转发干扰下DS/FH混合扩频测控信号检测性能

杨文革，路伟涛，卞燕山，洪家财

（装备学院，北京101416）

转发干扰下DS/FH混合扩频测控信号检测性能

杨文革，路伟涛，卞燕山，洪家财

（装备学院，北京101416）

分析直扩/跳频（DS/FH）混合扩频测控信号在干扰环境下的性能对该新测控体制的研究具有重要的意义。推导了转发干扰环境下DS/FH测控信号的检测概率和虚警概率表达式。以Matlab/Simulink为平台搭建了检测性能仿真系统，对检测概率、主副旁瓣比和相关系数进行了仿真分析，指出只要转发时延小于一个跳频驻留，就能实现“欺骗”干扰，验证了理论推导的正确性，为进一步研究提供了参考。

DS/FH；TT＆C；转发干扰；虚警概率；主副旁瓣比；相关系数；检测性能

1 Introduction

Combining the advantages of Direct Sequence Spread Spectrum（DSSS）system and Frequency Hopping Spread Spectrum（FHSS）system，DS/FH hybrid spread spectrum system has high viability and good reliability in complexly electronic environment，which is deemed to be best antijamming system for TT＆C.The synchronization of DS/FH signals for TT＆C has been analyzed to a certain degree in AWGN channel［1］，which is notenough to demonstrate its superiority on DS or other systems.In order to find out pertinent anti-jammingmeasures and offer advices for setting DS/FH system parameter［2－3］，it is necessary to explore its performance under jamming.

Aswe all know that DS/FH hybrid spread spectrum system is hardly interfered by blanket jamming because of its high processing gain.Repeater jamming is all of the same as the real signal but time delay or Doppler frequency，so it can obtain the system′s processing gain and interfere victim′s receiver effectively with lesser jamming power，which indicates great threat.Repeater jamming isusually based on DRFM（Digital Radio Frequency Memory），by current types ofwhich enough delay could be obtained for TT＆C signals［4］.

Reference［5］analyzed respectively the performance of acquisition and demodulation，converting jamming effect to the degradation of SNR，but the supposition that repeater jammingwas a reverse replica is not prevalent all the time.The effect of repeater jamming depends on the relative time delay，which is deemed to be not better exceed PN code chip duration［5－6］，but the reality is that the receiver doesn′t actually know the code phase of the real signal and makes judgment only by peak correlation value.When the relative time delay is shorter than chip duration，the existence of repeater jamming will promote acquisition of the signal if there is no further jamming measures［7］.

Though repeater jamming has partial correlation with local PN code［8］for TT＆C signals，partial peak correlation value is possibly large enough to affect receiver′s judgment and deteriorates the performance of acquisition，because the jammer could increase the power of interfering signal.So the relative delay time should be less than hop frequency duration other than chip duration to obtain effective jamming.Besides probability of detection and false alarming，PSLR（Peak Side Lobe Level Ratio）and correlation coefficient could also be used as parameters to characterize effect of jamming.

Based on former study，the performance of detection of DS/FH signals for TT＆C is discussed here.This paper is organized as following.Section 2 introduces the detection and acquisition model，simulation parameters are introduced in section 3，including probability of detection and false alarming，PSLR as well as correlation coefficient.Some cases are simulated in section 4，and conclusions are presented in last section.

2 Acquisition and Detection Model

Assuming that local hop frequency has synchronized with the receiver signals，the problem turns to be the detection performance of DSSS under repeater jamming.Correlation operation and square rule are usually adopted in the model，justas shown in Fig.1，where T is integral time，equaling to one period of the stochastic code usually.

Fig.1 Acquisition and detection for DSSS图1直扩捕获检测原理图

The received signal r（t）and local intermediate frequency signal l（t）are：

where s（t）is real signals and j（t）is repeater jamming signal；n（t）is Gausswhite noisewith limited band whose mean value is zero and two-side power spectral density is N0/2；P is signal power，and D（t）is transferred data with 1 as assumed value in acquisition phase；Pn（t）is stochastic codes，and m codes is adopted here；fIFis intermediate frequency；fdis remaining Doppler frequency after coarse acquisition withθSas remaining phase；J is jamming signal power with fJas frequency andθJas phase；τandτ′are real time delay and relative time delay，respectively.

3 Simulation Parameters

3.1 Probability of detection and false alarm ing

whereρequals toΔτ/Tc－［Δτ/Tc］，［·］denoting the integer portion of a number.N is the length of Pn（t）and Tcis chip duration of Pn（t）.

