# Full-Duplex UAV Legitimate Surveillance System against a Suspicious Source with Artificial Noise

Authors: Shen Yi; Pan Zhiwen; Liu Nan; You Xiaohu
Journal: Wireless Communications and Mobile Computing
 (2021)

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## Abstract

We propose a legal full-duplex unmanned aerial vehicle (UAV) surveillance system in the presence of the ground-to-ground suspicious link with antisurveillance technology. UAV performs passive surveillance and active jamming simultaneously, and the suspicious source with multiantenna employs artificial noise to avoid being monitored. In order to ensure effective surveilling, we adopt two beamforming schemes, namely, maximum ratio transmission (MRT)/receiving zero-forcing (RZF) and transmitting zero-forcing (TZF)/maximum ratio combing (MRC), for MIMO UAV. For the two beamforming schemes, we derive the surveilling nonoutage probability in a closed-form expression and analyze the surveilling performance under different system environments. Monte Carlo (MC) simulation validates the correctness of the formula.


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## Body

## 1. Introduction

Public safety is becoming more and more important. Illegal nodes transmit suspicious information to conduct actions that endanger public safety, such as illegal crimes and terrorist attacks. Public security agencies can use wireless monitoring equipment to surveil suspicious communication links. Wireless monitoring equipment consists of two categories: ground monitors and unmanned aerial vehicle (UAV) monitors.The study of ground monitors has been considered in [1–4]. In order to ensure effective surveilling, the authors in [1, 2] propose a legitimate surveilling system in the presence of a suspicious link, where the ground monitor performs proactive surveilling via cognitive jamming. A new proactive surveilling approach, namely, spoofing relay, is proposed in [3] to enhance the surveilling performance. For successful surveilling, the authors in [4] make use of full-duplex technology with self-interference cancellation and multi-antenna technology to increase the surveilling channel quality and reduce the suspicious transmission rate.Due to on demand deployment and flexible mobility, UAVs can be involved in wireless communication scenes including UAV legitimate terminals [5–7], UAV base station [8–10], UAV friendly jamming [11–13], and UAV friendly relays [14, 15].UAV can pretend a legitimate node that communicates with other nodes, and the existence of UAV does not draw attention from suspicious links.Due to the relatively high operation altitude, UAVs have a dominant line-of-sight (LoS) commutation channel compared to the ground monitors. As such, compared to ground-to-ground surveillance link with severe fading, the UAV-to-ground surveilling link provides an advantageous communication channel. Furthermore, UAVs can use spatial freedom to obtain the best surveillance performance. UAV monitor has been considered in [16–19]. Authors in [16] investigate a legal UAV monitoring system in the presence of suspicious UAV pairs, where the legal UAV’s trajectory is limited by energy. Authors in [17] propose a legitimate UAV surveilling scenario in the presence of a ground-to-ground suspicious relay network, where the suspicious source can only communicate with the suspicious destination through the suspicious relay. Multiple cooperated UAV surveilling scenario in the presence of a ground-to-ground suspicious relay network with multiple relays where all nodes operate in half-duplex mode is proposed in [18]. Authors in [19] consider two surveilling schemes, namely, proactive surveilling and spoofing relaying, in the UAV surveilling system. However, all above literatures [16–19] assume that the suspicious link is passive, and no antisurveillance technology is adopted to avoid being monitored.Suspicious nodes have become more and more cunning, and the suspicious source can use artificial noise to avoid being monitored. Artificial noise has been studied in [20–23]. In [20], the authors propose a secure transmission system in which the legitimate source transmits useful information to the legitimate destination in the presence of an eavesdropper. The legal source can use artificial noise to avoid being eavesdropped. Authors in [21] further consider a secure transmission system in the presence of multiple eavesdroppers operating in both noncollusion and collusion modes. In [22], the authors consider a secure transmission system based on [20]. The difference is that [20] knows the statistical characteristics of the eavesdropping channel state information (CSI), while [22] does not know the eavesdropping channel CSI. In [23], the authors further extend the secure transmission system of [22], and the assumption of the system environment changes from knowing the statistical characteristics of the eavesdropping channel CSI to not knowing the eavesdropping CSI channel. However, in the above literatures [20–23], they all stand from the perspective of legitimate nodes, not from the perspective of suspicious nodes, and artificial noise has not been adopted by the suspicious source.Full-duplex technology has been considered in [24–26]. In [24], the authors propose a beam-domain full-duplex massive MIMO to enable co-time co-frequency uplink and downlink transmission in the cellular system. In [25], the authors consider the benefits, feasibility, and limitations of inband full-duplex massive MIMO in the cellular system. In [26], the authors consider the hybrid time switching and power splitting simultaneous wireless information and power transfer protocol design in a full-duplex massive MIMO system to maximize system achievable sum rate. Therefore, full-duplex technology can be used in the surveillance system to enhance the surveilling performance.Based on the above investigations, in this paper, we propose a legal full-duplex UAV surveillance system in the presence of a ground-to-ground suspicious communication link with antisurveillance technology. UAV monitor operates in full-duplex mode, where passive surveilling aims to receive the suspicious information from the dubious source, and active jamming aims to reduce the channel capacity of the suspicious link, thus degrading the ability of the dubious source to transmit suspicious messages to the dubious destination. By using antisurveillance technology, the suspicious source with multiantenna employs artificial noise to avoid being monitored. Without loss of generality, LoS link with a certain probability is the most suitable for the UAV-to-ground channel model. We adopt the nonoutage probability to evaluate the surveilling performance of UAV monitor.The main contributions of this paper are summarized as follows:We propose a full-duplex UAV monitor scheme based on [27], where the suspicious source adopts a single antenna without artificial noise, while in this paper, the suspicious source with multi-antenna employs artificial noise to avoid being monitored.In order to improve surveilling performance, two low-complexity linear beamforming schemes, maximum ratio transmission (MRT)/receiving zero-forcing (RZF), and transmitting zero-forcing (TZF)/maximum ratio combing (MRC) are adopted for MIMO UAV. Furthermore, we derive the probability of surveilling non-outage in a closed-form expression.For various UAV surveilling environments, the optimal angle/radius/height to maximize the surveilling nonoutage probability is determined. The impact of the artificial noise power ratio in the suspicious source, the distance between the suspicious source, and the suspicious destination, as well as the transmitting power of the suspicious source and UAV on the surveilling non-outage probability, is analyzed. For different heights of UAV, configuration of the receiving antennas and transmitting antennas with fixed total number of antennas that maximizes the surveilling nonoutage probability of the UAV monitor is explored for two beamforming schemes.The optimal power ratio of artificial noise at the suspicious source which minimizes the surveilling non-outage probability is determined. When the power ratio of artificial noise of the suspicious source is unknown, the UAV surveillance system can be designed with reference to the worst case while ensuring surveillance performance.Notations:CN denotes the complex Gaussian distribution. ·H denotes the conjugate transpose. · denotes the absolute value. · denotes the Frobenius norm of the matrix or vector.


