# Impact of Hardware Impairments with Imperfect Channel Estimation for Cache-Enabled UAV Relaying Networks

Authors: Dan Deng; Yanyi Rao; Fusheng Zhu
Journal: Wireless Communications and Mobile Computing
 (2020)

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## Abstract

The effects of hardware impairments with imperfect channel estimation for cache-enabled UAV networks are studied in this paper. The effects of the setup parameters, such as the number of cached or relaying nodes, the hardware impairment factor, the channel estimation error, and the transmission SNR, on the outage probability are present by deriving the exact closed-form expressions on outage probability. Also, the asymptotic results are present when the transmission SNR is large enough. From the asymptotic analysis, we can see that there is an error floor introduced by the hardware impairments and imperfect channel estimation. Specifically, the error floor is dependent on the channel estimation error factor, the hardware impairment distortion factor, and the QoS requirements. And the diversity order of the error floor for the cached/relaying links is equal to the number of cached/relaying UAV nodes.


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## Body

## 1. Introduction

In recent years, wireless throughput is growing up exponentially [1–3] and wireless communication network is facing more and more challenges introduced by wireless big data [4–7]. Cache technology, which can both improve the quality of service (QoS) of wireless link and relieve the pressure of wireless throughput, has demonstrated as a remarkable enabling solution for wireless networks [8–10]. By exploiting interference neutralization, the authors in [11] proposed an optimal content placement method to improve the system capacity. Furthermore, the maximum distance separable coding is adopted in wireless cache networks in [12], which can improve the system performance in terms of successful retrieval probability.On the other hand, hardware impairments, which are introduced by phase noise of the RF components, show great effects on the system performance. Hardware impairments have been extensively studied and modeled as additive distortion noise [13] or nonlinear polynomial multiplicative factor [14, 15]. Considering amplify-and-forward (AF) relaying networks, the authors in [16] investigated the effects of hardware impairments on channel capacity by exact closed-form expression as well as the tight bounds, while Ref. [17] proved that larger hardware impairments can be used in massive MIMO due to the huge degrees of space freedom. By using iterative optimization algorithm, Ding et al. [18] proposed a solution to maximize the detection probability.Meanwhile, due to the high mobility, there exists imperfect channel estimation since the linear estimation methods are applied on pilot signals [19]. Considering correlated Rayleigh fading with imperfect channel status information, Al-Hussaibi and Ali [20] derived expressions on the ergodic capacity with antenna selection. The authors in [21] analyzed the impact of imperfect CSI estimation for Alamouti-OSTBC Wireless Cooperative Networks in terms of symbol error probability.However, the impacts of hardware impairments with imperfect channel estimation on relaying networks are still open questions. Considering unmanned aerial vehicle (UAV) networks, the UAV nodes work as a cache enable access point or an AF relaying node. To improve the QoS of the wireless channels, the best cached UAV nodes or AF relaying nodes are selected to help the message transmission from the macro BS to the user. The effects of the system parameters, such as the number of cached/relaying nodes, the hardware impairment factor, the channel estimation error, and the transmission SNR, on the outage probability are present by deriving the exact closed-form expressions on outage probability. Also, the asymptotic results are present when the transmission SNR is large enough. From the asymptotic analysis, we can see that there is an error floor introduced by the hardware impairments and imperfect channel estimation. Specifically, the error floor is dependent on the channel estimation error factor, the hardware impairment distortion factor, and the QoS requirements. And the diversity order of the error floor for the cached/relaying links is equal to the number of cached/relaying UAV nodes.The main contributions of this paper are as follows:(i)
Cache-enabled UAV relaying protocol is adopted to improve the QoS of the wireless links, where the UAV nodes work as a cache enable access point or an AF relaying node(ii)
We provide the deep insight on the effects of the system parameters, such as the number of cached/relaying nodes, the hardware impairment factor, the channel estimation error, and the transmission SNR, on the outage probability by deriving the exact closed-form expressions on outage probabilityThe organization of this paper is as follows. Section2 presents the system model of cache-enabled amplify-and-forward UAV networks, while the UAV selection algorithm and its performance analysis are given in Section 3. Furthermore, the asymptotical analysis is present in Section 4 with large transmission power. In Section 5, simulation results are present to validate the theoretical analysis. Finally, conclusion is given in Section 6.


