Optimization for UAV-assisted simultaneous transmission and reception communications in the existence of malicious jammers

In this paper, we study an unmanned aerial vehicle (UAV)-assisted communication system, where the UAV is dispatched to implement simultaneous transmission and reception (STR) in the existence of multiple malicious jammers. Two schemes are investigated, namely frequency band-division-duplex (FDD) and time-fraction (TF). Based on the FDD scheme, the UAV can transmit information by using the portion of the bandwidth and receive information within the remaining portion of the bandwidth simultaneously. To perform the STR within the whole bandwidth, the TF-based scheme is considered by using a fraction of a time slot for the downlink, while the remaining fraction of the time slot is allocated for the uplink. We aim to maximize the worst-case throughput by optimizing the UAV three-dimensional (3D) trajectory and resource allocation for each scheme. The optimization problem is non-convex and thus computationally intractable. To handle the nonlinear problem, we use the block coordinate decomposition method to disaggregate the optimization problem into four subproblems and adopt the successive convex approximation technique to tackle non-convex problems. The simulation results demonstrate the performance of the TF-based scheme over the benchmark schemes.


Introduction
In the B5G/6G wireless communication network, unmanned aerial vehicles (UAVs) are prominent owing to their advanced agility and potential capability in disasters, transportation, or complex environments [1][2][3].Unlike terrestrial communication facilities, UAVs can improve the quality of service, due to the high controllability and dominance of line-of-sight (LoS) links at moderate heights [4][5][6].Thus, UAVs not only act as aerial base stations to send information to ground users [7][8][9] but also are utilized to collect data from terrestrial nodes [10][11][12].
Recently, many studies have been devoted to the optimization of UAV-based uplink (UL) and downlink (DL) communication [13][14][15].Based on half-duplex communication, resource allocation has been optimized to improve the network throughput [16].For simultaneous transmission and reception (STR), frequency band-division-duplex (FDD) with fixed bandwidth allocation was considered [17].To perform STR in the whole bandwidth, two UAVs' cooperative communication network was considered in [18], where one UAV was dispatched to send information and the other UAV was used to receive information from ground users.By applying the full-duplex (FD) technology, the optimization of resource allocation between DL and UL communication is important [19][20][21][22][23][24].In [19], one UAV was deployed to simultaneously serve multiple downlink users (DLUs) and uplink users (ULUs), where four different STR schemes were investigated to maximize the throughput of the system.A novel joint uplink-downlink resource allocation algorithm that optimizes the power allocation for uplink and downlink to achieve balanced average rates for both UL and DL communications was proposed [20].A cellular network in [21] was investigated comprising a UAV-mounted aerial base station and multiple terrestrial base stations, each serving multiple users.The balance between DL throughput and UL throughput in the UAV-based communication networks was investigated [22].The UL and DL resource allocation were jointly optimized to improve spectrum efficiency [23].Similarly, [24] improved the overall capacity by considering scheduling, UAV trajectory, and ULU power allocation.Full-duplex communication faces challenges due to self-interference, where the transmit signal can interfere significantly with the received signal.This strong interference hinders the performance of FD systems [25].It is a remarkable fact that the quality of service in FDbased communication depends on self-interference, which cannot be neglected in the network.Instead of utilizing the FD communication, FDD and time-fraction (TF) are investigated to implement the simultaneous transmission and reception within a time slot in this paper.Besides, resource allocation such as bandwidth allocation and time slot scheduling are considered in the optimization [26,27].
In addition, the security of UAV-based communications is more susceptible to interference from malicious terrestrial nodes due to the physical properties of the air-ground broadcast channel [28].In [29], the secrecy rate of DL and UL communication was optimized considering the security of UAV-based communication in the existence of eavesdroppers.Additionally, considering both unfriendly jammers and eavesdroppers in [30], the UAV trajectory and power allocation were optimized to improve the secrecy rate of DL and UL communications.However, [29] and [30] considered scenarios where users can only act as uplink or downlink nodes during a one-time slot (TS).The scenario of the UAV simultaneously serving ULUs and DLUs in the presence of malicious jammers has not been investigated.
Motivated by the aforementioned issues, a UAV-assisted STR communication system in the existence of multiple jammers is considered.We aim to maximize the worst communication throughput among DLUs and ULUs.The main contributions of this investigation can be captured as follows: • To perform the STR, we first investigate the FDD-based scheme for UAV-assisted downlink-anduplink communication.The available bandwidth is divided for DL and UL communication within a single time slot.The presence of multiple jammers adds complexity to the system, as they send malicious interference signals to both the UAV and users.To address these challenges, we propose a joint optimization approach.Specifically, we optimize the UAV's three-dimensional trajectory, downlink scheduling, uplink scheduling, bandwidth allocation, and UAV's transmission power.Our objective is to maximize the worst throughput among DLUs and ULUs, considering the impact of interference from the jammers.• Furthermore, instead of the bandwidth allocation for DL and UL communication, a time fraction (TF) based transmission scheme to maximize the worst throughput by utilizing the fraction of a time slot for the DL communication and the remaining fraction for the UL communication [31].In the TF-based scheme, we optimize the time fraction to balance DL and UL communication.To address each non-convex optimization problem, we develop the mathematically soluble optimization algorithm for each scheme based on the block coordinate decomposition (BCD) method and successive convex approximation (SCA) technique.• Finally, we analyze the convergence of the proposed approaches and examine the system performance by adopting different schemes through numerical simulations.
The organization of the paper is as follows.The channel model and FDD-based UAV-assisted system model are presented in Section 2, whereas TF-based UAV-assisted STR is constructed in Section 3 to optimize downlink scheduling, uplink scheduling, 3D trajectory, UAV transmission power, and time

