QoE-Driven Video Transmission: Energy-Efficient Multi-UAV Network Optimization

Many recent studies on UAV network optimization for effective video transmission have been conducted. For example, in [19], the authors introduced a relay placement mechanism to find the ideal locations for UAVs acting as relay nodes, and thus avoided the effects of UAV movements on the video dissemination. The authors in [20] investigated the joint optimization of UAV trajectory and transmission rate allocation for reliable video streaming delivery in UAV networks. In [21], the authors considered the joint optimization of the UAV deployment and the content placement of a cache-enabled UAV for the maximization of link throughput when delivering multimedia data. In conclusion, the above works of transmitting video streams using UAV networks mainly focused on improving the link throughput by optimizing the UAVs’ locations, trajectories, and network resources without considering the proprietary characteristics of video streaming.

QoE, which can effectively capture the unique characteristics of video streaming, is an important measure of the performance of video transmission. Recently, many researchers have paid attention to the QoE-driven UAV network optimization. For instance, in [22], the authors created a QoE utility model and studied an average QoE maximization problem for video transmission in a UAV relay system by optimizing the system bandwidth and power allocation. However, the work assumed that QoE depended only on the video transmission rate. In [23], the authors proposed a QoE-driven dynamic pseudo analog wireless video broadcasting scheme, and the goal was to maximize the peak signal-to-noise ratio (PSNR) of a subscriber’s reconstructed videos by jointly optimizing the UAV’s transmit power and trajectory. Nevertheless, the evaluation metric (exactly, PSNR), which does not consider the overall video sequences, is typically used to quantify the distortion degree of video images. For video streaming, the key performance indicators include video bitrates, frame freezing, and latency.

To this end, the authors in [17] studied a scenario of the UAV-assisted live video streaming transmission and modeled the QoE using latency, video resolution, and smoothness. The authors in [24] presented a QoE-guided content delivery framework for providing subscribers with on-demand content in a multi-UAV network and aimed to maximize the QoE by improving the average end-to-end delay for each subscriber and the average throughput of each UAV. The work in [25] proposed to model QoE by the bitrate together with the frozen time of videos and formulated a problem of optimizing the system bandwidth along with UAVs’ transmit power to maximize the total long-term QoE. Compared with the previous works [22, 23], the studies in [17, 24, 25] exploited more indicators in constructing a QoE model. However, the energy efficiency of the UAV networks were not investigated in [17, 22, 23, 24, 25]. Compared to traditional BSs, UAVs are sharply energy-sensitive, and then it is essential to optimize the energy consumption of the UAV networks.

Therefore, the work in [26] jointly optimized video level selection and power allocation to maximize the energy efficiency of a UAV network, which was defined as the ratio of video bitrate to UAV power consumption. The authors in [27] jointly optimize subscriber communication scheduling, UAV trajectory, transmit power, and bandwidth allocation to maximize the energy efficiency of the UAV network and satisfy subscribers’ QoE requirements. Besides, the issue of energy-efficient trajectory optimization for aerial video surveillance under QoS constraints was investigated in [28]. Although the issue of energy-efficient UAV video streaming was investigated in [26, 27, 28], they just discussed the case of deploying a single UAV, which had restricted coverage, limited communication capacity, and stringent energy limitation. The availability of a single UAV network is also not guaranteed during the entire mission. In contrast, multiple or a swarm of UAVs can serve subscribers collaboratively to achieve communications of higher throughput and lower latency. The availability and efficiency of communications can also be improved by deploying a multi-UAV network. Nevertheless, the scheduling of communication resources of a multi-UAV network is much more challenging than that of a single UAV network [29]. The problem of deploying a multi-UAV network to provide efficient services for subscribers by jointly optimizing the association among UAVs and subscribers, UAVs’ trajectories, and UAVs’ transmit power was investigated in [30]. However, this work did not look into the particularities of video transmission. The authors in [31] designed an intelligent and distributed allocation mechanism to allocate uplink bandwidth for multi-UAV video streaming. Nevertheless, they just aimed to resolve the insufficiency of wireless channel resources when a cluster of UAVs executed the video shooting and uploading mission, nor did they consider the interference between UAVs.

