Power-Efficient UAV Positioning and Resource Allocation in UAV-Assisted Wireless Networks for Video Streaming with Fairness Consideration

Abstract

This work proposes a power-efficient framework for adaptive video streaming in UAV-assisted wireless networks specially designed for disaster-hit areas where existing base stations are nonfunctional. Delivering high-quality videos requires higher video rates and more resources, which leads to increased power consumption. With the increasing demand of mobile video, efficient bandwidth allocation becomes essential. In shared networks, users with lower bitrates experience poor video quality when high-bitrate users occupy most of the bandwidth, leading to a degraded and unfair user experience. Additionally, frequent video rate switching can significantly impact user experience, making the video rates’ smooth transition essential. The aim of this research is to maximize the overall users’ quality of experience in terms of power-efficient adaptive video streaming by fair distribution and smooth transition of video rates. The joint optimization includes power minimization, efficient resource allocation, i.e., transmit power and bandwidth, and efficient two-dimensional positioning of the UAV while meeting system constraints. The formulated problem is non-convex and difficult to solve with conventional methods. Therefore, to avoid the curse of complexity, the block coordinate descent method, successive convex approximation technique, and efficient iterative algorithm are applied. Extensive simulations are performed to verify the effectiveness of the proposed solution method. The simulation results reveal that the proposed method outperforms 95–97% over equal allocation, 77–89% over random allocation, and 17–40% over joint allocation schemes.

1. Introduction

The use of wireless communication has had significant growth in the previous decade, leading to the expansion of its service capabilities to a wide range. The tremendous growth is also accelerating the pace of developing sophisticated wireless communication networks. Unmanned aerial vehicles (UAVs) are revolutionizing wireless communication by offering faster and more flexible wireless networking capabilities compared to traditional networks, demonstrating strong resilience in natural disaster situations. During busy times, conventional base stations cannot handle heavy communication traffic and they do not provide sufficient communication coverage in remote areas. UAV networks serve as a superior alternative to terrestrial base stations, utilizing UAVs as airborne base stations or relay networks [1,2]. UAVs have the ability to establish active communication links for line-of-sight (LoS) propagation between UAVs and ground users such that the performance of the communication network can be significantly improved. UAV communication networks are often used in emergencies and high-demand regions because they are cost-effective, easy to deploy, and can quickly restore wireless communication services [3,4].

The UAV networks have also achieved vast attention in the fields of research and industrial setup, and extensive research has been explored in the field of UAV-aided communication in terrestrial communication networks during the previous several years [5]. UAV-enabled networks offer a range of services, including video streaming. Video streaming is particularly favored and dominant in providing information, especially in emergencies for rescue purposes [6]. Furthermore, due to the growth of broadband cellular networks and the rising popularity of smart mobile gadgets, video media streaming has become a major part of communication network services. Furthermore, it is predicted that the share of video transmission will continue to rise in the upcoming 6G age.

With the rapid growth of technology, the UAV has a wide range of applications, including intelligent video surveillance, image detection, forest fire prevention, power line detection, agriculture information, video monitoring, etc. A UAV-enabled target detection method, YOLOv4, can be applied for road traffic detection and intelligent video monitoring and can identify small targets in aerial videos [7], wind turbine blade crack inspection applications [8], deep learning-based aerial applications for forest area classification [9], and UAV use in disaster management [10]. Video service transmission refers to the process of transmitting large volumes of video data with playback information, necessitating a high-performing network with increased throughput and minimal latency, particularly for high-definition video transmission services. Video streaming communication quality is highly dependent on the accomplishment of the network, which in UAV-based transmission is dependent on changing network topologies, interference, and the time-dependent fading channel. These diverse characteristics pose a significant challenge in the research of the transmission of video services in UAV-assisted networks [11].

Adaptive streaming over HTTP, taking into consideration the user’s current state and network conditions to ensure a high quality of experience even with sudden decreases in bandwidth, is investigated in [12]. To ensure fairness of quality of experience in adaptive video streaming, a server-based technique which controls bandwidth allocation among associated users is proposed in [13,14]. The repetitive selection of video rates leads to a degradation in the performance of QoE. The impact on the QoE caused by abrupt shifts is greater than the seamless selection or transition between video rates [15]. To enhance the overall user experience, it is crucial to ensure fair distribution of bandwidth among users in a shared network where a user with a lower video rate experiences poor viewing experience while most of the bandwidth may be occupied by users with higher video rates.

It is a challenging task to deploy a UAV as an aerial base station in wireless networks because charging or replacement of its batteries is not an easy job. On the other hand, enhanced video quality requires a high bitrate, bandwidth, and power. Therefore, efficient power management and control in UAV-assisted networks are challenging issues and very important to be addressed. In addition, the efficient placement of a UAV to better exploit its deployment flexibility is also a challenging task. Similarly, the inefficient and unfair allocation of bandwidth among users can negatively affect video streaming quality, thereby causing interruptions and delays in video services. In this work, we aim to address the aforementioned challenges in UAV-assisted wireless networks for video transmission.

Motivated by the above discussion, this work focuses on efficient UAV positioning, fair allocation of resources among users, and improving power efficiency in a UAV-assisted wireless network for video streaming with enhanced user experience by fair distribution and smooth transition of video rates.

Organization

The organizational framework of the remainder of this paper is summarized as follows: The related work and contributions are presented in Section 2, the proposed system model and the formulated problem are illustrated in Section 3, whereas the mathematical model with its mathematical illustrations of the proposed solution is expressed in Section 4. Simulations are discussed in Section 5. Finally, the conclusions of the proposed approach are presented in Section 6.

2. Related Work and Contribution

Quality of experience (QoE) is the performance metric for video transmission and it can effectively measure the distinctive features of video streaming. Therefore, many researchers have considered it carefully in QoE-driven UAV-enabled network optimization schemes. For instance, the authors developed a model in [16] that combines adaptive video streaming and power efficiency considerations for delivering adaptive video transmission to multiple ground users. The model also takes into account resource allocation, optimization of the UAV’s horizontal location, information causality constraints, and available energy limitations. A novel framework is presented to optimize the quality of experience for clients and reduce the power dissipation of the system by utilizing multiple UAVs [17].

A quality of experience-based study is presented in [18], which utilizes numerous UAVs to provide on-demand media transmission in a communication network, with the goal of maximizing quality of experience (QoE) by reducing user delay and increasing communication throughput for all UAVs. The authors in [19] suggested a model for maximizing long-term QoE by optimizing the transmission power and system bandwidth of unmanned aerial vehicles (UAVs), taking into account the bitrate and video freezing time. In the comparison made with the previous studies, however, the crucial feature of UAV networks, energy efficiency, was not considered in [19,20]. Compared to traditional base stations, UAV-aided networks are more sensitive to energy constraints due to their limited onboard energy capacity and inability to carry heavy energy sources. Therefore, optimizing power consumption is a crucial feature of UAV-aided communication networks.

Therefore, the authors in [21] presented a power efficiency optimization model comprising the ratio between the video bitrate and power consumption of the UAV while jointly optimizing allocated power and video level selection. In [22], the authors have explored the optimization framework of joint optimization of user communication scheduling, transmit power, trajectory, and allocated bandwidth for maximizing the energy efficiency of an aerial-enabled system while satisfying QoE demands for users. The energy efficiency framework of UAV trajectory optimization for mobile video monitoring while considering quality-of-service constraints is presented in [23]. Even though the matter of energy efficiency in UAV-aided video streaming networks is explored in [16], a single-UAV deployment case is studied which has limitations in coverage and communication capacity and strict energy constraints. A lone UAV cannot guarantee the completion of the whole mission due to limited energy sources. Alternatively, the utilization of many UAVs can enable clients to collectively achieve increased communication capacity with minimal latency. These strategies can also improve the efficiency of communication services by utilizing several UAVs in a communication network. However, in multi-UAV-assisted networks, communication resource scheduling is significantly challenging in comparison to a network of single deployed UAVs [24].

A study of the deployment of multiple UAVs in communication networks for delivering valuable services to clients by joint optimization of the UAVs and client associations, UAV trajectories, and transmit power is explored in [25]. However, in this work, the features of video transmission are not elaborated. An unmanned aerial vehicle (UAV) is used to create a video streaming network that delivers video services to users on the ground. This network takes into account the balance between video quality and playback rate and aims to enhance user experience by optimizing the transmission schedule, UAV trajectory, and playback rate simultaneously [26]. The optimization model is presented in [27] for the maximization of the achievable sum rate through the efficient placement of the UAV and transmit power allocation while meeting the available energy budget. An aerial communication network is explored in [28] to improve the minimum throughput of the system for respective users by adjusting the aerial location of the UAVs.

