• 学术论文 •

### 基于LSTM特征提取的有限新息率畸变信号重构

1. 1.福州大学物理与信息工程学院，福建 福州 350108
2.南京大学电子科学与工程学院，江苏 南京 210023
• 收稿日期:2020-10-10 修回日期:2021-06-16 出版日期:2022-01-25
• 作者简介:
• 刘 狄 男，1994年10月生，福建福州人.2017年和2021年分别在武汉大学和福州大学获得工学学士和工学硕士学位.主要从事智能信息处理方面的研究工作. E-mail:526920885@qq.com
钱 慧（通信作者） 女，1977年11月生，湖北荆州人.2004年和2012年分别在华中师范大学和福州大学获得工学硕士和工学博士.目前任福州大学副教授，主要从事低功耗信号采样理论以及模数混合系统设计方面的研究工作. E-mail:qianhui@fzu.edu.cn
王中风 男，1963年10月生，安徽省安庆人.教授、博士生导师、IEEE会士.1988年和1990年在清华大学获得工学学士和工学硕士学位.2000年在美国明尼苏达大学获得工学博士学位.目前任南京大学特聘教授，主要从事信号处理系统的低功耗设计方面的研究工作. E-mail:zfwang@nju.edu.cn
• 基金资助:
• 数字福建物联网工程应用实验室建设项目 (82917002); 工业物联网感知识别技术创新平台项目 (82317241)

### Reconstruction of Distorted Signal with Finite Innovation Rate Based on LSTM Feature Extraction

LIU Di1, QIAN Hui1, WANG Zhong-feng2

1. 1.College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China
2.School of Electronic Science and Engineering, Nanjing University, Nanjing, Jiangsu 210023, China
• Received:2020-10-10 Revised:2021-06-16 Online:2022-01-25 Published:2022-01-25
• Supported by:
• “Digital Fujian” Internet of Things Engineering Application Laboratory Construction Program (82917002); Industrial Internet of Things Perception Recognition Technology Innovation Platform (82317241)

Abstract:

The finite rate of innovation(FRI) samples signal at rate of sub-Nyquist rate by using the known waveform structure, which has a wide application prospect in wideband information systems. However, in the real-world information system, the signal waveform structure is often distorted by the non-ideal factors, such as noise and long-distance transmission, which leads to fail to reconstruct the FRI waveform. According to the principle of waveform regeneration, an FRI reconstruction method based on long and short-term memory(LSTM) is proposed in this paper. This method replaces the sampling kernel of FRI sampling system by an automatic LSTM encoder, and the distorted waveform with unknown structure is obtained by off-line training. Thus, the waveform sequence is projected to a Dirac signature sequence. The FRI sampling and reconstruction of waveform distortion signal are realized. The results show that the proposed method can effectively reconstruct the FRI signals, which distorted by the multipath effect, by exploiting the standard annihilating filter.

Extended Abstract
Nowadays, the Shannon sampling theorem is fundamental for contemporary data acquisition systems, which require an analog signal to be sampled at Nyquist rate. Nyquist rate samples can perfectly represent the signal waveform, but include a large amount of data redundancy. For cost-effective transmission and storage, data acquisition systems typically compress these Nyquist rate samples at high compression ratios. This processing framework of first sampling and then discarding wastes a large amount of limited hardware resources. With the appearance of the Internet of Things (IoTs), the amount of data is still growing. This impacts an enormous challenge for data acquisition systems with Nyquist rate. Over the past three decades, sub-Nyquist sampling has become a prominent topic in the field of sampling methods that use some prior information about an analog signal and thus support sampling the analog signal below its Nyquist rate.
Finite rate of innovation (FRI) is one of the popular sub-Nyquist frameworks. It simultaneously samples and compresses an analog signal by using its known waveform structure. It uses the innovation rate of the signal, rather than the bandwidth of the signal, as the sampling criterion. In this way, it should be possible to sample a wideband signal at a rate below its Nyquist rate. Classical FRI sampling systems rely on a priori knowledge of the structure of the signal waveform. It mainly preprocesses an analog FRI signal by using a sampling kernel such as a Gaussian sampling kernel. In ideal conditions, the sampling kernel compresses the bandwidth of an FRI signal and extracts its feature parameters into the discrete time domain. However, in practical information systems, non-ideal factors such as noise and long-distance transmission mostly distort the known waveform structure of the signal, which results in the failure of reconstructing the sparse parameters of the signal from its sub-Nyquist samples. Recently, there have been a number of studies related to this issue. These methods often assume that the FRI signal is processed with white Gaussian noise. The noise signal is incoherent with the original FRI signal. In reality, some complex factors, such as multipath transmission, may generate waveform overlaps of multiple FRI signals, causing the reconstruction of the FRI sampling system to fail.
In order to eliminate the effect of overlapping distortion, researchers have proposed a number of methods that employ model fitting based on waveform reproduction. In general, the distorted signal incorporates multiple versions of the original signal. According to the theory of reproducible sampling, a sub-Nyquist sample of a certain FRI signal can be mapped to a particular combination of Dirac streams that include features of the FRI signal. This means that a distorted signal can be translated into a linear combination of Dirac streams with unknown combinatorial coefficients. These existing methods commonly obtain the best combined model by searching for various fitting parameters of the fitted model, such as the order or bandwidth of the fitting function. Since the distortion of FRI signals is various, subtle model biases can dramatically degrade the performance of FRI sampling systems. To date, sub-Nyquist sampling and reconstruction of FRI signals with overlapping distortions remains an open topic.
In this paper, we handle the challenge by constructing the long and short-term memory (LSTM) based auto encode (AE) to acquire the feature of the distorted waveform, and realizes the sub-Nyquist sampling and reconstruction of the distorted FRI signal. We consider the distorted signal as a signal with unknown structure and construct an LSTM based AE to replace the sampling kernel. By using off-line training, the LSTM based AE is able to map the sub-Nyquist samples of a distorted FRI signal into a learned linear combination of Dirac streams. Then, the perturbations of the overlapping distortion are removed from these samples. Hence, our proposed FRI sampling system includes two stags. The first stage is offline training, where an LSTM based AE is constructed to learn a distortion model for the distorted FRI signal. The second stage is the online reconstruction. At this stage, the sampling system firstly uses the learned distorted model to extract the Dirac streams with the feature parameters and then reconstruct FRI signal by using standard annihilating filter (AF) algorithm with Cadzow denoising.
Our major contribution consists of the following aspects. First, we propose a novel learned model fitting based sampling framework for distorted FRI signals. This framework uses a neural network to construct a relationship between a sub-Nyquist sample of a FRI signal and a sequence of Dirac streams containing its feature parameters. Second, we construct an LSTM based AE neural network with three layers by exploiting the linear regression property of the distorted FRI signal. The LSTM based AE can extract sub-optimal combinations of Dirac flows from sub-Nyquist samples in the case where the known waveform structure of an FRI signal has been distorted.
In this paper, a large number of simulation experiments have been carried out to investigate the proposed sampling framework. The results show that our approach can efficiently mitigate the degradation of reconstruction performance due to waveform distortion. Existing frameworks for FRI sampling are susceptible to waveform overlapping, which is typically caused by the well-known multipath effect. Simulations on distorted FRI signal data show that our method can still efficiently reconstruct the distorted FRI signal using a standard annihilation filter, even if their pulses overlap by 50 per cent. Moreover, our LSTM based AE is a simple three-layer network, which requires relatively small hardware resources to operate its inference model. Thus, our approach can be easily implemented by contemporary data systems. It may also facilitate practical applications of FRI systems.