FANG Zheng,LI Haitao,and QIAN Yiming

1.School of Electronic,Information and Electrical Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;

2.China Science and Technology on Avionics Integration Laboratory,Shanghai 200233,China;

3.Faculty of Information Technology,Beijing University of Technology,Beijing 100124,China;

4.China Nuclear Control System Engineering CO.,LTD,Beijing 100176,China

1.Introduction

In modern military wars, the operational system of the battlefield calls for involvement of assets from army,navy,air,and special forces to work together in joint action.There are varieties of information warfare weapons used in the joint operational system,which makes the battle field electromagnetic environment become more and more complicated and wicked.Therefore,the tactical data links(TDLs)suffer from serious electromagnetic interference.These interferences stem from two aspects:one is the external jamming which is determined by the essence of the battle field electronic countermeasure,the other is from the internal interference which is generated by a large number of electronic warfare equipment operating in crowded electromagnetic spectrum resources.The interference will result in the communication interruption of data links.

In order to effectively reduce these interferences,cognitive radio based anti-jamming(CAJ)communication technology was put forward recently.The basic principle of this scheme can be described as follows:the electromagnetic environment is percepted firstly,then the characteristic of jamming signals is analyzed,and the best frequency hole is dynamically chosen as the operating frequency to transmit message,so as to enhance the anti-jamming capability of tatical radio.In general,cognitive radio(CR)is mainly used to improve the spectrum efficiency of the commercial communication system.While in the field of tactical wireless communication section,through sensing,understandingand learning the electromagnetic environment based on CR,the radio timely adjusts its configuration to adapt to the variation of the battle field timely,then the reliability of TDLs communication can be improved.

In recent years,the use of low frequency(LF)bands CR based anti-jamming technology for tactical wireless networks has been investigated and some new progress has been reported.For example,the simultaneous transmission and reception based full-duplex cognitive anti-jamming(SCAJ)scheme was proposed in[1,2],which can enhance the anti-jamming capability of military radio and improve its system capacity.With the rapid development of space and terrestrial integrated network technology,especially the emergence of inter-satellite links,the Ka-band,X-band and other high frequency(HF)bands are utilized for the joint operation communication system.Therefore,it is im-perative to explore the high frequency band SCAJ communication scheme.

For the cognitive anti-jamming communication system in high frequency bands, the spectrum sensing of the SCAJ receiver, namely the spectrum detection of jamming source is the key to implement cognitive anti-jamming,which directly affects the performance of data links.It is necessary to design high performance SCAJ receiver for data links.By far,many researchers have carried out beneficial exploration on CAJ technology,most of which only considered the ideal transceiver.However,radio-frequency(RF)impairments exist in the practical transceiver,including the nonlinear distortion of power amplifier,the local oscillator(LO)phase noise,in-phase and quadrature(IQ)imbalance and so on,seriously reducing the performance of military wireless communication.Therefore,we focus on these hardware impairments,and especially investigate the performance of HF bands SCAJ receiver impaired by LO phase noise.

specifically,the RF signal of the SCAJ receiver needs to be turned into intermediate frequency(IF)signal by LO.For a signal source with center frequency f0,the output signal is not distorted under ideal conditions,this is because that the total energy of the output signal concentrates on f0.However,the jitter also called phase noise may be created in the time domain when the receiver signal frequency f0is not equal to the transmitter frequency,which leads some energy spitted into the frequency around f0in the frequency domain.And the IF noise is generated when the phase noise is mixed with the jamming signal,which causes receiver blocking,thereby the SCAJ receiver performance is degraded.

The phase noise of the radio receiver has been discussed deeply.For example,a method estimation Gaussian colored phase noise maximum a posteriori probability was proposed in[3],which is suitable for the feedback oscillator.Based on above,literature[4]designed a greatly simplified model for the prediction of phase noise in oscillators which use a negative resistance as the active element,and compared it with feedback oscillators.However,these studies are limited to the additive white Gaussian noise(AWGN)channel,and the findings are not suitable for fading channels.The signal-to-noise ratio of the receiver with phase noise in the Rayleigh fading channel is analyzed in[5],but it is only for the traditional half-duplex(HD)communication system.And to the best of our knowledge,it has no report about the receiver LO phase noise problem of the full-duplex communication system.