Assumingτ＝kTc＋ε，0≤ε≤Tc，τ′＝k′Tc，k，k′is an integer，namely the real signaland repeater jamming have integral chip delay time，fJ－fIF＝fd，

So themean value of~J，which is the peak value of the correlation between repeater jamming and local signal is：

Equation（7）shows that there is always peak of correlation between repeater jamming and local signal，whose height depends on jamming power and relative delay time τ′.Themore the jamming power is and the less the relative delay time is，the higher the peak is.It is because of existence of the peak that repeater jamming increases probability of false alarming remarkably，deteriorating system′s performance，but doesn′t affect probability of detection.Therefore it is doable to study effectof repeater jamming by analyzing changes of probability of false alarming.Repeater jamming is all the same as the real signal but the time delay，so peak after correlation must have jitter too，which is supposed as that of real peak in（5）.Only special case whenε＝0 is discussed here.

Here come the two hypotheses：

It is easy to see that the outputof the complex correlator nearly obeys Rice distribution，the probability density function of decision variable x＝｜z｜2is［9］：

Here are obtained the probability of detection，Pd，and false alarming，Pfa，of DS/FH signal for TT＆C under repeater interference：

where Ec/N0is chip signal power to noise power density ratio，C is normalizing threshold.Considering range of normalizing threshold［10］and existence of interference，it is reasonable to set10 as the value of C，which nearly is the value in AWGN channelwhen Pfais10－3and Ec/N0is－10 dB-Hz.

3.2 PSLR and Correlation Coefficient

The effectof jammingwasgained by deteriorating the correlation performance，because its existence doesn′tonly reduce the realmain lobe，but increases side lobes. Repeater jamming is so alikewith the real signal that they are highly correlative with each other，and there are two peaks in correlation figure，just as shown in Fig.2，in which the real one is located at nearly 150 chips.Thus the study of changes in correlation under jamming is ofgreat importance.

Fig.2 Correlation value under different condition图2 不同环境下的相关图

where f（Δτi，Δfdj）and g（Δτi，Δfdj）stand for Time-Doppler two-dimensional correlation figure.

PSLR stands for the peak of side lobe andmain lobe ratio in correlation figure，defined in（12），which describes effect of jamming on correlation.The smaller the PSLR is，the better the performance is.PSLR equals to－20lg N in ideal situation，and approximately is－48 dB when N＝255.

Usually used in study of imaging radar to evaluate effect of jamming，the Correlation Coefficient（CC）describes the correlation degree between two images which are correlation figures before and after being jammed. Similarly，correlation coefficient can be adopted here，defined in（13）.The more closely the value of CC approaches 1，the less the jammed effect is.Only time dimension is considered here.

4 Simulation and Analysis

The aforementioned deduction is simulated in numerical and Mote Carloways here based on Matlab/Simulink. In order to lower the sampling frequency and simulation time，the period of stochastic code，T，is set to 1 ms，moreover，the remaining Doppler frequency after coarse acquisition and T have relationship of fd*T＝0.3.It surelymakes no difference to conclusion under these assuming factors.Ec/N0is set to－10 dB-Hz in the following simulations.

Fig.3 Probability of false alarming versus relative time delay with different JSR图3 不同时延下的虚警概率

4.1 Probability of false alarm ing

As shown in Fig.3，Pfanearly equals to 0 with relative delay timeτ′less than chip duration，denoting jamming doesn′t worsen system′s performance，but promotes the acquisition of real signals；Pfaincreases quickly up to 1 whenτ′is littlemore than chip duration，because repeater jamming obtains almost all the processing gain comparing real signal，which results in the highest jamming power；peak side lobe slowly decreases withτ′increasing，because FH pattern delays largely and only partial correlation exists between repeater jamming and local PN code，that iswhy Pfakeeps decreasing.Whenτ′in-creases to hop duration，FH pattern of repeater jamming is completely stagger with that of local signal，so repeater jamming can′t be dehoped and deteriorates to common blanking jamming，then Pfais back down nearly to 0 when JSR is not large enough.

Fig.4 shows that Pfaalways approximately equals to 0 whenτ′is little，here just the special caseτ′＝0 is considered.Repeater jamming doesn′t deteriorate system′s performance，contrarily promotes acquisition in this situation.Whenτ′becomes a little larger than chip duration，Pfais increasing with JSR larger and larger. Moreover，the longer repeater jamming delays，themore power needed to increase Pfa，because partial correlation peak is smaller under the same conditions when relative delay time is larger.

4.2 PSLR and Correlation Coefficient

Fig.5 shows that the correlation coefficientand PSLR are almost the same valuewith thatof no jamming situation whenτ′is smaller.The larger the JSR is，themore slowly the performance get better with increasingτ′.When jamming power is little enough，PSLR is around－20 dB in Fig.5，which hasmuch differencewith theoretical value（－48 dB），because of the existence of noise.

