Fuzzy Jamming Pattern Recognition Based on Statistic Parameters of Signal’s PSD

NIU Ying-tao(牛英滔)，YAO Fu-qiang(姚富强)，CHEN Jian-zhong(陈建忠)

(Nanjing Telecommunication Technology Institute，Nanjing 210007，Jiangsu，China)

Introduction

During past 30 years，a variety of wireless communication systems was widely deployed.Since the wireless channel is open，the communication systems have to face all kinds of man-made and natural interference.These interferences，especially the malicious jamming has severe effect on reliability and efficiency of communication［1］.If the jamming pattern can be recognized and different anti-jamming strategies for different jamming patterns can be exploited in the communication process，the reliability and efficiency of communication can be improved prominently［2］.Currently，literatures on jamming pattern recognition are rather limited.Ref.［3］introduced a jamming pattern recognition algorithm based on high order accumulation and neural network，and it extracted high order accumulation as the characters and recognizes jamming pattern by neural network.Ref.［4］proposed a compound jamming pattern recognition algorithm by fast independent component analysis(FICA)and support vector machine(SVM).Ref.［5］extracted characters by wavelet packet decomposition，and then SVM was used to classify the jamming.Ref.［6］exploited thirteen characters to recognize several jamming patterns and their modulations in direct sequence spread spectrum(DSSS)system.Ref.［7］investigated the separation and recognition of four jamming patterns and two kinds of communication signals based on FICA.The literatures mentioned above investigated the jamming pattern recognition in complex electromagnetic environment preliminarily. But， they have many shortcomings，such as high complexity，few kinds of recognized jamming patterns，etc.Furthermore，some of them can only work effectively in special system，or recognize special jamming pattern.Therefore，practical application of these algorithms is restricted.

This paper proposes a fuzzy jamming recognition method based on statistic parameters of received signal’s power spectral density(PSD).It can recognize single-tone jamming (STJ)，multi-tone jamming(MTJ)，narrow-band jamming(NBJ)，pulse jamming(PJ)，broad-band noise jamming(BBNJ)，frequency hopping jamming(FHJ)，sweep jamming(SJ)，and no jamming(NJ)considered as a jamming pattern，in wireless communication system.First，the received signal in time domain is transformed to PSD in frequency domain，and its shape factor and skewness is calculated.After training by using some jamming samples，the mean center and variance of each jamming pattern are found out.Then，an exponential fuzzy membership function is used to calculate the membership value of the recognized sample.The jamming pattern of received signal is recognized by using the maximum membership principle.

1 System Model

1.1 Block Diagram of System Model

An intermediate frequency communication system model is adopted in this paper.Its block diagram is shown in Fig.1.The binary information sequence from random information source is modulated as base-band QPSK signal.The base-band QPSK signal is modulated as intermediate frequency signal，and then the intermediate frequency signal is transmitted to the wireless channel.The intermediate frequency signal is added additive white Gaussian noise(AWGN)as ambient noise and the jamming is also added to the communication signal.The discrete-time received signal can be given as

where s(n)denotes the communication signal，v(n)denotes AWGN，J(n)is the jamming signal.The received signal is preprocessed in receiver firstly，and the jamming pattern is recognized then.

1.2 Common Jamming Patternsin Wireless Communication

Common jamming patterns in wireless communication systems mainly include STJ，MTJ，NBJ，PJ，BBNJ，FHJ，SJ and NJ［2］.They will be investigated in this paper.Their characteristics are introduced briefly.

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STJ is a carrier with single frequency.It is the simplest jamming pattern which can jam one communication channel.It can be written as

where WJ，fJand θ are the jamming signal’s power，carrier frequency and initial phase，respectively，θ∈［0，2π)，and θ is uniform distribution.

MTJ can be considered as a combination of several STJ with equal power.It can jam several channels at the same time.It can be expressed as

where NJis the carrier frequency number of MTJ，usually NJ≤10 to achieve jamming effect［2］，fiand θiare the ith carrier frequency and initial phase of MTJ，respectively.

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BBNJ is also called as barrage jamming.It is one of the most popular jamming patterns.It adds noise energy to the whole band of communication.BBNJ can increase receiver’s noise level，decrease SNR，even intermit communication.It can be generated by AWGN usually and written as

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where x(t)is AWGN with probability distribution function

where σ2is variance of x(t)，and σ2=1 usually.

