QoE-Driven UAV-Enabled Pseudo-Analog Wireless Video Broadcast: A Joint Optimization of Power and Trajectory
11 QoE-Driven UAV-Enabled Pseudo-Analog WirelessVideo Broadcast: A Joint Optimization of Powerand Trajectory
Xiao-Wei Tang,
Student Member, IEEE , Xin-Lin Huang*,
Senior Member, IEEE , and Fei Hu,
Member, IEEE
Abstract —The explosive demands for high quality mobile videoservices have caused heavy overload to the existing cellularnetworks. Although the small cell has been proposed to alleviatesuch a problem, the network operators may not be interested indeploying numerous base stations (BSs) due to expensive infras-tructure construction and maintenance. The unmanned aerialvehicles (UAVs) can provide the low-cost and quick deployment,which can support high-quality line-of-sight communications andhave become promising mobile BSs. In this paper, we propose aquality-of-experience (QoE)-driven UAV-enabled pseudo-analogwireless video broadcast scheme, which provides mobile videobroadcast services for ground users (GUs). Due to limitedenergy available in UAV, the aim of the proposed scheme isto maximize the minimum peak signal-to-noise ratio (PSNR)of GUs video reconstruction quality by jointly optimizing thetransmission power allocation strategy and the UAV trajectory.Firstly, the reconstructed video quality at GUs is defined underthe constraints of the UAVs total energy and motion mechanism,and the proposed scheme is formulated as a complex non-convex optimization problem. Then, the optimization problemis simplified to obtain a tractable suboptimal solution with thehelp of the block coordinate descent model and the successiveconvex approximation model. Finally, the experimental resultsare presented to show the effectiveness of the proposed scheme.Specifically, the proposed scheme can achieve over 1.6dB PSNRgains in terms of GUs minimum PSNR, compared with the state-of-the-art schemes, e.g., DVB, SoftCast, and SharpCast.
Index Terms —Unmanned aerial vehicles, video broadcast, peaksignal-to-noise ratio, and joint power and trajectory optimization.
I. I
NTRODUCTION A CCORDING to Cisco’s latest report [1], mobile videotraffic accounted for of global mobile data trafficin 2017 and will reach by 2022. In particular, ofthe mobile video traffic belongs to hotspot contents (e.g., theAmerican Super Bowl, the World Cup, etc.) which are usuallyrequested by many users simultaneously. How to efficientlydeliver these hotspot videos to ground users (GUs) becomesa non-trivial problem. Point-to-point (P2P) communicationis first excluded due to its high power consumption and
Xiao-Wei Tang (email: [email protected] ) is with the De-partment of Control Science and Engineering, Tongji University, Shanghai201804, China.Xin-Lin Huang (email: [email protected] ) is with the De-partment of Information and Communication Engineering, Tongji University,Shanghai 201804, China (Corresponding Author).Fei Hu (e-mail: [email protected] ) is with the Department of Electricaland Computer Engineering, University of Alabama, Tuscaloosa, AL 35487USA. low bandwidth utilization. Broadcast communication can effi-ciently save the bandwidth and the transmission power, whichmakes it seem like a better choice compared with P2P [2].In the conventional digital video broadcast (DVB) system,the base station (BS) transmits the video at the rate whichmatches the throughput of the GU with the worst channelquality to ensure that most users can successfully decode thevideo. However, the cliff effect may occur in DVB whenGUs’ channel qualities vary a lot [3]. The pseudo-analogvideo transmission (PAVT) techniques have been proposed toeffectively alleviate the cliff effect [4-8]. Specifically, PAVTadopts the joint source-channel coding instead of separatesource and channel coding [9,10]. Since video signals areprocessed linearly in PAVT, the video demodulation qualityis approximately proportional to the corresponding channelquality. Therefore, PAVT can provide continuous scalablevideo quality, which makes it suitable for video broadcast[11,12].Many novel schemes on PAVT have been proposed in recentyears. In [7], Katabi et al. proposed a cross-layer designfor wireless video broadcast named SoftCast which was thefirst work on PAVT. In [8], He et al. proposed a structure-preserving video delivery system named SharpCast to improveboth the objective and subjective visual quality. In [9], a PAVTscheme called D-Cast was proposed where the correlationamong videos could be fully utilized. In [10], a data-assistedcloud radio access PAVT network named DAC-RAN wasproposed, which separated the control and data planes in theconventional digital transmission infrastructure, and integrateda new data plane into the virtual BS. In [11], Huang et al.proposed a knowledge-enhanced wireless video transmissionsystem called KMV-Cast which could exploit the hierarchicalBayesian model to integrate the correlated information into thevideo reconstruction.The above PAVT schemes provide new feasible solutionsto video broadcast and users can enjoy the video qualitiesmatching their own channel qualities. However, PAVT schemescan not solve this problem, that is, cell-edge users far awayfrom BSs suffer from unsatisfactory quality of experience(QoE) due to poor channel qualities [13,14]. Although thecellular offloading technique has been proposed to alleviatesuch a problem, its high cost of deploying new BSs makes itunsuitable for the scenarios with temporary traffic (e.g., an on-demand concert) [15,16]. Furthermore, the cellular offloadingtechnique is usually applied in the conventional networkarchitectures with fixed infrastructure such as ground BSs, a r X i v : . [ c s . MM ] J un access points and relays, which makes it difficult to serve GUsin an energy-efficient manner.Nowadays, unmanned aerial vehicles (UAVs), which canprovide Internet access from the sky, have been considered asa promising solution to improve the communication qualityof cell-edge GUs. Particularly, the technology advances inaviation and artificial intelligence have enhanced the functionsof UAVs and made them smaller, lighter, and smarter [17-19]. Therefore, UAVs have been widely used to implementcomplex tasks such as post-disaster reconnaissance, agricultureprecision, cargo transportation, etc., due to their advantagesincluding rapid deployment, high flexibility, controllable mo-bility, and easily available line-of-sight (LoS) channels [20-24]. Specially, LoS channels can make the communicationprocess suffer less path loss, shadowing and fading [25-27].In addition, the coverage area of the UAV can be easilyadjusted by changing the UAV’s height, transmission power,and antenna orientations.To the best of our knowledge, the existing studies onUAV-enabled video transmission are generally limited to theconventional digital systems, e.g., P2P and DVB. Therefore,these schemes inevitably suffer from some problems, e.g.,lack of scalability/reliability, caused by the inherent defectsof the digital systems. For example, in the UAV-enabled P2Pvideo transmission scenario, the UAV usually stores multipleversions of the same video content encoded at different codingrates. The GU can only request the UAV for the videocontent which matches its instantaneous end-to-end throughput[28,29] or playback buffer status [30]. Switching betweendifferent video rates frequently inevitably causes visual qualityfluctuations that affect the QoE [31,32]. Moreover, the UAV’shigh mobility often results in time-varying channel qualityand network topology. The video demodulation quality reactsstrongly to the link degradation when streaming videos oversuch unreliable channels, and a single packet loss may leadto video freezing for several seconds [33-37]. In addition,existing work simply assumes that the GUs’ QoE only dependson the video transmission rate, and do not measure the videodemodulation quality from the perspective of objective imageevaluation metric.Motivated by the above limitations of existing studies, wepropose a QoE-driven UAV-enabled pseudo-analog wirelessvideo broadcast (QUPWV-Cast) system, in which the UAV isdispatched as a mobile BS to provide video broadcast servicesfor a group of GUs. The goal is to maximize the minimumpeak signal-to-noise ratio (PSNR) of GUs’ video demodulationquality by jointly optimizing the transmission power allocationstrategy and the UAV trajectory. Contributions : The main contributions of this paper are two-fold:1) This is the first work to integrate the UAV techniqueinto the PAVT system. UAV’s advantages including highmobility, promising LoS channel, and fast deployment arefully utilized to enhance the QoE of cell-edge GUs, whichprovides a feasible solution to video broadcast from thesky.2) The proposed QUPWV-Cast system is modelled as a non-convex optimization problem to maximize the minimum PSNR of GUs by jointly optimizing the transmissionpower allocation strategy and the UAV trajectory. Specif-ically, an effective optimization algorithm based on theblock coordinate descent (BCD) and successive convexapproximation (SCA) techniques is proposed to obtainthe sub-optimal solution.The reminder of the paper is organized as follows. SectionII introduces related work and fundamental knowledge onthe proposed QUPWV-Cast. In Section III, the details ofthe system model are presented. In Section IV, an effectiveBCD and SCA-based algorithm is proposed to maximize theminimum PSNR of GUs. In Section V, the simulation resultsare provided to show the effectiveness of the proposed system.In Section VI, we conclude this paper.