Frequency band-division-duplex based scheme
We establish a UAV-based joint DL and UL communication network with K D terrestrial downlink users and K U uplink users in the presence of K M jammers as shown in Figure 1.
The frequency band-division-duplex is proposed for simultaneous transmission and reception, where the downlink channel is orthogonal to the uplink channel [32].The planned flight time T is evenly separated into N time slots δ and FDD-based UAV can communicate with a DLU and a ULU during one TS.Therefore, the constraints for DLU's scheduling and ULU's scheduling can be given by where x DL j,n and x UL i,n represent user scheduling of j-th DLU j ∈ {1, . . ., K D } and i-th ULU i ∈ {1, . . ., K U }, respectively.
Different from the fixed bandwidth segmentation in [17], we define τ n as the portion of the normalized bandwidth, which is allocated to the downlink communication during n-th TS.Meanwhile, ζ denotes the portion for guarding, while (η − τ n ) with η = 1 − ζ is denoted by us as the rest of the bandwidth for uplink communication.Define τ = {τ n , ∀n}, ∀n}.P is the transmit power of UAV.Q is the 3D UAV-assisted coordinate, where Q n and H n are denoted as the horizontal coordinate and the flight height, respectively.Let [Q ini H ini ] denote the initial point, while [Q end H end ] denotes the end location.The UAV's mobility is limited by where V xy max is the maximum horizontal velocity and V z max is the maximum vertical velocity.The UAV-toground (U2G) channel, and the ground-to-UAV (G2U) channel are assumed to be dominated by LoS [4].Due to the characteristics of wireless channels, the channel from the UAV to the j-th DLU, the channel from the i-th ULU to the UAV and the channel from the m-th jammer to the UAV during the n-th TS can be regarded as Rician fading [18]: where the large-scale attenuation can be expressed as Let K r be the Rician factor, while ρn denotes the deterministic LoS component with |ρ n | = 1, ρn ∼ CN (0, 1) is the small-fading fraction and β 0 indicates the channel gain at the reference distance.
The small-scale fading can be expressed as ρ n = Kr Kr+1 ρn + 1 Kr+1 ρn [18].For the ground-to-ground (G2G) channels between m-th jammer and j-th DLU within one TS, the channels are largely subject to Rayleigh fading, which can be defined as h DL m,j = β 0 d −α m,j [24].Additionally, is a random value that follows an exponential distribution with a unit mean.
The FDD-based network downlink throughput within the n-th TS can be formulated as [33] ṘFDD where p b n is denoted as the transmission power of the UAV, while P m is the interference power of m-th jammer.σ 2 is the white Gaussian noise power.Also, the FDD-based network uplink throughput is given by where P i represents the ULU's transmission power.However, because of the randomness of the channel gain, the achievable throughput is random.We aim to investigate the average throughput of the network and the approximated throughput expression is given by [18], the FDD throughput of the downlink during n-th TS is formulated as where σ 2 denotes the white Gaussian noise power.Besides, the FDD throughput of the uplink during n-th TS is given by The binary constraints (3)-( 4) make it inefficient to obtain a global feasible solution.According to the approach in the study [24], the binary constraints can be rewritten as Considering the 3D trajectory design, the ULU/DLU scheduling, and the UAV transmission power, to find the balance between DL and UL communication, we aim to maximize the worst average throughput of the network.The optimization problem of FDD-based communication can be formulated as max XD ,XU ,Q,P,τ (1)−( 2), ( 5)−( 8), ( 16)−( 17), where denote the average throughput of j-th downlink and i-th uplink communication, respectively.P max denotes the transmission power allocation budget.

