Parameter Measurement of LFM Signal With FRI Sampling and Nuclear Norm Denoising

• Published in: IEEE transactions on instrumentation and measurement Vol. 71; pp. 1 - 17
• Main Authors: Wei, Zhiliang, Fu, Ning, Jiang, Siyi, Li, Xiaodong, Qiao, Liyan
• Format: Journal Article
• Language: English
• Published: New York IEEE 2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Baseband; Chirp; Estimation; Finite rate of innovation (FRI); Frequency estimation; Frequency modulation; Innovations; linear frequency modulation (LFM); Measurement methods; Noise measurement; Noise reduction; nuclear norm; Parameter estimation; Quadratures; Sampling; Signal processing; sub-Nyquist sampling; Subspace methods; Technological innovation; Time measurement; Time-frequency analysis
• ISSN: 0018-9456; 1557-9662
• DOI: 10.1109/TIM.2022.3158986

Measurement of linear frequency modulation (LFM) signal is significant for radar, communication, and electronic reconnaissance fields. An LFM signal is a wideband signal whose frequency varies linearly with time, and traditional measurement methods require very high sampling rates and heavy processing to estimate parameters of the LFM signal. In this article, we propose a multichannel cooperative sampling (MCS) system based on the finite rate of innovation (FRI) theory to sample and estimate the parameters of the real-valued LFM pulse sequence (LFMPS). The MCS system consists of three parts: the autocorrelation sampling structure (ACSS), the time-delayed ACSS, and the quadrature time-staggered sampling structure (QTSS). These three parts can sample the LFMPS with sub-Nyquist sampling rate, and using the subspace method in time or frequency domain, the discontinuity locations (DLs), chirp rates, and initial frequencies (IFs) of the LFMPS can be estimated with the sub-Nyquist samples, respectively. The sampling rate of the MCS system is determined by the rate of innovation of the LFMPS, instead of signal bandwidth (BW). The minimum number of samples required for parameter estimation is proven by theoretical analysis. In addition, a nuclear norm denoising algorithm is proposed based on the low-rank property of the signal subspace, which significantly improved the performance of the measurement system in the noise environment. Simulation and hardware experimental results demonstrate the effectiveness and robustness of the proposed method.