In [29], an optimization framework of energy efficiency is investigated for providing efficient transmission services to surficial users. In an IRS-aided UAV communication framework, the enhancement of the communication rate through optimizing aerial position, power, and IRS beam forming for transmission is presented in [30]. The paper [16] investigates a communication framework that utilizes a power-efficient aerial base station to deliver video services to surficial users. The framework takes into account several communication parameters like communication resources and UAV position. A power-efficient positioning of UAVs in a public safety network is investigated in [31]. A study of rate adaptation and controlling power for the provisioning of video streaming services with consideration of time-variable interference in a communication network is explored in [32]. An optimization study is elaborated in [33], in which power is allocated for a communication network for total rate enhancement, where the designed problem is decomposed into several parts and then solved iteratively. In the study [34], an optimization model of the total energy minimization of UAVs is investigated together with the optimization of trajectory by using successive convex approximation solution techniques. A study of quadrotor energy efficiency is presented in [35], in which a power consumption model is designed which indicates power consumption during field inspections tasks. The energy-saving aerial communication network is examined in [36], in which the minimum remaining energy is maximized. Moreover, it also describes that UAV wireless coverage is adaptive by adjusting UAV altitude.

A multi-UAV-enabled communication work is explored for providing clients with on-demand communication services by maximizing communication throughput by optimal resource allocation and UAV positioning in [37]. The paper [38] investigates the efficient allocation of resources to meet user requirements. The study focuses on maximizing system throughput by optimizing power, UAV position, and transmission time utilizing the standard technique of successive convex approximation (SCA). Considerable simulations are conducted for validating the effectiveness of the designed approach. The work of the authors in [16] has examined a UAV-aided communication network for optimization of allocated resources and aerial position. The application of a UAV-enabled network in emergency scenarios is investigated in [39], where the max-min rate of ground users is improved. A delay-sensitive communication network equipped with a UAV is investigated for disaster-affected areas in [40].

The UAV’s flexible and mobile deployment qualities are highly desirable in UAV-enabled communication networks. However, the delay requirements provide a significant challenge for UAV mobility. The paper [41] investigates the use of the 3D positioning of UAVs to address limitations in delay requirements, such as those found in online games and video streaming, while also maximizing throughput. Additionally, the paper [42] conducts an in-depth investigation of the optimization problem of minimizing video access delay. The study presented in [43] explores video transmission in a public-safety aerial network with efficient resource allocation and UAV positioning. An aerial framework is presented in [44] for the provisioning of video streaming services in emergency communication networks through joint optimization of trajectory and resources. A study on improving the quality of experience in terms of video streaming for multiple video users through a mechanism of practically allocating bandwidth is presented in [45].

2.1. Fairness in Quality of Experience

The research work conducted in [15] explores the effect of content-aware optimization on quality of experience, as well as the optimization of fairness and the utilization of bandwidth for video streaming in mobile edge computing environments. The algorithm is meant to adjust video rates by taking into account information from all users of the cell-wide HTTP Adaptive Streaming (HAS) system, as well as specific details about the video content and the characteristics of the user’s device. In addition, the suggested design employs multiple techniques to modify video rates for streaming videos of short and long duration. The quality of experience for clients is influenced by various factors, including video quality, its variations, and interruptions during playback. A linear-based QoE model is investigated while considering video bitrate, ongoing video quality, and re-buffering time [46].

The paper [47] introduces a research study focused on enhancing the overall quality of experience (QoE) in terms of fairness. The approach involves reducing the disparity among users through increasing the low bitrates of users prior to the bottleneck link bandwidth becoming heavily utilized for communication by users with high bitrates. A quality of experience optimization work is presented in [48], which investigates fairness-aware bitrate allocation among multiple users for reducing the difference in user experience. The work conducted in [49] explains the joint optimization framework of fairness for adaptive video streaming in mobile environments while considering the efficient utilization of bandwidth for all respective users.

2.2. Video Quality

HTTP-based Dynamic Adaptive Streaming (DASH) necessitates the organization of high-quality videos for selected viewpoints. The issue arises when there is a need to switch and the desired video may not be present in the buffer. Hence, a comprehensive examination of multi-view video quality of experience (QoE) is being conducted [50] to determine the impact of viewpoint quality on the user’s QoE and to identify methods for enhancing video quality and smoothness during video switching sessions. Bitrate switching and buffering events immediately affect user quality of experience, which the conventional linear-based quality of experience (QoE) model might not be able to accurately capture. In the paper [46], the presented model illustrates the sequential nature of the quality of experience.

An experimental research investigation has been performed for the assessment of video quality in two different environments to measure quality assessment scores. The experimental evaluation is conducted by employing various video bitrates and different image resolutions [51]. The study [52] investigates an adaptive medical video streaming method that incorporates super-resolution in a telemedicine network. The goal is to provide high-quality video services to medical professionals while conserving network bandwidth and ensuring a decent quality of experience (QoE). The study [53] utilizes a QoE model to compute the QoE performance of individual video streaming sessions. This model is both straightforward and widely utilized, encompassing all the pertinent characteristics like bitrate, smoothness, and re-buffering that impact the QoE during a video streaming session over the HTTP protocol.

The study conducted in [54] examines the utilization of UAVs as relays in a communication system. The purpose is to aid in establishing connections among users and the BS in situations where communication is impeded. This work aims to maximize the UAVs’ energy efficiency through joint optimization communication scheduling, allocated transmission power, and UAV trajectory. The optimization is subject to a buffer constraint with a given flight time, taking into account the limited energy resources of UAVs [54]. Another study examines the power-efficient adaptive video streaming in a UAV wireless communication network, in which a UAV is used as a relay to deliver video services from a base station to ground users in crisis scenarios when the existing communication setup has been destroyed or is unable to function effectively [16]. This study successfully evaluates the effectiveness of power-aware adaptive video streaming for various video scenarios. This optimization strategy involves the allocation of a specific power level to provide certain video services to consumers on the ground.

This research work offers an improved advantage compared to previous UAV-assisted networks by providing power-efficient video streaming transmission with QoE fairness and video quality. Additionally, it optimizes power allocation for specific video transmissions.

2.3. Contributions

The objective of this work is to enhance the overall quality of experience in adaptive video streaming in UAV-assisted wireless networks by ensuring fairness of video rate distribution and smoothness of video quality with respect to video rate switching and improving power efficiency. In this system, an aerial/UAV relay is employed to enable communication among a terrestrial BS and multiple ground users, as direct links between the base station and ground clients are obstructed. The most related studies discussed in Section 2 are as follows: ref. [15] considers optimization of QoE comprising the fairness, video rate, video quality, and bandwidth utilization; ref. [27] considers maximization of achievable sum rate through efficient placement of UAV and transmit power allocation while meeting energy budget constraints; ref. [45] considers improving QoE with respect to video streaming for multiple video users through allocating bandwidth; and [47] improves the overall quality of experience (QoE) in terms of fairness. It is noted that the solution in [15] does not study power efficiency, aerial networks, or adaptive video streaming. The work in [27] does not consider bandwidth, adaptive video streaming, fairness, or video quality. The work presented in [45] does not evaluate power efficiency, fairness, or UAV networks, and the work in [47] does not consider power efficiency or transmit power, while in the proposed work, we consider UAV-assisted networks, overall user experience in terms of adaptive video streaming, fairness and video quality, resource allocation, and power efficiency. A summarized comparison extracted from the most related works with our proposed work is presented in Table 1. This comparison shows the uniqueness of the proposed work is that the parameters and objectives it considered for UAV-assisted networks have not been considered before. The details of the main contributions of the proposed study are illustrated below.

