Research of Hybrid Modulation Radar Signal

Kai-Feng Guo，Yun Lin，Meng Wang，Xiao-Chun Xu

(Unit 91635 of the Chinese People Liberation Army，Beijing，102249，China)

1 Introduction

In the high resolution radar system，phase coded signal and stepped frequency signal are the two most commonly used pulse compression signals［1－2］，and they have some features of one’s own respectively.For example，the ambiguity function of the phase code(PC)signal is mostly approximate pushpin shape with large time delay and high Doppler resolution ability，and the signal is also easy to generate and handle.Meantime it is easy to implement waveform agility.But when the echo signal and the matched filter mismatch with Doppler frequency，the filtering can’t get the effect of pulse compression，so it is suitable for the situation of small change with the target Doppler frequency.Stepped-frequency(SF)signal can obtain large bandwidth and high resolution one-dimensional range resolution by IDFT coherent processing［3－4］.Using this signal，the instantaneous bandwidth of receiver is relatively narrow，which will significantly reduce the hardware requirements of digital signal processing speed.But its accumulation period is relatively long and the system data rate is low，even with the same speed of the targets，its Doppler frequency shift of the echo signal are different，which will affect the effect of high resolution one-dimensional range，and it is often called Distance—Doppler coupling［5－6］.

The impact of Distance—Doppler coupling can be well mitigated through two different methods which is motion compensation and redesigning waveform.If the target velocity is estimated precisely，target motion can be used to compensate by removing the motion-induced phase terms.Thus，for non-cooperative targets in MMW SF radar，many motion compensation methods are presented based on velocity estimation.Two motion compensation methods based on time domain and waveform entropy were presented，but they have low estimation accuracy and are only effective in high SNR and low-speed moving targets［7－8］.An effective algorithm of motion compensation based on SF and Pulse Doppler system was presented，and the simulation results showed that this method have high compensation accuracy and good anti-noise performance.However，it will increase the complexity of radar system.

To sum up，the motion compensation has a large computation amount which is hard to be used in application.In Ref.［10－12］，they give three new kinds of waveform which can reduce the Distance—Doppler coupling.Therefore，according to the analysis of these references and different radar signals，a hybrid modulation signal with intra-pulse phase coded and extra-pulse stepped frequency(PCSF)is presented in this paper.It can overcome the shortcomings of the phase coded(PC)signal and the stepped frequency(SF)signal，and the simulation results have proved the conclusions.

2 Definition and Ambiguity Function of the PCSF Signal Waveform

2.1 Definition of the PCSF Signal Waveform

For the SF signal，if it wants to get a larger bandwidth，the frequency step Δf or the number of synthesis pulse N should be increased.To increase Δf，the pulse width T must be reduced，so it will affect the average transmit power of the radar.Increasing N will reduce the data rate of the radar system，which will exacerbate the problem of Distance-Doppler coupling.

The PCSF signal is a new hybrid modulation signal.Through the phase modulation with the subpulse of the stepped frequency signal， Δf changes with the phase coding sub-pulse width T1，and T=KT1，where K is the number of coding bits.So a larger Δf than ordinary SF signal can be gotten，and under the premise of the average transmitted power of a radar system to achieve the same bandwidth with fewer number of pulses，and solve the confliction among the distance，the bandwidth of the system and the data rate of the system output.

The analytical expression of the PCSF signal is as follows:

where uc(t)=()－1rect(t/T1);N is the number of pulses;Tris the period of the stepped sub-pulse;Δf is frequency step;T is stepped sub-pulse width;T1is the width of each bit of phase coded sub-pulse;K is code length，and T=KT1;cmis the phase code sequence，which commonly use Barker code sequence，Frank code sequence，P code sequence and so on in radar systems［1］.

The waveform of the PCSF signal is shown in Fig.1，where TPis the frame period of the PCSF signal.

2.2 Ambiguity Function of PCSF Signal

Signal’s ambiguity function［1］is an effective tool for the analysis of radar signal and the design of waveform，and it describes as launching a certain waveform under the condition of optimal signal processing，the performances of resolution measurement accuracy and clutter suppression for radar system.The classic definition of the ambiguity function is shown as follows:

Fig.1 Waveform of the PCSF signal

Substituting Eq.(1)into Eq.(2)，the ambiguity function of PCSF can be gotten，which is shown in Eq.(3).

Carrier frequency f0=94 GHz，frequency step Δf=40 MHz，sub-pulse width T1=0.13μs，stepped frequency sub-pulse use Barker code sequence with K=13，pulse repetition period Tr=20μs，pulse number N=13，the simulation result is shown in Fig.2.Under the same pulse repetition period，the same effective width and the same work width，the ambiguity function of stepped frequency signal is shown in Fig.3.

Fig.2 Fuzzy graph and time-frequency distribution image of PCSF signal

Fig.3 Fuzzy graph and time-frequency distribution image of SF signal

The comparison of the results between Figs.2 and 3，some conclusions can be gotten as follows:

1)The three-dimensional fuzzy diagram of the PCSF signal and SF signal are both composed by nonoverlapping fuzzy band，and between the parallel fuzzy bands there exists some blank stripes，and these blank stripes do not produce"itself clutter".However，the fuzzy diagram of the PCSF signal is closer to thumbtack shape，thus it has a higher two-dimension resolution of Distance-Doppler.