## 2. System Model

The system model of cache-enabled amplify-and-forward unmanned aerial vehicle (UAV) networks is present in Figure1, where there is one destination user, one macro base station (BS) and N cache-enabled UAV relaying nodes. We assumed that all nodes are equipped with only one antenna. Furthermore, because of the shadow fading, there is no direct link from the macro BS to the destination user. In order to improve the QoS of the links, one of the UAV nodes is selected to assist the message transmission. Since the UAV nodes hold limited cache memory, the backhaul load from the macro BS to the UAV nodes can be relieved if the requested files from the user are hit in the UAV nodes. In this case, one of the UAV nodes is selected and directly transmits message to the user. On the other hand, if the requested file is not cached, the selected UAV node will work as an amplify-and-forward relaying node to help the data transmission. It is assumed that all links are block Rayleigh fading channel and independent with each other.Figure 1
System model of cache-enabled amplify-and-forward UAV networks.


## 3. Selection Algorithm and Performance Analysis

### 3.1. Cached Links

If the requested file is cached by the UAV nodes, the power normalized transmission signal from the UAV node can be modeled as [13]
(1)si=11+κηs^i+κηηi,where s^i is the information bearing signal with unit power, ηi∈CN0,1 is the distortion noise introduced by hardware impairments [22–25], and κη is the hardware impairment distortion factor.Since the classical MMSE channel estimation algorithm is adopted, there exists some estimation error between the real channel fading coefficient and the estimated version [26–29]. It is assumed that the estimation error is independent with the imperfect CSI [30–35]. Thus, the relationship between the imperfect channel status information and the ideal version is given as
(2)hu,i=11+κeh^u,i+κeei,where hu,i∈CN0,1 is the CSI from the ith UAV node to the user, while h^u,i∈CN0,1 denotes the imperfect estimation of hi, ei∈CN0,1 is the difference between h^u,i and hu,i, and κe is the channel estimation error factor. Specifically, κe=0 means the perfect channel estimation.Given that theith UAV relaying node is selected, the requested file is cached by the selected node. Then, the received signal of the user can be given as
(3)yi=PRhu,isi+ni=PR1+κe1+κηh^u,i+κeeis^i+κηηi+ni,where PR is the transmission power of the UAV node, and ni∈CN0,σ2 is the received white Gauss noise.Then, the signal to interference plus noise ratio (SINR) can be given as(4)γc,i=ρu,iρu,iκη+d1,where
(5)ρu,i=h^u,i2,λR=PRσ2,d1=κe1+κη+1+κe1+κηλR.Obviously,γc,i is a monotone increasing function of ρu,i. In this case, the optimal UAV node can be given as follows:
(6)n1∗=argmaxi∈ΩCρu,i.Due to the independence between differentρu,i’s, according to the ordered statistics, we have
(7)Fρu,n1∗x=Fρu,ixNR=1−e−xNR,where NR is the number of relaying nodes.Then, the outage probability of the cached links can be given as(8)PO,C=PrCC<C0=Prγr,n1∗<γ0=Prρu,n1∗<d1γ01−κηγ0,where γ0=2C0−1 and C0 are the required capacity.Substituting (7) into (8), we obtain
(9)PO,C=Prρu,n1∗<d1γ01−κηγ0=1−expd1γ01−κηγ0NR,γ0<1κη.


