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In order to solve the recognition of polyphase code radar signal, this paper gives two methods based on Frank code, i.e. the high-order spectrum recognition method and the fractional Fourier transform (FRFT) method, by analyzing the micro characteristics of polyphase code signals in time and frequency domain respectively. And a recognition algorithm based on Wigner-Hough transform (WHT) is developed in this paper. We verify the validity of each method by computer simulation and give relative merits and demerits. A set of results demonstrate that the algorithm based on Wigner-Hough transform has better recognition performance in low signal-to-noise (SNR) than others.

In recent years, a class of polyphase code radar signals (Frank, P1, P2, P3, P4 code) which is derived from linear frequency modulation (LFM) have wide applications in field of radar anti-interference system. Combining the doppler tolerance features of LFM and high range resolution of phase encoding, polyphase code signals have excellent pulse compression performance [

Polyphase code signals have similar time-frequency characteristics with LFM signals. Referring to the methods of LFM recognition, a mass of research results have been acquired for polyphase code signals detection and parameter estimation. For example, paper [

In this paper, we focus on the detection and estimation of Frank code in polyphase code signals by high-order spectrum recognition method, fractional Fourier transform (FRFT) and Wigner-Hough transform (WHT) respectively. The detection based on high-order spectrum recognition method is easy to practice theoretically but difficult implementation on hardware design. The one based on FRFT is achieved by rotating coordinate axis to get the optimum status of signal gathering. It has an excellent filter performance. The detection and parameter estimation to polyphase code signals using WHT are done by taking example by detecting LFM signal using WHT. The recognition performance is great especially in low SNR.

Phase coded signal is a kind of pulse radar signal, usually expressed in the form of complex signal

where

Supposing a coding cycle is

The paper mainly uses Frank code as an example to carry on the simulation and the discussion.

The phase transition diagram for the Frank code when

Frank | |
---|---|

P1 | |

P2 | |

P3 | |

P4 |

The high-order spectrum recognition method and the FRFT recognition method are widely used in LFM and two-phase and four-phase coded signals, and they have been gradually applied to the polyphase code signal. The paper introduces the application of the two methods in the polyphase code firstly.

Perform a quadratic operation on Frank codes

Remove the mean after the quadratic operation, and then take the Fourier transform of operation results. From the following simulation,

But, the second-order and the fourth-order computing are not easy to achieve in the hardware design. The consumption of hardware resources of the detection system is very high when do the corresponding calculation and recording of multiphase code signals with certain pulse width. And the output of the Fourier transform of the Frank code doesn’t make sense for subsequent data analysis.

The Fractional Fourier Transform (FRFT) of the signal

where

The rotation angle is

The FRRT of the signal can be seen as the rotation of the axis of the signal on the time-frequency plane around the origin by counterclockwise rotation of the

gregation of signals at different orders [

The FRFT three-dimensional distribution of the Frank code signal is shown as

The bandwidth of the Frank code signal

The coding cycles of codes

The width of codes

The number of codes

The estimated value of carrier frequency

where

The time-frequency curve of the Frank code signal can be regarded as the time-frequency curve of the LFM signal shifted by a certain delay. So we can draw on the LFM signal detection method based on fractional Fourier transform [

Wigner distribution is a time-frequency analysis method, which is usually used to analyze the non-stationary signal. The Hough transform is a method for detecting the graphical features in image processing. The Frank code is detected by performing the Hough transform for the Wigner distribution results, and mean- while the parameters of the signal can be estimated [

The Hough transforms’ principle of extracting straight lines.

On any point in the image space

to transform it into a curve,

This

The time-frequency distribution of the detected signal is taken as an image, then using Hough transform to detect straight line in this image. This translates the problem of the detection and parameter estimation of the Frank code signal into the problem of searching for the local maximum and its corresponding coordinate in the parameter space. The time-frequency distribution of the Frank code signal is a number of parallel ridge lines. And it exhibited multiple peak points on the parameter plane after Hough transform [

The definition of signal’s WVD

Perform Wigner-Hough transform of the signal by a straight line equation,

In order to verify the effectiveness and feasibility of the method, using Frank code to do the following simulation analysis. The center frequency is

The two spectrum distribution figures can be got by performing the second- order and the fourth-order operation for Frank code and then doing Fourier transform after removing the mean value. They are shown as

The FRFT three-dimensional distribution of the Frank code signal is shown as (a) of

Due to phase quantization, the WVD distribution of Frank code is multi-ridge distribution on the Wigner time-frequency plane. The three-dimen- sional distribution of the signal through Wigner-Hough transform is shown as

When the noise is increased to

As is shown in

Non-stationary signal is one of the main research objects of modern signal processing, and there are many kinds of theoretical analysis methods for it. In this paper, it is introduced the characteristics of polyphase code in time and frequency domain, and the three kinds of recognition methods of polyphase code signal, i.e. high-order spectrum, fractional Fourier transform recognition method and recognition method based on Wigner-Hough transform. The effectiveness of each method is verified by simulation, and the method based on WHT has great performance in low SNR, Which can provide reference for the identification of multi-phase code radar signals.

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., Wang, B. and Sun, F.L. (2017) Recognition Method Based on Wigner-Hough Transform for Poly-Phase Code Radar Signal. Int. J. Communications, Network and System Sciences, 10, 128-137. https://doi.org/10.4236/ijcns.2017.108B014