• A UAV-assisted network is considered where a UAV is acting as an aerial relay for relaying video communication between the BS and ground users.
• The investigation focuses on the total power dissipation of UAVs, including the transmission power of UAVs for ground users and the amount of power required for signal processing in the circuitry of UAV systems.
• Bitrate unfairness among users causes degradation of quality of experience; therefore, to improve overall quality of experience among users, this study also considers the quality of experience metrics in terms of fairness among multiple ground users.
• The variability in video quality is a significant factor to consider, as frequent changes in video rate can lead to a drop in quality of experience (QoE). On the other hand, seamless switching results in improved QoE performance [15]. Thus, the extent of variations in video rate quality, specifically in terms of video rate switching, is evaluated on a session-by-session basis.
• This study aims to optimize resource allocation, UAV 2D position, and informational causality constraints while considering the available energy budget. Nevertheless, the core problem at hand is non-convex and intricately interconnected, making it challenging to solve using conventional methods. To address this matter, the main problem is split into two sub-problems, and optimization techniques like Dinkelbach, which is used to solve convex fractional programming problems by transforming them into non-fractional form; the block coordinate descent technique, which is used to solve blocks of sub-optimization problems in an alternative way; and the successive convex approximation (SCA) method, which is used to solve non-convex optimization problems iteratively, are employed to obtain the efficient solution.
• Finally, an efficient iterative algorithm is used to solve both sub-problems iteratively. Moreover, the proposed design sets up a good tradeoff between system throughput in terms of video data rate for adaptive video streaming and power consumption while ensuring the fairness and quality of video transmission for providing valuable video streaming services among multiple ground users.
• Extensive simulations are performed by using MATLAB version R2024b software and the proposed method is evaluated for performance and efficiency with other benchmark schemes, with different video scenarios, etc.

  Table 1. Summarized comparison of the proposed work with related works.

  Paper	Objective	UAV	Power	Bandwidth	Positioning
  [15]	max QoE(rate, fairness, video quality)	No	No	Yes	No
  [17]	Max QoE (EE)	Yes	Yes	No	Yes
  [27]	Max sum Rate	Yes	Yes	No	Yes
  [29]	Max EE	Yes	Yes	No	Yes
  [34]	Min Energy cost	Yes	Yes	No	Yes
  [37]	Max sum Rate	Yes	Yes	No	Yes
  [45]	Max QoE (Fairness)	No	No	Yes	No
  [47]	Max QoE (fairness, adaptive video streaming)	No	No	Yes	No
  [54]	Max EE	Yes	Yes	No	Yes
  Proposed	Max QoE (adaptive video streaming, fairness, video quality, power efficiency)	Yes	Yes	Yes	Yes

  Table 1. Summarized comparison of the proposed work with related works.

  Paper	Objective	UAV	Power	Bandwidth	Positioning
  [15]	max QoE(rate, fairness, video quality)	No	No	Yes	No
  [17]	Max QoE (EE)	Yes	Yes	No	Yes
  [27]	Max sum Rate	Yes	Yes	No	Yes
  [29]	Max EE	Yes	Yes	No	Yes
  [34]	Min Energy cost	Yes	Yes	No	Yes
  [37]	Max sum Rate	Yes	Yes	No	Yes
  [45]	Max QoE (Fairness)	No	No	Yes	No
  [47]	Max QoE (fairness, adaptive video streaming)	No	No	Yes	No
  [54]	Max EE	Yes	Yes	No	Yes
  Proposed	Max QoE (adaptive video streaming, fairness, video quality, power efficiency)	Yes	Yes	Yes	Yes

3. System Model and Primary Problem

3.1. System Model

This paper considers a UAV-aided application model for providing video streaming services of high quality to multiple ground users. The system model includes a terrestrial BS, an aerial BS in the form of a UAV relay, and numerous ground users $\mathcal{M}$ = $\left\{m_1,m_2,\dots M\right\}$. Figure 1 shows a systematic sketch of the system model. The system model presents that the existing infrastructure has been disabled due to a disaster or because of functional disability and is ineffective for delivering wireless communication services to ground users. Therefore, in this proposed study, it is presumed that the aerial base station is launched as a relay of the decode-and-forward type [54] to enable the functionality of wireless communication links between a working base station and ground users in the affected region. In a three-dimensional Cartesian coordinate system, the coordinates for the functional terrestrial BS are $(x_s,y_s,H_s)$, where $(x_s,y_s)$ represent Cartesian coordinates on the horizontal plane, while $H_s$ is the height of the BS, and for the UAV/aerial BS are the coordinates $(x_a,y_a,H_a)$, in which $(x_a,y_a)$ represent Cartesian coordinates on the horizontal plane and $H_a$ is the altitude of the UAV, and the coordinates of the ground user “m” are expressed as $(x_m,y_m,0)$, where $(x_m,y_m)$ are the Cartesian coordinates of theground user.

Channel Model

The distance from the terrestrial BS to the aerial BS is calculated with the following numerical illustration:

$$d_s=\sqrt{{(H_s-H_a)}^2+{\parallel q_a-l_s\parallel }^2}$$

(1)

where $d_s$ presents the distance from the terrestrial BS to the UAV, and $H_s$ is the height of the terrestrial BS. $H_a$ is the altitude of the UAV, which is supposed as fixed to stay away from obstacles and elevated constructions to ensure safety measures [55]. The location points of the UAV on the horizontal plane are represented by $q_a={[x_a,y_a]}^T$ and that of the terrestrial BS by $l_s={[x_s,y_s]}^T$. Moreover, the expression $|q_a-l_s|$ calculates the Euclidean distance between the UAV and the terrestrial BS [56].

The wireless link established between the terrestrial BS and aerial relay is assumed to be a direct link, i.e., a line-of-sight (LoS) link, which goes along with the path-loss model of free space [57]. The gain of the channel between the terrestrial BS and aerial relay and its data rate are given as:

$$\begin{array}{cc}\hfill G_s& ={\beta }_0{\mathrm{d}}_s^{-2}\hfill \end{array}$$

(2)

$$\begin{array}{cc}\hfill R_s& =W{log}_2\left(1+{\displaystyle \frac{P_s{G}_s}{{\sigma }^2}}\right)\hfill \end{array}$$

(3)

$$\begin{array}{cc}\hfill R_s& =W{log}_2\left(1+{\displaystyle \frac{P_s{\chi }_s}{{(H_s-H_a)}^2+{∥q_a-l_s∥}^2}}\right)\hfill \end{array}$$

(4)

where in Equation (2), $G_s$ indicates the power gain of the channel, whereas ${\beta }_0$ expresses the gain of the communication channel with a 1 m reference distance. $R_s$ expresses the communication rate between the terrestrial BS and aerial BS, $P_s$ denotes the transmission power of the BS, and W presents the overall bandwidth of the communication channel. In Equation (3), ${\sigma }^2=W{N}_0$, $N_0$ indicates the noise spectral density of the AWGN on the side of the receiver, whereas in Equation (4), the parameter ${\chi }_s={\beta }_0/W{N}_0$.

The communication distance between the aerial relay and $m^{th}$ ground user is measured by the following mathematical expression.

$$d_m=\sqrt{{\mathrm{H}}_a^2+{∥q_a-l_m∥}^2}$$

(5)

where $l_m={[x_m,y_m]}^T$ denotes the location of ground user m in a two-dimensional specified region. The mathematical expression $|q_a-l_m|$ calculates the Euclidean distance between the UAV and the user ‘m’ [56].

The channel gain of the downlink transmission channel linking the aerial relay and the m ground user is measured as $G_m=\sqrt{{\Gamma }_m}{\Delta }_m$, where ${\Gamma }_m$ is the parameter assigned for large-scale fading like path loss, shadowing, etc., while ${\Delta }_m$ is the symbol for the small-scale fading component. ${\Delta }_m$ is a random variable having complex value and is expressed as $\mathrm{E}\left\{\right|{\Delta }_m{|}^2\}=1$, while the large-scale fading component for the downlink communication is dependent on the distance from the aerial relay to the ground user m is ${\Gamma }_m={\beta }_0{\mathrm{d}}_m^{-\alpha }$, where ${\beta }_0$ is channel gain, while $\alpha$ presents path loss [11].

$$\begin{array}{cc}\hfill |G_m{|}^2& ={\beta }_0{\mathrm{d}}_m^{-\alpha }\hfill \end{array}$$

(6)

$$\begin{array}{cc}\hfill R_m& =w_{m}W{log}_2\left(1+{\displaystyle \frac{p_m{\left|G_m\right|}^2}{w_m{\sigma }^2}}\right)\hfill \end{array}$$

(7)

$$\begin{array}{cc}\hfill R_m& =w_{m}W{log}_2\left(1+{\displaystyle \frac{p_m{\chi }_m}{w_m{(H_a^2+{∥q_a-l_m∥}^2)}^{\frac{\alpha }{2}}}}\right)\hfill \end{array}$$

(8)

In Equation (7), $R_m$ is denoted for the data rate of the downlink communication link from the UAV to the ${\mathrm{m}}^{th}$ ground user, $p_m$ is the power allocation for the m^th ground user, which is $p_m\ge 0$. The transmit power is constrained as ${\sum }_{m=1}^M{p}_m\le {\mathrm{P}}_{max}$ for all ground users $\left(m_1,m_2\dots M\right)$, where ${\mathrm{P}}_{max}$ is the total transmission power that the UAV can utilize for downlink communication. W is the bandwidth of the downlink transmission channel among the aerial BS and numerous ground users, whereas the notation $w_m$ is the portion of the bandwidth assigned to the m^th ground user, which is ranged as $0\le w_m\le 1$ subject to ${\sum }_{m=1}^M{w}_m\le 1$ and ${\chi }_m={\beta }_0/{\sigma }^2$.