### 3.2. Relaying Links

On the other hand, if the requested file is not cached in the selected UAV node, the original message will be transmitted from the macro BS to the user with the help of the UAV node by using amplify-and-forward relaying protocol.In this case, the received signal at theith UAV node can be given as
(10)ri=hr,iPS1+κηs^i+κηηi+nr,i,where PS is the transmission power of the macro BS, hr,i∈CN0,1 denotes the channel fading coefficient from the macro BS to the ith UAV node, and nr,i∈CN0,σ2 is the received Gauss noise at the UAV node.Then, the UAV node will amplify the received signal with powerPR and retransmit to the user. Thus, the received signal at the user through AF protocol can be given as
(11)yi=hu,iζiri+ni,where ζi is the power amplify factor as follows
(12)ζi=PRρr,iPS+σ2,and ρr,i=hr,i2 is the channel fading power of the first hop.By substituting (2) and (12) into (11), we can obtain the SINR at the user through AF protocol
(13)γr,i=ρr,iρu,iρr,iρu,iκη+ρr,iCr+ρu,iCu+Cn,where
(14)ρr,i=h^r,i2,λS=PSσ2,λR=PRσ2,cr=κe1+κη,cu=1+κe1+κηλR+σ2,cn=κeσ2+1+κe1+κηλS/λR.In order to obtain the best SINR, an UAV selection algorithm can be employed. Note that if the transmission power is large enough, i.e.,λS→0, λR→0, the high order items can be ignored. Then, γr,i in (13) can be simplified as
(15)γr,i≃κη+crρu,i+cuρr,i−1.To simply the complexity of theoretical analysis, we use the following approximation. Recall the following fact that [36]
(16)1minx,y≤1x+1y≤2minx,y,∀x,y>0.To obtain the best SINR through AF protocol, the selection criterion can be given as(17)n2∗=argmaxi∈ΩRminρu,i,ξρr,i,where ξ=cr/cu.Theorem 1.
The cumulative distribution functions ofρu,n2∗ and ρr,n2∗ are given as
(18)Fρu,n2∗x=NR∑k=1NR−1bk1ξ2−e−xξ3+e−ξ2xξ3ξ2,Fρr,n2∗x=NR∑k=1NR−1bk1ξ2−e−xξ4+e−ξ2ξxξξ2ξ4,for NR≥2.
(19)Fρu,n2∗x=Fρr,n2∗x=1−e−x,for NR=1, where
(20)ξ1=1+1ξ,ξ2=k+1ξ1,ξ3=kξ1+1ξ=ξ2−1,ξ4=kξ1+1=ξ2−1ξ,bk=CNR−1k−1k−1kξ1.
Taking the derivative of equations in Theorem1, we can obtain the following corollary.Corollary 2.
The probability distribution functions ofρu,n2∗ and ρr,n2∗ are given as
(21)fρu,n2∗x=NR∑k=1NR−1bkξ3e−x−e−ξ2x,fρr,n2∗x=NR∑k=1NR−1bkξ4e−x−e−ξ2ξx,for NR≥2, and
(22)fρu,n2∗x=fρr,n2∗x=e−x,for NR=1.Proof.
See Appendix VI-A.
Considering the SINR expression in (13), the outage occurs when γr,n2∗ falls below the quality-of-service requirement, i.e.,
(23)PO,R=PrCR<C0=Prγr,n2∗<γ0,where γ0=2C0−1.
Substituting (13) into (24), we have
(24)PO,R=Prρr,iρu,iρr,iρu,iκη+ρr,iCr+ρu,iCu+Cn<γ0=Prρr,iρu,i1−γ0κη<ρr,iCrγ0+ρu,iCuγ0+γ0Cn=Prρr,iρu,i1−γ0κη−Crγ0<ρu,iCuγ0+γ0Cn.
Applying conditional probability formula, we have(25)PO,R=Prρr,iρu,i1−γ0κη−crγ0<ρu,icuγ0+γ0cn=Prρu,i<c1+Prρr,i<c2ρu,i+cn/cuρu,i−c1,ρu,i≥c1=Prρu,i<c1⏟P1+Prρr,i≤c2,ρu,i≥c1⏟P2+Prc2<ρr,i<c2ρu,i+cn/cuρu,i−c1,ρu,i≥c1⏟P3,where
(26)c1=crγ01−γ0κη,c2=cuγ01−γ0κη,c3=cnc1cu.
Applying (18) on (25), we can obtain
(27)P1=Fρu,n2∗c1,(28)P2=Fρr,n2∗c21−Fρu,n2∗c1.
To derive the exact expression ofP3, firstly we give the following definition
(29)FZz=Prρu,i+cn/cuρu,i−c1<z,ρu,i≥c1,z>1=Prρu,i>c1z+cn/c1cuz−1,ρu,i≥c1,z>1=Prρu,i>c1z+cn/c1cuz−1,z>1=Prρu,i>c1z+c3z−1,z>1.
Applying (18) on (29), we can obtain
(30)FZz=Prρu,i>c1z+c3z−1,z>1=Fρu,n2∗c1z+c3z−1.
Thus, the itemP3 in equation (25) can be given as
(31)P3=Prc2<ρr,i<c2ρu,i+cn/cuρu,i−c1,ρu,i≥c1=∫x>c2+∞fρr,n2∗x1−FZxc2dx=∫x>c2+∞fρr,n2∗x1−Fρu,n2∗c1x+c3c2x−c2dx.
By using necessary mathematical derivation and applying equation (3.324-1) in [37], i.e.,
(32)∫0+∞expβ4x−γxdx=βγK1βγ,the closed-form expression of P3 can be obtained.
By substituting (27), (28), and (31) into (25), we can obtain the exact closed-form expression of PO,R.


