Hybrid Integration for Range Migration Target based on Time-frequency Method

Li Pin，Ni Jing

（Nanjing Research Institute of Electronics Technology，Nanjing，210039）

Abstract：The detection ability of range migration target is a key factor related to radar system.Based on time-frequency analysis method，coherent integration is realized first in this paper，and then combined to binary time-frequency images；a hybrid integration algorithm for range migration target is proposed.This algorithm can not only avoid envelope compensation and Doppler ambiguity estimation，but also reduce SNR requirement for detection.The simulation results show the efficiency of the algorithm.

Key words：target detection，range migration，time-frequency analysis.

1 Introduction

With the development of high-speed and stealth technology，ordinary signal processing methods can’t meet detection demands for battlefield，especially high-speed target and small RCS target.Increasing integration time is an effective way to improve radar detection ability，but coherent integration methods require target in the same range-gate，which limits the time of coherent integration.

Lots of work has been done to solve integration problem of range migration target.Most experts use non-coherent integration method to improve SNR，which also bring out envelope compensation and range division problems；some experts use keystone transform to achieve coherent integration ，but this method is restricted byVelocity ambiguity and acceleration；other experts utilize targets’linear character in range-time plane ，use Hough transform to achieve coherent integration，but this algorithm is not only based on detection processing twice，but also depend on SNR.In this paper，target motion model is introduced first，then a new algorithm is present，which not only use time-frequency method to realize target coherent integration and non-coherent integration，but also complete target detection with the projection of binary image；finally，simulations are taken to show the efficiency of the algorithm.

2 Echo Model of Motion Target

Relative movement between target and radar is usually ignored in signal processing，but to high-speed target or small RCS target，integration time is long enough that relative movement can cross several range-gates.

Suppose radar transmission signal is LFM（linear frequency modulation）pulse：

Where t is the time of transmission pulse，0T is the pulse width，K is the LFM coefficient.The spectrum of a（t）can be expressed by

Suppose there is a point target of uniform motion，the echo can be expressed by

Where n is the number of pulse，fc is the carrier frequency，fd is the Doppler frequency，is the delay time of nth pulse，R0 is the initialize range，v is theVelocity，T is the PRF，the frequency spectrum after pulse compression is

Corresponding time-domain signal can be expressed by

The envelope of x（t，n）is a sinc function，and the location of peakValue is .Obviously，different transmission pulse has different time delay；and the location of peakValue shift，called range migration.

3 Hybrid Integration and Target Detection

Infected by target motion，the location of target peakValue after pulse compression is not in the same range gate，a new algorithm is present in this paper，and the flow chart shows as follow.

3.1 Range Gate Division

Suppose target integration time isTs，then max integration pulse number is

N_max=Ts×PRF

Suppose sampling frequency isfs，target’s maxVelocity isVmax，then the number of pulse number in the same range gate is

The number of range-gate can be expressed by

3.2 Time-Frequency Integration

Range gate is divided to gain max number of pulses energy by coherent integration.Time-frequency window isN_range，and nf=ceil（log2（N_range））NFFT=2nf，then

Where Si is the time-frequency image of i-th range gate，and Nt=N_max−N_range+1

3.3 Non-Coherent Integration

Moving target may cross several range gates，but Doppler information is focused in the time-frequency plane.For uniform motion target，the energy is focused in the same frequency-gate，non-coherent integration can be realized by

3.4 Linear Projection and Detection

Target energy of all range-gates concentrates in the same frequency-gate by step 3，and binary time-frequency image can be advanced through background estimation.1-D projection to frequency axis can gain energy of all pulses，and detection can be done.

4 Simulation

Suppose transmission signal is LMF pulse，PRF is 125Hz，bandwidth 800KHz，sampling frequency 1MHz，targetVelocity 950m/s，max pulse number is 120，Fig.2 shows pulse compression result of a single pulse，and SNR is −4dB.Fig.3 is the result of coherent integration results of 120 pulses at range 1999，SNR is about 8dB，which is far less than theoretic result（16.8dB），when target don’t have range migration.

Combine to analysis is chapter 3，120 pulses cross M=6 range gates，then N_range=20，NFFT=32.

Fig4～9 show the time-frequency Figure-s of range-gate 1996—2001.It’s clear that target energy separate in these images，and the SNR in a single image is too low to detect.

Fig.10 is the non-coherent integration result of all range-gate，after background noise estimation，binary time-frequency image shows target energy distribution in fig11.It’s not hard to find out that energy in frequency-gate 20 is much greater than other frequency-gates.

After 1-D projection to frequency axis，Fig.11 can be transformed to Fig.12，and all target energy is concentrated in frequency-gate 20.Compared to Fig.3，target detection can be improved by SNR.

5 Conclusion

A hybrid integration algorithm based on time-frequency analysis for high-speed and low RCS target is present in this paper.This algorithm achieves integration for range migration target，it not only avoid envelope alignment，but also keep away from target Doppler ambiguity.Yet accelerate target may bring high side-lobe in projection result，and then target detection may be impacted，this work will be developed in further study.