## 2. System Model and Problem Formulation

The UAV legitimate surveillance system is shown in Figure1, where a suspicious ground source (S) transmits suspicious messages to a suspicious ground destination (D), and this suspicious communication link is surveilled by a full-duplex UAV legitimate monitor (M). However, the suspicious source with multi-antenna adopts artificial noise to avoid being monitored.Figure 1
(a). System model with 3-D view. (b). System model with top view.
(a)(b)Under a full-duplex mode, UAV performs passive surveillance and active jamming simultaneously. Suppose that the number of UAV receiving antennas used for surveilling isNr and the number of UAV transmitting antennas used for jamming is Nt, while the suspicious source has NS transmitting antennas and the suspicious destination has a single receiving antenna. In three-dimensional Cartesian coordinate system, S, D, and M are located at g,0,0, −g,0,0, and rcosθa,rsinθa,v, respectively, where the half separation between suspicious nodes is denoted by g, UAV circle radius r is in the range of 0 to rmax, UAV azimuth angle θa is in the range of 0 to 2π, and UAV altitude v is in the range of 0 to vmax. As in [1, 28], UAV knows all channel state information (CSI), while the suspicious nodes only know their own CSI.We denoteHSM, hMD, and hSD as the Nr×Ns channel matrix from the suspicious source to UAV, the 1×Nt channel vector from UAV to the suspicious destination, and the 1×Ns channel vector from the suspicious source to the suspicious destination, respectively. Model S-D channel as β1hSD/dSD4, where the ground-to-ground channel power gain at a reference distance of 1 m, is denoted by β1, hSD represents a Rayleigh fading with entries being independent and identically distributed (i.i.d.) zero-mean circular symmetric complex Gaussian (ZMCSCG) random variable with variance λ1, and dSD denotes the distances between S and D. Model the self-interference channel as ρHMM [29], where HMM denotes a Rayleigh channel with entries being i.i.d. ZMCSCG with variance λ2, and self-interference coefficient ρ is in the range of 0≤ρ≤1.Due to the high operating altitude of UAV, the UAV-to-ground channels typically have a high probability of LoS link [30] as
(1)prLOSθi=1+δ1e−δ2θi−1,where δ1 and δ2 are constant values determined by the environment, θi,i∈SM,MD is the elevation angle, and
(2)θi=arcsinvdi,i∈SM,MD,where the distance between S and M is denoted by dSM, and the distance between M and D is denoted by dMD, which can be, respectively, given by
(3)dSM=g2+r2+v2−2grcosθa1/2,dMD=g2+r2+v2+2grcosθa1/2.Note that the LoS probability in (1) increases as the elevation angle θi,i∈SM,MD increases.From [31], we model the UAV-to-ground channel as a Rice fading channel, and the Rice factor and path loss exponent are associated with the elevation angle and environment.We then express the Rician factor betweenS (or D) and M as Ki=α3eδ3θi,i∈SM,MD and the path loss exponent as τi=α1prLOSθi+α2,i∈SM,MD, where α1, α2, α3, and δ3 are constants related to frequency and environment. Therefore, we model the S-M channel as β2Hi/diτi,i∈SM [28], where the UAV-to-ground channel power gain at a reference distance of 1 m is denoted by β2, and Hi represents the small-scale fading of the UAV-to-ground channel, which can be expressed as
(4)Ηi=KiKi+1H¯i+1Ki+1H~i,i∈SM,where H¯SM is the deterministic LoS component of the channel between the suspicious source and UAV satisfying traceH¯SMH¯SM†=NrNs. H~SM∈ℂNr×Ns denotes the scattered component of the channel between the suspicious source and UAV with entries being i.i.d. ZMCSCG random variable with unit variance.Further, we model theM-D channel asβ2hi/diτi,i∈MD [28], where hi represents the small-scale fading in the air, which is given by
(5)hi=KiKi+1h¯i+1Ki+1h~i,i∈MD,where h¯MD is the deterministic LoS components of the channel between the suspicious destination and UAV satisfying traceh¯MDh¯MD†=Nt. h~MD∈ℂ1×Nt denotes the scattered components of the channel between the suspicious destination and UAV with entries being i.i.d. ZMCSCG random variable with unit variance.The suspicious source is equipped with multiple antennas, where one antenna is used to transmit useful information, while the remaining antennas are used to send artificial noise signals [32]. The transmitting information of the suspicious source can be expressed as
(6)xs=Wt,where W is the Ns×Ns beamforming matrix and can be expressed as
(7)W=wsWa,where ws denotes the Ns×1 beamforming vector to maintain the receiving signal quality of the suspicious destination, and ws=hSD†/hSD. Wa denotes the Ns×Ns−1 beamforming matrix, which is used for transmitting artificial noise signal to avoid being monitored and will not affect the receiving signal quality of the suspicious destination, hence, hSDWa=0. t composes of useful information and artificial noise signals and can be expressed by
(8)t=tsta,where ts is a useful information signal, and ta is Ns−1×1 artificial noise vector in the suspicious source. Define αs with 0≤αs≤1 as the power ratio allocated to the useful information signal. Therefore,
(9)Ets2=αs,Etata†=1−αsNs−1INs−1.Hence, the signal received by UAV is given by(10)yM=Psβ2dSMτSMHSMwsts+Wata+ρPMHMMwtx+nM,where the transmitting power of the suspicious source is denoted by Ps, and UAV jamming power PM is in the range of 0≤PM≤PJ. In addition, UAV jamming symbol is x with unit power. Furthermore, wt is the transmit beamforming vector at UAV monitor with wt=1. Finally, nM is additive white Gaussian noise (AWGN) at UAV, i.e., nM~CN0Nr×1,σM2INr.Assume that UAV adopts a linear receiverwr with wr=1 for signal detection, hence, the output of the linear filter wr is given by
(11)yM~=wrHyM=Psβ2dSMτSMwrHHSMwsts+Wata+ρPMwrHHMMwtx+wrHnM.Similarly, the receiving signal of the suspicious receiverD can be expressed as
(12)yD=Psβ1dSD4hSDwsts+PMβ2dMDτMDhMDwtx+nD,where nD is the zero-mean AWGN at the suspicious destination node D with variance σD2.Therefore, the signal-to-interference-plus-noise ratio (SINR) of the suspicious destination nodeD can be expressed as
(13)SINRD=αsPsβ1/dSD4hSDws2PMβ2/dMDτMDhMDwt2+σD2,and the SINR of UAV can be expressed as
(14)SINRM=αsPsβ2dSMτSMwsHHSMHwrR−1wrHHSMws,where
(15)R=Psβ21−αsdSMτSMNs−1wrHHSMwawaHHSMHwr+ρPMwrHHMMwtwtHHMMHwr+σM2INr.IfSINRM≥SINRD, the UAV surveillance system is successful, and suspicious messages can be decoded without error. If SINRM<SINRD, the UAV surveillance system fails, and suspicious messages cannot be decoded without error.


## 3. Performance Analysis

In order to improve the surveilling performance, two low-complexity linear beamforming schemes, maximum ratio transmission (MRT)/receiving zero-forcing (RZF), and transmitting zero-forcing (TZF)/maximum ratio combing (MRC) are adopted for MIMO UAV.