In this paper,the jamming sensing performance of HF bands SCAJ receiver impaired by LO phase noise under the Rayleigh fading channel is deeply investigated.The rest of this paper is organized as follows.In Section 2 the SCAJ system model is described in detail.And the performance of jamming sensing of the SCAJ receiver with and without phase noise under different channels is explored.Further,the bounds of jamming sensing are derived in this section.Also,the performance of jamming sensing is analyzed with simulations.Finally,the conclusions are drawn in Section 3.

2.Jamming sensing of SCAJ receiver impaired by phase noise

2.1 SCAJ system model

The transceiver of HF bands SCAJ communication system is shown in Fig.1.At the transmitter side(TX),the information bit streams are modulated,then up-converted to the RF frequency.The up-converted signal is then transmitted through the antenna to the channel after digital-to-analog conversion(DAC)and the amplification of RF chain.It is assumed that the power of the transmittes signal reaches the desired power after the amplification by the IQ mixer and the power amplifier(PA).

Fig.1 SCAJ transceiver model

For the SCAJ transceiver,the transmission and reception of the signal is operated simultaneously,therefore the transmit signal is coupled back to the receiver and acts as a powerful source of interference,i.e.so-called self-interference(SI).Specially,in case of simultaneous transmit and receive(STAR)applications in high power military radio,the SI should be eliminated to meet the requirement of military communication.The joint analog and digital interference cancellation(JADIC)scheme is introduced to cancel the SI which is proposed in[6].Therefore,the received signals are down-converted to baseband output through the ordinary receiver chain and SI cancellation,which include analog SI cancellation,band-pass filter(BPF),low noise amplifier(LNA),IQ de-hopping and low pass filter(LPF),variable gain amplifier(VGA),analog to-digital conversion(ADC),and digital SI cancellation.

In addition,the frequency channel activities are inspected by the spectrum sensing(SS)module in the receiver,and the characteristics of the frequency channel feeds back to the transmitter.If the strong jamming in current frequency band is detected,the frequency channel with lower interference would be deter mined as alternative operational frequency by the SCAJ system.

For an SCAJ radio pair composed of remote and local stations,assuming that there are no transmitting signals from the remote radio in the sensing interval,the kth re-ceived signal at the local receiver impaired by the oscillator phase noise is defined as

where the two hypotheses,namely absence/presence of jamming signals,will be denoted with parameter α∈{0 1}.θkrepresents the phase noise affecting the kth received signal due to the receiver local oscillators.Furthermore,hkrepresents the channel coefficient at time instant k,and hkkis the channel coefficient between the transmitter and the receiver at the SCAJ transceiver.Since the distance is quite small,path-loss is ignored in this case,|hkk|≈1.xkis the received jamming signal(assumed to be a zero-mean independent identical distribution(iid)random process with varianceskis the SI signal generated by TX side(assumed to be a zero-mean i id signal with variance.Let β be a factor that represents the degree of SI,namely the residual SI by the JADIC technique.wkis the zero-mean complex circularly symmetric AWGN with variance

2.2 JNR of SCAJ receiver

2.2.1 JNR in AWGN channel

Based on the above SCAJ receiver model,we analyze the jamming signal to noise ratio(JNR)of the receiver under oscillator phase noise.Firstly,in the AWGN channel hk=1,hkk=1,the received signal is

The LO generally include free and phase-locked loop(PLL)types.In this paper,we consider free LO and phase noise is modeled as a discrete Wiener process.The phase noise innovation process ζk= θk+1- θkis a white zero-mean Gaussian random process,i.eFor the Wiener phase noise,the single-sided bandwidth(SSB)spectrum[7]has a Lorentzian shape:

where Δf is the offset frequency,κ is Boltzmann constant,and the 3dB SSB of carrier noise power ratio measures the size of phase noise,which determines the change rate of phase noise,f3dB= κπ.By the formula in[4],its discrete sampled versionis given as

where the communication bandwidth BW=1/Ts,and Tsis the Nyquist sampling period.

In order to compensate the effect of phase noise on the received signal,letbe the estimation of θkin the k th time instant,rotated byat the receiver

where ε1,kdenotes the estimation error of phase noise.