Notations : in this paper, italics represent scalars, boldlowercases represent vectors, and bold uppercase representssets. R M × represents a M -dimensional real-value vector. Forvector a , || a || represents its Euclidean norm, and a T representsits transpose. E ( · ) represents the expectation of a randomvariable.II. R ELATED W ORK AND F UNDAMENTAL K NOWLEDGE
In this section, we will first introduce related work onthe UAV-enabled video transmission. Then, we will givefundamental knowledge on the PAVT scheme and UAV-GUchannel model.
A. UAV-Enabled Video Transmission
UAVs can capture videos via their equipped sensors, andthen deliver them to the GUs after compression and en-coding. Therefore, UAVs play an important role in manyvideo streaming applications such as live streaming, virtualreality/augmented reality, etc. These applications usually havehigh QoE requirements, such as low packet loss ratio (PLR)and ultra-high resolution [38-41]. Specifically, there are twokey issues in the design and implementation of UAV-enabledwireless video transmission: 1) The UAV trajectory needs to beproperly designed [42], so that the UAV can approach GUs asclosely as possible to obtain better channel quality and reduceenergy consumption; 2) The limited resource, e.g., energy,should be properly allocated during the UAV’s flight [43,44],in order to maintain the QoE and reduce the communicationoutage probability.Many studies have contributed to the development of UAV-enabled wireless video transmission by solving the above twokey issues. In [45], Wu et al. investigated a UAV-enabledorthogonal frequency division multiple access (OFDMA)scheme, in which the UAV was adopted as a BS. A minimum-rate ratio (MRR) was defined for each GU to represent theminimum required instantaneous rate to maintain the averagethroughput. The goal was to maximize the minimum averagethroughput of all GUs by jointly optimizing the UAV trajectoryand OFDMA resource allocation under the given constraintson GUs’ MRRs. In [46], Zeng et al. studied a UAV-enabledmulticasting system, in which a UAV transferred a commonfile to a set of GUs. The goal was to minimize the mission completion time by designing the UAV trajectory, while en-suring that each GU could successfully recover the file with adesired probability. In [47], Ludovico et al. improved the delayperformance for video streaming applications in congestedcellular macro-cells using a mobile micro-cell installed on aUAV. The mobile micro-cell was used to offload GUs froma congested macro-cell to optimize the bandwidth usage. In[48], He et al. designed an intelligent and distributed allocationmechanism to improve GUs’ QoE. Each UAV in a clustercould independently adjust and select its video encoding rate toachieve flexible uplink allocation. They built a potential gamemodel to maximize the GUs’ QoE through a low-complexitydistributed self-learning algorithm. In [49], Zhan et al. ex-tended the UAV applications to adaptive streaming servicesover fading channels. The objective was to maximize theoverall utility while guaranteeing the fairness among multipleGUs under the constraints of UAV energy budget and rateoutage probability. In [50], Wu et al. considered UAV-enabledtwo-user broadcast channel, where a UAV was deployed tosend independent information to two GUs at different fixedlocations. It aimed to characterize the capacity region over agiven UAV flight duration, by jointly optimizing the UAV’strajectory and transmission power/rate allocations over time,subject to the UAV’s maximum speed/power constraints. In[51], Colonnese et al. investigated the benefits of flexibleresource allocation when performing adaptive video streamingacross cellular systems. To guarantee the video smoothness inthe presence of fluctuations of the channel capacity, the authorsconsidered a proxy video manager and resource controllerlocated at the cellular BS. A cross-layer bandwidth allocationscheme was proposed to minimize the transmission delay,considering the channel quality, video quality requirementsand coding rate fluctuations.In summary, the above studies mainly focus on the UAV-enabled digital video transmission. They cannot avoid inherentdefects of the digital systems, such as the low bandwidth usagein P2P and the cliff effect in DVB. In order to provide aneffective solution to UAV-enabled broadcast scenario, we willintroduce the fundamental knowledge of PAVT scheme in thenext part.
B. PAVT Scheme
Conventional DVB systems with JPEG 2000/H.264 dividea video into groups of pictures (GOPs) and adopt predictivecoding. Then, intra- and inter-frame correlations of the videoenable high compression efficiency. The DVB system canselect a suitable channel modulation/coding scheme (MCS)to overcome the channel interference based on the channelconditions. However, due to the fluctuations of the channelquality, the selected MCS may not guarantee a predeterminedPLR. The cliff effect will occur under deep channel fading.Especially in the broadcast scenario, the receivers have differ-ent channel qualities, and the transmitter should select a MCSaccording to the worst channel quality to guarantee the correctdemodulation of all receivers.The PAVT scheme can be used to improve the effectivenessof video broadcast, in which the transmitter does not need to know the receivers’ channel quality since the video demod-ulation quality is proportional to its corresponding channelquality. Specifically, a video is first divided into multipleGOPs. Then, three-dimensional discrete cosine transform (3D-DCT) is performed for each GOP to remove the spatial andtemporal redundancy. Next, the transformed DCT coefficientsin each frame are divided into blocks with a uniform size andthe transmitter allocates different transmission power levelsfor each coefficient block according to its variance. After that,Hadamard transform is performed for each block to reduce thepeak-to-average power ratio (PAPR). Finally, the transmittersends those transformed coefficients in high-density modula-tion mode. At each receiver, it performs a series of operationsin order, including the signal demodulation, inverse Hadamardtransform, minimum mean squared error estimation, inverse3D-DCT transform, and finally reconstructs the entire video.