CRSwNP呈现高度异质性特征，临床表型通常无法洞察疾病本质，而内在型是建立在细胞、分子和免疫机制基础上的分型，也就是CRSwNP的发病机制。然而，内在型非常复杂，目前研究尚不透彻，通过CRS内在型的探索，可能找到特异性个体病情发展的关键因素，即某些特定的生物学分子标识物，以这些标志物为靶标可实现临床上对于CRSwNP个性化的精准治疗[15，17]。

where Filter［·］denotes filter operation.

PJ is a kind of outburst jamming.The jammer emits very large power in a very short moment.It is characterized by large peak power，broad jammed bandwidth and short jamming time.The ideal PJ can be written as

where δ(t)denotes Kronecker function.But，the practical pulse signal occupies some width of time.It can be written as

where Dτ(t)is a rectangle pulse with width of τ=t2－t1，T is its period，A is its amplitude，U(t)is a step signal.

SJ can jam very broad band in a short time by sweeping within wide frequency scope using single-tone signal or narrow-band signal.If T is the sweep period，fHis the highest frequency of sweeping，fLis the lowest frequency of sweeping，the linear SJ can be given as

FHJ can jam communication signal in a frequency hop set by a rapid hopping single-tone or narrow-band signal in the frequency hop set.It can jam several channels in a short time，and can be written as

where m(t)is a random noise usually，fnis the carrier frequency in frequency hopping set，φ(d，t，Δf)is the modulation phase，This the hop period which is reciprocal of hopping speed.

2 Jamming Pattern Recognition Algorithm

2.1 Preprocessing of Received Signal

The clearance factor is a measure of relative intensity of the peak value to the square root amplitude of PSD.It can be written as

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Firstly，the received signal’s PSD has to be generated.To reduce computational complexity，a modified periodogram is used to calculate the PSD of received signal.If the length of received signal r(n)is N，the modified periodogram can be written as［8］

NBJ can be considered as BBNJ passed narrowband filter.Its power focuses on a part band of wireless communication.It can be given as

where wlis a window sequence，Fsis the sampling frequency.Hamming window is used in this paper.

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Secondly，smoothen the PSD of received signal.One of the shortcomings of the periodogram is large fluctuation in the generated PSD.Hence，PSD needs to be smoothened.To lower the processing delay，a moving average filter is exploited，which can be written as

where Ssmooth(fn)is the smoothened PSD.In this filter，M is an important parameter.An excessively small M generates poor effect on the smoothening，while an excessively large M yields a good effect on the smoothening，but also produces a high error in the PSD with large curvature.In this paper，M=2.

Finally，the communication signal PSD should be eliminated possibly in order to reduce communication the signal’s effect on the jamming pattern recognition.Theoretically，it can be eliminated in frequency domain by subtraction of the communication signal’s PSD template Sqpsk(fn)from the smoothened PSD Ssmooth(fn)of received signal.However，the direct subtraction can only eliminate 40% ～50%of communication signal’s PSD because of the random fluctuation of PSD.The authors improved the algorithm based on the following aspects.

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1)The PSD sample data whose amplitudeis greater than Sqpsk(fn)can be thought as the overlap of PSD of communication signal and jamming signal.The jamming signal PSD can be obtained by direct subtraction the PSD template of communication signal from the smoothened received signal’s PSD.

2)The PSD sample data whose amplitude is less than Sqpsk(fn)can be processed by two approaches.If the PSD sample’s amplitude is larger than 1/2 of Sqpsk(fn)，the jamming signal PSD can be obtained by direct subtraction the PSD template from the received signal’s PSD.Otherwise，the PSD sample is taken as the jamming signal PSD.

Some simulation results show that the algorithm is simple and reliable.It can eliminate 65% ～70%energy of communication signal.

2.2 Fuzzy Jamming Pattern Recognition Algorithm Based on Shape Factor and Skewness

The impulse factor of PSD is a measure of relative intensity of peak value to mean value of PSD.It can be given as

2.2.1 Selection and extraction of jamming pattern’s characters

As mentioned above，the first problem of jamming pattern recognition is character extraction，which can reflect the characteristic of jamming pattern.All kinds of statistic parameters can reflect the whole characteristic of signal for classification and recognition.Furthermore，dimensionless statistic parameters should be exploited to avoid the effect of signal’s dimension on the recognition.Based on the above points，the authors investigated some common dimensionless statistic parameters［9］，such as shape factor，impulse factor，crest factor，skewness，kurtosis and clearance factor.These six parameters are introduced as follows.

