An Efficient Estimation Method for the Model Order of FRI Signal Based on Sub-Nyquist Sampling

• Published in: IEEE transactions on instrumentation and measurement Vol. 72; pp. 1 - 13
• Main Authors: Fu, Ning, Yun, Shuangxing, Qiao, Liyan
• Format: Journal Article
• Language: English
• Published: New York IEEE 2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Accuracy; Algorithms; Artificial neural networks; Estimation; Extraterrestrial measurements; Finite rate of innovation (FRI); low-rank matrix; Mathematical models; Measurement methods; model order estimation; Noise measurement; Parameter estimation; Resampling; Sampling; Signal reconstruction; Signal to noise ratio; singular value rectification (SVR); Technological innovation
• ISSN: 0018-9456; 1557-9662
• DOI: 10.1109/TIM.2023.3320730

The finite rate of innovation (FRI) sampling theory offers a pathway for the sub-Nyquist sampling of nonbandlimited parametric signals. However, the successful application of FRI-based techniques requires prior knowledge of the model order of the parameterized signal being sampled. This article presents an efficient method for measuring the model order of FRI signals by leveraging the low-rank features of Toeplitz matrices. In a noisy environment, we conduct an initial analysis and identify that the key factor affecting the estimation of model order is the problem of small singular values in the Toeplitz matrix caused by noise. In response to this, we present a plug-and-play convolutional neural networks (CNNs)-based denoising module as well as an efficient algorithm for singular value rectification (SVR). Compared to classical methods for measuring model order, the proposed approach does not require signal reconstruction or resampling. As a result, our proposed technique has lower complexity and achieves significantly improved accuracy and efficiency under the same signal-to-noise ratio (SNR). We validate our approach through simulation experiments and hardware testing, and the results demonstrate that our method substantially enhances the accuracy and robustness of model order estimation in noisy environments.