C. UAV-GU Channel Model
Consider the case with one UAV and N GUs (denotedas u n , n ∈ N = { , ..., N } ), where the coordinate of u n is known to the UAV and can be denoted as w n =[ x n , y n , T , ∀ n ∈ N . For ease of analysis, the flight durationof the UAV is divided into K time slots, and the lengthof each time slot k ∈ K = { , ..., K } is ∆ . Note that ∆ can be set small enough so that the distance between theUAV and u n can be regarded as a constant in each timeslot. Assume that the starting and ending points of UAV’sflight are predetermined, which can be denoted as w and w F , and the UAV flies at the altitude H . Consequently,the UAV trajectory can be approximately represented by theset Q = { q [ k ] = [ x [ k ] , y [ k ] , H ] T , ∀ k ∈ K} , where q [ k ] represents the coordinate of the UAV in time slot k . Thedistance between the UAV and u n in time slot k can be denotedas d k ( n ) = (cid:107) q [ k ] − w n (cid:107) . (1)Then, the average channel power gain β k ( n ) can be mod-elled as β k ( n ) = β d − αk ( n ) = β ( || q [ k ] − w n || ) α/ , (2)where β is the average channel power gain at a referencedistance of d = 1 m, and α is the path loss exponent thatusually has a value between 2 and 6. Thus, the instantaneouschannel gain from the UAV to u n in time slot k can be denotedas h k ( n ) = g k ( n ) (cid:112) β k ( n ) , (3)where g k ( n ) indicates the shadowing and small-scale fadingcomponent between the UAV and u n in time slot k , and E [ | g k ( n ) | ] = 1 . By considering different channel modelssuch as probabilistic LoS model and Rician fading model [52],we may rewrite g k ( n ) as different functions. For simplicity,we assume that the communication links from the UAV toGUs are dominated by LoS channels, and the Doppler effectcaused by the UAV’s mobility can be perfectly compensatedat the receiver. Therefore, to simplify the analysis, we assumethat g k ( n ) = 1 and α = 2 in this paper. III. S
YSTEM MODEL
The scenario of the considered QUPWV-Cast is shown inFig. 1, where a fixed-wing UAV is dispatched as a mobile BSto transmit the stored video to N GUs through OFDM system.The flight duration of the UAV is divided into K time slots. Forsimplicity, we take the time of transmitting a DCT coefficientblock through the OFDM system as the length of each timeslot k . Assume that the stored video has been processed as inSoftCast [7]. The goal of the proposed system is to maximizethe minimum video demodulation quality of GUs by jointlyoptimizing the transmission power allocation strategy and theUAV trajectory.In the following part, we will first introduce two basic mod-els including distortion estimation model and energy consump-tion model. Then, we will define the PSNR-based objectivefunction according to the estimated distortion. Finally, we willstate the optimization problem under the constraints of UAV’stotal energy and motion mechanism. Fig. 1 The overview of the QUPWV-Cast system.
A. Distortion Estimation Model
Denote the DCT coefficient blocks by the random variable { X m , m = 1 , · · · , M } , where M represents the total numberof coefficient blocks. Assume that X m ∼ N (0 , λ m ) where λ m represents the variance of X m . In addition, we assumethat X m is sorted in the descending order of variance, that is, λ ≥ ··· ≥ λ M . Let x k [ j ] , ≤ j ≤ N p denote the j th DCTcoefficient transmitted in time slot k , where N p represents thetotal number of coefficients contained in each block. Let s k denote the power scaling factor assigned for the coefficientblock transmitted in time slot k . The video signal x k [ j ] afterpower scaling can be represented as y k [ j ] = s k x k [ j ] , where E [ Y k ] = p k represents the average transmission power allo-cated for coefficients in X k . Obviously, we have p k = s k λ k .Consequently, the video signal received by u n in time slot k ,i.e., (cid:101) y n,k [ j ] , can be denoted as (cid:101) y n,k [ j ] = h k ( n ) y k [ j ] + z k ( n ) = h k ( n ) s k x k [ j ] + z k ( n ) , (4)where h k ( n ) represents the instantaneous channel gain be-tween the UAV and u n in time slot k , which has been The fixed-wing UAV consumes less propulsion energy than the rotor UAV,and has a longer communication range. given in Eq. (3). z k ( n ) is drawn i.i.d from a zero-meanGaussian distribution with variance σ , which can be denotedas z k ( n ) ∼ N (cid:0) , σ (cid:1) . As a consequence, the estimation ofthe demodulated video signal of u n can be denoted as (cid:98) x n,k [ j ] = (cid:101) y n,k [ j ] h k ( n ) s k = x k [ j ] + z k ( n ) h k ( n ) s k . (5)Eq. (5) indicates that the item z k ( n ) h k ( n ) s k determines the distor-tion of the transmitted video signals. In the PAVT scheme, wemay discard some coefficient blocks with small variances tomeet the bandwidth requirement without significantly affectingGUs’ QoE [7]. The receivers can treat the discarded DCTcoefficients as zeros when demodulating the video. As aconsequence, the distortion caused by discarding coefficientblocks with small variances is only the sum of the squares ofall discarded DCT coefficients. In this paper, we assume thatonly K of M coefficient blocks will be transmitted to GUs,and the remaining coefficient blocks will be discarded in orderto meet the bandwidth requirement. For u n , the expectation ofthe video reconstruction distortion can be denoted as follows D n = E K (cid:88) k =1 N p (cid:88) j =1 ( (cid:98) x n,k [ j ] − x k [ j ]) + M (cid:88) m = K +1 N p (cid:88) j =1 x m [ j ] , = K (cid:88) k =1 N p E ( z k ( n )) h k ( n ) s k + M (cid:88) m = K +1 N p (cid:88) j =1 x m [ j ] , = N p (cid:32) K (cid:88) k =1 σ λ k h k ( n ) p k + M (cid:88) m = K +1 λ m (cid:33) , ∀ n. (6) B. Energy Consumption Model
The UAV’s limited battery lifetime becomes the perfor-mance bottleneck of UAV-enabled video transmission systems.Therefore, it is critical to allocate the UAV’s limited energyproperly. In this section, we will discuss the UAV’s energyconsumption which is used to support the communicationswith GUs as well as the flight.
1) Energy Consumed by UAV’s Communications:
In theproposed QUPWV-Cast system, the UAV needs to properlyallocate certain transmission power for each coefficient block,aiming at minimizing the GUs’ video demodulation distortion.Then the GUs demodulate the video adaptively accordingto their own channel qualities. It should be noted that asmall amount of side information (e.g., the mean and varianceof each coefficient block) also needs to be transmitted toGUs besides the DCT coefficients [7]. The most reliableMCS is selected to ensure that each GU can decode theside information correctly. However, the energy consumed bytransmitting these side information is often far less than thatconsumed by transmitting DCT coefficients. Specifically, theenergy consumed by communications can be denoted as E c = N p ∆ K (cid:88) k =1 p k , (7) In natural videos, most DCT coefficients have a zero value because videoframes tend to be smooth. The coefficient block with small variance usuallycontains little useful information. where p k represents the average transmission power allocatedfor each coefficient of the block transmitted in time slot k . Inthis paper, we use P ∆ = { p k , ∀ k ∈ K} to represent the trans-mission power allocation strategy. The average transmissionpower allocated for coefficients is not supposed to exceed themaximum average transmission power P max . Therefore, theenergy consumed by UAV communications is upper boundedby E max = KN p ∆ P max .