It is assumed that the relaying operation by the UAV uses the frequency division duplex [57], where the same bandwidth is assigned for both the links from the terrestrial BS to the aerial BS and the aerial BS to the ground users. In addition, the downlink communication is presumed to use the frequency division multiple access (FDMA) technique, along with the allocated bandwidth among various ground users, which are randomly distributed in a specific region [16]. Furthermore, the delivery of video content to these randomly distributed ground users is assumed to be performed through adaptive video streaming over HTTP.

In this paper, we use a logarithmic utility model of video streaming which is a logarithmic function of the video transmission rate. In this utility model, the achievable data rate and required playback rate are two important parameters for adaptive video streaming [16].

$$U_m=\gamma log\left(\lambda {\displaystyle \frac{R_m}{r_m}}\right)$$

(9)

where $\gamma$ and $\lambda$ are controlling parameters having multiple values for videos with different characteristics, i.e., City, Soccer, Old Town, etc., ref. [58], and $R_m$ is the achievable transmission rate of the m^th ground user, while $r_m$ denotes the needed playback rate of ground user m, which corresponds to the user media device.

The QoE is adversely influenced because of the continuous switching of video rates and this instantaneous switching highly degrades the quality of experience performance compared to even switching. The magnitude of variations in the quality of the video rate in terms of the video rate switching from one session to another session is calculated with the following formula [15]:

$$Q_m={\displaystyle \frac{R_m-R_{m-1}}{S}}$$

(10)

where $Q_m$ is the magnitude of variation in the video data rate or quality from the current video data rate $R_m$ and the previous video data rate $R_{m-1}$ of the $m^{th}$ ground user, and S denotes the number of switches.

For the improvement of the fairness of the quality of experience in video streaming adaptation, we minimize the disparity in video rates among users on the ground. This can be achieved through improving the video transmission rate of the users who currently have lower video rates prior to the bandwidth allocation to the congested links which are mainly used by users with higher video rates [47]. The fairness of video rate differences can be calculated by the following mathematical expression [46]:

$$F_m=|R_m-{\overline{R}}_{m-1}|$$

(11)

where ${\overline{R}}_{m-1}$ is the average of the previous video data rate of ground user m.

To facilitate the proposed work, we formulate a model that comprises three individual performance metrics: (1) overall user experience, consisting of adaptive video streaming [59], (2) fairness in video quality, and (3) video rate switching [15]. To the best of our knowledge, each of the existing works considers only one of the aforementioned three metrics. Our model considers all these three metrics jointly in one objective function for terrestrial consumers through the utilization of a UAV-enabled relay network. The overall user experience for all ground users can be expressed mathematically by taking into account the adaptive video streaming utility, the number of fluctuations, and the fairness or smoothness of the video quality:

$$U_{Total}=\gamma \sum _{m=1}^{M}log\left(\lambda {\displaystyle \frac{R_m}{r_m}}\right)-\delta \sum _{m=1}^M{\displaystyle \frac{R_m-R_{m-1}}{S}}-\eta \sum _{m=1}^M|R_m-{\overline{R}}_{m-1}|$$

(12)

where $\delta$ and $\eta$ are the constant parameters for the magnitude of variations and fairness of video quality, respectively. Low values are desired for the magnitude of the differences in the variations in the video data rates and the fairness of the video data rates for improved user quality of experience; therefore, their respective terms are negative.

The overall power consumption for communication during the relaying operation of the UAV is determined by the aerial transmit power for ground users, as well as the power needed for the processing of communication signals in the UAV. This overall power consumption can be calculated by the following numerical expression:

$$P_{total}=P_{cir}+\sum _{m=1}^M{p}_m$$

(13)

where $P_{total}$ denotes overall power consumption during relaying communication for video communication services to ground users in terms of power utilized during the processing of the communication signal at the UAV circuit as $P_{cir}$ and the transmission power consumption for the downlink transmission from the UAV to ground users as $p_m$.

3.2. Primary Problem

The primary goal of this study is to maximize the quality of experience in adaptive video streaming with respect to ensuring fairness in video quality and video rate switching and improving the power efficiency of the proposed system by minimizing power consumption. This maximization is achieved through joint optimization of transmit power, allocated bandwidth, and the two-dimensional aerial position while adhering to specific constraints. The optimization variables consist of fractional bandwidth as $\mathcal{W}=\left\{w_m,\forall m\right\}$, transmit power as $\mathcal{P}=\left\{p_m,\forall m\right\}$, and two-dimensional aerial location $\mathcal{Q}=\left\{q_a\right\}$. The formulation and mathematical illustration of the primary problem comprising objective function and its designed constraints is as follows:

$$\mathcal{P}1:\underset{\mathcal{W},\mathcal{P},\mathcal{Q}}{max}\left[{\displaystyle \frac{\gamma {\sum }_{m=1}^{M}log\left(\lambda \frac{R_m}{r_m}\right)-\delta {\sum }_{m=1}^M\frac{R_m-R_{m-1}}{S}-\eta {\sum }_{m=1}^M|R_m-{\overline{R}}_{m-1}|}{P_{cir}+{\sum }_{m=1}^M{p}_m}}\right]$$

(14)

Subject to:

$$\begin{array}{cc}\hfill C1& :\sum _{m=1}^M{R}_m\le R_s\hfill \end{array}$$

(15)

$$\begin{array}{cc}\hfill C2& :\sum _{m=1}^M{w}_m\le 1\hfill \end{array}$$

(16)

$$\begin{array}{cc}\hfill C3& :0\le w_m\le 1,\forall m\hfill \end{array}$$

(17)

$$\begin{array}{cc}\hfill C4& :\sum _{m=1}^M{p}_m\le P_{max}\hfill \end{array}$$

(18)

$$\begin{array}{cc}\hfill C5& :p_m\ge 0,\forall m\hfill \end{array}$$

(19)

$$\begin{array}{cc}\hfill C6& :R_m\ge {\overline{R}}_{min},\forall m\hfill \end{array}$$

(20)

$$\begin{array}{cc}\hfill C7a& :x_{min}\le x_a\le x_{max}\hfill \end{array}$$

(21)

$$\begin{array}{cc}\hfill C7b& :y_{min}\le y_a\le y_{max}\hfill \end{array}$$

(22)

where in (14), $\mathcal{W}\circeq \left\{w_1,w_2,\dots w_M\right\}$ is the allocated bandwidth for ground users, $\mathcal{Q}$ is the horizontal location of the relay UAV, and $\mathcal{P}\circeq \left\{p_1,p_2,\dots p_M\right\}$ is the transmission power for the downlink communication from the aerial relay to various users. Equation (15) describes the information causality constraints at the aerial relay and that the sum of the achievable data rate for the aerial BS should not exceed the uplink transmission throughput of the terrestrial BS. Equation (16) illustrates that the sum of fractional bandwidth $w_m$ allocated to all ground users should not be greater than 1, whereas it ranges from 0 to 1 as expressed in (17). In (18), it is addressed that the total power consumed for communication from the aerial BS to the ground users should not be more than the maximum power $P_{max}$ assigned for aerial communication, while the transmit power $p_m$ cannot be negative, as shown in (19). Equation (20) explains the requirement of the communication data rate during the optimization process, that the achievable communication rate $R_m$ of an individual user m should be more than the minimum average communication rate ${\overline{R}}_{min}$ of user m. This minimum data rate requirement should be met during the optimization of resources and horizontal aerial placement so that all users on the ground can obtain useful communication services. The constraints presented in (21) and (22) are the ranges of horizontal coordinates assigned to the UAV for the optimization of the aerial location in the specified area.

4. Proposed Solution Method

The primarily formulated problem $\mathcal{P}1$ cannot be solved using the traditional solution methods because of its non-convexity. Therefore, by using the Dinkelback, block coordinate descent, and SCA techniques, the primary problem is decomposed and solved by an alternate optimization method through an iterative algorithm. Figure 2 presents the solution procedure of the iterative algorithm. Specifically, in the first sub-problem, only the bandwidth and transmit power $\left\{\mathcal{W},\mathcal{P}\right\}$ allocations are optimized with the given position of the UAV, and in the second sub-problem, the optimization of the UAV location $\left\{\mathcal{Q}\right\}$ is performed while the allocated bandwidth and transmission power are given.