### 3.1. MRT/RZF

Aiming to completely eliminate self-interference, the multiantenna receiving end of the UAV monitorM adopts the RZF scheme.According to [33], the compact form of wr can be expressed as
(16)wr=Π2HSMΠ2HSM,where Π2=INr−HMMhMD†hMDHMM†/HMMhMD†2 spans the null space of HMMhMD†.Furthermore, the MRT scheme is adopted by the transmitting antennas of UAV monitorM for jamming the suspicious destination, i.e.,
(17)wt=hMD†hMD.Since UAV completely eliminates its self-interference [4], active jamming has no effect on the UAV signal receiving end. Consequently, UAV can use the full power PJ for jamming the suspicious destination.The probability of UAV surveilling non-outage with TZF/MRC scheme is given by (39).Define(18)γSD=αsPsβ1dSD4hSDws2.γMD=hMDwt2.Then, it is obvious that γSD follows the central chi-squared distribution with 2NSNS−1 degrees of freedom, with CDF (cumulative distribution function) given by [34]
(19)FSDx=1−exp−xψSD×∑p=1NS1ΓpxψSDp−1,where
(20)ψSD=αsPSβ1dSD4.In addition, the PDF (probability density function) ofγMD is given by [28]
(21)fMDx=KMD+1e−KMD+1x+KMDNt×KMD+1xKMDNtNt−12×INt−12KMD+1KMDNtx.As such, the probability of surveilling non-outage can be written as(22)Pnonout=ProbSINRM≥αsPsβ1/dSD4hSDws2PMβ2/dMDτMDhMDwt2+σD2.Conditioning onγSD, we obtain
(23)Pnonout=1−exp−PMβ2/dMDτMDhMDwt2+σD2SINRMψSD×∑p1=1NS1Γp1PMβ2/dMDτMDhMDwt2+σD2SINRMψSDp1−1.Averaging overγMD and with the help of [35], we have the desired result.
(24)Pnonout=1−KMD+1Ntexp−KMDNt−b1c1∑p1=1NS1Γp1a1c1p1−1∑v1=0p1−1v1p1−1b1a1p1−1−v1×∑i1=0∞KMDNtKMD+1iΓNt+v1+i1a1c1+KMD+1Nt+v+iΓi1+1ΓNt+i1,where
(25)a1=PMβ2dMDτMDb1=σD2c1=SINRMψSD.As such,SINRM can be written as
(26)SINRM=z1wz2+σM2,where
(27)w=Psβ21−αsdSMτSMNs−1.Define(28)z1=αsPsβ2dSMτSMwrHHSMwswsHHSMHwr.z2=wrHHSMwawaHHSMHwr,Then, it is obvious that z1 follows the central chi-squared distribution with 2Nr−1 degrees of freedom, with CDF given by [34]
(29)Fz1=1−exp−z1ϕz1×∑p2=1Nr−11Γp2z1ϕz1p2−1,where
(30)ϕz1=2αsPsβ2NsdSMτSMKSM+1.Then, it is obvious thatγSD follows the central chi-squared distribution with 2NS degrees of freedom [28], and the pdf of z2 is given by
(31)fz2x=KSM+1e−KSM+1x+KSMNs−1Ns×KSM+1xKSMNs−1NsNs−1Ns−12×INs−1Ns−12KSM+1KSMNs−1Nsx.Conditioning onz1, we obtain the CDF of SINRM as
(32)FT=1−exp−SINRMwz2+σM2ϕz1×∑p2=1Nr−11Γp2SINRMwz2+σM2ϕz1p2−1.Averaging overz2 and with the help of [35], we have the desired result.
(33)FT=1−KSM+1Ns−1Nsexp−KSMNs−1Ns−b2c2×∑p2=1Nr−11Γp2a2c2p2−1∑v2=0p2−1v2p2−1b2a2p2−1−v2×∑i2=0∞KSMKSM+1Ns−1Nsi2ΓNs−1Ns+v2+i2a2c2+KSM+1Ns−1Ns+v2+i2Γi2+1ΓNs−1Ns+i2,where
(34)a2=Psβ21−αsdSMτSMNs−1,b2=σM2,c2=SINRMϕz1=SINRMdSMτSMKSM+12αsPsβ2NS.The probability of UAV surveilling non-outage with TZF/MRC scheme is given by(35)Pnonout=1−KMD+1Ntexp−KMDNt∑p1=1NS1Γp1a1p1−1∑v1=0p1−1v1p1−1b1a1p1−1−v1×∑i1=0∞KMDNtKMD+1i1ΓNt+v1+i1Γi1+1ΓNt+i1×KSM+1Ns−1Nsexp−KSMNs−1Ns×∑p2=1Nr−11Γp2a2p2−1∑v2=0p2−1v2p2−1b2a2p2−1−v2×∑i2=0∞KSMKSM+1Ns−1Nsi2ΓNs−1Ns+v2+i2Γi2+1ΓNs−1Ns+i2×Q1where
(36)Q1=∑k1=0∞k1Nt+v1+i1+k1−1−a1k1ψSD−k1+p1−1KMD+1−Nt+v1+i1−k1×∑k2=0∞k2NSNS−1+v2+i2+k2−1−a2k2ϕz1−k2+p2−1KSM+1−NSNS−1+v2+i2−k2×Γp1+p2+k1+k2−1b1/ψSD+b2/ϕz1−p1+p2+k1+k2−1×−b2ϕz1+p2−1b1/ψSD+b2/ϕz1p1+p2+k1+k2−2−a2NSNS−1+v2+i2ϕz1×∑k1=0∞k1Nt+v1+i1+k1−1−a1k1ψSD−k1+p1−1KMD+1−Nt+v1+i1−k1×∑k2=0∞k2NSNS−1+v2+i2+k2−a2k2ϕz1−k2+p2−1KSM+1−NSNS−1+v2+i2+1−k2×Γp1+p2+k1+k2−1b1/ψSD+b2/ϕz1−p1+p2+k1+k2−1