From the above works [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], we observe that optimizing the resource allocation to improve the video transmission performance of UAV networks has become an important and popular research topic. However, the issue of improving subscribers’ QoE, including video bitrates, latency, and frame freezing by controlling a multi-UAV network is not investigated. This paper proposes to completely control multiple UAVs in terms of their trajectories, transmit power, and serving UAV selection to proactively alter downlink video transmission channels. In this way, it is desired to achieve a significant improvement in the video transmission performance of the multi-UAV network, including higher video bitrates, lower latency, and alleviated frame freezing. The main contributions of this paper are summarized as follows:

1) We mathematically model the QoE of subscribers based on the comprehensive analysis of the characteristics of the multi-UAV network and video transmission. In particular, a novel video streaming utility model adaptively matching the video bitrate and the playback bitrate requirements of subscribers is designed. Besides, the time-varying startup and rebuffering latency is investigated and modeled, and a constraint on the minimum time-averaged achievable bitrate is enforced to alleviate frame freezing.

2) A dynamic multi-UAV network is desired to be deployed to deliver video streams to subscribers, considering the restricted UAV communication coverage. To this end, we formulate the problem of dynamically deploying a multi-UAV network to deliver video streams to subscribers as a sequential-decision problem. The goal of this problem is to maximize the QoE of subscribers and minimize the total power consumption of the multi-UAV network through the joint optimization and control of UAV transmit power, serving UAV selection, and UAV trajectory. The formulated problem is confirmed to be NP-hard or non-tractable, and solving the sequential-decision problem as a whole encounters the curse of dimensionality.

3) Considering the advantages of the Lyapunov technique in tackling sequential-decision optimization problems, we develop a Lyapunov-based network optimization algorithm with provable performance guarantees to solve the optimization problem. First, we decompose the optimization problem into several repeatedly optimized sub-problems to avoid the curse of dimensionality. Nevertheless, the sub-problems are still difficult to solve as they are mixed-integer and non-convex. We then introduce the key idea of iterative optimization to tackle the mixed-integer issue and explore Taylor expansions to identify the convex approximation of the non-convex feasible regions of the sub-problems.

4) Finally, we compare the proposed algorithm with various benchmarks to verify its effectiveness and design extensive simulations to discuss the impact of diverse parameters on the performance of the algorithm. Simulation results show that the proposed algorithm can effectively improve the QoE of subscribers and is 66.75% more energy-efficient than benchmarks.

This paper considers an application scenario for providing high-quality video streaming services for a number of ground subscribers by deploying a multi-UAV network, as shown in Fig. 1. In the considered scenario, there is a ground content provider acting as a video source station (VSS), several ground BSs, a multi-UAV network consisting of $N$ flying UAVs, the set of which is denoted by ${\mathcal{K}}=\{1,2,3,\ldots,N\}$, and $M$ subscribers, the set of which is ${\mathcal{I}}=\{1,2,3,\ldots,M\}$. The content provider has the capabilities of video collection, video transcoding, as well as video streaming push and can provide adaptive streaming services for subscribers. In this scenario, we investigate the issue that subscribers cannot directly access the VSS through BSs, mainly because of severe signal blocking. Considering that UAVs can establish LoS links with BSs, we propose to dynamically deploy a multi-UAV network with UAVs acting as flying relays to forward video streams from BSs to subscribers.

To facilitate the mathematical model of the video transmission task, the time domain is discretized into a sequence of time slots, denoted by $t=\{1,2,\ldots\}$. As the communication coverage of UAVs is limited, the trajectories of UAVs will be continuously optimized to provide transmission services for subscribers fairly. We denote the time-varying two-dimensional (2D) horizontal coordinate of UAV $k$ at time slot $t$ by $\bm{q_{k}}\left(t\right)=[{x_{k}^{(u)}}\left(t\right),{y_{k}^{(u)}}\left(t\right)]^{\rm T},1\leq k\leq N$. Denote the location of subscriber $i$ at time slot $t$ by $\bm{s_{i}}\left(t\right)={\left[{{x_{i}^{(s)}}\left(t\right),{y_{i}^{(s)}}\left(t\right)}\right]^{\rm T}},1\leq i\leq M$. All UAVs are deployed at the same altitude, $H$, and the altitudes of all subscribers are negligible compared to $H$. Thus, the distance between UAV $k$ and subscriber $i$ at time slot $t$ can be given by ${D_{ik}}\left(t\right)=\sqrt{{H^{2}}+{{\left\|{\bm{q_{k}}\left(t\right)-\bm{s_{i}}\left(t\right)}\right\|}^{2}}}$. Considering the stringent QoE requirements of subscribers, it is critical to provide video streaming services via air-to-ground (AtG) LoS links. The reliability and the throughput of non-line-of-sight (NLoS) propagation links cannot be guaranteed for video streaming services. High energy consumption will also be required to compensate for attenuation of NLoS propagation [32, 33]. Besides, according to the research results in [34], the probability of LoS propagation can exceed $90\%$ when the elevation angle between a UAV and a ground subscriber is greater than a threshold $\theta$, which is related to the propagation environment, such as rural area, urban area, and dense urban. Therefore, the following condition can be held in order to approximate the establishment of a LoS link between a UAV and a ground subscriber.