4.1. Optimization of Bandwidth and Transmit Power Allocation

In this sub-problem, the bandwidth $\mathcal{W}$ and transmit power $\mathcal{P}$ are optimized, while the UAV position $\mathcal{Q}$ remains fixed. To optimize the initial sub-problem, the primary problem $\mathcal{P}1$ is redefined as $\mathcal{P}2$.

$$\mathcal{P}2:\underset{\mathcal{W},\mathcal{P}}{max}\left[{\displaystyle \frac{\gamma {\sum }_{m=1}^{M}log\left(\lambda \frac{R_m}{r_m}\right)-\delta {\sum }_{m=1}^M\frac{R_m-R_{m-1}}{S}-\eta {\sum }_{m=1}^M|R_m-{\overline{R}}_{m-1}|}{P_{cir}+{\sum }_{m=1}^M{p}_m}}\right]$$

(23)

Subject to:

$$\mathrm{C}1\mathrm{to}\mathrm{C}6$$

The redefined problem $\mathcal{P}2$ is a fractional programming problem and is nonlinear in nature [60] as the objective function is in fractional form and its numerator is an increasing nonlinear term, while the denominator is a linear-type increasing function of the decision variable $p_m$. Hence, this problem is not feasible to solve with traditional problem solution techniques.

The objective function has a numerator with the summations of the downlink data rates of the ground users and the logarithm of the data rates of the ground users. The Hessian matrix of the mth user data rate is negative semi-definite with respect to the control variables $p_m$ and $w_m$, confirming its concavity in $p_m$ and $w_m$ [61]. Furthermore, it is established that if a function is concave, then its logarithm will also be concave, and the summation of several concave functions also exhibits concave properties [61]. In the objective function of problem $\mathcal{P}2$, the numerator consists of the summation of the logarithms of concave functions; therefore, its concavity is defined in terms of transmit power $p_m$ and fractional bandwidth $w_m$, whereas in the objective function of problem $\mathcal{P}2$, the denominator is a linear function. Furthermore, as the objective function is a fractional term, we will utilize the Dinkelbach technique [60] to transform it into non-fractional form for initiating the solution of problem $\mathcal{P}2$. According to the Dinkelbach technique, the fractional objective function follows this relationship between its numerator $D\left(x\right)$ and denominator $E\left(x\right)$.

$$\underset{\underline{x}}{max}{\displaystyle \frac{D\left(x\right)}{E\left(x\right)}}\iff \underset{\underline{x}}{max}F\left({\psi }^{\ast }\right)$$

(24)

where

$$\underset{\underline{x}}{max}F\left({\psi }^{\ast }\right)=\underset{\underline{x}}{max}\left[D\left(\underline{x}\right)-{\psi }^{\ast }E\left(\underline{x}\right)\right]$$

(25)

and

$${\psi }^{\ast }={\displaystyle \frac{D\left(x^{\ast }\right)}{E\left(x^{\ast }\right)}}$$

(26)

The achieved results for the term ${max}_x{\displaystyle \frac{D\left(x\right)}{E\left(x\right)}}$ will only be optimum if $F\left({\psi }^{\ast }\right)={max}_x[D\left(x\right)-{\psi }^{\ast }E\left(x\right)]=0$ [62]. By applying the same procedure of the Dinkelbach technique on the objective function of the problem $\mathcal{P}2$, we will then obtain the problem form equivalent to $\mathcal{P}2$.

$$\begin{array}{cc}\hfill \mathcal{P}3& :\underset{\mathcal{W},\mathcal{P}}{max}[\left(\gamma \sum _{m=1}^{M}log\left(\lambda {\displaystyle \frac{R_m}{r_m}}\right)-\delta \sum _{m=1}^M{\displaystyle \frac{R_m-R_{m-1}}{S}}-\eta \sum _{m=1}^M|R_m-{\overline{R}}_{m-1}|\right)\hfill \\ \hfill - & \psi \left(P_{cir}+\sum _{m=1}^M{p}_m\right)]\hfill \end{array}$$

(27)

Subject to:

$$\mathrm{C}1\mathrm{to}\mathrm{C}6$$

The reformulated problem $\mathcal{P}3$ obtained by the above procedure is a non-convex optimization problem and cannot be solved easily, and therefore the slack variable $\widehat{\mathcal{R}}=\left\{{\widehat{R}}_m,\forall m\right\}$ is introduced to transform it into a feasible form for solving it with standard solution techniques. The slack variable is introduced in the objective function and its constraints $C1$ and $C6$ and re-written below:

$$\begin{array}{cc}\hfill \mathcal{P}4& :\underset{\mathcal{W},\mathcal{P},\widehat{\mathcal{R}}}{max}[\left(\gamma \sum _{m=1}^{M}log\left(\lambda {\displaystyle \frac{{\widehat{R}}_m}{r_m}}\right)-\delta \sum _{m=1}^M{\displaystyle \frac{{\widehat{R}}_m-{\widehat{R}}_{m-1}}{S}}-\eta \sum _{m=1}^M|{\widehat{R}}_m-{\widehat{\overline{R}}}_{m-1}|\right)\hfill \\ \hfill & -\psi \left(P_{cir}+\sum _{m=1}^M{p}_m\right)]\hfill \end{array}$$

(28)

Subject to:

$$C8:w_{m}W{log}_2\left(1+{\displaystyle \frac{p_m{\chi }_m}{w_m{(H_a^2+{∥q_a-l_m∥}^2)}^{\frac{\alpha }{2}}}}\right)\ge {\widehat{R}}_m,\forall m$$

(29)

$$\begin{array}{cc}\hfill \widehat{C}1& :\sum _{m=1}^M{\widehat{T}}_m\le R_s\hfill \end{array}$$

(30)

$$\begin{array}{cc}\hfill \widehat{C}6& :{\widehat{R}}_m\ge {\overline{R}}_{min}\forall m\hfill \end{array}$$

(31)

and

$$\mathrm{C}2\mathrm{to}\mathrm{C}5$$

Now, the optimization problem $\mathcal{P}4$ is a convex optimization problem with a given constant $\psi$ of the Dinkelbach algorithm and its solution is easy by applying the standard solvers for convex optimization or by utilizing the CVX toolbox [63].

From the definition of the C8 constraint, if the the optimal solution of $\mathcal{P}4$ satisfies C8 equality, then the optimal results of $\mathcal{P}4$ will be equal to those of $\mathcal{P}2$. Moreover, the optimality of the solution to $\mathcal{P}4$ can also be achieved when the equality for constraint C8 is met. However, contrary to this, if the optimum results for the problem $\mathcal{P}4$ do not justify equality for the C8 constraint, in this case the value of the transmit power $p_m$ can be reduced for the purpose of attaining equality. This decrease in the transmit power $p_n$ neither reduces the objective value nor breaches the remaining constraints. Hence, it confirms the solution optimality for $\mathcal{P}4$ can be obtained, which justifies the C8 constraint with equality. Accordingly, this explanation demonstrates the similarity of $\mathcal{P}4$ to $\mathcal{P}2$.