2) Energy Consumed by UAV’s flight:
Let v [ k ] ∈ R × and a [ k ] ∈ R × denote the UAV’s velocity and acceleration intime slot k , respectively. We assume that v min ≤ || v [ k ] || ≤ v max , ∀ k ∈ K and || a [ k ] || ≤ a max , ∀ k ∈ K , where v max and a max represent the UAV’s maximum velocity and accelera-tion, respectively; and v min represents the minimum velocityrequired by the fixed-wing UAV to maintain its flight. Inaddition, we define v [0] ∆ = v as the UAV’s initial velocityand a [0] ∆ = a as the UAV’s initial acceleration.According to the motion mechanism, we have v [ k ] − v [ k −
1] = a [ k − , and q [ k ] − q [ k −
1] = v [ k − a [ k − , ∀ k ∈ K . Therefore, for a given UAV trajectory Q ∆ = { q [ k ] , ∀ k ∈ K} , the UAV’s velocity V ∆ = { v [ k ] , ∀ k ∈ K} andacceleration A ∆ = { a [ k ] , ∀ k ∈ K} can be uniquely determined.Consequently, Q , V and A are a set of coupling variables, and Q can be represented by V and A . For each time slot k , thepropulsion power of the fixed-wing UAV (i.e., p fk ) measuredin joules can be approximately represented as follows [44] p fk = c || v [ k ] || + c || v [ k ] || (cid:18) || a [ k ] || g (cid:19) , ∀ k, (8)where c and c are constants related to air density, dragcoefficient, wing area, etc. g is the gravitational acceleration,and its value is . m/s . Therefore, the total energy consumedby UAV’s flight can be denoted as E f = ∆ K (cid:88) k =1 p fk . (9) C. Objective Function
In this paper, PSNR is adopted as the metric to measurethe GUs’ QoE of the reconstructed video [53]. It is a standardobjective image evaluation metric with a definition as follows
PSNR = 10log η MSE , (10)where η is a constant related to the pixel depth of the video . MSE represents the mean squared error of pixels between thereconstructed video and the original one. According to Eq. (6),the
MSE n of u n can be denoted as MSE n = K (cid:80) k =1 σ λ k h k ( n ) p k + M (cid:80) m = K +1 λ m M , ∀ n. (11)Combining Eq. (10) and Eq. (11), the PSRN n of thereconstructed video of u n can be formulated as PSNR n = 10log Mη K (cid:80) k =1 σ λk (cid:107) q [ k ] − w n (cid:107) β pk + M (cid:80) m = K +1 λ m , ∀ n. (12) The pixel depth means the number of bits used to hold a pixel. Forexample, if the pixel depth is 8 bits, then η = 2 − . From Eq. (12), one can see that the video demodulationquality is mainly affected by the following three factors:1)
The UAV trajectory . The UAV trajectory actually de-termines the instantaneous channel gain h k ( n ) . If the UAVis close enough to u n , h k ( n ) will increase and the videodemodulation quality will be improved accordingly. However,it is unlikely for the UAV to approach to all GUs at the sametime. Thus it is necessary to design an optimal UAV trajectoryto maximize the minimum PSNR of GUs.2) The transmission power allocation strategy . When moretransmission power is allocated to the coefficient block, thesignals decoded by GUs will be less error-prone. The trans-mission power allocation strategy is mainly related to thecharacteristics of the transmitted video data, e.g., λ m . It istypical to allocate more transmission power to the coefficientblocks with large variances since those blocks may containmore useful information than those with small variances.3) The bandwidth budget . In the proposed system, somecoefficient blocks need to be discarded due to the limitedbandwidth resources. Eq. (12) shows that less coefficientblocks may worsen the reconstruction distortion.
D. Problem Statement
It has been pointed out in [7] that the reconstructed videowith PSNR lower than 20 dB is unsuitable for high-resolutionvideo applications. Therefore, the goal of this paper is to max-imize the minimum PSNR of the video reconstructed by theGUs via jointly optimizing the transmission power allocationstrategy (i.e., P ) and the UAV trajectory (i.e., Q , V , A ) underthe constraints of UAV’s total energy and motion mechanism.The optimization problem can be expressed as follows: ( P
1) max P , Q , V , A min n PSNR n , (13) s . t . E c + E f ≤ E t , (14) ≤ E c ≤ E max , (15) v min ≤ || v [ k ] || ≤ v max , ∀ k, (16) || a [ k ] || ≤ a max , ∀ k, (17) v [ k ] − v [ k −
1] = a [ k − , ∀ k, (18) q [ k ] − q [ k − v [ k − a [ k − , ∀ k, (19) q [0]= w , q [ K ]= w F , v [0]= v , a [0]= a , (20)where E t represents the UAV’s total available energy includingthe energy consumed by communications (i.e., E c ) and flight(i.e., E f ). The constraint (14) indicates that the consumedenergy can not exceed the UAV’s total available energy.The constraint (15) stipulates that the consumed transmissionenergy must be greater than but no more than the maxi-mum allowable transmission energy E max . The constraint (16)specifies the UAV’s minimum and maximum velocity. Theconstraint (17) specifies the UAV’s maximum acceleration.The constraint (18) shows the relationship between the UAV’svelocity and acceleration in each time slot. The constraint(19) shows the relationship between the UAV’s coordinateand velocity/acceleration in each time slot. The constraint (20)gives the UAV’s starting point, ending point, initial velocity and acceleration, respectively. Since the constraints (14) and(16) as well as the objective function in Eq. (13) are non-convex, P OLUTION
In this section, BCD and SCA techniques will be appliedto obtain the sub-optimal solution to the original optimizationproblem P
1. Before solving P
1, we make the notation: µ ∆ =min n PSNR n . After combining Eqs. (7)-(9) and (12), we canrewrite P ( P
2) max P , Q , V , A ,µ µ (21) s . t . (15) − (20) , M η K (cid:80) k =1 σ λ k (cid:107) q [ k ] − w n (cid:107) β p k + M (cid:80) m = K +1 λ m ≥ µ, ∀ n, (22) ∆ K (cid:88) k =1 (cid:18) N p p k + c || v [ k ] || + c || v [ k ] || (cid:18) || a [ k ] || g (cid:19)(cid:19) ≤ E t . (23)Since the maximization function is a convex function,the objective function of P P transmission power allocation strategy optimization withfixed UAV trajectory , and 2) UAV trajectory optimization withfixed transmission power allocation . Then we could use aglobally iterative algorithm (discussion below) to obtain thesub-optimal solution to P A. Transmission Power Allocation Strategy Optimization withFixed UAV Trajectory
Given the UAV trajectory, i.e., Q , V , and A , we considerthe following sub-optimization problem of P P ( P
3) max P ,µ µ (24) s . t . (15) , (22) , (23) . In the sub-optimization problem P
3, we introduce the fol-lowing lemma to prove the convexity of the constraint (22).