The channel gain of an AtG LoS link can be calculated by the free-space path loss model[18], ${h_{ik}}(t)=\frac{{g_{ik}^{T}g_{ik}^{R}{c^{2}}}}{{{{\left({4\pi f_{c}{D_{ik}}\left(t\right)/{D_{0}}}\right)}^{2}}}}$ where ${h_{ik}}(t)$ denotes the channel gain from UAV $k$ to subscriber $i$ at time slot $t$, $g_{ik}^{T}$ and $g_{ik}^{R}$ respectively represent transmitting and receiving antenna gains, $c$ is the speed of light, $f_{c}$ is the carrier frequency, and ${D_{0}}$ is a far-field reference distance. Let ${\omega_{ik}}=\frac{{g_{ik}^{T}g_{ik}^{R}{c^{2}}D_{0}^{2}}}{{{{\left({4\pi f_{c}}\right)}^{2}}}}$, ${h_{ik}}(t)$ can be rewritten as

Owing to the movement of UAVs and their limited coverage, a subscriber’s serving UAV will be time-varying. We denote the serving UAV selection set at time slot $t$ as ${\mathcal{C}}(t)$. For any ${c_{ik}}\left(t\right)\in{\mathcal{C}}(t)$, ${c_{ik}}\left(t\right)=1$ indicates that subscriber $i$ can select UAV $k$ as its serving UAV at time slot $t$; otherwise, ${c_{ik}}\left(t\right)=0$. We assume that at time slot $t$, a subscriber can select at most one UAV as its serving UAV, and a UAV is allowed to deliver video streams to at most one subscriber. Mathematically, we have

As all UAVs share the frequency resource in the considered scenario, a subscriber $i$ will receive its intended signal from UAV $k$ and interference caused by other UAVs at each time slot. For subscriber $i$, the strength of its received interference can be calculated by ${I_{ik}}\left(t\right)=\sum\limits_{j\in{\mathcal{K}}\backslash\left\{k\right\}}{{p_{j}}\left(t\right){h_{ij}}\left(t\right)}$ where ${p_{j}}\left(t\right)$ denotes the instantaneous transmit power of UAV $j$ at time slot $t$. Then, the signal-to-interference-plus-noise ratio (SINR) experienced by subscriber $i$ at time slot $t$ can be given by $sin{r_{ik}}\left(t\right)=\frac{{{p_{k}}\left(t\right){h_{ik}}\left(t\right)}}{{{\sigma^{2}}+{I_{ik}}\left(t\right)}}$, where ${\sigma^{2}}$ is the noise power. According to Shannon’s channel capacity formula, we can calculate the achievable bitrate of subscriber $i$ at time slot $t$ by

For subscriber $i$, its time-averaged achievable bitrate during the first $t$ time slots can be given by ${{\bar{r}}_{i}}\left(t\right)=\frac{1}{t}\sum\nolimits_{\tau=1}^{t}{{r_{i}}\left(\tau\right)}$.