### 3.2. TZF/MRC

Different from the RZF scheme, the transmitter of UAV with multiple antennas adopts the TZF scheme to completely eliminate the self-interference.According to [33], the compact form of wt can be expressed as
(37)wt=Π1hMD†Π1hMD†,where Π1=INt−HMM†hSMhSM†HMM/hSM†HMM2 spans the null space of hSM†HMM.Furthermore, the MRC scheme is adopted by the receive antennas of UAV monitor M to maximize the receiving of the suspicious information, i.e.,(38)wr=HSMHSM.Since UAV completely eliminates its self-interference [4], active jamming has no effect on the UAV signal receiving end. Consequently, UAV can use the full power PJ for jamming the suspicious destination.By deriving similar to MRT/RZF, the probability of UAV surveilling non-outage with TZF/MRC scheme is given by(39)Pnonout=1−KMD+1Nt−1exp−KMDNt−1∑p1=1NS1Γp1a1p1−1∑v1=0p1−1v1p1−1b1a1p1−1−v1×∑i=0∞KMDNt−1KMD+1i1ΓNt+v1+i1−1Γi1+1ΓNt+i1−1×KSM+1Ns−1Nsexp−KSMNs−1Ns×∑p2=1Nr1Γp2a2p2−1∑v2=0p2−1v2p2−1b2a2p2−1−v2×∑i2=0∞KSMKSM+1Ns−1Nsi2ΓNs−1Ns+v2+i2Γi2+1ΓNs−1Ns+i2×Q2where
(40)Q2=∑k1=0∞k1Nt+v1+i1+k1−2−a1k1ψSD−k1+p1−1KMD+1−Nt+v1+i1−1−k1×∑k2=0∞k2NSNS−1+v2+i2+k2−1−a2k2ϕz1−k2+p2−1KSM+1−NSNS−1+v2+i2−k2×Γp1+p2+k1+k2−1b1/ψSD+b2/ϕz1−p1+p2+k1+k2−1×−b2ϕz1+p2−1b1/ψSD+b2/ϕz1p1+p2+k1+k2−2−a2NSNS−1+v2+i2ϕz1×∑k1=0∞k1Nt+v1+i1+k1−2−a1k1ψSD−k1+p1−1KMD+1−Nt+v1+i1−1−k1×∑k2=0∞k2NSNS−1+v2+i2+k2−a2k2ϕz1−k2+p2−1KSM+1−NSNS−1+v2+i2+1−k2×Γp1+p2+k1+k2−1b1/ψSD+b2/ϕz1−p1+p2+k1+k2−1