## 3.1. Cached Links

If the requested file is cached by the UAV nodes, the power normalized transmission signal from the UAV node can be modeled as [13]
(1)si=11+κηs^i+κηηi,where s^i is the information bearing signal with unit power, ηi∈CN0,1 is the distortion noise introduced by hardware impairments [22–25], and κη is the hardware impairment distortion factor.Since the classical MMSE channel estimation algorithm is adopted, there exists some estimation error between the real channel fading coefficient and the estimated version [26–29]. It is assumed that the estimation error is independent with the imperfect CSI [30–35]. Thus, the relationship between the imperfect channel status information and the ideal version is given as
(2)hu,i=11+κeh^u,i+κeei,where hu,i∈CN0,1 is the CSI from the ith UAV node to the user, while h^u,i∈CN0,1 denotes the imperfect estimation of hi, ei∈CN0,1 is the difference between h^u,i and hu,i, and κe is the channel estimation error factor. Specifically, κe=0 means the perfect channel estimation.Given that theith UAV relaying node is selected, the requested file is cached by the selected node. Then, the received signal of the user can be given as
(3)yi=PRhu,isi+ni=PR1+κe1+κηh^u,i+κeeis^i+κηηi+ni,where PR is the transmission power of the UAV node, and ni∈CN0,σ2 is the received white Gauss noise.Then, the signal to interference plus noise ratio (SINR) can be given as(4)γc,i=ρu,iρu,iκη+d1,where
(5)ρu,i=h^u,i2,λR=PRσ2,d1=κe1+κη+1+κe1+κηλR.Obviously,γc,i is a monotone increasing function of ρu,i. In this case, the optimal UAV node can be given as follows:
(6)n1∗=argmaxi∈ΩCρu,i.Due to the independence between differentρu,i’s, according to the ordered statistics, we have
(7)Fρu,n1∗x=Fρu,ixNR=1−e−xNR,where NR is the number of relaying nodes.Then, the outage probability of the cached links can be given as(8)PO,C=PrCC<C0=Prγr,n1∗<γ0=Prρu,n1∗<d1γ01−κηγ0,where γ0=2C0−1 and C0 are the required capacity.Substituting (7) into (8), we obtain
(9)PO,C=Prρu,n1∗<d1γ01−κηγ0=1−expd1γ01−κηγ0NR,γ0<1κη.


