arXiv subjects

Manuel S. Stein

Publications and source records attributed to Manuel S. Stein.

11 recordsLinked to original sources

arXiv2021

On Optimal Quantization in Sequential Detection

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.

cs.IT↗

arXiv2021

Sensitivity Analysis for Binary Sampling Systems via Quantitative Fisher Information Lower Bounds

The problem of determining the achievable sensitivity with digitization exhibiting minimal complexity is addressed. In this case, measurements are exclusively available in hard-limited form. Assessing the achievable sensitivity via the Cramér-Rao lower bound requires characterization of the likelihood function, which is intractable for multivariate binary distributions. In this context, the Fisher matrix of the exponential family and a lower bound for arbitrary probabilistic models are discussed. The conservative approximation for Fisher's information matrix rests on a surrogate exponential family distribution connected to the actual data-generating system by two compact equivalences. Without characterizing the likelihood and its support, this probabilistic notion enables designing estimators that consistently achieve the sensitivity as defined by the inverse of the conservative information matrix. For parameter estimation with multivariate binary samples, a quadratic exponential surrogate distribution tames statistical complexity such that a quantitative assessment of an achievable sensitivity level becomes tractable. This fact is exploited for the performance analysis concerning parameter estimation with an array of low-complexity binary sensors in comparison to an ideal system featuring infinite amplitude resolution. Additionally, data-driven assessment by estimating a conservative approximation for the Fisher matrix under recursive binary sampling as implemented in $ΣΔ$-modulating analog-to-digital converters is demonstrated.

cs.IT↗

arXiv2019

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

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.

eess.SP↗

arXiv2019

Spectral Power Parameter Estimation of Random Sources with Binary Sampled Signals

This paper investigates the problem of estimating the spectral power parameters of random analog sources using numerical measurements acquired with minimum digitization complexity. Therefore, spectral analysis has to be performed with binary samples of the analog sensor output. Under the assumption that the structure of the spectral power density of the analog sources is given, we investigate the achievable accuracy for power level estimation with likelihood-oriented processing. The discussion addresses the intractability of the likelihood with multivariate hard-limited samples by exploiting advances on probabilistic modeling and statistical processing of hard-limited multivariate Gaussian data. In addition to estimation-theoretic performance analysis, the results are verified by running an iterative likelihood-oriented algorithm with synthetic binary data for two exemplary sensing setups.

eess.SP↗

arXiv2019

Glancing Through Massive Binary Radio Lenses: Hardware-Aware Interferometry With 1-Bit Sensors

Energy consumption and hardware cost of signal digitization together with the management of the resulting data volume form serious issues for high-rate measurement systems with multiple sensors. Switching to binary sensing front-ends results in a resource-efficient layout but is commonly associated with significant distortion due to the nonlinear signal acquisition. In particular, for applications that require to solve high-resolution processing tasks under extreme conditions, it is a widely held belief that low-complexity $1$-bit analog-to-digital conversion leads to unacceptable performance degradation. In the Big Science context of low-frequency radio astronomy, we propose a telescope architecture based on simplistic binary sampling, precise probabilistic modeling, and likelihood-oriented data processing. The main principles, building blocks, and advantages of such a radio telescope system, which we refer to as The Massive Binary Radio Lenses, are sketched. The open engineering science questions which have to be answered before building a prototype are outlined. We set sail for the academic technology study by deriving a statistical algorithm for interferometric imaging from binary array measurements. The method aims at extracting the full discriminative information about the spatial power distribution embedded in a binary sensor data stream without bias. Radio measurements obtained with LOFAR are used to test the developed imaging technique and discuss visual and quantitative results. These assessments shed light on the fact that binary radio telescopes are suited for surveying the universe.

astro-ph.IM↗

arXiv2018

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

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.

eess.SP↗

arXiv2018

Performance Analysis for Channel Estimation with 1-bit ADC and Unknown Quantization Threshold

In this work, the problem of signal parameter estimation from measurements acquired by a low-complexity analog-to-digital converter (ADC) with $1$-bit output resolution and an unknown quantization threshold is considered. Single-comparator ADCs are energy-efficient and can be operated at ultra-high sampling rates. For analysis of such systems, a fixed and known quantization threshold is usually assumed. In the symmetric case, i.e., zero hard-limiting offset, it is known that in the low signal-to-noise ratio (SNR) regime the signal processing performance degrades moderately by ${2}/π$ ($-1.96$ dB) when comparing to an ideal $\infty$-bit converter. Due to hardware imperfections, low-complexity $1$-bit ADCs will in practice exhibit an unknown threshold different from zero. Therefore, we study the accuracy which can be obtained with receive data processed by a hard-limiter with unknown quantization level by using asymptotically optimal channel estimation algorithms. To characterize the estimation performance of these nonlinear algorithms, we employ analytic error expressions for different setups while modeling the offset as a nuisance parameter. In the low SNR regime, we establish the necessary condition for a vanishing loss due to missing offset knowledge at the receiver. As an application, we consider the estimation of single-input single-output wireless channels with inter-symbol interference and validate our analysis by comparing the analytic and experimental performance of the studied estimation algorithms. Finally, we comment on the extension to multiple-input multiple-output channel models.