Subproblem for the user scheduling
We fixed the feasible point the transmission power of the UAV P, the 3D trajectory Q, and the allocation portion τ to obtain the optimal DLU's scheduling X D and ULU's scheduling X U .The optimization subproblem can be expressed as max s.t. ( 16)−( 17), (1)−( 2), (20b) Obviously, the subproblem for user scheduling is a standard linear problem, which can be solved efficiently by using an optimization package [24].

Subproblem for the portion of bandwidth
With the achievable DLU's scheduling X D , ULU's scheduling X U , the transmission power of the UAV P and the 3D trajectory Q, the objective function (19) can be reformulated as follows To deal with constraint (21c) and constraint (21d) more efficiently, we apply the inequality (66) with [τ r n , ∀n] for them respectively.Next, the lower bound RFDD j,n (τ ) and the lower bound RFDD i,n (τ ) yield as follows ) ) where , and Analogously, the optimal subproblem (21) can be reformulated as The above subproblem (24) can be solved steadily and the local solution can be obtained efficiently.

Subproblem for the 3D trajectory design
In this part, we aim to optimize the 3D trajectory Q, while DLU's scheduling X D , ULU's scheduling X U , the transmission power of the UAV P, and the portion of bandwidth τ are fixed.The objective function (19) can be rewritten as max s.t. ( 5)−( 8), (25b) The constraint (25c) and the constraint (25d) are non-convex w.r.t the 3D trajectory Q.Firstly, we define the lower bound for the term where and With reference to the term R FDD i,n (Q) in the constraint (25d), by introducing slack variables L = {L FDD i,n , ∀n, i} and with extra constraints and Next, we apply inequality (64) for (27), and the lower bound RFDD,lb i,n (L, I) of ( 27) can be expressed as where ) .
To handle the extra non-convex constraint (29), we introduce the slack variable D = {d FDD m,n , ∀n, m} to transform the constraint (29) into the new constraints as follows The right-hand side (RHS) of the constraint ( 32) is non-concave, by using the first-order Taylor expansion, the lower bound is derived as The constraint (32) can be rewritten as The optimization problem( 25) can be revised as max Q,D,L,I,ϑ ϑ (36a) s.t.

Subproblem for UAV transmission power allocation
With the given DLU's scheduling X D , ULU's scheduling X U and the 3D trajectory of the UAV Q, the optimization problem ( 19) can be reformulated as follows max The left-hand side (LHS) of the constraint (37c) is concave w.r.t the UAV transmission power p b n .We can obtain the local solution by using CVX [34] expeditiously. where Similarly, by introducing the slack variable ϑ, the objective function (41) can be rewritten as follows max (1)−( 2), ( 5)−( 8), ( 16)−( 17), (42d) Again, by using the BCD technique, we alternately optimize the user scheduling X D , X U , the time fraction µ, the 3D trajectory of the UAV Q and the UAV transmission power P to obtain the optimal solution.

Subproblem for User Scheduling
Define the time fraction µ, 3D trajectory Q and the transmission power of the UAV P be fixed, the objective function (42) can be revised as max s.t.(1)−( 2), ( 16), ( 17), (43b) The linear subproblem (19) for DLU's scheduling X D and ULU's scheduling X D can be solved efficiently by using CVX [34].