## 3.1. MRT/RZF

Aiming to completely eliminate self-interference, the multiantenna receiving end of the UAV monitorM adopts the RZF scheme.According to [33], the compact form of wr can be expressed as
(16)wr=Π2HSMΠ2HSM,where Π2=INr−HMMhMD†hMDHMM†/HMMhMD†2 spans the null space of HMMhMD†.Furthermore, the MRT scheme is adopted by the transmitting antennas of UAV monitorM for jamming the suspicious destination, i.e.,
(17)wt=hMD†hMD.Since UAV completely eliminates its self-interference [4], active jamming has no effect on the UAV signal receiving end. Consequently, UAV can use the full power PJ for jamming the suspicious destination.The probability of UAV surveilling non-outage with TZF/MRC scheme is given by (39).Define(18)γSD=αsPsβ1dSD4hSDws2.γMD=hMDwt2.Then, it is obvious that γSD follows the central chi-squared distribution with 2NSNS−1 degrees of freedom, with CDF (cumulative distribution function) given by [34]
(19)FSDx=1−exp−xψSD×∑p=1NS1ΓpxψSDp−1,where
(20)ψSD=αsPSβ1dSD4.In addition, the PDF (probability density function) ofγMD is given by [28]
(21)fMDx=KMD+1e−KMD+1x+KMDNt×KMD+1xKMDNtNt−12×INt−12KMD+1KMDNtx.As such, the probability of surveilling non-outage can be written as(22)Pnonout=ProbSINRM≥αsPsβ1/dSD4hSDws2PMβ2/dMDτMDhMDwt2+σD2.Conditioning onγSD, we obtain
(23)Pnonout=1−exp−PMβ2/dMDτMDhMDwt2+σD2SINRMψSD×∑p1=1NS1Γp1PMβ2/dMDτMDhMDwt2+σD2SINRMψSDp1−1.Averaging overγMD and with the help of [35], we have the desired result.
(24)Pnonout=1−KMD+1Ntexp−KMDNt−b1c1∑p1=1NS1Γp1a1c1p1−1∑v1=0p1−1v1p1−1b1a1p1−1−v1×∑i1=0∞KMDNtKMD+1iΓNt+v1+i1a1c1+KMD+1Nt+v+iΓi1+1ΓNt+i1,where
(25)a1=PMβ2dMDτMDb1=σD2c1=SINRMψSD.As such,SINRM can be written as
(26)SINRM=z1wz2+σM2,where
(27)w=Psβ21−αsdSMτSMNs−1.Define(28)z1=αsPsβ2dSMτSMwrHHSMwswsHHSMHwr.z2=wrHHSMwawaHHSMHwr,Then, it is obvious that z1 follows the central chi-squared distribution with 2Nr−1 degrees of freedom, with CDF given by [34]
(29)Fz1=1−exp−z1ϕz1×∑p2=1Nr−11Γp2z1ϕz1p2−1,where
(30)ϕz1=2αsPsβ2NsdSMτSMKSM+1.Then, it is obvious thatγSD follows the central chi-squared distribution with 2NS degrees of freedom [28], and the pdf of z2 is given by
(31)fz2x=KSM+1e−KSM+1x+KSMNs−1Ns×KSM+1xKSMNs−1NsNs−1Ns−12×INs−1Ns−12KSM+1KSMNs−1Nsx.Conditioning onz1, we obtain the CDF of SINRM as
(32)FT=1−exp−SINRMwz2+σM2ϕz1×∑p2=1Nr−11Γp2SINRMwz2+σM2ϕz1p2−1.Averaging overz2 and with the help of [35], we have the desired result.
