Bayesian Information Criterion for Signed Measurements With Application to Sinusoidal Signals

Li, Changheng; Zhang, Rong; Li, Jian; Stoica, Petre

doi:10.1109/lsp.2018.2847559

Cited by 21 publications

(15 citation statements)

References 21 publications

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“…To determine the number of sinusoids, i.e., the model order K, from signed measurements, we will use the one-bit Bayesian information criterion (1bBIC) with 1bMMRELAX. Suppose that β K is the vector of parameter estimates obtained by the 1bMMRELAX algorithm for an assumed model order K; then the 1bBIC cost function is given by [54]:…”

Section: Determining the Number Of Sinusoidsmentioning

confidence: 99%

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Sinusoidal Parameter Estimation From Signed Measurements Via Majorization–Minimization Based RELAX

Ren

Zhang

et al. 2019

IEEE Trans. Signal Process.

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We consider the problem of sinusoidal parameter estimation using signed observations obtained via one-bit sampling with fixed as well as time-varying thresholds. In a previous paper, a relaxation-based algorithm, referred to as 1bRELAX, has been proposed to iteratively maximize the likelihood function. However, the exhaustive search procedure used in each iteration of 1bRELAX is time-consuming. In this paper, we present a majorization-minimization (MM) based 1bRELAX algorithm, referred to as 1bMMRELAX, to enhance the computational efficiency of 1bRELAX. Using the MM technique, 1bMMRELAX maximizes the likelihood function iteratively using simple FFT operations instead of the more computationally intensive search used by 1bRELAX. Both simulated and experimental results are presented to show that 1bMMRELAX can significantly reduce the computational cost of 1bRELAX while maintaining its excellent estimation accuracy.

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Section: Determining the Number Of Sinusoidsmentioning

confidence: 99%

“…3) For the case that the number of sinusoids, i.e., the model order, is unknown, we explain how the proposed algorithm can be used with the one-bit Bayesian information criterion (1bBIC) [54] to simultaneously estimate the sinusoidal parameters and determine the number of sinusoids.…”

Section: Introductionmentioning

confidence: 99%

Sinusoidal Parameter Estimation From Signed Measurements Via Majorization–Minimization Based RELAX

Ren

Zhang

et al. 2019

IEEE Trans. Signal Process.

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“…For the case that the number of RFI sources, i.e., the true model order K, is unknown, we consider extending the single-PRI based one-bit Bayesian information criterion (1bBIC) in [21] to the multiple-PRI based cases so that the extended 1bBIC can be used with the extended 1bMMRELAX to determine the RFI model order. Suppose that β K is parameter vector estimated by the extended 1bMMRELAX algorithm for an assumed model order K, where 1 ≤ K ≤ K max .…”

Section: Bbicmentioning

confidence: 99%

“…Under mild conditions (see, e.g., [21], [34] and the references therein), the matrix Ĵ(Y, β) has the following asymptotic relationship with the Fisher information matrix (FIM) J for the parameter vector β [21]:…”

Section: Appendix a Derivation Of 1bbic For Multiple-pri Based Signed...mentioning

confidence: 99%

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RFI Mitigation for One-Bit UWB Radar Systems

Zhang

Ren

Gianelli

et al. 2019

2019 53rd Asilomar Conference on Signals, Systems, and Computers

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Radio frequency interference (RFI) mitigation is critical to the proper operation of ultra-wideband (UWB) radar systems since RFI can severely degrade the radar imaging capability and target detection performance. In this paper, we address the RFI mitigation problem for one-bit UWB radar systems. A one-bit UWB system obtains its signed measurements via a low-cost and high rate sampling scheme, referred to as the Continuous Time Binary Value (CTBV) technology. This sampling strategy compares the signal to a known threshold varying with slow-time and therefore can be used to achieve a rather high sampling rate and quantization resolution with rather simple and affordable hardware. This paper establishes a proper data model for the RFI sources and proposes a novel RFI mitigation method for the one-bit UWB radar system that uses the CTBV sampling technique. Specifically, we first model the RFI sources as a sum of sinusoids with frequencies fixed during the coherent processing interval (CPI) and we exploit the sparsity of the RFI spectrum. We extend a majorization-minimization based 1bRELAX algorithm, referred to as 1bMMRELAX, to estimate the RFI source parameters from the signed measurements obtained by using the CTBV sampling strategy. We also devise a new fast frequency initialization method based on the Alternating Direction Method of Multipliers (ADMM) methodology for the extended 1bMMRELAX algorithm to significantly improve its computational efficiency. Moreover, an ADMM-based sparse method is introduced to recover the desired radar echoes using the estimated RFI parameters. Both simulated and experimental results are presented to demonstrate that our proposed algorithm outperforms the existing digital integration method, especially for severe RFI cases.

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Signal Recovery From 1-Bit Quantized Noisy Samples via Adaptive Thresholding

Khobahi

Soltanalian

2018

2018 52nd Asilomar Conference on Signals, Systems, and Computers

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In this paper, we consider the problem of signal recovery from 1-bit noisy measurements. We present an efficient method to obtain an estimation of the signal of interest when the measurements are corrupted by white or colored noise. To the best of our knowledge, the proposed framework is the pioneer effort in the area of 1-bit sampling and signal recovery in providing a unified framework to deal with the presence of noise with an arbitrary covariance matrix including that of the colored noise. The proposed method is based on a constrained quadratic program (CQP) formulation utilizing an adaptive quantization thresholding approach, that further enables us to accurately recover the signal of interest from its 1-bit noisy measurements. In addition, due to the adaptive nature of the proposed method, it can recover both fixed and time-varying parameters from their quantized 1-bit samples.

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Bayesian Information Criterion for Signed Measurements With Application to Sinusoidal Signals

Cited by 21 publications

References 21 publications

Sinusoidal Parameter Estimation From Signed Measurements Via Majorization–Minimization Based RELAX

Sinusoidal Parameter Estimation From Signed Measurements Via Majorization–Minimization Based RELAX

RFI Mitigation for One-Bit UWB Radar Systems

Signal Recovery From 1-Bit Quantized Noisy Samples via Adaptive Thresholding

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