Estimation and Classification of NLFM Signals Based on the Time–Chirp Representation
A new approach to the estimation and classification of nonlinear frequency modulated (NLFM) signals is presented in the paper. These problems are crucial in electronic reconnaissance systems whose role is to indicate what signals are being received and recognized by the intercepting receiver. NLFM s...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/22/21/8104 |
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| author | Ewa Swiercz Dariusz Janczak Krzysztof Konopko |
| author_facet | Ewa Swiercz Dariusz Janczak Krzysztof Konopko |
| author_sort | Ewa Swiercz |
| collection | DOAJ |
| description | A new approach to the estimation and classification of nonlinear frequency modulated (NLFM) signals is presented in the paper. These problems are crucial in electronic reconnaissance systems whose role is to indicate what signals are being received and recognized by the intercepting receiver. NLFM signals offer a variety of useful properties not available for signals with linear frequency modulation (LFM). In particular, NLFM signals can ensure the desired reduction of sidelobes of an autocorrelation (AC) function and desired power spectral density (PSD); therefore, such signals are more frequently used in modern radar and echolocation systems. Due to their nonlinear properties, the discussed signals are difficult to recognize and therefore require sophisticated methods of analysis, estimation and classification. NLFM signals with frequency content varying with time are mainly analyzed by time–frequency algorithms. However, the methods presented in the paper belong to time–chirp domain, which is relatively rarely cited in the literature. It is proposed to use polynomial approximations of nonlinear frequency and phase functions describing signals. This allows for applying the cubic phase function (CPF) as an estimator of phase polynomial coefficients. Originally, the CPF involved only third-order nonlinearities of the phase function. The extension of the CPF using nonuniform sampling is used to analyse the higher order polynomial phase. In this paper, a sixth order polynomial is considered. It is proposed to estimate the instantaneous frequency using a polynomial with coefficients calculated from the coefficients of the phase polynomial obtained by CPF. The determined coefficients also constitute the set of distinctive features for a classification task. The proposed CPF-based classification method was examined for three common NLFM signals and one LFM signal. Two types of neural network classifiers: learning vector quantization (LVQ) and multilayer perceptron (MLP) are considered for such defined classification problem. The performance of both the estimation and classification processes was analyzed using Monte Carlo simulation studies for different SNRs. The results of the simulation research revealed good estimation performance and error-free classification for the SNR range encountered in practical applications. |
| first_indexed | 2024-03-09T18:41:02Z |
| format | Article |
| id | doaj.art-5ef8a250d4b54fc59f20f9f614661730 |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-09T18:41:02Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-5ef8a250d4b54fc59f20f9f6146617302023-11-24T06:42:47ZengMDPI AGSensors1424-82202022-10-012221810410.3390/s22218104Estimation and Classification of NLFM Signals Based on the Time–Chirp RepresentationEwa Swiercz0Dariusz Janczak1Krzysztof Konopko2Faculty of Electrical Engineering, Bialystok University of Technology, 15-351 Bialystok, PolandFaculty of Electrical Engineering, Bialystok University of Technology, 15-351 Bialystok, PolandFaculty of Electrical Engineering, Bialystok University of Technology, 15-351 Bialystok, PolandA new approach to the estimation and classification of nonlinear frequency modulated (NLFM) signals is presented in the paper. These problems are crucial in electronic reconnaissance systems whose role is to indicate what signals are being received and recognized by the intercepting receiver. NLFM signals offer a variety of useful properties not available for signals with linear frequency modulation (LFM). In particular, NLFM signals can ensure the desired reduction of sidelobes of an autocorrelation (AC) function and desired power spectral density (PSD); therefore, such signals are more frequently used in modern radar and echolocation systems. Due to their nonlinear properties, the discussed signals are difficult to recognize and therefore require sophisticated methods of analysis, estimation and classification. NLFM signals with frequency content varying with time are mainly analyzed by time–frequency algorithms. However, the methods presented in the paper belong to time–chirp domain, which is relatively rarely cited in the literature. It is proposed to use polynomial approximations of nonlinear frequency and phase functions describing signals. This allows for applying the cubic phase function (CPF) as an estimator of phase polynomial coefficients. Originally, the CPF involved only third-order nonlinearities of the phase function. The extension of the CPF using nonuniform sampling is used to analyse the higher order polynomial phase. In this paper, a sixth order polynomial is considered. It is proposed to estimate the instantaneous frequency using a polynomial with coefficients calculated from the coefficients of the phase polynomial obtained by CPF. The determined coefficients also constitute the set of distinctive features for a classification task. The proposed CPF-based classification method was examined for three common NLFM signals and one LFM signal. Two types of neural network classifiers: learning vector quantization (LVQ) and multilayer perceptron (MLP) are considered for such defined classification problem. The performance of both the estimation and classification processes was analyzed using Monte Carlo simulation studies for different SNRs. The results of the simulation research revealed good estimation performance and error-free classification for the SNR range encountered in practical applications.https://www.mdpi.com/1424-8220/22/21/8104NLFM signal classificationNLFM signal estimationcubic phase functionmulticlass classificationinstantaneous frequency rate |
| spellingShingle | Ewa Swiercz Dariusz Janczak Krzysztof Konopko Estimation and Classification of NLFM Signals Based on the Time–Chirp Representation Sensors NLFM signal classification NLFM signal estimation cubic phase function multiclass classification instantaneous frequency rate |
| title | Estimation and Classification of NLFM Signals Based on the Time–Chirp Representation |
| title_full | Estimation and Classification of NLFM Signals Based on the Time–Chirp Representation |
| title_fullStr | Estimation and Classification of NLFM Signals Based on the Time–Chirp Representation |
| title_full_unstemmed | Estimation and Classification of NLFM Signals Based on the Time–Chirp Representation |
| title_short | Estimation and Classification of NLFM Signals Based on the Time–Chirp Representation |
| title_sort | estimation and classification of nlfm signals based on the time chirp representation |
| topic | NLFM signal classification NLFM signal estimation cubic phase function multiclass classification instantaneous frequency rate |
| url | https://www.mdpi.com/1424-8220/22/21/8104 |
| work_keys_str_mv | AT ewaswiercz estimationandclassificationofnlfmsignalsbasedonthetimechirprepresentation AT dariuszjanczak estimationandclassificationofnlfmsignalsbasedonthetimechirprepresentation AT krzysztofkonopko estimationandclassificationofnlfmsignalsbasedonthetimechirprepresentation |