## 3.2. Relaying Links

On the other hand, if the requested file is not cached in the selected UAV node, the original message will be transmitted from the macro BS to the user with the help of the UAV node by using amplify-and-forward relaying protocol.In this case, the received signal at theith UAV node can be given as
(10)ri=hr,iPS1+κηs^i+κηηi+nr,i,where PS is the transmission power of the macro BS, hr,i∈CN0,1 denotes the channel fading coefficient from the macro BS to the ith UAV node, and nr,i∈CN0,σ2 is the received Gauss noise at the UAV node.Then, the UAV node will amplify the received signal with powerPR and retransmit to the user. Thus, the received signal at the user through AF protocol can be given as
(11)yi=hu,iζiri+ni,where ζi is the power amplify factor as follows
(12)ζi=PRρr,iPS+σ2,and ρr,i=hr,i2 is the channel fading power of the first hop.By substituting (2) and (12) into (11), we can obtain the SINR at the user through AF protocol
(13)γr,i=ρr,iρu,iρr,iρu,iκη+ρr,iCr+ρu,iCu+Cn,where
(14)ρr,i=h^r,i2,λS=PSσ2,λR=PRσ2,cr=κe1+κη,cu=1+κe1+κηλR+σ2,cn=κeσ2+1+κe1+κηλS/λR.In order to obtain the best SINR, an UAV selection algorithm can be employed. Note that if the transmission power is large enough, i.e.,λS→0, λR→0, the high order items can be ignored. Then, γr,i in (13) can be simplified as
(15)γr,i≃κη+crρu,i+cuρr,i−1.To simply the complexity of theoretical analysis, we use the following approximation. Recall the following fact that [36]
(16)1minx,y≤1x+1y≤2minx,y,∀x,y>0.To obtain the best SINR through AF protocol, the selection criterion can be given as(17)n2∗=argmaxi∈ΩRminρu,i,ξρr,i,where ξ=cr/cu.Theorem 1.
The cumulative distribution functions ofρu,n2∗ and ρr,n2∗ are given as
(18)Fρu,n2∗x=NR∑k=1NR−1bk1ξ2−e−xξ3+e−ξ2xξ3ξ2,Fρr,n2∗x=NR∑k=1NR−1bk1ξ2−e−xξ4+e−ξ2ξxξξ2ξ4,for NR≥2.
(19)Fρu,n2∗x=Fρr,n2∗x=1−e−x,for NR=1, where
(20)ξ1=1+1ξ,ξ2=k+1ξ1,ξ3=kξ1+1ξ=ξ2−1,ξ4=kξ1+1=ξ2−1ξ,bk=CNR−1k−1k−1kξ1.
Taking the derivative of equations in Theorem1, we can obtain the following corollary.Corollary 2.
The probability distribution functions ofρu,n2∗ and ρr,n2∗ are given as
(21)fρu,n2∗x=NR∑k=1NR−1bkξ3e−x−e−ξ2x,fρr,n2∗x=NR∑k=1NR−1bkξ4e−x−e−ξ2ξx,for NR≥2, and
(22)fρu,n2∗x=fρr,n2∗x=e−x,for NR=1.Proof.
See Appendix VI-A.
Considering the SINR expression in (13), the outage occurs when γr,n2∗ falls below the quality-of-service requirement, i.e.,
(23)PO,R=PrCR<C0=Prγr,n2∗<γ0,where γ0=2C0−1.
Substituting (13) into (24), we have
(24)PO,R=Prρr,iρu,iρr,iρu,iκη+ρr,iCr+ρu,iCu+Cn<γ0=Prρr,iρu,i1−γ0κη<ρr,iCrγ0+ρu,iCuγ0+γ0Cn=Prρr,iρu,i1−γ0κη−Crγ0<ρu,iCuγ0+γ0Cn.
Applying conditional probability formula, we have(25)PO,R=Prρr,iρu,i1−γ0κη−crγ0<ρu,icuγ0+γ0cn=Prρu,i<c1+Prρr,i<c2ρu,i+cn/cuρu,i−c1,ρu,i≥c1=Prρu,i<c1⏟P1+Prρr,i≤c2,ρu,i≥c1⏟P2+Prc2<ρr,i<c2ρu,i+cn/cuρu,i−c1,ρu,i≥c1⏟P3,where
(26)c1=crγ01−γ0κη,c2=cuγ01−γ0κη,c3=cnc1cu.
Applying (18) on (25), we can obtain
(27)P1=Fρu,n2∗c1,(28)P2=Fρr,n2∗c21−Fρu,n2∗c1.
To derive the exact expression ofP3, firstly we give the following definition
(29)FZz=Prρu,i+cn/cuρu,i−c1<z,ρu,i≥c1,z>1=Prρu,i>c1z+cn/c1cuz−1,ρu,i≥c1,z>1=Prρu,i>c1z+cn/c1cuz−1,z>1=Prρu,i>c1z+c3z−1,z>1.
Applying (18) on (29), we can obtain
(30)FZz=Prρu,i>c1z+c3z−1,z>1=Fρu,n2∗c1z+c3z−1.
Thus, the itemP3 in equation (25) can be given as
(31)P3=Prc2<ρr,i<c2ρu,i+cn/cuρu,i−c1,ρu,i≥c1=∫x>c2+∞fρr,n2∗x1−FZxc2dx=∫x>c2+∞fρr,n2∗x1−Fρu,n2∗c1x+c3c2x−c2dx.
By using necessary mathematical derivation and applying equation (3.324-1) in [37], i.e.,
(32)∫0+∞expβ4x−γxdx=βγK1βγ,the closed-form expression of P3 can be obtained.
By substituting (27), (28), and (31) into (25), we can obtain the exact closed-form expression of PO,R.