cs.IT↗

arXiv2018

Asymptotic Signal Detection Rates with 1-bit Array Measurements

This work considers detecting the presence of a band-limited random radio source using an antenna array featuring a low-complexity digitization process with single-bit output resolution. In contrast to high-resolution analog-to-digital conversion, such a direct transformation of the analog radio measurements to a binary representation can be implemented hardware and energy-efficient. However, the probabilistic model of the binary receive data becomes challenging. Therefore, we first consider the Neyman-Pearson test within generic exponential families and derive the associated analytic detection rate expressions. Then we use a specific replacement model for the binary likelihood and study the achievable detection performance with 1- bit radio array measurements. As an application, we explore the capability of a low-complexity GPS spectrum monitoring system with different numbers of antennas and different observation intervals. Results show that with a moderate amount of binary sensors it is possible to reliably perform the monitoring task.

cs.IT↗

arXiv2018

Joint Transmit and Receive Filter Optimization for Sub-Nyquist Delay-Doppler Estimation

In this article, a framework is presented for the joint optimization of the analog transmit and receive filter with respect to a parameter estimation problem. At the receiver, conventional signal processing systems restrict the two-sided bandwidth of the analog pre-filter $B$ to the rate of the analog-to-digital converter $f_s$ to comply with the well-known Nyquist-Shannon sampling theorem. In contrast, here we consider a transceiver that by design violates the common paradigm $B\leq f_s$. To this end, at the receiver, we allow for a higher pre-filter bandwidth $B>f_s$ and study the achievable parameter estimation accuracy under a fixed sampling rate when the transmit and receive filter are jointly optimized with respect to the Bayesian Cramér-Rao lower bound. For the case of delay-Doppler estimation, we propose to approximate the required Fisher information matrix and solve the transceiver design problem by an alternating optimization algorithm. The presented approach allows us to explore the Pareto-optimal region spanned by transmit and receive filters which are favorable under a weighted mean squared error criterion. We also discuss the computational complexity of the obtained transceiver design by visualizing the resulting ambiguity function. Finally, we verify the performance of the optimized designs by Monte-Carlo simulations of a likelihood-based estimator.

cs.IT↗

arXiv2017

Analog Transmit Signal Optimization for Undersampled Delay-Doppler Estimation

In this work, the optimization of the analog transmit waveform for joint delay-Doppler estimation under sub-Nyquist conditions is considered. Based on the Bayesian Cramér-Rao lower bound (BCRLB), we derive an estimation theoretic design rule for the Fourier coefficients of the analog transmit signal when violating the sampling theorem at the receiver through a wide analog pre-filtering bandwidth. For a wireless delay-Doppler channel, we obtain a system optimization problem which can be solved in compact form by using an Eigenvalue decomposition. The presented approach enables one to explore the Pareto region spanned by the optimized analog waveforms. Furthermore, we demonstrate how the framework can be used to reduce the sampling rate at the receiver while maintaining high estimation accuracy. Finally, we verify the practical impact by Monte-Carlo simulations of a channel estimation algorithm.

cs.IT↗

arXiv2017

Performance Analysis for Time-of-Arrival Estimation with Oversampled Low-Complexity 1-bit A/D Conversion

Analog-to-digtial (A/D) conversion plays a crucial role when it comes to the design of energy-efficient and fast signal processing systems. As its complexity grows exponentially with the number of output bits, significant savings are possible when resorting to a minimum resolution of a single bit. However, then the nonlinear effect which is introduced by the A/D converter results in a pronounced performance loss, in particular for the case when the receiver is operated outside the low signal-to-noise ratio (SNR) regime. By trading the A/D resolution for a moderately faster sampling rate, we show that for time-of-arrival (TOA) estimation under any SNR level it is possible to obtain a low-complexity $1$-bit receive system which features a smaller performance degradation then the classical low SNR hard-limiting loss of $2/π$ ($-1.96$ dB). Key to this result is the employment of a lower bound for the Fisher information matrix which enables us to approximate the estimation performance for coarsely quantized receivers with correlated noise models in a pessimistic way.

cs.IT↗