as folding transient. Both these effects are motivated by our hardware experiments and also occur in previous, domain-specific applications. We show that the effect of hysteresis is beneficial for the USF and we leverage it to derive the first recovery guarantees in the context of our generalized USF model. Additionally, we show how the proposed recovery can be directly generalized for the case of lower sampling rates. Our theoretical work is corroborated by hardware experiments that are based on a hysteresis enabled, modulo ADC testbed comprising off-the-shelf electronic components. Thus, by capitalizing on a collaboration between hardware and algorithms, our paper enables an end-to-end pipeline for HDR sampling allowing more flexible hardware implementations.

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