Lemma Given the feasible UAV trajectory, i.e., Q , V , and A , the constraint (22) is convex with respect to P .Proof. Please see
Appendix A for the proof details.The constraints (15) and (23) are also convex with respectto Q . Consequently, the sub-optimization problem P B. UAV Trajectory Optimization with Fixed TransmissionPower Allocation Strategy
Given the feasible transmission power allocation strategy P ,we consider the following sub-optimization problem of P Q , V , and A . ( P
4) max Q , V , A ,µ µ (25) s . t . (16) − (20) , (22) , (23) . The sub-optimization problem P P
4, we firstintroduce a set of slack variables O = { o [ k ] , ∀ k } . Note that o [ k ] is a scalar. Then P ( P
5) max Q , V , A , O ,µ µ (26) s . t . (17) − (20) , (22) , || v [ k ] || ≤ v , ∀ k, (27) v ≤ || v [ k ] || , ∀ k, (28) o [ k ] ≤ || v [ k ] || , ∀ k, (29) o [ k ] ≥ , ∀ k, (30) ∆ K (cid:88) k =1 (cid:18) c || v [ k ] || + c o [ k ] (cid:18) || a [ k ] || g (cid:19)(cid:19) ≤ E t − E c . (31)Note that only the reciprocal term of || v [ k ] || is replacedby o [ k ] , and the cubic term of || v [ k ] || is reserved under theconstraint (31). As a consequence, the left-hand side of theconstraint (31) is monotonically decreasing with respect to o [ k ] . Lemma Without compromising the optimality, the optimalsolution to P5 must meet: || v [ k ] || = o [ k ] , ∀ k .Proof. Please see Appendix B.According to Lemma 2, we can conclude that the solutionof P P P P
4. Afterintroducing the slack variable set O , the constraint (31) is nowconvex with respect to V and A . However, P P || v [ k ] || , and the left-hand side of the constraint (22), i.e., Mη K (cid:80) k =1 σ λk (cid:107) q [ k ] − w n (cid:107) β pk + M (cid:80) m = K +1 λ m , at a given point in eachiteration.In the constraints (28)-(29), || v [ k ] || is convex with respectto v [ k ] . Since the first-order Taylor approximation of a convexfunction is a global under-estimator, || v [ k ] || can be lowerbounded as follows || v [ k ] || ≥ || v r [ k ] || + 2( v r [ k ]) T ( v [ k ] − v r [ k ]) , ∀ k, (32) where v r [ k ] represents the given approximation point in the r th iteration. The equality holds at the point v [ k ] = v r [ k ] . Ac-cording to Eq.(32), the constraints (28)-(29) can be rewrittenas v ≤ || v r [ k ] || + 2( v r [ k ]) T ( v [ k ] − v r [ k ]) , ∀ k, (33) o [ k ] ≤ || v r [ k ] || + 2( v r [ k ]) T ( v [ k ] − v r [ k ]) , ∀ k. (34)In Lemma 1, we have proved that the left-hand side ofthe constraint (22) is a concave function with respect to P .Therefore, it can be inferred from the proof in Appendix A thatthe left-hand side of the constraint (22) can not be a concavefunction with respect to Q . For simplicity, we omit the proofprocess since it is similar to Lemma 1. In order to solve thenon-convexity of the constraint (22), we still use the first-orderTaylor approximation to obtain the lower bound of the left-hand side of the constraint (22) as follows PSNR n ( Q ) ≥ PSNR n ( Q r )= I n − K (cid:88) k =1 J n [ k ] (cid:0) || q [ k ] − w n || −|| q r [ k ] − w n || (cid:1) , ∀ n, (35)where Q r ∆ = { q r [ k ] , ∀ k } is defined as the given feasible UAVtrajectory in the r th iteration. The equality holds at the point q [ k ] = q r [ k ] . The coefficients I n and J n [ k ] can be denotedas I n = 10log M η K (cid:80) k =1 σ λ k (cid:107) q r [ k ] − w n (cid:107) β p k + M (cid:80) m = K +1 λ m , ∀ n, (36) J n [ k ] = 10 · σ λ k β p k ln10 (cid:18) K (cid:80) k =1 σ λ k (cid:107) q r [ k ] − w n (cid:107) β p k + M (cid:80) m = K +1 λ m (cid:19) , ∀ k, n. (37)According to Eqs. (35)-(37), the constraint (22) in P I n − K (cid:88) k =1 J n [ k ] (cid:0) || q [ k ] − w n || −|| q r [ k ] − w n || (cid:1) ≥ µ, ∀ n. (38)Since the left-hand side of Eq. (38) is a concave functionwith respect to || q [ k ] − w n || , the constraint (38) is now aconvex constraint. By combining Eqs. (33), (34) and (38), P ( P
6) max Q , V , A , O ,µ µ (39) s . t . (17) − (20) , (27) , (30) , (31) , (33) , (34) , (38) . In P
6, all constraints now satisfy the convexity require-ments. Therefore, P P P vice versa . Therefore, the feasible solutionto P P C. Complexity and Convergence Analysis
Based on the results of the above two sub-optimizationproblems, the overall algorithm for computing the sub-optimalsolution to P Algorithm 1 . The complexityof
Algorithm 1 is analyzed as follows. In each iteration,the transmission power allocation strategy P and the UAVtrajectory Q are iteratively optimized using the convex solverbased on the interior-point method, and thus their individualcomplexity can be represented as O (( K ) . log(1 /ς )) and O ((3 K ) . log(1 /ς )) , respectively. Specifically, K representsthe total time slots and ς represents the predetermined solutionaccuracy. Then accounting for the BCD iterations with thecomplexity in the order of log(1 /ς ) , the total computationcomplexity of Algorithm 1 is O ((3 K ) . log (1 /ς )) [52]. Algorithm 1
Iterative Optimization for P and Q . Initialize P , Q , V , and A . Set up a convergence threshold ς > . Let r = 0 . repeat Solve P Q r , V r , and A r ,and denote the optimal solution to the transmission powerallocation strategy as P r +1 . Solve P P r +1 , and denote the optimal solution to the UAVtrajectory as Q r +1 , V r +1 , and A r +1 . Update r = r + 1 . Break : if µ ( P r +1 , Q r +1 , V r +1 , A r +1 ) − µ ( P r , Q r , V r , A r ) µ ( P r , Q r , V r , A r ) ≤ ς .Next, we investigate the convergence property of Algorithm1 . Let µ ( P r , Q r , V r , A r ) denote the objective value of P r th iteration. Therefore, the following inequality holds, µ ( P r , Q r , V r , A r ) ( a ) ≤ µ ( P r +1 , Q r , V r , A r ) ( b ) ≤ µ ( P r +1 , Q r +1 , V r +1 , A r +1 ) ( c ) ≤ µ ∗ ( P r +1 , Q r +1 , V r +1 , A r +1 ) . (40)where µ ∗ ( P r +1 , Q r +1 , V r +1 , A r +1 ) represents the optimal solu-tion to P
2. The inequality (a) holds since Step 5 in
Algorithm1 can obtain the optimal solution to P
3. The inequality (b)holds as Step 6 in
Algorithm 1 can obtain the optimal solutionto P
6. Since the SCA technique is used to achieve the lowerbounds of the constraints (32) and (35), the optimal solutionto P P P P Algorithm 1 can converge to a locally optimal solution to P ERFORMANCE A NALYSIS
We have conducted simulations to verify the effectiveness ofthe proposed system. Particularly we investigate the influenceof three factors, e.g., K , E t , and N , on the system perfor-mance. For each case, we present the simulation results about1) the transmission power allocation strategy, 2) the UAVtrajectory, 3) the convergence of the proposed algorithm, and4) the PSNRs of GUs, respectively. Finally, we compare the performance of the proposed system with three other systems,e.g., DVB, SoftCast, and SharpCast, from the perspectives ofsubjective visual quality and objective evaluation metric. A. Parameter Settings
We assume that the UAV flies at a fixed altitude as H =100 m . The average noise power is σ = − dBm and themaximum average transmission power for each coefficient isset to dBm . β is assumed to be − dB . According tothe energy-consumption model of the fixed-wing UAV [43], c and c are set to . × − and . × , respectively.To ensure the safety, the UAV’s velocity is restricted to bewithin the range of m/s to m/s and the UAV’s maximumacceleration is set to a max = 10 m/s .In the simulations, we require that the UAV flies fromthe starting point (i.e., w = [0 , , T m ) to the end-ing point (i.e., w F = [300 , , T m ). The initial UAVtrajectory is designed to fly straight from the starting pointto the ending point at a constant speed. Therefore, theinitial UAV trajectory can be denoted by the set Q = { q [ k ] = w + kK ( w F − w ) , ∀ k ∈ K} . Consequently, theinitial feasible velocity set for the UAV is V = { v [ k ] = w F − w K ∆ , ∀ k ∈ K} . The initial acceleration set for the UAVis A = { a [ k ] = [0 , , T , ∀ k ∈ K} . For simplicity, theUAV’s initial velocity v is also set to w F − w K ∆ , and the UAV’sinitial acceleration a is set to [0 , , T m/s , respectively.In addition, we assume that each transmitted coefficient isallocated with the maximum average transmission power at thebeginning of the iteration, i.e., p k = 10 dBm, ∀ k ∈K . Thus theinitial transmission power allocation strategy can be denotedas P = { p k = 10 dBm, ∀ k ∈ K} . For ease of reference, allof the parameters are provided in Table I .Six classic testing video sequences including “Foreman”,“Akiyo”, “Coastguard”, “Container”, “Hall”, and “Mother-daughter” are used to verify the effectiveness of the proposedsystem. These video sequences are open source and have beenwidely used for simulation analysis in multimedia research[53]. The details of these six video sequences are providedin