It is worth noting that the onboard energy of UAVs is limited and needs to be efficiently utilized. In this paper, we mainly consider the communication power consumption of UAVs (exactly, for forwarding video streams) and model the total communication power consumption of UAV $k$ at time slot $t$ as [32]

where $p_{k}^{c}$ is the onboard circuit power consumption of UAV $k$. The time-averaged transmit power of UAV $k$ in the first $t$ time slots can be computed by ${{\bar{p}}_{k}}\left(t\right)=\frac{1}{t}\sum\limits_{\tau=1}^{t}{{p_{k}}\left(\tau\right)}$. Accordingly, the time-averaged total communication power consumption of UAV $k$ in the first $t$ time slots can be written as $\bar{p}_{k}^{tot}\left(t\right)={{\bar{p}}_{k}}\left(t\right)+p_{k}^{c}$. The upper-bounded constraints of $p_{k}^{tot}\left(t\right)$ and $\bar{p}_{k}^{tot}\left(t\right)$ can be written as $p_{k}^{tot}\left(t\right)\leq{{\hat{p}}_{k}}$ and $\bar{p}_{k}^{tot}\left(t\right)\leq{{\tilde{p}}_{k}},\forall k,t$, where ${{\hat{p}}_{k}}$ and ${{\tilde{p}}_{k}}$ denote the maximum instantaneous total power consumption and the maximum time-averaged total power consumption of UAV $k$, respectively[35].

At any time slot $t$, to avoid the UAV collision, the distance between any two UAVs must be greater than a value [29],[36], i.e.,

where ${d_{\min}}$ denotes the minimum safety distance.

In addition, limited by the flight speed, the moving distance of a UAV in a time slot is constrained[29],[36], i.e.,

where ${s_{\max}}$ denotes the UAV’s maximum flight distance in a time slot.

QoE has become an acknowledged performance evaluation standard in video streaming services. The accurate analysis of the key factors influencing QoE will be beneficial for enhancing subscriber satisfaction and improving the utilization of network resources. In the research field of video streaming, high resolution, fluency, low latency, and smoothness of video streaming are four universal factors affecting QoE. These influencing factors, however, are challenging to be optimized simultaneously, especially in a time-varying multi-UAV network. Meanwhile, the dominant influencing factors are diverse for various network services. For example, some applications are sensitive to latency, while others are greatly affected by packet loss ratio. The smoothness of video streaming is closely related to subscribers’ switching strategies towards video streaming of diverse quality and cannot be directly optimized by controlling the multi-UAV network. Considering the time-varying characteristics of the multi-UAV network and the continuous playback requirements of video streaming, we create a novel QoE model incorporating the video bitrate, the latency, and the frame freezing in this paper.

The decoding capabilities and screen sizes of subscriber terminals may be different, and their playback bitrate requirements for the same video streaming may be diverse. In this case, implementing adaptive transmission and playback of video streaming is an effective way of improving QoE. Based on the throughput of the multi-UAV network and the receiving capabilities of subscribers, we design an adaptive video streaming utility model that implements the adaptive matching between subscribers’ required playback bitrates and video bitrates. For a subscriber, its available video bitrate is upper-bounded by its achievable bitrate; otherwise, packet loss or frame freezing will occur. Therefore, the video streaming utility model $\phi\left({\bm{\bar{r}}\left(t\right)}\right)$ for all subscribers $i\in{\mathcal{I}}$, which also represents the profit of the multi-UAV network, can be written as

where ${\bm{\bar{r}}\left(t\right)}=\left({{{\bar{r}}_{1}}\left(t\right),\ldots,{{\bar{r}}_{M}}\left(t\right)}\right)$, ${{R_{i}}}$ represents the required playback bitrate of subscriber $i$, $B$ represents the total bandwidth, and $\alpha$, $\beta$ are both positive values that are different for various types of applications.

Latency, especially the startup latency and the rebuffering latency in video streaming, is a crucial factor affecting QoE. The startup latency and the rebuffering latency are closely related to subscribers’ achievable bitrates. The greater the achievable bitrate, the shorter the latency to receive a sufficient amount of video data. Latency is also greatly affected by a subscriber’s selection of serving UAV in the considered application scenario. Hence, the startup and rebuffering latency (briefly, latency) model ${d_{i}}\left(t\right)$ for any subscriber $i\in{\mathcal{I}}$ at time slot $t$ is given by

where ${\delta t}$ denotes the duration of a time slot, and $L$ is the length of transmitted video data in a time slot. According to (9), we will obtain the latency ${d_{i}}\left(t\right)=\frac{L}{{B{{\log}_{2}}\left({1+sin{r_{ik}}\left(t\right)}\right)}}$, when subscriber $i$ can select a certain UAV $k$ as its serving UAV at time slot $t$; otherwise, the latency ${d_{i}}\left(t\right)$ is $\delta t$, namely the interval of one time slot. $d\left(t\right)=\sum\nolimits_{i}{{d_{i}}\left(t\right)}$ denotes the total latency of all subscribers $i$ at time slot $t$.