Subproblem for time fraction
With the provided user scheduling X D , X U , P and the 3D trajectory of the UAV Q, the optimization problem (42) can be rewritten as follows Obviously, the subproblem for the time fraction µ is a linear programming problem and can be solved directly.

Subproblem for 3D Trajectory Design
With feasible DLU's scheduling X D , ULU's scheduling X U , time fraction µ and the transmission power of the UAV P, the objective function (42) can be expressed as max s.t. ( 5)−( 8), (45b) Since the constraints (45c) and (45d) are non-convex, this subproblem seems non-trivial and nonlinear.About the constraint (45c), by employing the first-order Taylor expansion, the lower bound RTF,lb j,n (Q) with feasible point [Q r n H r n , ∀n] can be derived by where and To handle the non-convex constraint (45d), introducing slack variables L = {L TF i,n , ∀n, i} and I = {I TF n , ∀n}, R TF i,n (Q) of constraint (45d) can be rewritten as with extra constraints and To solve the problem (45), utilize the inequality (64) for (47) with [L TF,r i,n  the fairness between the DL and UL communication.In order to investigate the fairness among users, we investigate the average throughput of each user.
In Figure 4, the benchmark "FDD Fixed Band" refers to the traditional algorithm in [17] without optimal bandwidth allocation, in which bandwidth for DL and UL communication is divided into two fixed parts, while "TF Fixed Time Fraction" refers to the algorithm in [19] with equal time fraction.Obviously, the average throughput of each ULU is less than or equal to each DLU's throughput.Therefore, the UAV flies closer to the ULUs to improve the throughput of the uplink.Besides, in Figure 4, it can be seen that each user is fair and enjoys the same throughput in the "TF" scheme.
Meanwhile, we can observe that the "FDD" scheme has better performance than the "FDD Fixed Band" scheme in Figure 4.As demonstrated in Figure 5, the "FDD" scheme is able to adjust its bandwidth allocation to improve the throughput of the system to guarantee fairness between the DL and UL communication.Especially, with the jammer transmission power increasing, the adjustment of the bandwidth allocation is more evident.Also, as can be seen in Figure 6, TF-based UAV communication can improve the throughput by changing the time fraction in different slots.
Figure 7 shows the average throughput achieved by different schemes versus the flight time T .One can observe that the performance of the TF-based scheme outperforms other schemes.As expected, the "FDD Fixed Band" scheme is the worst performer.Besides, we compare the TF-based average  throughput achieved by the polyblock outer approximation method (POA) in [18] and our proposed Considering the same trajectory, our proposed scheme demonstrates a performance that is closely with that of the POA-based method.Furthermore, to examine the performance of different schemes in the existence of malicious jammers, we simulate average throughput versus the transmission power of jammers in Figure 8.As can be seen, the average throughput of each proposed algorithm decreases when the jammer transmission power gradually rises.Nevertheless, the performance of the TF-based scheme is superior to other schemes.
Finally, Figure 9 characterizes the convergence of the proposed algorithms.The "FDD Fixed Band" algorithm and the "TF Fixed Fraction" algorithm achieve the same convergence throughput.The TFbased algorithm and FDD-based algorithm require 40 and 19 iterations, respectively.

Conclusions
In this paper, a joint downlink and uplink communication system in the presence of multiple malicious jammers has been considered, where a UAV is designed to transmit the signal to DLUs and receive the signal from ULUs simultaneously.The possible schemes for jointly optimizing the DL and UL communication to maximize the worst throughput among users are proposed, namely the FDD-based scheme and TF-based scheme.Our numerical results demonstrate the advantage of the TF-based scheme over other schemes.x ), x > 0. It can be verified that g 1 (x) is concave with respect to x and g 2 (x) is convex with respect to x.Based on Jensen's inequality, the inequalities are given by [18] log 2 (1 + 1 Define x = X Y (X > 0, Y > 0), and X and Y are independent, we have where the (62) follows the convexity of function 1 Y .Hence we can derive the following approximation result log 2 (1 + 1 From ( 61) and (63), it can be seen that E{log   which can be proved in [38],