The shape factor is a measure of relative intensity of effective value to mean value of PSD.It can be defined as

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where SJ，evand SJare the effective value and mean value of PSD respectively.They can be expressed as

where N is the sample number of PSD，SJ(fn)is the jamming signal PSD after elimination communication signal PSD.

Compared with the general definition of pattern recognition，the definition of jamming pattern recognition can be given as follows.According to the jamming pattern’s characters or attributes，the jamming pattern is identified automatically by machine system centralized with computer.Similar to general pattern recognition，it includes three basic aspects，i.e.choice and extraction of jamming pattern’s character，learning and training and classification and recognition.

The crest factor of PSD is a measure of relative intensity of peak value to effective value of PSD.It can be written as

The skewness of PSD is a measure of the asymmetry of the PSD around the PSD’s mean.It can be defined as where σJis the standard deviation of SJ(fn).

The kurtosis is a measure of the probability distribution of PSD bias against normal distribution.It can be defined as

The preprocessing of received signal transforms the received signal in time domain to PSD in frequency domain and eliminates the communication signal PSD possibly to reduce communication signal’s influence on jamming pattern recognition.To accomplish these two functions，the preprocessing signalincludesthree steps，i.e.PSD generation，smooth of PSD and elimination of communication signal’s PSD.

where SJ，srais a square root’s amplitude.It can be defined as

To compare the classification ability of six statistic parameters mentioned above，100 jamming samples of each jamming pattern are generated randomly from 7 to 15 dB in JSR，jamming-to-signal ratio.Then，the six parameters are calculated respectively according to Eq.(13)～(17).The ranges of six parameters are shown in Table 1.

From Table 1 each parameter’s differentiation for the jamming pattern can be found.The impulse factor has a good differentiation to STJ and MTJ.But，its distributions for the other jamming patterns have considerable overlap.The crest factor has poor differentiation to NBJ and FHJ，BBNJ and SJ.The kurtosis has poor differentiation to NBJ，BBNJ and SJ.The clearance factor has excessively large range and its distributions for different jamming patterns have some overlap.Comparatively，the shape factor and skewness have good differentiation to various jamming patterns and little overlap of distribution.Hence，the shape factor and skewness are exploited as the characters of jamming patterns recognition.

Table 1 PSD statistic parameters of common jamming pattern

To illustrate the difference of eight jamming patterns which is reflected by two-dimensional character S=(Sx，Sk)，plot of character distribution is generated as Fig.2 by 100 jamming samples of every jamming pattern within JSR=0～15 dB.Sxand Skdenote shape factor and skewness respectively.

式中：Dx、Dy分别为泥沙扩散系数沿x、y方向的取值；s为含沙量；Fs为底部冲刷函数，采用切应力理论表达式如下：

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带壳、不带壳烘焙种籽衣提取液全波长扫描结果如图 5-a和图 5-b。所有样品吸收峰波长都位于274～279 nm之间。其中，未处理种籽衣提取液吸收峰波长为275.5 nm，吸光值为1.00；带壳烘焙40 min种籽衣提取液吸收峰波长为275.0 nm,吸光值最高1.13；不带壳烘焙20 min种籽衣提取液吸收峰波长为278.5 nm，吸光值为1.12。说明烘焙过程中活性成分种类以及含量是发生变化的。Alasalvar等[26]研究的榛子种籽衣提取物吸收峰波长为282 nm，说明两者活性成分较为接近。

2.2.2 Pattern recognition based on exponential fuzzy membership function

Figure 2 shows that the other jamming patterns have clear confines except PJ has little overlap with SJ.Especially，STJ and MTJ are far from the others.Thus，(Sx，Sk)can reflect the difference of jamming patterns clearly.