Table II , including resolution, frame number, frame rate,and size. All of them have a 8-level pixel depth (i.e., the pixelvalue ranges from 0 to 255). Similar to SoftCast, we divideeach frame into blocks with uniform size of × . Therefore,each frame contains 64 coefficient blocks and each coefficientblock contains 396 DCT coefficients. For simplicity, we selectthe st , th , and th frames from each video sequence asthe signal source. B. Influence of K on the performance of the proposed scheme In DVB, GUs can only request the BS for the videoswith a bit rate matching their channel bandwidth. It has beenshown that the video quality can be modelled as a logarithmicfunction with respect to the bit rate [49]. Therefore, GUs withlow channel quality may suffer from low QoE when requestingvideos from the BS. The PAVT scheme can perform efficientlyeven when the channel bandwidth is limited, since it is allowedto discard some coefficient blocks with small variances, in order to meet the bandwidth budget while causing little impacton the GUs’ QoE.Here we study the impact of available channel bandwidthon the performance of the proposed scheme. We only changethe value of K while maintaining other parameters constant.Specifically, we set the UAV’s total energy E t to J .Assume that there are four GUs which are randomly generatedby Monte-Carlo method. Specifically, both the x-coordinatesand y-coordinates of these GUs range from 0m to 1200m. Theperformance of the proposed system is investigated under fourcases: K = { , , , } . The simulation results areshown in Fig. 2.Fig. 2(a) shows the transmission power allocation strategiesunder different values of K . One can see that the averagetransmission power allocated for the coefficients in each blockdecreases with the decline of the variance (here the coefficientblocks are sorted in descending order of variance). It hasbeen proved in SoftCast scheme that the optimal transmissionpower for the coefficients in each block is approximatelyproportional to the standard deviation. Therefore, the proposedalgorithm can obtain a sub-optimal power allocation strategyas in SoftCast. However, the location relationship between theBS and GUs are not considered in SoftCast when allocatingthe transmission power. In this paper, the UAV can adjust thetransmission power allocation according to the channel qualityof GUs in each time slot. Therefore, our proposed transmissionpower allocation scheme is more practical and effective. Fig.2(b) shows the UAV trajectory under four cases. We can seethat the UAV approaches the GU in the furthest location (i.e., u ) to maximize the video demodulation quality of the GU.Since the UAV’s flight duration is limited by K , it can be seenfrom Fig. 2(b) that the UAV’s flight distance increases withthe increment of K .Fig. 2(c) shows the convergence of the proposed algorithm.We can see that the proposed algorithm has a fast convergencespeed. We have shown in Section IV that the complexity of theproposed algorithm is O (( K ) . log(1 /ς )) which scales with K . From Fig. 2(c), one can see that with the increase of K ,the algorithm needs more iterations to achieve the predeter-mined convergence accuracy. In addition, as K increases, theGUs’ minimum video demodulation quality keeps improving.However, the PSNR gain with the increase of K becomeslimited, which indicates that the proposed system can achievesatisfactory performance even under the condition of limitedbandwidth. Fig. 2(d) shows the video demodulation qualitiesof four GUs under different values of K . It can be seen thatthe PSNR of four GUs under each case can achieve smallimprovement with the increase of K . Specifically, the PSNRof u (which suffers from the worst demodulation quality dueto the largest distance from the UAV trajectory) can also getimproved with the increase of K . C. Influence of E t on the performance of the proposed scheme It has been analysed in Section III that the video demodula-tion qualities of GUs are mainly determined by the followingthree aspects: 1)
UAV transmission power allocation strategy,i.e., P , 2) UAV trajectory , i.e., Q , and 3) Channel bandwidth , TABLE I The parameter settings.
Parameter Value Parameter ValueUAV’s altitude H = 100 m Number of transmitted blocks K = 120 / / / UAV’s starting point w = [0 , , T m Number of coefficients in each block N p = 396 UAV’s ending point w F = [300 , , T m Maximum average transmission power P max = 10 dBm UAV’s maximum velocity v max = 100 m/s Length of each time slot ∆ = 0 . s UAV’s minimum velocity v min = 3 m/s UAV’s total energy E t = 3000 / / / J UAV’s maximum acceleration a max = 10 m/s Index of transmitted frames
Index = 1 st , th , th UAV’s initial velocity v = w F − w K ∆ m/s Number of GUs N = 4 / / / UAV’s initial acceleration a = [0 , , T m/s Constant 1 for UAV’s energy-consuming model c = 9 . × − Noise power σ = − dBm Constant 2 for UAV’s energy-consuming model c = 2250 Referenced channel gain β = − dB Gravity acceleration g = 9 . m/s Path loss exponent α = 2 Constant related to PSNR formulation η = 255 Total block number M = 192 Convergence threshold ς = 10 − TABLE II Details of testing video sequences.
Sequences Resolution Frame number Frame rate SizeForeman ×
300 25fps 5.88MBAkiyo ×
300 25fps 1.86MBCoastguard ×
300 25fps 5.74MBContainer ×
300 25fps 4.06MBHall ×
300 25fps 5.72MBMother-daughter ×
300 25fps 10.8MB i.e., K . The influence of K on the performance of the proposedsystem has been analysed. Since both P and Q are constrainedby E t , we will study the influence of E t on the performanceof the proposed system in this section. Again, we assume thatthere are four GUs with coordinates the same as before. K isset to 180 here. The performance of the proposed system isstudied under four cases of E t = { , , , } J .The simulation results are given in Fig. 3.Fig. 3(a) shows the transmission power allocation strategiesunder different cases of E t . We can see that the transmissionpower allocated for those coefficient blocks with large vari-ances is almost the same in all cases. As the total energyincreases, the coefficient blocks with small variances canobtain more transmission power. Fig. 3(b) shows the UAVtrajectory with different values of E t . It shows that as theUAV’s total energy increases, the UAV can fly closer to thefarthest GU to maximize the video demodulation quality ofthe GU. In addition, one can also find that with the increaseof E t , the UAV’s turning radius is getting smaller and smaller,which means consuming more propulsion energy .Fig. 3(c) shows the convergence of the proposed algorithmunder different values of E t . With the increase of UAV’s totalenergy, the sub-optimal solution obtained by the proposedalgorithm is also increasing, and the increasing amplitude isapproximately proportional to the energy increment. Fig. 3(d)shows the video demodulation qualities of the four GUs. FromFig. 3(d), one can conclude that with the increase of E t , theminimum video demodulation quality of GUs (i.e., u ) can beimproved to some extent. Meanwhile, the video demodulationquality of u gets lower since the distance is getting largerfrom the UAV. According to [44], the energy consumed by the UAV’s flight is approxi-mately proportional to the square of the UAV’s acceleration.
