Contents Introduction
The rise in connectivity of intelligent devices such as smartphones and tablets has raised the challenge of managing the increasing number of on-demand service requests. It has created opportunities to implement the Internet of Things (IoT) to improve the efficiency of service delivery in areas such as home automation, smart city, and smart healthcare. Unlike the traditional mobile networks, the IoT has the potential to provide built-in intelligence system for our daily lives. The massive amount of data collected by cellular networks can lead to congestion due to limited spectrum resources. As the amount of data being collected by cellular networks increases, the need for efficient data caching becomes more critical. This technology can reduce the traffic load on the network by caching data on the device. The vast majority of the information collected through the IoT is cacheable, making it a type of reusable content. This content can be stored in smart objects with high storage capacity can reduce back-haul costs and improve download latency. The possibility of Device-to-Device (D2D) communication to improve the effectiveness and reliability of wireless communication networks has gained significant attention in recent years. Devices can connect directly over D2D networks without intervention of the base station[1], [2]. This technology has the potential to reduce latency, improve network capacity, and provide better quality of service for users. There have been significant advancements in D2D communication technology, including new protocols, algorithms, and hardware designs have made D2D communication more reliable, secure, and efficient. Moreover, the emergence of Beyond Fifth-Generation (B5G) networks [3] has created new opportunities for D2D communication[4], as these networks offer higher bandwidth, lower latency, and more advanced features for direct communication[5]. Through D2D communication, devices with close proximity can connect more efficiently, maximizing spectrum reuse and enhancing cellular coverage. D2D also offers advantages such as content privacy and robust anonymity, as shared information is not stored in a central repository. D2D communications can improve energy efficiency, throughput, spectral efficiency, resource allocation, and minimize the delay and interference[5]. Additionally, D2D can provide lower power consumption due to the shorter communication range[6]. However, in a cellular network with underlay D2D communication, mutual interference between D2D and cellular communication can be occurred, as D2D users are given access to share the spectrum that is reserved for cellular users. Efficient allocation of resources, in terms of spectrum bandwidth and power, is the most effective way to mitigate this interference. The convergence of mobile communication and IoT technologies has led to the concept of the Social Internet of Things (SIoT)[7], where smart devices, sensors, and objects are interconnected through wireless communication networks, enabling seamless data sharing and intelligent interactions. As the SIoT ecosystem continues to evolve, the proliferation of D2D communication has emerged as a promising paradigm to enhance communication efficiency, reduce latency, and improve overall network performance. One of the key challenges in D2D communication for SIoT applications is efficient resource allocation.
In D2D communication, perturbation refers to the introduction of disturbances or variations in the communication system that can affect its performance and characteristics. Perturbations can arise from various sources and can impact D2D communication in several ways. Perturbations during resource allocation in D2D communication can affect several parameters crucial for maximizing throughput, including signal strength, link stability, latency, and Quality of Service (QoS), respectively[8]. To mitigate the effects of perturbations in D2D communication, various techniques such as resource management, channel equalization, power control, interference management, and link adaptation algorithms can be employed [9]–[13], These techniques aim to enhance the robustness, reliability, and performance of D2D communication in the presence of perturbations.
Resource allocation plays a critical role in optimizing the use of network resources, such as bandwidth, power, and spectrum, to meet the diverse and dynamic communication demands of IoT devices[14]. The tripartite graph is a powerful mathematical framework that represents complex relationships between three distinct sets of entities. In the context of D2D communication for SIoT applications, the tripartite graph can capture the intricate interactions between IoT devices, social relationships, and available resources. By integrating social context into resource allocation decisions, this approach enables more context-aware and personalized communication, contributing to the efficient deployment of D2D links. In this paper, we delve into the implementation of our proposed resource allocation strategy. We present a detailed exploration of the tripartite graph's theoretical foundation and its practical applicability in SIoT networks. Additionally, we outline the timescale D2D association and resource management mechanism[15], providing insights into how it enhances the adaptability and responsiveness of the networks. To evaluate the performance and effectiveness of our strategy, we conduct extensive simulations and performance analyses. The results demonstrate significant improvements in communication efficiency, resource utilization, and overall network performance compared to conventional resource allocation schemes. The main aim is to optimize the allocation of spectrum resources while considering social relationships among IoT devices. By leveraging this approach, we intend to improve communication performance in terms of throughput, enhance user experience, and alleviate network congestion.