## 4. Asymptotical Analysis

To get a deep insight on the impact of hardware impairments with imperfect channel estimation, we will conduct the asymptotical analysis of outage probability. Note that if the transmission power is large enough, i.e.,1/λS→0,1/λR→0, and κe→0,κη→0.Thus, we have(33)cr≃κe1+κη,cu≃σ2,cn≃κeσ2d1≃κe1+κη,ξ≃κe1+κησ2,c1≃κe1+κηγ01−γ0κη,c2≃σ2γ01−γ0κη,c3≃1−γ0κη1+κηγ0.Applying the approximation that1−e−x≃x, if x→0 on (9), we have
(34)PO,C≃d1γ01−κηγ0NC≃γ0κe1+κη1−κηγ0NC.According to the asymptotical expression on outage probability for cached links, we can conclude the following remarks:Remark 3.
There is an error floor for the cached links when the transmission power is large enough. Meanwhile, the diversity order with respect to the transmission power is zero.Remark 4.
The error floor for the cached links is dependent on the channel estimation error factorκe, the hardware impairment distortion factor κη, and the QoS requirements γ0.Remark 5.
The diversity order of error floor for the cached links is equal to the number of cached UAV nodes.Considering the SINR expression in (15), we have
(35)PO,R≃Prmaxi∈ΩRminρu,i,ξρr,i<γ0ξcu1−γ0κη=Prminρu,i,ξρr,i<c4NR.By using the result in (A.3), we have
(36)PO,R≃1−e−ξ1c4NR≃ξ1c4NR≃γ01+ξσ21−γ0κηNR≃γ0σ2+κe1+κη1−γ0κηNR,where
(37)c4=γ0ξcu1−γ0κη≃γ0ξσ21−γ0κη.Remark 6.
There also exists an error floor for the relaying links when the transmission power is large enough.Remark 7.
The diversity order of error floor for the relaying links is equal to the number of relaying UAV nodes.