D. Influence of N on the performance of the proposed scheme Besides the total energy E t , the UAV trajectory is alsoaffected by the number of GUs. The goal of the proposedsystem is to maximize the minimum PSNR of GUs. Therefore,we should consider the distribution of GUs when designingthe UAV trajectory. We set K to and E t to J ,respectively. Assume that there are GUs which are ran-domly generated by Monte-Carlo method. Specifically, boththe x-coordinate and y-coordinate of these GUs range from0m to 1200m. We study the performance of the proposedsystem under the following four cases: N = { , , , } . Thecorresponding simulation results are shown in Fig. 4.Fig. 4(a) shows the transmission power allocation strategiesunder different values of N . We can see that the increaseof N does not have a big impact on the transmission powerallocation strategy. From Fig. 4(b), one can see that due to theincrease of N and the dispersion of users’ distribution, theUAV’s trajectory gradually deviates from the users with thefarthest distance. The UAV manages to fly as close as possibleto the farthest GU to maximize its video demodulation quality.Fig. 4(c) shows the convergence of proposed algorithmunder different values of N . One can find that the convergedvalue has a close relationship with the distribution of GUs.Specifically, the proposed system has similar performanceunder the cases of N = 6 and N = 8 since u and u have almost the same distance from the BS which suffers fromthe worst demodulation quality in each case. Fig. 4(d) showsthe video demodulation qualities of all GUs under differentvalues of N . With the increase of N , the GUs’ minimum videodemodulation quality gradually decreases. This is because withthe increase of N , the distance between the cell-edge GU andthe starting point also gets longer. However, the distance thata UAV can reach is limited by E t and K . Therefore, the videodemodulation quality of the edge GU gradually declines as N increases. E. Performance comparisons with different systems
In this section, we compare the performance of the proposedsystem with three other classical video transmission systems,e.g., DVB, SoftCast [7], and SharpCast [8]. In DVB, we gen-erate MPEG4 streams using the H.264/AVC codec providedby the FFmpeg software and the X264 codec library [54].To ensure that all of the systems occupy the same channel k -50510152025 p k ( d B m ) K=120K=140K=160K=180 (a) x(m) y ( m ) K=120K=140K=160K=180 u u u u (b) r ( d B ) K=120K=140K=160K=180 (c)
120 140 160 180 K PS NR ( d B ) u u u u (d) Fig. 2 Performance comparisons under conditions of different channel bandwidth: (a) transmission power allocation strategy, (b) UAVtrajectory, (c) convergence of the proposed algorithm, and (d) PSNRs of GUs. bandwidth, the MPEG4 streams are encoded into the bitstreams at / code rate and mapped into complex signalsusing 16QAM. According to [8], we decompose the videointo a content part and a structure part in SharpCast. Thestructure part is compressed by HEVC codec and is protectedwith a robust digital transmission scheme. The content partin SharpCast is transmitted in PAVT scheme. We assume thatthe BS is located at the origin of the coordinate axis in DVB,SoftCast, and SharpCast. For the sake of fairness, the foursystems transmit the video signals with the same total energy.The performance of the four systems are compared from theperspectives of both subjective visual quality and objectiveevaluation metric.Figs. 5-7 show the demodulated frames of four GUs usingthe four systems. One can conclude that u , u and u canalways obtain excellent subjective visual qualities in all thefour systems. u gets high visual qualities in both SoftCast,SharpCast, and our proposed system. However, DVB cannot provide u with satisfactory subjective visual qualitiescompared with three other systems. Specifically, one can seefrom Figs. 5-7 that frames disorder when u demodulates thevideo using DVB system. This is because DVB adopts theinter-frame compression and motion compensation, resulting in a high correlation between frames . The demodulation errorof a single frame may result in the loss of several seconds ofvideo clips.The detailed individual PSNR values of each GU usingdifferent testing sequences are provided in Table III . Theminimum PSNR value in each method is marked with blue.One can see that the video demodulation quality of eachGU using DVB is lower than three other systems. Table IIIalso clearly demonstrates the cliff effect in DVB: when thechannel quality is greater than a certain threshold, GUs’ videodemodulation quality can no longer be improved (the locationsof u and u are different, but their video demodulationqualities are the same). This is due to the inherent loss causedby the lossy compression technology adopted by DVB. Amongthe four systems, the proposed system can obtain the bestperformance in terms of the poorest GU’s reconstructed videoquality (see Eq. (13)). Therefore, the proposed system canovercome the defect of GUs’ geographical location with thehelp of the UAV’s mobility. In order to achieve high compression rate, the video is often divided intoI-frames and P-frames in DVB. The demodulation of P-frames often relies onthe I-frames. k -50510152025 p k ( d B m ) E t =3000JE t =4000JE t =5000JE t =6000J (a) x(m) y ( m ) E t =3000JE t =4000JE t =5000JE t =6000J u u u u (b) r ( d B ) E t =3000JE t =4000JE t =5000JE t =6000J (c) E t PS NR ( d B ) u u u u (d) Fig. 3 Performance comparisons under conditions of different total energy: (a) transmission power allocation strategy, (b) UAV trajectory,(c) convergence of the proposed algorithm, (d) PSNRs of GUs.TABLE III Individual PSNR values of GUs with different systems.
Sequences Systems Average PSNR (dB) u u u u Foreman DVB 19.50 33.36 36.81 36.81SoftCast 39.56 40.57 44.79 43.45SharpCast 40.44 41.38 45.26 43.99QUPWV-Cast 43.29 45.15 46.91 51.51Akiyo DVB 36.45 40.09 45.22 45.22SoftCast 40.65 41.66 45.84 44.51SharpCast 42.04 43.05 47.22 45.21QUPWV-Cast 44.52 46.36 48.11 52.43Coastguard DVB 18.76 33.94 34.93 34.93SoftCast 40.28 41.27 45.36 44.07SharpCast 40.99 41.88 45.66 44.52QUPWV-Cast 44.07 45.82 47.66 51.27Container DVB 18.71 27.04 42.40 42.40SoftCast 38.38 39.38 43.47 42.18SharpCast 39.37 40.28 44.24 42.87QUPWV-Cast 42.11 43.83 45.77 49.17Hall DVB 21.63 36.07 41.30 41.30SoftCast 38.82 39.81 43.89 42.61SharpCast 39.99 41.28 44.66 43.88QUPWV-Cast 42.72 44.45 46.30 49.80Mother-daughter DVB 23.82 32.02 43.47 43.47SoftCast 43.29 44.29 48.45 47.13SharpCast 45.31 46.16 49.69 48.58QUPWV-Cast 46.99 48.80 50.60 54.72
In order to study the effect of the number of GUs on thesystem performance, we observe the average PSNR values ofGUs in each method under the four cases: N = { , , , } (please note that the GUs has the same coordinates with thosein Part D). From Fig. 8, one can see that the proposed systemcan always achieve the best average PSNR performance indifferent cases. SharpCast can achieve a performance gainin terms of GUs’ average PSNR compared with SoftCast.This is because SharpCast can preserve more structure-relatedinformation. DVB performs the worst in terms of the averagePSNR among the four systems. Therefore, one can concludethat the PAVT system is more suitable for broadcast scenariosthan DVB system. In addition, we can see from Fig. 8 thatwith the increase of the number of GUs, the average PSNR ofGUs in each scheme has not changed much. This is becausethat we aim at minimizing the minimum PSNR of GUs ratherthan average PSNR. However, according to our analysis inPart D of Section V, we can conclude that the distribution ofGUs rather than the number directly affects the performanceof the proposed system. k -50510152025 p k ( d B m ) N=4N=6N=8N=10 (a) x(m) y ( m ) N=4N=6N=8N=10 u u u u u u u u u u (b) r ( d B ) N=4N=6N=8N=10 (c) N PS NR ( d B ) u u u u u u u u u u (d) Fig. 4 Performance comparisons under conditions of different numbers of GUs: (a) transmission power allocation strategy, (b) UAVtrajectory, (c) convergence of the proposed algorithm, (d) PSNRs of GUs.