(33)FT=1−KSM+1Ns−1Nsexp−KSMNs−1Ns−b2c2×∑p2=1Nr−11Γp2a2c2p2−1∑v2=0p2−1v2p2−1b2a2p2−1−v2×∑i2=0∞KSMKSM+1Ns−1Nsi2ΓNs−1Ns+v2+i2a2c2+KSM+1Ns−1Ns+v2+i2Γi2+1ΓNs−1Ns+i2,where
(34)a2=Psβ21−αsdSMτSMNs−1,b2=σM2,c2=SINRMϕz1=SINRMdSMτSMKSM+12αsPsβ2NS.The probability of UAV surveilling non-outage with TZF/MRC scheme is given by(35)Pnonout=1−KMD+1Ntexp−KMDNt∑p1=1NS1Γp1a1p1−1∑v1=0p1−1v1p1−1b1a1p1−1−v1×∑i1=0∞KMDNtKMD+1i1ΓNt+v1+i1Γi1+1ΓNt+i1×KSM+1Ns−1Nsexp−KSMNs−1Ns×∑p2=1Nr−11Γp2a2p2−1∑v2=0p2−1v2p2−1b2a2p2−1−v2×∑i2=0∞KSMKSM+1Ns−1Nsi2ΓNs−1Ns+v2+i2Γi2+1ΓNs−1Ns+i2×Q1where
(36)Q1=∑k1=0∞k1Nt+v1+i1+k1−1−a1k1ψSD−k1+p1−1KMD+1−Nt+v1+i1−k1×∑k2=0∞k2NSNS−1+v2+i2+k2−1−a2k2ϕz1−k2+p2−1KSM+1−NSNS−1+v2+i2−k2×Γp1+p2+k1+k2−1b1/ψSD+b2/ϕz1−p1+p2+k1+k2−1×−b2ϕz1+p2−1b1/ψSD+b2/ϕz1p1+p2+k1+k2−2−a2NSNS−1+v2+i2ϕz1×∑k1=0∞k1Nt+v1+i1+k1−1−a1k1ψSD−k1+p1−1KMD+1−Nt+v1+i1−k1×∑k2=0∞k2NSNS−1+v2+i2+k2−a2k2ϕz1−k2+p2−1KSM+1−NSNS−1+v2+i2+1−k2×Γp1+p2+k1+k2−1b1/ψSD+b2/ϕz1−p1+p2+k1+k2−1


## 3.2. TZF/MRC

Different from the RZF scheme, the transmitter of UAV with multiple antennas adopts the TZF scheme to completely eliminate the self-interference.According to [33], the compact form of wt can be expressed as
(37)wt=Π1hMD†Π1hMD†,where Π1=INt−HMM†hSMhSM†HMM/hSM†HMM2 spans the null space of hSM†HMM.Furthermore, the MRC scheme is adopted by the receive antennas of UAV monitor M to maximize the receiving of the suspicious information, i.e.,(38)wr=HSMHSM.Since UAV completely eliminates its self-interference [4], active jamming has no effect on the UAV signal receiving end. Consequently, UAV can use the full power PJ for jamming the suspicious destination.By deriving similar to MRT/RZF, the probability of UAV surveilling non-outage with TZF/MRC scheme is given by(39)Pnonout=1−KMD+1Nt−1exp−KMDNt−1∑p1=1NS1Γp1a1p1−1∑v1=0p1−1v1p1−1b1a1p1−1−v1×∑i=0∞KMDNt−1KMD+1i1ΓNt+v1+i1−1Γi1+1ΓNt+i1−1×KSM+1Ns−1Nsexp−KSMNs−1Ns×∑p2=1Nr1Γp2a2p2−1∑v2=0p2−1v2p2−1b2a2p2−1−v2×∑i2=0∞KSMKSM+1Ns−1Nsi2ΓNs−1Ns+v2+i2Γi2+1ΓNs−1Ns+i2×Q2where
(40)Q2=∑k1=0∞k1Nt+v1+i1+k1−2−a1k1ψSD−k1+p1−1KMD+1−Nt+v1+i1−1−k1×∑k2=0∞k2NSNS−1+v2+i2+k2−1−a2k2ϕz1−k2+p2−1KSM+1−NSNS−1+v2+i2−k2×Γp1+p2+k1+k2−1b1/ψSD+b2/ϕz1−p1+p2+k1+k2−1×−b2ϕz1+p2−1b1/ψSD+b2/ϕz1p1+p2+k1+k2−2−a2NSNS−1+v2+i2ϕz1×∑k1=0∞k1Nt+v1+i1+k1−2−a1k1ψSD−k1+p1−1KMD+1−Nt+v1+i1−1−k1×∑k2=0∞k2NSNS−1+v2+i2+k2−a2k2ϕz1−k2+p2−1KSM+1−NSNS−1+v2+i2+1−k2×Γp1+p2+k1+k2−1b1/ψSD+b2/ϕz1−p1+p2+k1+k2−1


