Estimating the Instantaneous Frequency of Linear and Nonlinear Frequency Modulated Radar Signals—A Comparative Study

Abstract

Automatic modulation recognition plays a vital role in electronic warfare. Modern electronic intelligence and electronic support measures systems are able to automatically distinguish the modulation type of an intercepted radar signal by means of real-time intra-pulse analysis. This extra information can facilitate deinterleaving process as well as be utilized in early warning systems or give better insight into the performance of hostile radars. Existing modulation recognition algorithms usually extract signal features from one of the rudimentary waveform characteristics, namely instantaneous frequency (IF). Currently, there are a small number of studies concerning IF estimation methods, specifically for radar signals, whereas estimator accuracy may adversely affect the performance of the whole classification process. In this paper, five popular methods of evaluating the IF–law of frequency modulated radar signals are compared. The considered algorithms incorporate the two most prevalent estimation techniques, i.e., phase finite differences and time-frequency representations. The novel approach based on the generalized quasi-maximum likelihood (QML) method is also proposed. The results of simulation experiments show that the proposed QML estimator is significantly more accurate than the other considered techniques. Furthermore, for the first time in the publicly available literature, multipath influence on IF estimates has been investigated.

Estimation and Classification of NLFM Signals Based on the Time–Chirp Representation

“…Compared to other methods of estimation of the IF, the method based on CPF shows a similar estimation quality. For example, comparing the obtained results with those presented in [ 2 ], it can be noticed that, for LFM, the MSE obtained using the CPF method for dB is smaller than for the QML method, which, according to [ 2 ], shows lower estimation errors than methods such as the backward finite difference (BFD) method, central finite difference (CFD) estimator, Kay estimator, estimators based on the Choi–Williams distribution (CWD) and pseudo-Wigner distribution (PWD). However, for a higher noise level, QML provides better results.…”

“…The MSE defined in this way allows for determining the estimation error for the entire signal (the entire pulse) and enabling the comparison of the obtained results with the results presented in the publication [ 2 ]. Figure 6 presents the MSE of estimation of the instantaneous frequency in various SNR conditions.…”

“…The analysis and processing of NLFM signals are exploited in a wide range of applications for example in Electronic Support Measures/Electronic Intelligence (ESM/ELINT), Electronic Warfare (EW), Electronic Reconnaissance (ER) systems, as well as in passive bistatic radar (PBR) [ 1 ]. Modern electronic intelligence and electronic support are designed to automatically distinguish the modulation type of an intercepted radar signal, which can be utilized in early warning systems or give more information about hostile radars [ 2 , 3 , 4 , 5 , 6 , 7 ]. Passive bistatic radar uses emissions from communications, broadcast, or radionavigation transmitters instead of dedicated, cooperative radar transmitters.…”

“…However, the most known quadratic T-F distributions, such as the pseudo Wigner–Ville distribution and the Choi–Williams distribution, contain cross-term components, and the estimation of the instantaneous frequency modulation is performed with unacceptable accuracy. Therefore, they are practically useless [ 2 ]. For analysis of the PPS, the high order ambiguity function (HAF) or the product HAF (PHAF) seems to be attractive.…”

Low‐sidelobe waveform design for integrated radar‐communication systems based on frequency diversity array

“…The traditional baseband waveform (such as LFM) has a high auto-correlation SLL. [32] Therefore, we select the NLFM signal with low SLL as the baseband waveform for angle resolution recovery. In contrast with the LFM signal, the NLFM signal has a much lower SLL [33].…”