The most ordinary pattern recognition uses the method based on distance.First，the mean center or median center Ci(k)of each jamming pattern’s character is calculated.Then，the distance between the recognized sample Z and ith center is calculated as follows

Fig.2 Characteristic distribution of jammingthe distance between recognizing sample and the center

where SZ(k)denotes kth character of sample Z.Eq.(18)denotes Manhattan distance，Euclidean distance and Chebyshev distance respectively，if m=1，2，∞.Finally，the jamming pattern is recognized according to of each jamming pattern.However，although the jamming pattern is determinate，the boundary of each jamming pattern’s distribution can not be determined rigorously because different parameters of jamming and JSR induce great difference in shape and range of each jamming pattern’s character distribution.It leads to the fuzziness of jamming pattern recognition.Therefore，it is not reasonable that a point of center represents the character distribution of one jamming pattern.Moreover，though the character distribution of each jamming pattern is fuzzy，it is difficult to determine the fuzzy membership and kernel function of jamming pattern for one jamming sample.Hence，an exponential fuzzy membership function is exploited［10］，

where μiis the fuzzy membership of a recognized jamming sample Z to ith jamming pattern，SZ(k)denotes kth character of sample Z，Ci(k)and σ2i，kdenote kth character mean center and variance of ith jamming pattern.In this paper，there are two characters and K=2.It can be seen that both the distance between sample and center of jamming pattern and the variance of training samples’characters are considered in the exponential fuzzy membership function.It is simple and clear，and needs not to determine the weight factor，correlation matrix，etc.After the fuzzy membership of recognizing sample Z is found out，the jamming pattern of sample Z can be recognized by the maximum membership principle

where Zjis jth jamming pattern，N1is the number of jamming patterns.

To sum up，the block diagram of jamming pattern recognition is shown in Fig.3.After the received signal preprocessing which includes PSD generation，PSD smooth and communication signal PSD elimination，the shape factor and skewness of recognized jamming samples are calculated respectively.Before the recognition，the characters have to be trained by using some samples for each jamming pattern，and the mean and variance of each character have to be calculated.After training，Eq.(19)can be used to calculate the fuzzy membership of recognized sample，and Eq.(20)can be used to recognize the jamming pattern.

Fig.3 Block diagram of jamming pattern recognition

2.3 Computation Complexity Analysis

The computation complexity of the proposed algorithm can be estimated according to the algorithm principle.If the length of received signal sequence is N，it is easy to find that the computation complexity of the proposed algorithm is about 11N addition and 6N multiplication.Contrastively，the computation complexity of high order accumulation in Ref.［3］is 5N addition and 15N multiplication.The computation complexity of neural networks in Ref.［3］is related to the number of neuron.If the number of neuron is M，the computation complexity is about O(M2+M).Hence，the algorithm in Ref.［3］is more complex than the proposed algorithm.The computation complexity of wavelet transform in Ref.［5］is 2N2.If the number of samples for classification is Np，the computation complexity of each SVM is.It is obvious that the algorithm in Ref.［5］is more complex than the proposed algorithm if N and Npare larger.

Furthermore，the proposed algorithm can recognize eight jamming patterns more than that in Ref.［3－5，7］.It exploits only two characters less than that in Ref.［4 － 7］and reduces computation complexity greatly and effectively.

3 Simulation Results

In the simulation，the communication signal is assumed as QPSK signal whose rate is 100 kbit/s.After base-band modulation，it is modulated to an intermediate frequency of 500 kHz，and added by AWGN and jamming signal.In this way，the received signal in jamming environment can be simulated.The center frequency of STJ changes from 400 to 600 kHz randomly.The frequency number of MTJ changes from 2 to 10 randomly.Their frequencies are taken between 100 kHz and 900 kHz.Its power is normalized.BBNJ substitutes for AWGN.NBJ is generated by broad-band noise passing narrow-band filter with center frequency of 500 kHz and random bandwidth of 10 kHz to 50 kHz.The duty ratio of PJ changes from 0.001%to 0.01%.FHJ is generated as BPSK/FH(frequency hopping)signal whose hop speed is 1 000 hop/s.The minimum interval of hopping frequency is 10 kHz.The number of frequency set is chosen as 16，24 or 32 randomly.The center frequency of SJ is 500 kHz，and its sweep bandwidth is chosen as 500 kHz，400 kHz，300 kHz or 200 kHz randomly.The simulation’s sampling frequency is 2 MHz.The jamming signal segment of 50 ms，i.e.105samples，is used as recognition data.100 jamming samples with JSR=7～15 dB of each jamming pattern is generated as training samples.