Note that in(5),(ejε1,k-1)αxkrepresents the additive noise term due to the residual phase noise estimation error.Assuming that the SI is fairly small,Gaussian noise approximately has similar statistics for different channels[8 – 11],we can consider that,the JNR of the SCAJ receiver under phase noise in the AWGN channel is written as

2.2.2 JNR in fading channel

Next analyze the effort of channel estimation errors on the JNR in the receiver.In absence of oscillator phase noise,i.e.θk=0,the received signal is rewritten as

where hkis Rayleigh fading channel coefficient,and realand imaginaryare modeled as zero-mean Gaussian random variables independently.By setting the variancewe obtain

The cross-correlation and auto-correlation functions betweenand[12]are defined as

where J0is the zero-order Bessel function of the first kind,and fDis the maximum Doppler frequency,given by fD=vf0/c.v is the relative velocity between the transmitter and the receiver,c=3×108m/s is the speed of light,and f0is the center frequency of the SCAJ system.

In order to compensate for the effect of the Rayleigh fading channel,consider an estimate of the channel coefficient?hk,then multiply the received signal by the conjugate of?hk:

After equalization processing in(15),the JNR under oscillator phase noise in the Rayleigh fading channel can be expressed as(16).

2.3 Jamming sensing performance

2.3.1 Probability of detection and false alarm

Based on the above theoretical results,the performance of the jamming sensing receiver impaired by the LO phase noise is further investigated.In the following analysis,we focus on energy detection(ED)based sensing where the main idea of ED is to calculate the average energy of K received signal samples within a sampling period,and compare it with a threshold λ to determine whether the channel is being jammed or not,i.e.the channel is available if the power is smaller than the threshold or not available otherwise.Two metrics to measure the performance of the ED algorithm are analyzed,namely the jamming detection and false-alarm probabilities[13–15].The average energy of K received signal samples is defined as

where Re(·),Im(·)denote the real and the imaginary part of complex variables(·)respectively.For a large K,using the central limit theorem,the probability density function(PDF)of Tαcan be approximated by a Gaussian distribution

with the following mean and variance when α=0 and α=1:

Accordingly,the false-alarm probability in the SCAJ receiver[1,2]can be expressed as

Similarly,the detection probability[1,2]can be expressed as

For a target false-alarm probability,the threshold can be solved from(21):

Based on the above derivation,the jamming detection and false alarm probabilities of the SCAJ receiver can be achieved.We find that the performance of the CAJ receiver mainly depends on the variancesandThe next work is to analyze the bounds of the variances in order to obtain optimal jamming sensing.

2.3.2 Upper bounds of jamming sensing

We firstly consider the AWGN channel, denote K jamming signal symbols by the vector x =[x1,...,xk,...,xK]T,and the PDF of phase noise vector θ =[θ1,...,θk,...,θK]Tis f(θ).By utilizing mean square error(MSE)to estimate the varianceof phase noise estimation error,the Bayesian Cram˙er-Rao bound(BCRB)can satisfy the following inequality:

where BPNis the Bayesian information matrix(BIM),F(θ)is the modified Fisher information matrix(FIM),the diagonal elements ofprovide a lower bound,i.e.the modified Bayesian Cramer-Rao bound(MBCRB).

As seen from(24)and(25),the bound ofis determined by f(θ)and f(y|θ,x).For the discrete phase noise innovations ζkare uncorrelated,

where I1is a K×K identity matrix,anddenotes the phase noise variance associated with the first received signal,θ1is uniformly distributed over[0,2π).

Assuming that the phase noise estimate achieves an MSE performance close to the MBCRB and by substituting(26)and(27)in(7),the JNR for the received signal after phase noise compensation is determined as

For further study in the Rayleigh fading channel,denotingwe obtain the BIM and FIM respectively

As we observe from(29)and(30),BCHis determined by prior distributionand the likelihood function.Because noise wkand the SI signals skare independent,is written as

where

By substituting(31)and(32)in(30),then

In order to reduce the computational complexity,by using(10)and(11),we obtain,where

By substituting(33)–(35)in(29),then

From all above analysis,the bound of JNR in the Rayleigh fading channel absence of phase noise is

Further,from(16),(25)and(37),we obtain the bound of JNR in the Rayleigh fading channel under phase noise as

By substituting(25),(37)and(39)in(21)and(22),then the bounds of false-alarm probability and detection probability under phase noise are

