Computational Array Signal Processing via Modulo Non-Linearities

Fernández-Menduiña, Samuel; Krahmer, Felix; Leus, Geert; Bhandari, Ayush

doi:10.1109/tsp.2021.3101437

Cited by 27 publications

(9 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…7: Obtain the pseudo spectrum of Capon according to (30). 8: Construct Â Â Â using (31) 9: Calculate the power of noise according to (34). 10: Construct f Capon obj according to (35).…”

Section: This Work Uses the Generalized Pattern Search (Gps) [37] To ...mentioning

confidence: 99%

“…Recently, data processing methods based on unlimited sensing (US) [30][31][32] have gained much attention with their extremely high data dynamic range. In the meantime, US-based array signal processing theory [33][34][35] also has a lot of room for improvement. Motivated by the finite difference employed there, a generalized noise reconstruction approach to robust DOA estimation is proposed in this paper, which can improve the performance of DOA estimation by removing the noise reconstructed in the receiving domain.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Generalized Noise Reconstruction Approach to Robust DOA Estimation

Cong¹,

Wang²,

Liu³

et al. 2023

Preprint

View full text Add to dashboard Cite

<p>A generalized noise reconstruction approach is proposed for improved direction-of-arrival (DOA) estimation. The objective function kernel of the noise reconstruction problem can be made up of many distinct DOA estimation algorithms, making it an optimization problem. First, a coarse estimation of the received domain noise is calculated based on the cumulative sum of an approximate noise first-order finite difference. In particular, the generalized pattern search algorithm is used to find the best initial value. The objective function is constructed with the total noise power estimated by least squares (LS), minimized. After that, a brand-new cumulative sum constructed with the solution from the previous step is used to precisely reconstruct the received data-domain noise. Finally, DOA estimation is obtained using Capon algorithm. The efficiency of suppressing sidelobes and pseudo-peaks and the accuracy of DOA estimation are evaluated. In simulations, different scenarios, such as non-uniform noise, colored noise, impulsive noise, and K-distribution sea clutter, are considered. Real-world frequency-modulated continuous wave (FMCW) radar multiple-input multiple-output (MIMO) data is used to confirm the effectiveness of the proposed approach.</p>

show abstract

“…7: Obtain the pseudo spectrum of Capon according to (30). 8: Construct Â Â Â using (31) 9: Calculate the power of noise according to (34). 10: Construct f Capon obj according to (35).…”

Section: This Work Uses the Generalized Pattern Search (Gps) [37] To ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Generalized Noise Reconstruction Approach to Robust DOA Estimation

Cong¹,

Wang²,

Liu³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…since the above difference operation does not destroy the information in the spatial dimension [41], the reconstructed noise can be obtained by the following cumulative sum:…”

Section: Robust Noise Reconstructionmentioning

confidence: 99%

A Generalized Noise Reconstruction Framework for DOA Estimation in Received Data Domain

Cong¹,

Wang²,

Liu³

et al. 2022

Preprint

View full text Add to dashboard Cite

<p>The performance of direction-of-arrival (DOA) estimation algorithms is affected by noise and clutter, but conventional noise reduction methods are difficult to adapt a variety of DOA estimation algorithms in different noise/clutter environments. To address this issue, a generalized robust framework for noise reconstruction in the received data domain is proposed to enhance DOA estimation performance. The problem of noise reconstruction is formulated as an optimization problem, whose objective function kernel may consist of many different DOA estimation algorithms. First, based on the cumulative sum of an approximate noise first order finite difference, a coarse estimation of the received domain noise is then calculated. In particular, the optimal initial value is obtained using the generalized pattern search algorithm, where the objective function, constructed with the distance between the normalized spatial spectrum peaks and the desired spatial spectrum peaks or the total noise power estimated by least squares (LS), is minimized. Then, exact reconstruction of the received data-domain noise is realized by a new cumulative sum formed using the solution from the previous step. Finally, using the denoised data, the DOA estimation is obtained via different algorithms. The effectiveness of the proposed framework is verified by simulations, with the objective function kernel of the propagator method (PM), Capon, sparse Bayesian learning (SBL), and parallel factorization (PARAFAC), both in terms of accuracy of DOA estimation and effectiveness in suppressing sidelobe and pseudo-peaks, for different cases, including white Gaussian noise, non-uniform noise, colored noise, impulsive noise, and K-distribution sea clutter. In addition, the effectiveness of the proposed framework is verified on the FMCW MIMO radar real-world data. The relevant codes are available online: https://github.com/CJYLostviews/Robust-Noise-Reconstruction/</p>

show abstract

“…The conceptualization of the USF triggered a number of follow-up studies. A wider class of measurement scenarios were covered including computed tomography [14], [15], sensor array processing [16], [17], and event-driven sampling [18]. For bandlimited signals, which are the main focus in our work, the folded measurements are proven to be injective: a bandlimited function is mapped one-to-one to its modulo samples for sampling rates just above the critical Nyquist rate [19], [20].…”

Section: Related Workmentioning

confidence: 99%

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

Florescu,

Krahmer,

Bhandari

2021

Preprint

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Computational Array Signal Processing via Modulo Non-Linearities

Cited by 27 publications

References 36 publications

A Generalized Noise Reconstruction Approach to Robust DOA Estimation

A Generalized Noise Reconstruction Approach to Robust DOA Estimation

A Generalized Noise Reconstruction Framework for DOA Estimation in Received Data Domain

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

Contact Info

Product

Resources

About