3.1 Simulation of Communication Signal PSD Elimination Algorithm

In the simulation，a QPSK signal segment with length of 1 s，i.e.2 ×106sample data，is used to generate PSD as communication signal PSD template.A QPSK signal segment with length of 50 ms，i.e.105sample data，is used to generate PSD as the practical communication signal PSD.The communication signal PSD is subtracted by the communication signal PSD template as the algorithm in section 2.1.The simulation results are shown in Fig.4.

Limited by the length of paper，the algorithm of direct subtraction is not shown in Fig.4.From Fig.4，it can be seen that only 35%of communication power is remained.In contrast，the direct subtraction algorithm can only eliminate 40%～50%of communication power.

Fig.4 Simulation of communication signal PSD elimination

3.2 Influence of JSR on Jamming Recognition Rate

In the simulation，40 000 jamming signals including communication signal are generated for each jamming pattern.JSRs of these signals are between －7 and 15 dB.For convenience，the communication signal power keeps constant，and the jamming signal power changes with JSR.Fig.5 shows the recognition performance of eight jamming patterns of the proposed algorithm as a function of JSR.

It can be seen from Fig.5(a)that the proposed algorithm has better recognition performance for STJ when JSR≥ －1 dB.In contrast，the algorithm in Ref.［3］has fine recognition performance in low JSR，but it has ceiling and can not reach recognition rate of 100%in high JSR.Fig.5(b)shows that the proposed algorithm has so good recognition performance for MTJ that the recognition rate keeps 100%when JSR≥ －7 dB.From Fig.2(b)，it can be found that the character distribution of MTJ is far from the others.Therefore，its recognition performance is satisfied.In contrast，the performance of the algorithms in Ref.［3，5］falls obviously in low JSR.Fig.5(c)shows that the performance of the proposed algorithm for NBJ is slightly better than the algorithm in Ref.［5］，and is obviously better than the algorithm in Ref.［3］.Fig.5(d)shows that the proposed algorithm has satisfied performance for BBNJ when JSR≥3 dB，while the algorithm in Ref.［3］has slightly better performance than the proposed algorithm.The reason lies in that BBNJ is easy to be misrecognized as PJ or communication signal(NJ).Fig.5(e)shows the recognition performance for communication signal(NJ).It can be seen that the proposed algorithm is better than the algorithm in Ref.［5］.Fig.5(f)shows the recognition performance for SJ，PJ，and FHJ which has not been investigated in the present literature.From Fig.5(f)，it can be found that the recognition performance of the proposed algorithm exceeds 90%for SJ when JSR≥ －1 dB，95%for PJ when JSR≥1 dB，and 90% for FHJ when JSR≥4 dB.However，the character distribution of FHJ is close to narrow-band jamming.Therefore，there is limitation of recognition for FHJ，which is about 90%.In order to solve the problem，the characters with better differentiation should be exploited.

Fig.5 Recognition rates for different jamming

3.3 Recognition Performance of Jamming Pattern Without Communication Signal

If there is not communication signal in the environment，the main factor which affects the recognition rate is ambient noise.This section simulates the ambient noise effect on the recognition rate.To measure the noise power，a jamming-to-noise ratio(JNR)similar to JSR can be defined as

where WJis the jamming power，WNis the ambient noise power.In the simulation，40 000 jamming signals are generated for each jamming pattern from JNR= －7 dB to 15 dB.Fig.6 shows the jamming recognition performance of the proposed algorithm without communication signal.Generally speaking，it is consistent with the recognition performance when the communication signal exists.The recognition rate of BBNJ always keeps 100%because BBNJ and the ambient noise are all AWGN.

4 Conclusions

A novel fuzzy jamming recognition method based on the statistic parameters of received signal’s PSD was proposed.Its shape factor and skewness are exploited as characters.An exponential fuzzy membership function is used to calculate the membership value of the recognized sample，and the jamming pattern is recognized by using the maximum membership principle.Compared to the existing methods，the proposed method can recognize more jamming patterns with clear procedure and low complexity.The simulation results show that it can recognize common eight jamming patterns with high recognition rate.Furthermore，the existence of communication signal has little effect on recognition rate which is propitious to application.

Fig.6 Jamming recognition rate without communication signal

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