## 4. Numerical and Simulation Results

In this part, we analyze the surveilling performance of the UAV monitor through numerical and simulation results.ρ=0.1 represents the self-interference coefficient, and the Rayleigh channel variances are λ1=λ2=1. The ground-to-ground channel power gain at a reference distance of 1 m is β1=−5dB, and the UAV-to-ground channel power gain at a reference distance of 1 m is β2=−65dB. The maximize height of UAV is 4000 m, the maximized circle radius of UAV is 1200 m, and the maximized distance between suspicious nodes is 6000 m. In [31], we obtain the system environment and frequency parameters as follows: α1=1, α2=3, α3=5, δ1=44, δ2=9, and δ3=2ln3/π. We obtain the simulation results through Monte Carlo (MC) simulation. In order to ensure the accuracy of the simulation, the number of simulations is 100,000. The detailed parameters in the simulations will be introduced in the description of the figures. Curves without (MC) represent numerical results, and curves with (MC) represent simulated results.Figure2 shows the probability of UAV surveilling non-outage with MRT/RZF and TZF/MRC schemes versus θa. The numerical results and the simulation results completely agree, which verifies our derivation. It is obvious that the surveilling performance of MRT/RZF scheme outperforms that of TZF/MRC scheme, since for facing artificial noise from the suspicious source, it is more effective to use more transmitting antennas to degrade the channel capacity of the suspicious link than improving the surveilling channel capacity by employing the more receiving antennas. When the azimuth angle θa is in the range of 0 to π, since UAV moves in a half circle and is getting closer to the suspicious destination, thus the jamming power on the suspicious destination becomes larger, the artificial noise power on the receiving of UAV becomes smaller, and the monitoring performance of the UAV becomes better. However, as the azimuth angle θa is in the range of π to 2π, the monitoring performance of the UAV becomes worse.Figure 2
The probability of UAV surveilling nonoutage with MRT/RZF and TZF/MRC schemes versusθa, PS=10W, PJ=10W, v=1000m, d=600m, r=400m, αs=0.1, Ns=10, Nr=Nt=5, and σD2=σM2=−115dBm.Figure3 shows the probability of UAV surveilling non-outage with MRT/RZF and TZF/MRC schemes versus radius r. The numerical results and the simulation results completely agree, which validates our derivation. The surveilling non-outage probability increases with the radius until 400 m, since UAV starts linear motion from the origin and is getting closer to the suspicious destination; thus, the jamming power on the suspicious destination becomes larger, and the artificial noise power on the receiving of UAV becomes smaller. Then, as the monitoring distance becomes larger and the channel quality of the legal monitoring link becomes worse, the surveilling non-outage probability decreases as the radius increases.Figure 3
The probability of UAV surveilling nonoutage with MRT/RZF and TZF/MRC schemes versus radiusr, PS=10W, PJ=10W, v=1000m, d=600m, θa=π, αs=0.1, Ns=10, Nr=Nt=5, and σD2=σM2=−115dBm.Figure4 shows the probability of UAV surveilling non-outage with MRT/RZF and TZF/MRC schemes versus the distance between suspicious nodes dSD. The numerical results and the simulation results completely agree, which validates our derivation. Since the distance between suspicious nodes increases and the monitoring link has better channel quality than the suspicious link, the probability of surveilling nonoutage increases with dSD increasing until 2000 m, where the probability of surveilling nonoutage is the largest. Then, as the monitoring distance becomes larger and the channel quality of the legal monitoring link becomes worse, the possibility of UAV surveilling non-outage decreases as dSD increases.Figure 4
The probability of UAV surveilling non-outage with MRT/RZF and TZF/MRC schemes versusdSD, PS=10W, PJ=10W, v=1000m, r=400m, θa=0, αs=0.1, Ns=10, Nr=Nt=5, and σD2=σM2=−115dBm.Figure5 shows the comparison of the surveilling performance versus height when UAV adopts three schemes, that is, active monitoring with the MRT/RZF beamforming scheme, active monitoring with the TZF/MRC beamforming scheme, and the passive monitoring scheme. It is obvious that the surveilling nonoutage probability of passive monitoring scheme is 0, while MRT/RZF and TZF/MRC beamforming schemes with maximum jamming power have better monitoring performance. This shows that UAV passive monitoring scheme is not suitable for the case where the suspicious source uses artificial noise. Only by using the MRT/RZF and TZF/MRC beamforming schemes can UAV improve the surveilling performance. Since the monitoring link has better channel quality than the suspicious link and the active jamming signal received at the suspicious destination becomes larger, the probability of surveilling nonoutage increases with height until 900 m, where the surveilling performance is the best, and then the surveilling performance decreases as the UAV height increases, since the monitoring distance becomes larger, while channel quality keeps unchanged, and active jamming signal received at the suspicious destination becomes smaller. It indicates that reasonable height control can improve UAV surveillance performance.Figure 5