4.2. Optimization of UAV’s Aerial Position

The next decomposed part of our primary problem $\mathcal{P}1$ can be restructured for the optimization of the aerial location $\mathcal{Q}$ of the UAV and the transmission power $\mathcal{P}$ and the fractional bandwidth allocation $\mathcal{M}$ are given.

$$\mathcal{P}5:\underset{\mathcal{Q}}{max}\left[{\displaystyle \frac{\gamma {\sum }_{m=1}^{M}log\left(\lambda \frac{R_m}{r_m}\right)-\delta {\sum }_{m=1}^M\frac{R_m-R_{m-1}}{S}-\eta {\sum }_{m=1}^M|R_m-{\overline{R}}_{m-1}|}{P_{cir}+{\sum }_{m=1}^M{p}_m}}\right]$$

(32)

Subject to:

$$\begin{array}{cc}\hfill C1& :\sum _{m=1}^M{R}_m\le R_s\hfill \end{array}$$

(33)

$$\begin{array}{cc}\hfill C6& :R_m\ge {\overline{R}}_{min}\hfill \end{array}$$

(34)

$$\begin{array}{cc}\hfill C7a& :x_{min}\le x_a\le x_{max}\hfill \end{array}$$

(35)

$$\begin{array}{cc}\hfill C7b& :y_{min}\le y_a\le y_{max}\hfill \end{array}$$

(36)

The redefined optimization problem $\mathcal{P}5$ is also non-convex in nature and its solution is not easy without introducing slack variables. Therefore, the slack variable $\widehat{\mathcal{R}}=\left\{{\widehat{R}}_m,\forall m\right\}$ is introduced to obtain a feasible form of $\mathcal{P}5$ which can be easily solved by utilizing available optimization solvers.

$$\mathcal{P}6:\underset{\mathcal{Q},\widehat{\mathcal{R}}}{max}\left[{\displaystyle \frac{\gamma {\sum }_{m=1}^{M}log\left(\lambda \frac{{\widehat{R}}_m}{r_m}\right)-\delta {\sum }_{m=1}^M\frac{{\widehat{R}}_m-{\widehat{R}}_{m-1}}{S}-\eta {\sum }_{m=1}^M|{\widehat{R}}_m-{\widehat{\overline{R}}}_{m-1}|}{P_{cir}+{\sum }_{m=1}^M{p}_m}}\right]$$

(37)

Subject to:

$$C9:w_{m}W{log}_2\left(1+{\displaystyle \frac{{\Pi }_m}{{(H_a^2+{∥q_a-l_m∥}^2)}^{\frac{\alpha }{2}}}}\right)\ge {\widehat{R}}_m,\forall m$$

(38)

$$C10:W{log}_2\left(1+{\displaystyle \frac{{\Pi }_s}{{(H_s-H_a)}^2+{∥q_a-l_s∥}^2}}\right)\ge \sum _{m=1}^M{\widehat{R}}_m$$

(39)

$$\widehat{C}6:{\widehat{R}}_m\ge {\overline{R}}_{min},\forall m$$

(40)

and

$$\mathrm{C}7\mathrm{a}\mathrm{to}\mathrm{C}7\mathrm{b}$$

where ${\Pi }_m=p_m{\chi }_m/w_m$ and ${\Pi }_s=P_s{\chi }_s$.

The objective function of the problem $\mathcal{P}6$ is concave in terms of ${\widehat{R}}_m$ because the second derivative is less than zero [64], while constraints at C9 and C10 are still non-convex. For the purpose of transforming the non-convex constraints into convex form, we will apply the successive convex approximation and Taylor series expansion techniques. Consequently, after transformation, the problem $\mathcal{P}6$ will be converted to convex form and its solution with standard solvers will be feasible. The function $f\left(z\right)$ can be written by using Taylor series expansion as below:

$$f\left(z\right)=f\left(c\right)+{\displaystyle \frac{f^{\prime }\left(c\right)}{1!}}(z-c)+{\displaystyle \frac{f^{″}\left(c\right)}{2!}}{(z-c)}^2+\dots$$

(41)

To proceed, let

$$x_m={∥q_a-l_m∥}^2$$

(42)

$${\displaystyle \frac{tial{R}_m}{tial{x}_m}}={\displaystyle \frac{w_{m}W{log}_{2}e}{1+\frac{{\Pi }_m}{{(H_a^2+x_m)}^{\frac{\alpha }{2}}}}}.{\displaystyle \frac{-{\Pi }_m\frac{\alpha }{2}}{{(H_a^2+x_m)}^{(\frac{\alpha }{2}+1)}}}={\displaystyle \frac{-w_{m}W{\Pi }_m{log}_{2}e\alpha }{2({(H_a^2+x_m)}^{\frac{\alpha }{2}}+{\Pi }_n)(H_a^2+x_m)}}$$

(43)

By substituting value of $x_m$ from Equation (42):

$${\displaystyle \frac{tial{R}_m}{tial\left({∥q_a-l_m∥}^2\right)}}={\displaystyle \frac{-w_{m}W{\Pi }_m{log}_{2}e\alpha }{2({(H_a^2+{∥q_a-l_m∥}^2)}^{\frac{\alpha }{2}}+{\Pi }_m)(H_a^2+{∥q_a-l_m∥}^2)}}$$

(44)

Notice that it is the property of the Taylor series expansion that the first-order Taylor expansion of a convex function is the function’s global lower bound [61]. The Taylor series approach requires derivatives, which are obtained either numerically or analytically and is usually limited to a first-order analysis for convex functions [65]. Therefore, we use the first-order Taylor approximation for $R_m$ and its expression is written as below;

$$R_m^{lb}=R_m\left(x^r\right)+{\displaystyle \frac{tial{R}_m}{tial{x}_m}}{|}_{x_m=x^r}(x_m-x^r)$$

(45)

$$R_m^{lb}=w_{m}W(A_m^r-I_m^r({∥q_a-l_m∥}^2-{∥q_a^r-l_m∥}^2))$$

(46)

where

$$A_m^r={log}_2\left(1+{\displaystyle \frac{{\Pi }_m}{(H_a^2+{∥q_a^r-l_m∥}^2)\frac{\alpha }{2}}}\right)$$

(47)

and

$$I_m^r={\displaystyle \frac{{log}_{2}e\alpha {\Pi }_m}{2({(H_a^2+{∥q_a^r-l_m∥}^2)}^{\frac{\alpha }{2}}+{\Pi }_m)(H_a^2+{∥q_a^r-l_m∥}^2)}}$$

(48)

The same procedure as illustrated above will be applied for constraint $C9$ for obtaining $R_s^{lb}$.

$$R_s^{lb}=W\left(A_s^r-I_s^r({∥q_a-l_s∥}^2-{∥q_a^r-l_s∥}^2)\right)$$

(49)

where

$$A_s^r={log}_2\left(1+{\displaystyle \frac{{\Pi }_s}{({(H_s-H_a)}^2+{∥q_a^r-l_s∥}^2)}}\right)$$

(50)

and

$$I_s^r={\displaystyle \frac{{log}_{2}e{\Pi }_s}{(({(H_s-H_a)}^2+{∥q_a^r-l_s∥}^2)+{\Pi }_s)({(H_s-H_a)}^2+{∥q_a^r-l_s∥}^2)}}$$

(51)

With the lower bounds at (46) and (49), and the given UAV location $q_a^r$, the problem $\mathcal{P}6$ can be written as follows:

$$\mathcal{P}7:\underset{\mathcal{Q},\widehat{\mathcal{R}}}{max}\left[{\displaystyle \frac{\gamma {\sum }_{m=1}^{M}log\left(\lambda \frac{{\widehat{R}}_m}{r_m}\right)-\delta {\sum }_{m=1}^M\frac{{\widehat{R}}_m-{\widehat{R}}_{m-1}}{S}-\eta {\sum }_{m=1}^M|{\widehat{R}}_m-{\widehat{\overline{R}}}_{m-1}|}{P_{cir}+{\sum }_{m=1}^M{p}_m}}\right]$$

(52)

Subject to:

$$\begin{array}{cc}\hfill R_m^{lb}& \ge {\widehat{R}}_m,\forall m\hfill \end{array}$$

(53)

$$\begin{array}{cc}\hfill R_s^{lb}& \ge \sum _{m=1}^M{\widehat{R}}_m\hfill \end{array}$$

(54)

$$\begin{array}{cc}\hfill {\widehat{R}}_m& \ge {\overline{R}}_{min},\forall m\hfill \end{array}$$

(55)

Now, the redefined problem $\mathcal{P}7$ is obtained in convex form and its solution with standard convex solvers is possible.