In summary, this paper introduces a novel resource allocation strategy based on the tripartite graph and timescale D2D association and resource management for D2D communication in SIoT networks. By combining the tripartite graph for resource allocation with adaptive time scaling for power management with minimum delay. The proposed strategy contributes to enhancing communication throughput, optimizing resource utilization, and enabling context-aware interactions in SIoT networks by minimizing the impact of perturbation. Paving the way towards a more connected D2D-enabled SIoT devices and intelligent IoT ecosystem. Abbreviations and symbols used in this article are given in Table 1.
Related Work and Motivation
2.1 Related Work
A resource distribution scheme can be used for resource allocation and Particle Swarm Optimization (PSO)-based power allocation method for D2D-supporting cellular networks with insufficient Channel State Information (CSI). Authors of Ref. [16] presented an innovative solution to address spatial and social mismatch issues. They utilized a 3-D-Social Identifier Structure (3-D-SIS) model to analyze the link between the various sensors and devices connected to the SIoT ecosystem. In Ref. [17], utilized a matching-method approach to analyze the users' attributes and determine the factors that affected their satisfaction. They then utilized the same approach to improve the efficiency of their platform. The algorithm makes an educated determination of the capabilities of the Cellular User Devices (CUD) and D2D pair sharing the same channel. They used the maximum weight matching algorithm, which was based on the results of the particle swarm optimization (PSO)-based power allocation strategy, to solve the channel assignment problem[18], [19]. Through the use of the Non-Orthogonal Multiple Access (NOMA) protocol, two D2D receivers can connect with a D2D transmitter. However, in cellular networks based on NOMA, the power distribution employed for D2D communication is not optimal. In Ref. [20], the authors introduced a solution that supports D2D communication that provide high-quality service to time-critical applications by integrating social ties into the communication process. They used heuristic algorithm to analyze the tasks and improve their efficiency. The authors of Ref. [21] focused on the issue of establishing an effective and stable connection between various social users based on their mobility across different networks. They developed an adaptive framework for D2D communication that can handle the complexity of this issue. The authors of Ref. [22] proposed an algorithm that can help identify and recommend users who can interact with smart objects on the IoT. In Ref. [23], a Lagrange pairwise method is used to solve the transformed problem after it is divided into two subproblems using an alternating optimization strategy. Successive Interference Cancellation (SIC) is suggested for real-world scenarios when the SIC decoding process may be inaccurate, taking into account both user equity and energy efficiency in great detail. The authors of Ref. [24] used a Partly Observable Markov Decision Process (POMDP) to concentrate largely on the battery life of cellular users, in addition to the deployment of transmitters and the mode selection[13]. There are many ways to approach it. To be more specific, creating sophisticated optimization issues can be difficult to achieve in a decentralized setting, entail a significant amount of overhead, and/or demand a significant amount of processing and resources. In particular, the work presented here focuses on different ways to use a power-efficient method adaptation to improve the standard of resource allocation for D2D networks[16], [25], [26].
Perturbation in the allocation of resources causes inaccuracies. An increase in interference may conflict on assigning resources. Perturbation may cause an imbalance in resource allocation[27]. Perturbation effect may longer the route or cause long delay in device discovery time. These concepts include perturbed and unperturbed D2D user channel links due to multipath propagation. Furthermore, Signal-to-Interference-plus-Noise Ratios (SINRs) also affect due to perturbation for both D2D and cellular users. Therefore, we have two types of SINR in our system model, that is perturbed SINR and unperturbed SINR. Due to perturbation, channel state information of the system also effects. CSI can be Multi-path Channel State Information (MCSI) and Unobstructed Path Channel State Information (UCSI) [28]–[30]. Effect on CSI[12] due to perturbationincludes the impact of resource allocation, signal blockages caused by environmental dynamics, link failures due to instability, and challenges in satisfying QoS constraints. None of these studies consider the perturbation effect on CSI with low-latency devices that can be used to control the interference in the D2D network between the SIoT and the underlay pair. Researchers have been trying to optimize the utilization of the available spectrum to address the increasing interference between SIoT and D2D. Various strategies have been proposed to address this issue, such as resource pooling[31], bargaining games through bipartite graphs[32], cluster partitioning[33], [34], greedy optimization[35], [36], and Hungarian-based methods[5], [37]. These techniques require a high amount of time computation and may lead to an increase in the signal overhead. Some of the major research gaps are identified from the extensive literature works:
Lack of consideration of the effect of perturbation on CSI: The SIoT relies on minimal delay and high throughput to perform at its best. This is due to how time-sensitive the system is. Due to the increasing number of complex SIoT components and the need for faster and more accurate computation, the creation of D2D software for the education sector is being considered.