The probability of surveilling nonoutage with different jamming schemes versus the height of UAV,PS=10W, PJ=10W, d=600m, r=400m, αs=0.1, θa=0, Ns=10, and σD2=σM2=−115dBm.Figure6 shows the probability of UAV surveilling non-outage versus the number of receiving antennas for the MRT/RZF beamforming scheme with different jamming powers. It is obvious that the probability of surveilling nonoutage increases with the number of receiving antennas until Nr=5, since it is more effective to improve the surveilling channel capacity than degrading the channel capacity of the suspicious link. Then, the probability of surveilling non-outage decreases as the number of receiving antennas increases, since it is more effective to degrade the channel capacity of the suspicious link than improving the surveilling channel capacity. For UAV monitor with the MRT/RZF beamforming scheme, it should adopt reasonable Nr to improve the surveilling performance.Figure 6
The probability of UAV surveilling nonoutage versus the number of receiving antennas for the MRT/RZF beamforming scheme with different jamming powers,PJ=10W, d=600m, r=400m, θa=0, αs=0.1, σD2=σM2=−115dBm, Ns=10, and Nr+Nt=10.Figure7 shows the probability of UAV surveilling non-outage versus the number of receiving antennas for the TZF/MRC beamforming scheme with different jamming powers. The reason why the surveilling performance of the TZF/MRC scheme increases with Nr and then decreases with Nr is the same as that of the MRT/RZF scheme. For UAV monitor with the TZF/MRC beamforming scheme, it should adopt reasonable Nr to improve the surveilling performance.Figure 7
The probability of UAV surveilling nonoutage versus the number of receiving antennas for the TZF/MRC beamforming scheme with different jamming powers,PJ=10W, d=600m, r=400m, θa=0, αs=0.1, σD2=σM2=−115dBm, Ns=10, and Nr+Nt=10.Figure8 shows the probability of UAV surveilling non-outage with different αS versus UAV maximized jamming power PJ for MRT/RZF and TZF/MRC beamforming schemes. It is obvious that the probability of UAV surveilling non-outage increases with PJ increasing. Furthermore, the probability of UAV surveilling non-outage increases with αS increasing. The MRT/RZF beamforming scheme has a little better surveilling performance than the TZF/MRC beamforming scheme. For UAV monitor, it should adopt larger PJ to improve the surveilling performance.Figure 8
The probability of UAV surveilling nonoutage with differentαS versus UAV maximized jamming power PJ for the MRT/RZF and TZF/MRC beamforming scheme, v=1000m, d=600m, r=400m, θa=0, Nr=Nt=5, Ns=10, and σD2=σM2=−115dBm.Figure9 shows the probability of UAV surveilling non-outage with different Nr and Nt versus PS for MRT/RZF and TZF/MRC beamforming schemes. It is obvious that the probability of UAV surveilling non-outage decreases with PS increasing. Furthermore, when Nr=Nt=5, the probability of UAV surveilling non-outage is the largest. The MRT/RZF beamforming scheme has a little better surveilling performance than the TZF/MRC beamforming scheme.Figure 9
The probability of UAV surveilling nonoutage with differentNr and Nt versus PS, PJ=10W, v=1000m, d=600m, r=400m, αs=0.1, θa=0, Ns=10, and σD2=σM2=−115dBm.For the suspicious source, it should adopt largerPS to avoid being monitored.Figure10 shows the probability of UAV surveilling non-outage with different Nr and Nt versus αS for MRT/RZF and TZF/MRC beamforming schemes. It is obvious that the probability of UAV surveilling non-outage increases with αS increasing. Furthermore, when Nr=Nt=5, the probability of UAV surveilling non-outage is the largest. The MRT/RZF beamforming scheme has a little better surveilling performance than the TZF/MRC beamforming scheme.Figure 10
The probability of UAV surveilling nonoutage with differentNr and Nt versus αS, PS=10W, PJ=10W, v=1000m, d=600m, r=400m, θa=0, Ns=10, and σD2=σM2=−115dBm.For the suspicious source, it should adopt lowerαS to avoid being monitored.


## 5. Conclusion

We propose a legal full-duplex UAV surveillance system in the presence of the ground-to-ground suspicious link with antisurveillance technology. UAV performs passive surveillance and active jamming simultaneously. However, the suspicious source with multiantenna adopts artificial noise to avoid being monitored. The probability of surveilling non-outage is derived for MRT/RZF and TZF/MRC beamforming schemes. For different heights of UAV, the optimal number of receiving antennas with a fixed total number of antennas that maximizes the probability of UAV surveilling non-outage is determined. Impact of angle/radius/height on the surveilling non-outage probability is analyzed. For the suspicious source, impact of the distance between suspicious nodes on the surveilling non-outage probability is analyzed.



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*Source: 5565213-2021-05-12.xml*