Non-Bayesian estimation with partially quantized observations

Harel, Nadav; Routtenberg, Tirza

doi:10.1109/icdsp.2017.8096150

Cited by 5 publications

(4 citation statements)

References 16 publications

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“…Since the vectors θ, w da , w dq , w a , and w q are all mutually independent, then it can be shown, similar to the derivation of ( 4) and (6), that (33) and (34) imply, in this case, the following covariance matrices of the measurements:…”

Section: Optimization With Ditheringmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

“…In addition to purely-quantized or purely-analog data, a few works have been using schemes with multiple quantization resolution data [4], [13], [33]. For example, the ML and CRB for non-Bayesian estimation with partially quantized observations is considered in [33]. For the Bayesian case, the minimum MSE (MMSE) estimation of a uniformly distributed parameter, based on both quantized and unquantized observations, has been suggested in [4] and linear MMSE (LMMSE) in specific applications is discussed in [11], [12], [15].…”

Section: Introductionmentioning

confidence: 99%

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Resource Allocation and Dithering of Bayesian Parameter Estimation Using Mixed-Resolution Data

Berman,

Routtenberg

2020

Preprint

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Quantization of signals is an integral part of modern signal processing applications, such as sensing, communication, and inference. While signal quantization provides many physical advantages, it usually degrades the subsequent estimation performance that is based on quantized data. In order to maintain physical constraints and simultaneously bring substantial performance gain, in this work we consider systems with mixedresolution, 1-bit quantized and continuous-valued, data. First, we describe the linear minimum mean-squared error (LMMSE) estimator and its associated mean-squared error (MSE) for the general mixed-resolution model. However, the MSE of the LMMSE requires matrix inversion in which the number of measurements defines the matrix dimensions and thus, is not a tractable tool for optimization and system design. Therefore, we present the linear Gaussian orthonormal (LGO) measurement model and derive a closed-form analytic expression for the MSE of the LMMSE estimator under this model. In addition, we present two common special cases of the LGO model: 1) scalar parameter estimation and 2) channel estimation in mixed-ADC multiple-input multiple-output (MIMO) communication systems. We then solve the resource allocation optimization problem of the LGO model with the proposed tractable form of the MSE as an objective function and under a power constraint using a one-dimensional search. Moreover, we present the concept of dithering for mixed-resolution models and optimize the dithering noise as part of the resource allocation optimization problem for two dithering schemes: 1) adding noise only to the quantized measurements and 2) adding noise to both measurement types. Finally, we present simulations that demonstrate the advantages of using mixed-resolution measurements and the possible improvement introduced with dithering and resource allocation.

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Section: Optimization With Ditheringmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Resource Allocation and Dithering of Bayesian Parameter Estimation Using Mixed-Resolution Data

Berman,

Routtenberg

2020

Preprint

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“…Additionally, we mention that a further realistic complication is represented by the need for fusing sensors with different quantization resolutions, and, in some cases, able to provide their unquantized analog data to the FC, as recently studied in [34], [35] for a decentralized estimation problem. The need for considering this type of sensors can be motivated by sensors being very close to the FC, then capable of transmitting their unquantized data with little cost in terms of battery depletion (as opposed to further sensor nodes, whose measurements need to be quantized).…”

Section: Introductionmentioning

confidence: 99%

Multibit Decentralized Detection Through Fusing Smart and Dumb Sensors Based on Rao Test

Cheng

Ciuonzo

Rossi

2020

IEEE Trans. Aerosp. Electron. Syst.

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We consider Decentralized Detection (DD) of an unknown signal corrupted by zero-mean unimodal noise via Wireless Sensor Networks (WSNs). We assume the presence of both smart and dumb sensors: the former transmit unquantized measurements, while the latter employ multi-level quantizations (before transmission through binary symmetric channels) in order to cope with energy and/or bandwidth constraints. The data are received by a Fusion Center (FC), which relies on a proposed Rao test, as a simpler alternative to the Generalized Likelihood Ratio Test (GLRT). The asymptotic performance analysis of the multi-bit Rao test is provided and exploited to propose a (signalindependent) quantizer design approach by maximizing the noncentrality parameter of the test-statistic distribution. Since the latter is a non-linear and non-convex function of the quantization thresholds, we employ the particle swarm optimization algorithm for its maximization. Numerical results are provided to show the effectiveness of Rao test in comparison to GLRT and the boost in performance obtained by (multiple) threshold optimization. Asymptotic performance is also exploited to define detection gain measures allowing to assess gain arising from (a) use of dumb sensors and (b) increasing their quantization resolution.

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When Less Is More$\ldots$ Few Bit ADCs in RF Systems

Rodenbeck¹,

Martinez

Beun³

et al. 2019

IEEE Access

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Digitizing RF signals using few bit ADCs can provide system advantages in terms of reduced power dissipation, wider sampling bandwidth, and decreased demand for digital throughput. The diversity of established applications based on few bit ADCs, together with the recent surge of interest in the topic for 5G wireless communications and millimeter-wave radar, has created a need for practical design guidance governing their use in general RF systems. This paper, therefore, summarizes the state-of-the-art in few bit ADCs, comparing the dynamic range considerations involved with those of conventional RF receiver design. A simple analytic model for the monobit ADC is extended to multiple bits. Parametric analysis, independent of sampling considerations and system-specific signal processing, is used to illustrate the variation in the ADC output signal-to-noise-and-distortion ratio (SNDR) versus both the number of quantization bits and the input signal-to-noise ratio (SNR). At low and negative input SNR, increasing ADC resolution beyond 3-4 bits yields little advantage in output SNDR. Experiment confirms analytic predictions for the specific conditions under which the loss of signal fidelity due to quantization can be made negligible. In addition, parametric analysis of two-tone intermodulation distortion shows clear disadvantages to quantizing with <4 bits in the presence of strong blockers. The results reported in this paper, which are general and independent of system application, can be used to customize the number of ADC bits in an RF system based on system-specific performance requirements for receiver dynamic range. INDEX TERMS Analog-to-digital converters (ADCs), 5G, low resolution ADCs, quantization, coherent receivers, radiofrequency integrated circuits, wireless communications, radar.

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Non-Bayesian estimation with partially quantized observations

Cited by 5 publications

References 16 publications

Resource Allocation and Dithering of Bayesian Parameter Estimation Using Mixed-Resolution Data

Resource Allocation and Dithering of Bayesian Parameter Estimation Using Mixed-Resolution Data

Multibit Decentralized Detection Through Fusing Smart and Dumb Sensors Based on Rao Test

When Less Is More$\ldots$ Few Bit ADCs in RF Systems

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