4.3. Review of Efficient Iterative Algorithm

On the basis of the preceding investigation, the proposed efficient iterative Algorithm 1 utilizes the block coordinate descent technique [66,67] for solving the decomposed sub-problems $\mathcal{P}4$ and $\mathcal{P}7$ in an alternate way and hence obtains the optimum solution of our primary problem $\mathcal{P}1$. Particularly, the decision variables of the primary problem $\mathcal{P}1$ are decomposed into two parts. In the first part, the fractional bandwidth and transmit power $\left\{\mathcal{W},\mathcal{P}\right\}$ are optimized with the given aerial position by solving $\mathcal{P}4$. In the second part, having the transmit power and fractional bandwidth obtained from the solution of $\mathcal{P}4$, the aerial location $\left\{\mathcal{Q}\right\}$ is optimized by solving $\mathcal{P}7$. Both the sub-problems are alternatively solved in every iteration of our proposed algorithm. The step-by-step procedure of the proposed optimization method with alternating technique is established in efficient iterative Algorithm 1. The solution procedure for $\mathcal{P}4$ is presented in lines 4 to 8 and the solution of $\mathcal{P}7$ is expressed in line 9 of our proposed efficient Algorithm 1. In the convergence condition in step 4 of Algorithm 1, the first term represents the numerator $D({\mathcal{W}}^{i+1},{\mathcal{P}}^{i+1},{\mathcal{Q}}^i)$ and the next term is the denominator $E\left({\mathcal{P}}^{i+1}\right)$ of the objective function of the problem $\mathcal{P}4$. The optimal results of the problem $\mathcal{P}4$ will be obtained if and only if $\left|D({\mathcal{W}}^{i+1},{\mathcal{P}}^{i+1},{\mathcal{Q}}^i)-\psi \left(E\left({\mathcal{P}}^{i+1}\right)\right)\right|=0$. However, to accelerate the procedure of the iterative algorithm, we stop the execution process from lines 4 to 8 after the term reaches $\left|D({\mathcal{W}}^{i+1},{\mathcal{P}}^{i+1},{\mathcal{Q}}^i)-\psi \left(G\left({\mathcal{P}}^{i+1}\right)\right)\right|\le \kappa$, where $0<\kappa <<1$ is a very small value.

The convergence analysis in [66,67] confirms the optimality of the results obtained using the block coordinate descent (BCD) technique. That is, the optimum results for every sub-problem during each iteration can be achieved when the convexity of the reformulated sub-problems is confirmed. Consequently, the convergence is guaranteed, leading to the global optimality. As both the sub-problems $\mathcal{P}4$ and $\mathcal{P}7$ are convex, the proposed iterative algorithm will therefore find the global optimum solutions of the two sub-problems in every iteration of the algorithm while promising convergence.

Algorithm 1 Efficient Iterative Algorithm $\left(\mathcal{P}1\right)$

1: Initialization; $P_{max},p_m^0,w_m^0,\kappa ,{\psi }^0$, ${\mathcal{W}}^0$, ${\mathcal{P}}^0$, $i=0$  2: Repeat  3: Set $j=0$  4: while  $\left|D({\mathcal{W}}^{i+1},{\mathcal{P}}^{i+1},{\mathcal{Q}}^i)-\psi \left(E\left({\mathcal{P}}^{i+1}\right)\right)\right|\le \kappa$  do  5:    Solve $\left(\mathcal{P}4\right)$ for the given ${\psi }^j$ and ${\mathcal{Q}}^i$ to get $({\mathcal{W}}^{i+1},{\mathcal{P}}^{i+1})$  6:    Update ${\psi }^{j+1}$ by using ${\psi }^{j+1}={\displaystyle \frac{D({\mathcal{W}}^{i+1},{\mathcal{P}}^{i+1},{\mathcal{Q}}^i)}{E\left({\mathcal{P}}^{i+1}\right)}}$  7:    $j=j+1$  8: end while Loop  9: Solve $\left(\mathcal{P}7\right)$ for the given $({\mathcal{W}}^{i+1},{\mathcal{P}}^{i+1})$ and ${\mathcal{Q}}^r$ to get optimal solution as ${\mathcal{Q}}^{i+1}$ 10: $i=i+1$ 11: Until the convergence achieved for the objective value of primary problem $\mathcal{P}1$.

4.3.1. Convergence Analysis of Iterative Algorithm 1

For the comprehensive explanation of the iterative algorithm convergence procedure, we assume that $U_{\psi }\left\{{\mathcal{W}}^i,{\mathcal{P}}^i,{\mathcal{Q}}^i\right\}$ and $U_{lb}\left\{{\mathcal{W}}^i,{\mathcal{P}}^i,{\mathcal{Q}}^i\right\}$ are the objective values of sub-problems $\mathcal{P}4$ and $\mathcal{P}7$ with the given ${\mathcal{W}}^i,{\mathcal{P}}^i$, and ${\mathcal{Q}}^i$ for the $i^{th}$ iteration of Algorithm 1, respectively. Furthermore, the procedure of convergence for the proposed algorithm can also be described by means of the following illustrations of inequalities.

$$\begin{array}{cc}\hfill U\{W^i,P^i,Q^i\}& \stackrel{\left(a\right)}{\le }{U}_{\psi }\{W^{i+1},P^{i+1},Q^i\}\hfill \end{array}$$

(56)

$$\begin{array}{cc}\hfill & \stackrel{\left(b\right)}{\le }{U}_{lb}\{W^{i+1},P^{i+1},Q^i\}\hfill \end{array}$$

(57)

$$\begin{array}{cc}\hfill & \stackrel{\left(c\right)}{\le }{U}_{lb}\{W^{i+1},P^{i+1},Q^{i+1}\}\hfill \end{array}$$

(58)

$$\begin{array}{cc}\hfill & \stackrel{\left(d\right)}{\le }U\{W^{i+1},P^{i+1},Q^{i+1}\}\hfill \end{array}$$

(59)

Firstly, the inequality (a) exists in step 5 of the proposed iterative Algorithm 1 when the optimum solution $\left\{{\mathcal{W}}^{i+1},{\mathcal{P}}^{i+1}\right\}$ is obtained for the problem $\mathcal{P}4$ with the given ${\mathcal{Q}}^i$. Further, the power efficiency value ${\psi }^j$ of the proposed solution method is updated in the sixth step of the iterative Algorithm 1 as ${\psi }^{j+1}$ when the output of the objective function value of $\mathcal{P}4$ reaches $\le \kappa$.

Secondly, in the ninth step of iterative Algorithm 1, the optimum solution is achieved as $Q^{i+1}$ for the problem $\mathcal{P}7$ with the given values of bandwidth ${\mathcal{W}}^{i+1}$ and power ${\mathcal{P}}^{i+1}$. The inequality presented in (59) describes that the obtained value of the objective function of the problem $\mathcal{P}7$ is consistently non-decreasing after the execution of every iteration. In view of the fact that the use of the successive convex approximation technique always guarantees monotonic convergence [63,68], then the inequalities (b–d) must hold. Additionally, the solution of the objective function of the proposed problem $\mathcal{P}1$ is finite and upper-bounded and, consequently, guarantees the convergence of the proposed iterative Algorithm 1.

4.3.2. Complexity Analysis of Iterative Algorithm 1

The decomposed parts $\mathcal{P}4$ and $\mathcal{P}7$ of the primary problem $\mathcal{P}1$ are convex nature optimization problems, while the proposed Algorithm 1 is an iterative method and has polynomial complexity which is discussed below:

The first sub-problem $\mathcal{P}4$ of the primary problem $\mathcal{P}1$ is solved from line 4 to line 8 of the proposed iterative Algorithm 1. The problem has 3M variables and 4M + 3 constraints, where M represents the number of users. The solution is guaranteed to converge with polynomial-time complexity, given by $O(\sqrt{3M}(4M+3)log{\displaystyle \frac{1}{\varphi }})$, where $\varphi >0$ is the accuracy tolerance [61]. Furthermore, the ninth line of Algorithm 1 provides the solution of the second convex problem $\mathcal{P}7$, which has M+2 variables and 2M + 1 constraints. Its computational complexity is given by $O(\sqrt{M+2}(2M+1)log{\displaystyle \frac{1}{\varphi }})$ [61]. The total computational complexity of Algorithm 1 is $O(\sqrt{3M}(4M+3)log{\displaystyle \frac{1}{\varphi }})+O(\sqrt{M+2}(2M+1)log{\displaystyle \frac{1}{\varphi }})$. Ignoring constant parameters, the complexity simplifies to approximately $O(M^{3.5}log{\displaystyle \frac{1}{\varphi }})$. This accounts for the number of users, system constraints, and accuracy tolerance.

5. Results and Discussion

This section presents the evaluation of the simulation results of the proposed solution method by comparing other existing schemes for performance assessment. Users are uniformly distributed in a region of 1000 × 1000 m² in a random manner. The utility parameters chosen for the adaptive video streaming are $\gamma$ = 0.8, $\lambda$ = 100, and the individual playback rate is taken as $r_m$ = 0.5 Mbps [57,58]. The controlling parameter for the video rate switching is $\delta =0.4$, and for the fairness of video quality, it is $\eta =0.1$, [15]. The location of the terrestrial BS for the provisioning of uplink communication is positioned as $l_s$ = ${[0,500]}^T$, whereas the location of the UAV/aerial BS is set as $q_a$ = ${[0,500]}^T$. The transmit power budget of the terrestrial BS is $P_s$ = 20 dBm and $\chi =P_s{\beta }_0/W{N}_0$ is taken as 70 dB, which is the reference SNR at a distance of $d_0$ = 1 m. The terrestrial BS is mounted with a height of $H_s$ = 20 m, while the aerial BS is at an altitude of $H_a$ = 100 m. The channel bandwidth for both the uplink and downlink communication links is taken as W = 1 MHz, while the noise power at the receiver end for the AWGN is $N_0$ = −170 dBm/Hz, and the channel power gain with 1 m reference distance is ${\beta }_0$ = −60 dB [57].