The exhaustion of resources in a subscriber’s playback buffer will lead to annoying frame freezing. When the playback bitrate remains unchanged, either the decrease of link throughput or the link interruption can result in the exhaustion of buffer resources. To tackle this issue, it is essential to constrain the time-averaged achievable bitrate ${{\bar{r}}_{i}}\left(t\right)$ by

where, $r_{i}^{th}$ denotes the threshold of time-averaged achievable bitrate of subscriber $i$. In order to meet this constraint, the optimization of UAV trajectories and network resources is desired and should be investigated.

Considering that UAVs are energy-sensitive, our goal is to maximize subscribers’ QoE and minimize the total power consumption of the multi-UAV network. To achieve this goal, we propose to jointly optimize the serving UAV selection ${\mathcal{C}}(t)$, the UAVs’ trajectories ${\mathcal{Q}}(t)$, and the UAVs’ transmit power ${\mathcal{P}}(t)$. According to the above analysis, the optimization problem can be mathematically formulated as follows

where ${{\rho_{1}}}$ and ${{\rho_{2}}}$ are both positive values that reflect the trade-off among the network profit, the total latency, and the total power consumption. One can choose ${{\rho_{1}}}$ and ${{\rho_{2}}}$ based on preferences of network operators and subscribers and the Pareto frontier of the formulated multi-objective optimization problem, as depicted in Fig. 2.

The formulated problem is confirmed to be a sequential-decision optimization problem, the solution of which is highly challenging. The video streaming utility model in the objective function is a logarithm function of time-averaged achievable bitrates of subscribers during the first $t$ time slots, which not only makes the problem highly time-coupled but also greatly increases the computational complexity of solving the problem. For example, the number of time-varying decision variables of the problem will grow exponentially with the increase of time slot $t$. As a result, to solve this problem directly by exploring some conventional optimization algorithms is unacceptable in terms of computational complexity. Besides, this optimization problem includes the summation term of 2-norm, complex fractional terms, continuous and integer variables, logarithmic-quadratic functions, and non-convex constraints. Thus, the formulated problem is also a mixed-integer non-convex optimization problem that may be NP-hard or even undecidable [37].

To alleviate this highly challenging problem, we first employ the Jensen’s inequality to decouple the time-coupled objective function. Next, considering the advantages of Lyapunov optimization approach in tackling time-averaged problems, we decompose the sequential-decision problem into multiple repeatedly optimization sub-problems at different time slots using the Lyapunov approach. In this way, the curse of dimensionality can be effectively tackled, and the computational complexity of solving the original problem can be greatly reduced. Next, we transform the complex fractional terms into rotated quadratic cones by introducing some slack variables. Finally, alternative and approximate optimization mechanisms with provable performance guarantees are explored to handle the mixed-integer and the non-convex properties of the sub-problems, respectively.

As the auxiliary function $\phi\left(\bm{\lambda}\left(t\right)\right)$ is the total of all individual logarithmic functions, we can then divide this sub-problem into $M$ individually optimized sub-problems, each of which can be formulated as

(23a) is a convex function of ${\lambda_{i}}\left(t\right)$, and its closed-form solution can be obtained by calculating the derivative. Let $\frac{{\partial f}}{{\partial{\lambda_{i}}\left(t\right)}}={[{Z_{i}}\left(t\right)]^{+}}-\frac{{V\alpha}}{{\beta\left({\frac{{{R_{i}}}}{B}+{\lambda_{i}}\left(t\right)}\right)\ln 2}}=0$, we can obtain

It can be observed that (22) includes some logarithmic-quadratic terms and non-convex constraints. It is also a multi-objective optimization problem involving both integer and continuous decision variables. As a result, (22) is difficult to be solved directly. To this end, an iterative optimization scheme is adopted to solve (22) in this paper.