Analysis and impact of perturbation on resource allocation, signal blockages due to environment dynamics, and latency while deciding on resource allocation: Even if the transmission delay is longer, some devices prefer a higher computation rate in order to cope with the issue. On the other hand, devices with lower capacities may need to implement a resource management strategy to cope with the delays. Even though a device has a lower capacity, it can still cope with the delays provided they implement a resource management strategy.
Lack of analysis of QoS assurance in dynamic environments: Dynamic environments pose a challenge when it comes to analyzing and monitoring the quality of service provided by D2D-enabled IoT networks. These environments are characterized by varying user demands and network conditions, which can make it difficult to maintain consistent service levels. It can be hard to develop effective mechanisms to cope with sudden changes in network traffic without thorough analysis. This can also affect the efficiency of the system. In addition to prioritizing data flows, managing resources properly and responding to network traffic can help guarantee QoS.
To overcome the identified gaps in the existing work, we propose a tripartite graph-based resource allocation algorithm that utilizes time scaling concept to optimize the power consumption and minimize the signaling overhead, thereby maximizing the throughput. Further research on QoS assurance in dynamic environments can improve the efficiency and resilience of IoT networks. The proposed work is utilized by developing a resource allocation model that is comparable to traditional resource allocation procedure, considering the perturbation effects. The proposed work takes into account the three key components of the tripartite matching process: resource sharing, throughput, and low power consumption. There has been a limited number of studies on the D2D-SIoT communication capabilities of various applications in the field of SIoT. These studies have primarily focused on the efficiency of the resource allocation process for the transmission of information between nodes with higher throughput.
2.2 Motivations
Due to the numerous advantages of distributed caching and SIoT, it is important to take advantage of the platform to improve the quality of service and download latency. Various D2D User Equipment's (DUEs) and Cellular User Devices (CUDs) in a distributed fashion can be linked using D2D connections. The spectrum of cellular users can be utilized to match the three graph attributes of the linked DUEs. When a CUD requests to pair with SIoT and D2D, the latter typically delivers the requested information to the nearby base station. However, if the link fails to deliver, the device will be able to access the requested data from the neighboring station, which leads to higher download latency[38], [39]. Since a CUD can provide a service to a single D2D user at the same time, the allocation of resources should be modeled as a tripartite problem. In addition, we consider the sharing of information between DUE and CUD in the context of the SIoT. For instance, if a cellular network has the same spectrum allocation for multiple D2D links, the utilization of that spectrum can be improved. The channel state information is affected by the perturbation[40], which can lead to co-channel interference[11], [12], [41] between D2D users when they reuse the same cellular spectrum. Perturbation effects are considered one of the most challenging issues when it comes to the design and implementation of social connections. The key contributions of this work as follows:
An optimal throughput formulation under the constraints of QoS and transmit power has been derived. This optimization problem is a Mixed Integer Non-Linear Programming (MINLP) problem which makes it hard to solve directly. Hence, it can be handled by decomposes into subproblems and solved in a tractable manner.
A tripartite graph-based resource allocation strategy is proposed in first stage. Then, time scaling optimization strategy is proposed in the next stage.
The subproblems are formulated to achieve the sum throughput maximization by minimizing the impact of perturbation effect on CSI and enhance the allocation of resources, the device re-association, and reduction of power consumption within each time slot.
Latency and power get optimized by using Lagrange dual method in a given period by identifying the power variable that meets the immediate QoS of the users.
The remaining part of this article is organized as follows: Section 3 presents the D2D based SIoT framework and problem formulation to achieve the objective. In Section 4, we detail the mathematical analysis and implementation of the proposed resource allocation algorithm covering the tripartite graph representation and the timescale D2D association and resource management approach. Section 5 presents extensive simulation results and performance evaluations. Finally, Section 6 concludes the paper, highlighting the improvements from the proposed approach and discussing the potential future research directions.
System Model and Problem Formulation
A framework for conceptualizing D2D-SIoT networks is presented in Fig. 1. It comprises the applications under social and physical domains. The physical domain includes various wireless devices and SIoT devices that are involved in establishing direct links and sharing spectrum to communicate with each other. The paper proposes a method for allocating resources through a tripartite graph in interconnected cellular networks. The application domain is composed of the physical domain that's responsible for determining if the requesting devices will allow data transmission using the Resource Block (RB) and caching device. It takes into account various factors such as the relevance of the social relationships of the users and the mobile relevance of the devices.