Fig.5 Correlation coefficientand PSLR versus relative time delay with different JSR图5 不同时延下的相关系数

Fig.6 Correlation coefficient versus JSR with different relative time delay图6 不同干信比下的相关系数

Fig.6shows that correlation coefficient is decreasing while PSLR is increasing with JSR becoming larger and largerwhenτ′is less than hop duration.Correlation co-efficient and PSLR could be worsened with large enough jamming power whenτ′exceeds hop duration，because repeater jamming has deteriorated to common blanket jamming now.

5 Conclusions

This paper analyzed the performance of DS/FH signals for TT＆C under repeater jamming.Existence of repeater jamming will promote acquisition of real signal when relative delay timeτ′is less than chip duration. Whereas FH patterns of repeater jamming and local signalswillmiss a little and become partially correlativewith each other whenτ′is a little larger than chip duration，but as long as the jammer enhances jamming power enough，it is also possible toworsen system′s performance，including Correlation Coefficient decreasingwhile Pfaand PSLR increasing quickly.Ifτ′is too large，FH pattern willmiss somuch and peak of partial correlation will become so little or even to zero that repeater jamming will deteriorate to common blanket jamming which is to be spread seriously by DS/FH system and couldn′t interfere effectively.

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Biography：

YANG Wen-ge was born in Jinxi，Jiangxi Province，in 1966.He received the B.S.degree from National University of Defense Technology，the M.S.degree from Beijing University of Aeronautics and Astronautics and the Ph.D.degree from Beijing Institute of Technology in 1994，1997 and 2000，respectively.He is now a professor and also the Ph.D.supervisor.His research concerns TT＆C and radar signal processing.

杨文革（1966—），男，江西金溪人，1994年于国防科技大学获学士学位，1997年于北京航空航天大学获硕士学位，2000年于北京理工大学获博士学位，现为教授、博士生导师，主要研究方向为航天测量与控制、雷达信号处理；

LUWei-taowas born in Xihua，Henan Province，in 1985.He received the B.S.degree from Peking University in 2008.He is currentlyworking toward the Ph.D.degree.His research interests include TT＆C and interfermetry technology.

路伟涛（1985—），男，河南西华人，2008年于北京大学获学士学位，现为博士研究生，主要研究方向为航天测控、干涉测量技术；

Email：lwteecspku＠126.com

BIANYan-shan was born in Hubei Province，in 1986.He received the B.S.degree from Wuhan University and the M.S.degree from National University of Defense Technology in 2008 and 2010，respectively.He is currently working toward the Ph.D.degree.His research interests include signal processing and image processing.

卞燕山（1986—），男，湖北人，2008年于武汉大学获学士学位，2010年于国防科技大学获硕士学位，现为博士研究生，主要研究方向为信号处理、图像处理；

HONG Jia-caiwas born in Anhui Province，in 1967.He received the M.S.degree and the Ph.D.degree from Beijing University of Aeronautics and Astronautics in 1996 and 2002，respectively. He is now an associate professor and also the instructor of graduate students.His research concerns TT＆Cand interfermetry technology.

洪家财（1967—），男，安徽人，1996年、2002年于北京航空航天大学获硕士学位和博士学位，现为副教授、硕士生导师，主要研究方向为航天测控技术、干涉测量技术等。

Detection Performance of DS/FH Hybrid Signals for TT＆C under Repeater Jamm ing❋

YANGWen-ge，LUWei-tao❋❋，BIAN Yan-shan，HONG Jia-cai
（The Academy of Equipment Command＆Technology，Beijing 101416，China）

Studying the performance deterioration of DS/FH signals for TT＆C（Telemetry Tracking＆Command）in interfered environment is of great importance to this novel system.Expressions for probability of detection and false alarming of DS/FH（Direct Spread/Frequency Hopping）signals for TT＆C under repeater jamming are deduced.The probability of false alarming，PSLR（Peak Side lobe Level Ratio）and Correlation Coefficient are simulated and analyzed with different configuration of DS（Direct Spread）and FH（Frequency Hopping）spreading gain based on Matlab/Simulink.It is concluded that victim′s receiver is suffered“deception jamming”as long as relative delay time is less than frequency hop duration，which denotes correctness of deduce and offers references for following work.

DS/FH；TT＆C；repeater jamming；PFA；PSLR；correlation coefficient；detection performance

10.3969/j.issn.1001－893x.2013.01.004

TN973.2；V55

A

1001－893X（2013）01－0016－06

❋Received date：2012－06－21；Revised date：2012－10－23

2012－06－21；修回日期：2012－10－23

❋❋Corresponding author：lwteecspku＠126.com通讯作者：lwteecspku＠126.com