## 5. Simulation Results

In this section, simulation results are provided to verify the accuracy of the theoretical analysis. For the sake of simplicity, we setκe=κη=σ2. The impacts of the system parameters, such as the number of UAV nodes N, the transmission SNR of the cached links and the relaying links λS,λR, and the capacity threshold C0, are investigated.Figure2 shows the impacts of transmission SNR λS on outage performance for cached links. In this simulation, we have the following system parameters: NC=2,κe=κη=0.01,C0=1bps/Hz, and the transmission SNR λS changes from 12 dB to 39 dB. The simulation results and the theoretical analysis as well as the asymptotic analysis are compared in this figure. As shown in this figure, in all SNR regions, the simulation results match well with the theoretical analysis. Furthermore, an error floor appears when the transmission SNR grows large, which coincides with the asymptotic performance analysis. The reason is that when SNR is large enough, the bottleneck of the system performance is the hardware impairments and the channel estimation error. The detailed relationship between the error floor and κη and κe is given as in equations (34) and (36). When the requested file is not hit by the UAV nodes, amplify-and-forward protocol is adopted and the simulation results are present in Figure 3, where similar conclusion can be obtained for relaying links with NR=2.Figure 2
Outage probability for cached link withNC=2.Figure 3
Outage probability for AF relaying links withNR=2.Figures4 and 5 show the effects of the capacity threshold C0 on outage probability for cached links and relaying links, respectively. The system parameters are set as follows: NC=NR=2,κe=κη=0.01, and the capacity threshold C0 changed from 1 bps/Hz to 3 bps/Hz. From the two figures, we can observe that C0 shows significant impact on outage probability for all of the SNR regions. Specifically, the diversity order of outage probability is zero with respect to the transmission SNR λS or λR.Figure 4
Outage probability versus capacity threshold for cached links withNC=2.Figure 5
Outage probability versus capacity threshold for relaying links withNR=2.Figures6 and 7 show the effects of the hardware impairment factor κη on outage probability for cached links and relaying links, respectively. The system parameters are set as follows: NC=NR=2,κe=κη=0.01,C0=1bps/Hz, and the hardware impairment factor κη changed from 0.01 to 0.03. From these figures, we can observe that C0 shows considerable impact on outage probability especially in high SNR regions. Specifically, the larger κη will introduce higher error floor. The reason is that, in the considered scenario, the bottleneck of the system performance is the hardware impairments. When the hardware impairment factor κη grows larger, the noise power will be higher, which will deteriorate the system performance.Figure 6
Outage probability versusκη for cached links with NC=2.Figure 7
Outage probability versusκη for relaying links with NR=2.The effect of the number of cached UAV nodes is present in Figure8, where the system parameters are set as follows: κe=κη=0.01,C0=1bps/Hz, and the number of cached UAV nodes NC changed from 2 to 3. We can see from this figure that NC shows great impact on system performance. As mentioned by the remarks of asymptotic analysis, the diversity order of error floor for the cached/relaying links is equal to the number of cached/relaying UAV nodes.Figure 8
Outage probability versusNC for cached links.


## 6. Conclusions

The impacts of hardware impairments with imperfect channel estimation for cache-enabled UAV relaying networks are investigated in this paper. To improve the QoS of the wireless channels, the best cached UAV nodes or AF relaying nodes are selected to help the message transmission from the macro BS to the user. The impacts of the setup parameters, such as the number of cached/relaying nodes, the hardware impairment factor, the channel estimation error, and the transmission SNR, on the outage probability are present by deriving the exact closed-form expressions on outage probability. Also, the asymptotic results are present when the transmission SNR is large enough. From the asymptotic analysis, we can see that there is an error floor introduced by the hardware impairments and imperfect channel estimation. Specifically, the error floor is dependent on the channel estimation error factor, the hardware impairment distortion factor, and the QoS requirements. In future works, we will introduce deep learning-based [38–40] or Q-learning-based algorithms [41, 42] to further improve the system performance. Moreover, we will apply the considered wireless techniques into some practical IoT systems [43, 44] to achieve the green energy applications.



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*Source: 8891793-2020-08-10.xml*