DVBSoftCastSharpCastQUPWV-Cast
Fig. 5 Demodulated subjective visual quality of the st frame usingthe four systems. VI. C
ONCLUSIONS
In this paper, a novel QoE-driven UAV-enabled pseudo-analog wireless video broadcast system called QUPWV-Cast,
DVBSoftCastSharpCastQUPWV-Cast
Fig. 6 Demodulated subjective visual quality of the th frameusing the four systems. has been proposed to enhance the QoE of cell-edge GUs. Theproposed system was modelled as a challenging non-convexoptimization problem, aiming at maximizing the minimum DVBSoftCastSharpCastQUPWV-Cast
Fig. 7 Demodulated subjective visual quality of the th frameusing the four systems. N A v e r age PS NR ( d B ) DVBSoftCastSharpCastQUPWV-Cast
Fig. 8 The average PSNR under each case with different number ofGUs.
PSNR of GUs by jointly optimizing the transmission powerallocation strategy and the UAV trajectory. An efficient BCDand SCA-based algorithm was proposed to divide the originaloptimization problem into two sub-optimal problems. A sub-optimal solution could be obtained by iteratively solving thetwo sub-optimal problems. Comprehensive simulation resultshave been provided to prove the effectiveness of the proposedsystem. The results have shown that the proposed QUPWV-Cast system has the best performance, compared with threeother systems, e.g., DVB, SoftCast, and SharpCast, in terms ofboth subjective visual quality and objective evaluation metric.VII. A
CKNOWLEDGEMENT
The authors would like to thank all reviewers for their effortsin reviewing this manuscript. A
PPENDIX
AFor ease of proof, we first rewrite the constraint (22) asfollows Mη K (cid:80) k =1 σ λk (cid:107) q [ k ] − w n (cid:107) β pk + M (cid:80) m = K +1 λ m ≥ µ , ∀ n. (41)In Eq. (41), it is obvious that the right-hand side is convex.Therefore, we only need to prove that the left-hand side ofEq. (41) is concave. For simplicity, we make the followingdefinition ϕ n ( p k ) ∆ = γ (cid:18) K (cid:80) k =1 ω n [ k ] p k (cid:19) + γ , ∀ k, n, (42)where γ = M η , γ = M (cid:80) m = K +1 λ m , and ω n [ k ] ∆ = σ λ k (cid:107) q [ k ] − w n (cid:107) β , ∀ k, n , respectively. The first-order andsecond-order partial derivatives of ϕ n with respect to p k canbe denoted as follows ∂ϕ n ∂p k = γ ω n [ k ] p k (cid:18)(cid:18) K (cid:80) k =1 ω n [ k ] p k (cid:19) + γ (cid:19) , ∀ k, (43) ∂ ϕ n ∂p k = − γ ω n [ k ] (cid:18) K (cid:80) k =1 ωn [ k ] pk + γ (cid:19)(cid:18) p k (cid:18) K (cid:80) k =1 ωn [ k ] pk + γ (cid:19) − ω n [ k ] (cid:19) p k (cid:18)(cid:18) K (cid:80) k =1 ωn [ k ] pk (cid:19) + γ (cid:19) , ∀ k, n. (44)In Eq. (44), the inequality p k (cid:18)(cid:18) K (cid:80) k =1 ω k [ n ] p k (cid:19) + γ (cid:19) − ω k [ n ] ≥ p k (cid:16) ω k [ n ] p k + γ (cid:17) − ω k [ n ] = γ ≥ holds. In addition, wehave − γ ω n [ k ] (cid:18) K (cid:80) k =1 ω n [ k ] p k + γ (cid:19) < . Therefore, it is true that ∂ ϕ∂p k < . Consequently, ϕ n is a concave function with respectto p k . A PPENDIX
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Xiao-Wei Tang ( S’16, IEEE ) received the B.E.degree in Communication Engineering from TongjiUniversity in 2016, where he is currently pursuingthe Ph.D. degree. He has published several researchpapers on IEEE Transactions on Multimedia, IEEETransactions on Vehicular Technology, IEEE Access,IEEE Globecom, and Mobile Networks & Applica-tions. He was a recipient of the Excellent BachelorThesis of Tongji University in 2016, the NationalScholarship for Graduate Students by Ministry ofEducation of China in 2017, the Outstanding Stu-dents Award of Tongji University in 2017, the Outstanding Freshman Schol-arship of Tongji University in 2018, the Chinese Government Scholarship byChina Scholarship Council in 2019, the Outstanding Students Award of TongjiUniversity in 2019, and the National Scholarship for Graduate Students byMinistry of Education of China in 2019. From Aug. 2019, he is doing researchon UAV-enabled wireless video transmission in the Department of Electricaland Computer Engineering, the National University of Singapore, as a visitingscholar. His research interests include pseudo-analog video transmission, UAVcommunication, convex optimization, and deep learning.
Xin-Lin Huang ( S’09-M’12-SM’16, IEEE ) is cur-rently a professor and vice-head of the Departmentof Information and Communication Engineering,Tongji University, Shanghai, China. He receivedthe M.E. and Ph.D. degrees in information andcommunication engineering from Harbin Institute ofTechnology (HIT) in 2008 and 2011, respectively.His research focuses on Cognitive Radio Networks,Multimedia Transmission, and Machine Learning.He published over 70 research papers and 8 patentsin these fields. Dr. Huang was a recipient of Schol-arship Award for Excellent Doctoral Student granted by Ministry of Educationof China in 2010, Best PhD Dissertation Award from HIT in 2013, ShanghaiHigh-level Overseas Talent Program in 2013, and Shanghai Rising-StarProgram for Distinguished Young Scientists in 2019. From Aug. 2010 toSept. 2011, he was supported by China Scholarship Council to do researchin the Department of Electrical and Computer Engineering, University ofAlabama (USA), as a visiting scholar. He was invited to serve as SessionChair for the IEEE ICC2014. He served as a Guest Editor for IEEE WirelessCommunications and Chief Guest Editor for International Journal of MONETand WCMC. He serves as IG cochair for IEEE ComSoc MMTC, andAssociate Editor for IEEE Access. He is a Fellow of the EAI.