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With the new system radar put into practical use, the characteristics of complex radar signals are changing and developing. The traditional analysis method of one-dimensional transformation domain is no longer applicable to the modern radar signal processing, and it is necessary to seek new methods in the two-dimensional transformation domain. The time-frequency analysis method is the most widely used method in the two-dimensional transformation domain. In this paper, two typical time-frequency analysis methods of short-time Fourier transform and Wigner-Ville distribution are studied by analyzing the time-frequency transform of typical radar reconnaissance linear frequency modulation signal, aiming at the problem of low accuracy and sen-sitivity to the signal noise of common methods, the improved wavelet transform algorithm was proposed.

The characteristics of modern complex radar signals penetrate into the time domain, frequency domain, airspace, two-dimensional transformation domain, which contains rich content; it is reflected in the subtle differences of the signal itself as well as in the characteristics and changes of the overall signal [

The time-frequency analysis method is the most widely used method in the two-dimensional transform domain. The time-frequency analysis method can reflect the time-varying nature of the non-stationary signal more accurately [

The literature [

The linear frequency modulation (LFM) signal is one of the modern radar signals that are frequently used with a simple structure. It obtains a large time-bandwidth product by the linear frequency modulation. It is a typical signal type that is widely used in pulse compression signals. The LFM signal has the advantage of Doppler shift insensitivity, which means that even if the Doppler shift of the echo signal is large, the matched filter still has the effect of pulse pressure [

Short-time Fourier transform (STFT) is a linear transformation, which is a typical representation of the current time-frequency analysis. The small calculation and conceptual simplicity make Short-time Fourier transform a widely used time-frequency analysis in engineering [

In order to introduce time-dependency in the Fourier transform, a simple and intuitive solution consists in pre-windowing the signal

where

The STFT may also be expressed in terms of signal and window spectra:

where

In contrast with the linear time-frequency representations which decompose the signal on elementary components, the purpose of the energy distributions is to distribute the energy of the signal over the two description variables: time and frequency. The starting point is that since the energy of a signal

we can interpret

which is an intermediary situation between those described by (4). As the energy is a quadratic function of the signal, the time-frequency energy distributions will be in general quadratic representations. Two other properties that an energy density should satisfy are the following marginal properties:

which mean that if we integrate the time-frequency energy density along one variable, we obtain the energy density corresponding to the other variable.

A time-frequency energy distribution which is particularly interesting is the Wigner-Ville distribution (WVD) defined as:

or equivalently as:

This distribution satisfies a large number of desirable mathematical properties, as summarized in the next sub-section. In particular, the WVD is always real-va- lued, it preserves time and frequency shifts and satisfies the marginal properties.

Wavelet analysis is a kind of time-frequency analysis aiming to describe the signal with time-scale plane based on the idea of replacing the representation of frequency domain with scale field, which has the characteristics of multiresolution analysis together with the ability to indicate the local characteristics of the signal. Wavelet analysis is a localized analysis method of time and frequency in which the size of time?frequency window is fixed but the shape can be adjusted [

The idea of the continuous wavelet transform (CWT) is to project a signal

where

The variable

The basic difference between the wavelet transform and the short-time Fourier transform is as follows: when the scale factor

Morlet wavelet is chosen as the wavelet basis function to extract the characteristic parameters of radar signals because of its good time-frequency characteristics; its expression is [

and its Fourier transforms is:

So:

The improved wavelet transform has two purposes: 1) transform the time signal into time-frequency domain instead of time scale domain by means of wavelet transform with kernel function of Morlet wavelet; 2) each parameter of the wavelet has definite physical meaning.

The improved Morlet basic wavelet is as follow:

In the formula,

The family of Morlet wavelet deduced from the mother wavelet by translations and dilations:

In the formula, the parameters

The wavelet transform using Morlet wavelet as kernel function can be used for time-frequency analysis of signals. Morlet wavelet is a double window function. The time window center

The time-frequency window is:

and

The modified Morlet wavelet approximation satisfies the admissible conditions, and

The function space composed of the function family generated by the improved Morlet wavelet function is equal to the function space generated by the original Morlet wavelet function family.

Without going into details about this representation we can see that the linear progression of the frequency with time is clearly shown in

The improved wavelet transform has introduced the scalable parameters in the window function to obtain the automatic resolution, that is, in the part of low frequency obtain the higher frequency resolution and the lower time resolution, and in the part of high frequency obtain the higher time resolution and the lower frequency resolution. Thus it is suitable for detecting the transient anomalies in the normal signal entrainment and shows its details, which is very useful for detecting the trip points of frequency coded and phase coded signal. And the effect of continuous wavelet analysis has not changed considerably with the existence of noise, which indicates that wavelet analysis is not sensitive to noise, as is shown in

Aiming at the problem of low accuracy and sensitivity to the signal noise of short-time Fourier transform and Wigner-Ville distribution, this paper proposed the improved wavelet transform algorithm. The results of simulation show that the performance of the extraction of the extraction of radar signal features which is based on the improved wavelet transform algorithm better than the others, and the method is feasible. The optimal feature extraction method used for different modulation signals is different. At present, feature extraction methods of complex radar reconnaissance signal proposed by researchers at home and abroad involve signal detection, parameter estimation and classification of modulation style. In the future, the characteristics of different coded modulation

signals will be studied in a systematic, comprehensive and in-depth way, and the optimal corresponding intra-pulse feature extraction method are expected in the multidimensional transformation domain.

This work is supported partly by National Natural Science Foundation of China under Grant No. 61301205 and No. 61571146, National Defense Based Science Research Program under Grant No. JCKY2013604B001. This paper is funded by the International Exchange Program of Harbin Engineering University for Innovation-oriented Talents Cultivation.

Zhang, W.X., Sun, F.L. and Wang, B. (2017) Radar Signal Intra- Pulse Feature Extraction Based on Improved Wavelet Transform Algorithm. Int. J. Communications, Network and System Sciences, 10, 118-127. https://doi.org/10.4236/ijcns.2017.108B013