2.4 Numerical results

In this section,the performance of jamming sensing of the HF bands SCAJ receiver impaired by phase noise is presented by numerical simulation.Firstly,we provide the lower bounds on the innovation variance for the Wiener phase noise.Considering that fully integrated Si CMOS LO is widely used in wireless communication system,next the performance of the SCAJ receiver based on Si CMOS LO is analyzed.The innovation variance is affected by LO current Id,voltage Vdand the unloaded quality factor Q0([8]Vd=1 V,Id=5 mA,Q0=15).By using equation(28)in[5]and f3dB= κπ,we obtain the Wiener phase noise innovation variance

As observed from(42),the lower bound of phase noise innovation variance grows quadratically with the center frequency f0and decreases linearly with the BW of the radio signal.

Next,the upper bound of the JNR of the SCAJ receiver is analyzed.We suppose the number of signal samples K=104,narrow bandwidth BW1=1 MHz,wide bandwidth BW2=0.001f0,the JNRdB and the original SI to noise ratiodB.Consider the residual SI is eliminated by JADIC technique and becomes smaller,that is,we can set SI factor β=0.05.Fig.2 illustrates the upper bound of JNR after phase noise compensation of the SCAJ receiver impaired by phase noise,a JNR loss of 0.05 dB and 0.5 dB can be seen for BW1=1 MHz and BW2=0.001f0,respectively.When increasing the center frequency f0from 1 GHz to 100 GHz,it is higher than the conventional radio system where the center frequency is generally below 1 GHz.

Fig.2 Upper bound of JNR with phase noise

Fig.3 shows the upper bound of JNR of the ideal SCAJ receiver after channel fading compensation for relative velocities of v=1 km/h and v=50 km/h,the JNR is calculated by using(38),and its value is kept a constant for both relative velocities when BW2=0.001f0.On the other hand,when the increasing f0with BW1=1 MHz,JNR drops 0.1 dB and 0.14 dB for v=1 m/h and v=50 km/h,respectively.This comparison shows that channel fading has a more prominent effect on the SCAJ performance when the relative velocity is slightly higher.And the similar results of the upper bound of JNR under phase noise in the Rayleigh fading channel is shown in Fig.4.From Fig.3 and Fig.4,we can clearly see that the degradation of the JNR due to phase noise is more severe than that due to the channel fading when BW is a constant.

Fig.3 Upper bound ofJNR without phase noise under fading channel

Fig.4 Upper bound of JNR with phase noise under fading channel

Under the Rayleigh fading channel,we set the center frequency f0=10 GHz,the false-alarm probability Pfa=0.1,the channel estimation error variance0.4.Fig.5 shows the jamming detection probability of the SCAJ receiver with phase noise under differentAs is shown that the smaller phase noise variance of estimation error is,the higher jamming detection probability of the SCAJ receiver is.And the detection probability is lower than the theoretical optimal MBCRB bound and matches the theoretical analysis.It also can be observed that the jamming sensing performance is not ideal under low,this is because that the jamming signal cannot be correctly distinguished from noise and SI based on the ED scheme.

Fig.5 Jamming detection probability of SCAJ receiver with phase noise

3.Conclusions

Since the SCAJ receiver is seriously affected by the LO phase noise,in order to evaluate the anti-jamming performance of HF band SCAJ radio employed by TDL in the complex electromagnet environment,we investigate the SCAJ receiver impaired by phase noise in LO under the fading channel.Firstly,ED based JNR of the SCAJ receiver with phase noise under different channels is analyzed.Then,the jamming detection and false alarm probabilities in closed-form for the SCAJ receiver are derived.Finally,the MBCRB for the channel and phase noise estimators are studied.Simulation results show that the performance degradation of the SCAJ system due to phase noise is more severe than that due to the channel fading when BW is a constant in HF bands.Moreover,the signal BW has an effect on the phase noise in LO,and the jamming detection probability of the wide band SCAJ receiver with lower phase noise outperforms the narrow band receiver in the same operation frequency band.Furthermore,an accurate phase noise estimation and compensation scheme can improve the jamming detection probability of the SCAJ receiver and approach to the upper bound.Thus,a precise phase noise estimation and compensation technology would be developed to improve the anti-jamming capability of the SCAJ system,which is our research work in the future.

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