2)From the time-frequency distribution image，we can see that PCSF signal and SF signal are both have time frequency coupling characteristic，therefore the relative motion between the target and radar will affect the matching output signal of time-domain receiver，the attenuation extension and time-shifting of the signal.But under the same pulse repetition period，the same effective width，the same work width，PCSF signal’s time frequency coupling effect is much smaller than that of SF signal;therefore PCSF signal has a much lower Distance-Doppler sensitivity.

3)PCSF signal and SF signal both have distance and doppler ambiguity sidelobe，which come from other ambiguity bands.But because PCSF signal adopts hybrid modulation mode，which will effectively inhibit the distance and Doppler ambiguity side lobe，and make distance and Doppler ambiguity side lobe decay faster，hence PCSF signal has a better clutter suppression ability.

3 The PCSF Signal’s Processing Method

PCSF signal is a hybrid modulation signal，which combines phase coded modulation during the pulse with stepped frequency modulation between the pulses;the processing method of this signal should also combine the processing methods of phase coded pulse train signal with the stepped frequency pulse train.Therefore，in this paper，a solution method which can get high resolution range profile through pulse compression is presented;the block diagram of signal processing is shown in Fig.4.

Fig.4 Block diagram of PCSF signal

After frequency mixing with the local oscillator signal which has the same carrier frequency as the transmitted pulse，the PCSF signal’s echo is processed in each pulse repetition period by using matched filtering.Through sampling the compressed signal，a pulse sequence compose of N pulses can be gotten，and then handle with IDFT coherent processing to this pulse sequence.Finally，the high resolution range profile of the target can be gotten.

Assuming that the parameter of PCSF is shown as follows:Carrier frequency f0=94 GHz，frequency step Δf=40 MHz，sub-pulse width T1=0.13μs，stepped frequency sub-pulse use Barker code sequence with K=13，pulse repetition period Tr=20μs，pulse number N=13.The target exists three strong scattered points，respectively in 50 m，51 m，51.8 m.Fig.5 shows the high resolution one-dimensional range profile when the target’s radial velocity is v=0.We can get the conclusion that the high resolution one-dimensional range profile of PCSF signal can clearly distinguish these three scattered points of the target，and the location of the target range profile is also accurate，so the method as shown in Fig.4 to process PCSF signal is feasible，effective and accurate.

Fig.5 PCSF signal’s one-dimensional range profile when v=0

4 Target Imaging Analysis on PCSF Signal’s Relative Movement

Fig.5 shows that the PCSF signal has the problem of Distance-Doppler coupling，so the radial motion of the target will affect the target’s high resolution onedimensional range profile，and the main influence are the attenuation，divergence and time shift of the range profile.Here，divergence phenomenon has the biggest influence on target identification，defining divergence factor P as:

Therefore it can be seen that target’s radial motion makes PCSF signal’s high resolution onedimensional range profile extend P distance resolution cells which will lead the distortion of range resolution，the reduction and divergence of range profile peak，and even producing“spurious peak”.All of these will seriously affect the recognition ability of the target，so when designing the PCSF signal waveform，we should consider to reduce the P value as much as possible.

According to Eq.(4)，in order to reduce P value，we should reduce the number of pulse train’s media-pulse and increase pulse repetition frequency.PCSF signal’s sub-pulse adopts phase coded modulation，so comparing with SF signal，PCSF signal can obtain larger stepped frequency Δf.Under the same range resolution，the number of pulse can be reduced greatly，and the data rate of the radar system will rise，so PCSF signal has much lower Doppler sensibility.

If P≤1/4，the condition of range profile does not need speed compensation，substituting for Eq.(4)will obtain the target radial velocity which is shown as follows:

Based on the preceding simulation parameters，using Eq.(5)can obtain the tolerated speed range of PCSF signal is v≤277 m/s.

In Fig.6，when the target’s radial velocity is v=200 m/s，the high resolution one-dimensional range profile of PCSF signal and SF signal are shown.In Fig.6，the solid line represents the range profile of the static target，while dashed line represents the range profile of moving target.It shows that，target movement will produce the migration and distortion of range profile.With the increase of the target radial velocity，the peak value of the SF signal’s one-dimensional range profile will reduce and diverge which will hardly be used for the detection and recognition for target.While PCSF signal’s high resolution one-dimensional range profile has slightly expansion，but the scatter points are still clearly visible.Therefore，the motion of target does not affect the matching identification.The simulation result shows that comparison with the SF signal，PCSF signal’s has much better Doppler performance.

Fig.6 Signal’s one-dimensional range profile when v=200 m/s

5 Conclusions

In this paper，a new hybrid modulation signal which is named as PCSF signal is presented;it combines an intra-pulse phase coded with extra-pulse stepped frequency.The math model，waveform，parameter，ambiguity function，processing method and Doppler performance are analyzed in detail.PCSF signal adopts intra-pulse and extra-pulse two-level modulation mode，which can get a higher stepped frequency than that of SF signal，realize the same equivalent bandwidth with less pulse number，and solve the problem of conflicting among the stepped frequency.It also decreases the number of pulse，and enhances the average power.Under the premises of a certain range resolution，this method not only raises the data rate of radar system，but also reduces Doppler sensitivity with a good prospect.Therefore，this new signal can be widely used in radar system.However，in order to obtain accurate distance information，or if the target has a very large radial velocity，the speed compensation algorithm should be gone further study.

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