Asymptotic Signal Detection Rates with 1-Bit Array Measurements

Stein, Manuel

doi:10.1109/icassp.2018.8461559

Cited by 4 publications

(6 citation statements)

References 23 publications

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“…Note, that an ADC (flash architecture) with b bits requires 2 b −1 comparators per sample, while the A/B converter (ABC) modeled by the nonlinear operation ( 21) can be realized by a single comparator per sample. However, the characterization of the multivariate Bernoulli distribution at the quantizer output (21) forms a challenge [26]. In general, for all 2 M output constellations the integral…”

Section: Analog-to-binary Receive Modelmentioning

confidence: 99%

“…by arguing that this choice maximizes the distance between the expected values of (32) under p z (z; γ 0 ) and p z (z; γ 1 ) [26].…”

Section: Llr Approximation In Exponential Familiesmentioning

confidence: 99%

“…As the number of sufficient statistics for the multivariate Bernoulli distribution (23) scales O(2 M ), we base our SPRT analysis on a pessimistic replacement model, also residing within the exponential family [26]. This model holds a reduced set of sufficient statistics…”

Section: B Approximate Sprt -Multivariate Bernoulli Data Modelmentioning

confidence: 99%

“…Here we discuss a sequential procedure with collocated antennas featuring A/B front-ends. Therefore, the detector does not have access to the exact observations and has to base its decision exclusively on hard-limited sensor data [25], [26]. For sequential tests, this case is less well studied and the focus of existing works is on the design of optimal quantizers [27]- [29].…”

Section: Introductionmentioning

confidence: 99%

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In a One-Bit Rush: Low-Latency Wireless Spectrum Monitoring With Binary Sensor Arrays

Stein

Faub

2018

2018 IEEE Statistical Signal Processing Workshop (SSP)

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Detecting the presence of a random wireless source with minimum latency utilizing an array of radio sensors is considered. The problem is studied under the constraint that the analog-to-digital conversion at each sensor is restricted to reading the sign of the analog received signal. We formulate the resulting digital signal processing task as a sequential hypothesis test in simple form. To circumvent the intractable probabilistic model of the multivariate binary array data, a reduced model representation within the exponential family in conjunction with a log-likelihood ratio approximation is employed. This approach allows us to design a likelihood-based sequential test and to analyze its analytic performance along Wald's classical arguments. In the context of wireless spectrum monitoring for satellite-based navigation and synchronization systems, we study the achievable processing latency, characterized by the average sample number, as a function of the binary sensors in use. The practical feasibility and potential of the discussed low-complexity sensing and decision-making technology is demonstrated via simulations.

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Section: Analog-to-binary Receive Modelmentioning

confidence: 99%

“…by arguing that this choice maximizes the distance between the expected values of (32) under p z (z; γ 0 ) and p z (z; γ 1 ) [26].…”

Section: Llr Approximation In Exponential Familiesmentioning

confidence: 99%

Section: B Approximate Sprt -Multivariate Bernoulli Data Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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In a One-Bit Rush: Low-Latency Wireless Spectrum Monitoring With Binary Sensor Arrays

Stein

Faub

2018

2018 IEEE Statistical Signal Processing Workshop (SSP)

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“…Quantized (sequential) detection is a well-known problem in the literature [13]- [17]. However, in most works the focus is on scenarios in which the quantizers are either given or fixed, that is, the quatization rules are identical for every sample.…”

Section: Introductionmentioning

confidence: 99%

On Optimal Quantization in Sequential Detection

Fauß¹,

Stein²,

Poor³

2021

Preprint

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The problem of designing optimal quantization rules for sequential detectors is investigated. First, it is shown that this task can be solved within the general framework of active sequential detection. Using this approach, the optimal sequential detector and the corresponding quantizer are characterized and their properties are briefly discussed. In particular, it is shown that designing optimal quantization rules requires solving a nonconvex optimization problem, which can lead to issues in terms of computational complexity and numerical stability. Motivated by these difficulties, two performance bounds are proposed that are easier to evaluate than the true performance measures and are potentially tighter than the bounds currently available in the literature. The usefulness of the bounds and the properties of the optimal quantization rules are illustrated with two numerical examples.

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Latency Analysis for Sequential Detection in Low-Complexity Binary Radio Systems

Stein

Faub

2019

IEEE Trans. Commun.

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We consider the problem of making a quick decision in favor of one of two possible physical signal models while the numerical measurements are acquired by sensing devices featuring minimal digitization complexity. Therefore, the digital data streams available for statistical processing are binary and exhibit temporal and spatial dependencies. To handle the intractable multivariate binary data model, we first consider sequential tests for exponential family distributions. Within this generic probabilistic framework, we identify adaptive approximations for the log-likelihood ratio and the Kullback-Leibler divergence. The results allow designing sequential detectors for binary radio systems and analyzing their average run-time along classical arguments of Wald. In particular, the derived tests exploit the spatio-temporal correlation structure of the analog sensor signals engraved into the binary measurements. As an application, we consider the specification of binary sensing architectures for cognitive radio and GNSS spectrum monitoring where our results characterize the sequential detection latency as a function of the temporal oversampling and the number of antennas. Finally, we evaluate the efficiency of the proposed algorithms and illustrate the accuracy of our analysis via Monte-Carlo simulations.

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Asymptotic Signal Detection Rates with 1-Bit Array Measurements

Cited by 4 publications

References 23 publications

In a One-Bit Rush: Low-Latency Wireless Spectrum Monitoring With Binary Sensor Arrays

In a One-Bit Rush: Low-Latency Wireless Spectrum Monitoring With Binary Sensor Arrays

On Optimal Quantization in Sequential Detection

Latency Analysis for Sequential Detection in Low-Complexity Binary Radio Systems

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