The circuitry power consumed for signal processing in the UAV is $P_{cir}$ = 0.001 Watt [69], while the minimum user average data rate required is set as ${\overline{R}}_{min}$ = 10 Kbps [70]. The accuracy of tolerance for the Dinkelbach procedure used in our proposed iterative Algorithm 1 is taken as $\kappa$ = 10⁻⁴. Moreover, in the proposed work, the power-efficient QoE is defined as the QoE perceived by the user per watt, as QoE/power, and therefore, its unit is defined as QoE/Watt [71], and according to the objective function of P4, the power efficiency will be calculated by the expression QoE/power and the unit for power efficiency will also be defined as QoE/Watt. The path loss exponent is a real positive number.

The proposed algorithm is a successive convex approximation method which works iteratively, and with each iteration, the approximation improves. We illustrate this fact by performing simulations, as shown in Figure 3. In this figure, the proposed iterative algorithm’s performance evaluation is expressed by taking ground users M = 10 and maximum transmission power for UAV communication $P_{max}$ = 0.1 Watt. The lower bound of the objective function value of our method is compared with the original value of our primary formulated problem $\mathcal{P}1$ prior to its decomposition into sub-parts. The lower bound of our designed method is computed through the solution of two sub-parts as convex optimization problems $\mathcal{P}4$ and $\mathcal{P}7$ presented in (28) and (52), while the exact value is calculated based on (14). The curves show that the result of the proposed solution method is very close to the exact solution and converges after a few iterations, indicating the efficiency of our decomposition-based approach for solving problem $\mathcal{P}1$.

We compare our proposed solution with multiple ground users and different transmit powers using the following methodologies: (1) The proposed solution is obtained using Algorithm 1. (2) Equal allocation involves equally allocating transmit power and bandwidth among ground users [37], while aerial position is optimized by solving of the second sub-problem $\mathcal{P}7$. (3) In random allocation, resources are randomly distributed among ground users [37], while aerial position is optimized by solving of the second sub-problem $\mathcal{P}7$. (4) Joint transmit power and bandwidth allocation, which transmit power and bandwidth, are optimized with a fixed UAV position [37].

Figure 4 shows the findings of our proposed approach in terms of performance with M = 10 as the number of users and the increasing transmission power. The graphical results demonstrate that with the increase in the transmission power, the output of the objective function in the proposed method improves. Furthermore, the proposed objective value reaches saturation when the minimum requirement of our objective is achieved. In the proposed method, the allocation of power is efficient and the required amount of power is allocated according to the power requirements of the services, along with efficient placement of the UAV. On the other hand, in equal and random allocation schemes, the power is allocated unnecessarily and, therefore, consumed without requirement, which consequently degrades the overall performance of the system, as shown in the figure, whereas in the joint allocation scheme, transmit power and bandwidth are optimized with fixed UAV position and show better results with comparison to equal and random allocation. The performance of the proposed solution method improves 89%, 97%, and 17% compared to the equal allocation, random allocation, and joint allocation schemes, respectively.

Figure 5 shows the power efficiency of the proposed method with M = 10 ground users and $P_{max}$ = 0.1 Watt maximum transmission power. The figure represents the rapid increase in the power efficiency with the increasing iterations, and hence it achieves the convergence within a few iterations, which shows the performance efficiency of the proposed algorithm.

In Figure 6, the achievement of the proposed solution method is validated for the increasing path-loss exponent with maximum transmit power $P_{max}$ = 0.1 Watt and M = 10 ground users. It is clear from the figure that the objective value decreases with the increase in the value of the path-loss exponent. Moreover, it exceeds in performance in comparison to other methods, which shows the performance efficiency of our proposed method. Moreover, in the proposed scheme, the power allocation is optimal and efficient, so a specific amount of power is allocated for a certain service, while for the comparative schemes of equal and random allocation, the power is allocated unnecessarily, which degrades their performance as shown in the figure, whereas in the case of joint allocation where resources are optimized but the UAV position is fixed, it shows better performance than the equal and random method but lower performance than the proposed method. The performance achievement of the proposed method outperforms by 77%, 95%, and 40% over the equal allocation, random allocation, and joint allocation techniques, respectively.

In the Figure 7, the efficiency of the proposed method is validated with M = 10, $P_{max}$ = 0.1 Watt and multiple video scenarios. These varying video scenarios have videos with different characteristics; therefore, their controlling parameters $\gamma$ and $\lambda$ are also different, i.e., for Crew ($\gamma$ = 0.802, $\lambda$ = 419.6), Soccer ($\gamma$ = 0.777, $\lambda$ = 352.3), Parkjoy ($\gamma$ = 0.872, $\lambda$ = 290.3), City ($\gamma$ = 0.976, $\lambda$ = 143.2), Ice ($\gamma$ = 0.765, $\lambda$ = 297.3), and Old Town ($\gamma$ = 0.787, $\lambda$ = 218.1). The results of various curves in the figure show that the convergence is achieved up to the second iteration, which shows the effectiveness of our proposed solution method and algorithm, which is not only effective for a specific system but also works for other systems too, determining that the proposed method is versatile and effective for various video scenarios.

In Figure 8, the efficacy of power efficiency is validated for numerous video environments by taking $P_{max}$ = 0.1 Watt and M = 10. It shows that our proposed power-efficient solution method is also valid for other video scenarios. It shows that the power efficiency of all the video scenarios converges quickly in few iterations. This shows the convergence efficiency of our proposed technique and iterative algorithm.

In Figure 9, the proposed design is evaluated for different video environments for the increasing path-loss exponent $\alpha$ with M = 10 and $P_{max}$ = 0.1 Watt. This validation shows that the output of the objective value decreases with the increasing intensity of the path loss. The validation results highlight that the proposed solution method has varying performance for videos with different features and distinctive constant parameters $\gamma$ and $\lambda$ for each video [16].

Figure 10 shows the effect of increasing path loss on transmit power consumption with M = 10 and $P_{max}$ = 0.1 Watt. As the value of the path-loss intensity increases, the consumption of transmission power increases but within the allocated power budget.

In Figure 11, Figure 12, Figure 13, Figure 14, Figure 15 and Figure 16, the performance of the proposed method is evaluated with various video environments. It is described in this evaluation that videos with different characteristics have different controlling parameters, as expressed with figures. Moreover, the performance of the proposed solution method is compared with other existing schemes. The comparison results reveal that the proposed method outperforms the existing schemes. This performance evaluation also shows the algorithm convergence and shows that the proposed algorithm not only works for a specific video scenario, but it is generalized and performs efficiently for any video scenario. In Figure 1, the results show the performance evaluation of our proposed method by comparing it with existing schemes and varying video scenarios, which shows the effectiveness and convergence of our proposed method and algorithm, respectively.

6. Conclusions

In this study, the overall quality of experience is maximized in terms of power-efficient adaptive video streaming, fairness of video rate distribution, and smoothness of video quality with respect to video rate switching, together with the joint optimization of resource allocation and UAV position in UAV-assisted wireless networks. In this proposed model, the formulated primary problem is non-convex in nature and its solution with traditional methods is not feasible. Therefore, it is divided into sub-problems to find a feasible solution. To this end, we have used several optimization techniques such as successive convex approximation, the Dinkelbach method, block coordinate descent, and an efficient iterative algorithm. The performance of the proposed model is assessed by comparing it with other existing benchmark methods, i.e., equal allocation, random allocation, and joint allocation. The proposed method outperforms the other comparative schemes. The proposed method is evaluated with varying transmit power, number of ground users, and path loss. The evaluation results show that the increasing transmission power improves the power efficiency and quality of experience, whereas it is saturated when the minimum requirement is achieved. Moreover, the increase in path loss decreases power efficiency and quality of experience. Also, the proposed method is validated for different video scenarios as well to verify its effectiveness, which shows very good results. The proposed model is employed for a scenario where the UAV acts as a relay base station for transmitting videos from the terrestrial BS to multiple ground users. However, this model can be extended and utilized with a UAV as an autonomous aerial BS with multiple ground users to provide fair quality video streaming services in crowded environments.