3.1 Social Network Model
A social network model consists of various users and devices that are connected through a communication network. D2D users can help social users to communicate and monitor objects within the network. Users can easily connect with various smart devices, such as smart cameras, and operate these objects directly from their own devices if a direct link is available. This establishes a social relationship between people and objects. In this section, we will discuss various models of communication and social networks, including interference and communication models. This paper explores the use of D2D technology in an urban environment for the development of SIoT. Most communication within the network is carried out through the use of D2D and cellular connections. Each device autonomously chooses the appropriate link for the communication task at hand. We assume that there are
3.2 Physical Network Model
The communication domain of SIoT networks is responsible for the allocation of spectrum and the establishment of D2D-SIoT and D2D connections. The RB's collection mark is responsible for establishing and maintaining the communication link between the data request and the RB. It also allocates the spectrum resources for the transmissions of both D2D-SIoT and D2Ds within the range of the communication device. On the other hand, as the cacher for establishing and maintaining the link between the RB and the collection number is responsible for the reuse of the resources for both D2D-SIoT and D2Ds.
The physical network model is utilized to model the various elements of a D2D-SIoT network. For example, the channel gain in a social network can be affected by both slow and fast fading. The channel gain between the D2D-SIoT source and destination is determined by the social network's boundary. Calculation of channel gain is expressed as
\begin{equation*}h_{i,j}=vu_{i,j}D_{i,j}d_{i,j}^{-z}\tag{1}\end{equation*}\begin{gather*}\text{SINR}_{i,m}^{C}=\frac{P_{i,m}^{C} h_{i,B}^{C}}{I_{CD_{i}}+ \sigma_{o}^{2}}\tag{2}\\ I_{CD_{i}}= \sum\limits_{i=1}^{M} P_{i,n}^{D} h_{D_{i}}^{C}\tag{3}\end{gather*}
Similarly, the SINR of the D2D user is given as
\begin{equation*}\text{SINR}_{i,j,n}^{D}=\frac{P_{i,n}^{D}h_{i,n}^{D}}{I_{D_{i}B}+I_{CD_{i}}+\sigma_{o}^{2}}\tag{4}\end{equation*}
3.3 Perturbation-Based Interference Model
The allocation of the D2D mode is also important to mitigate the intruder caused by the large number of users connectivity in the network. When a link pair is activated, devices can start distribution of information to the other D2D user pair. The D2D mode is primarily used to reduce the network's interference. Whenever a link pair is activated to transmit information, inference is performed. It is calculated as
\begin{align*}I_{D_{i}B}+ I_{D_{i} S_{j}}+ I_{CD_{i}}= \sum\limits_{i,j=1,i\neq j}^{M,N}A_{i,j} P_{i,n}^{D} h_{D_{i,n}}^{B}+ & \\ \sum\limits_{i,j=1,i\neq j}^{M,N} A_{i,j} P_{i,n}^{D} h_{D_{i,j}}^{S}+ \sum\limits_{i,j=1,i\neq j}^{M} A_{i,j} P_{i,n}^{D} h_{D_{i}}^{C} &\tag{5}\end{align*}\begin{equation*}A_{i,j}=\begin{cases}
1, & \mathrm{D}2\mathrm{D}\ \text{mode};\\ 0, & \text{otherwise}\end{cases}\tag{6}\end{equation*}
In a network that supports D2D, users can select any one of the following:
Reuse mode: Because the communication distance between the kth D2D pair's transmitter and receiver fully satisfies the fundamental requirements, in reuse mode, two DUEs transmitters and the receiver can have direct communication with one another. The
$n-\text{th}$ $m-\text{th}$ $m-\text{th}$ $n-\text{th}$ Dedicated mode: The
$n-\text{th}$ $k-\text{th}$ Cellular mode: Two DUEs that would normally communicate over the Base Station (BS) do so because they are too far apart and do not match the requirements for D2D communication distance. In this scenario, we give the D2D pair two uplink RBs and consider it safe to assume that no additional CUDs or DUEs will be able to use the RBs.
The signal strength for the D2D-SIoT pairs can be expressed as
\begin{equation*}\text{SINR}_{i,j,n,S}^{D}=\frac{P_{i,n}^{D}h_{D_{i,n}}^{S}}{I_{D_{i}B}+I_{D_{i}S_{j}}+I_{CD_{i}}+\sigma_{o}^{2}}\tag{7}\end{equation*}
The achievable throughput gained by the underlay D2D communication in the network is given as
\begin{equation*}T_{i,j}=W\log_{2}\left(1+\text{SINR}_{i,j}^{D}\right)\tag{8}\end{equation*}
We assume that the total bandwidth of a D2D-SIoT network is
3.4 Problem Formulation
This work aims to raise the sum throughput of the D2D system while maintaining the immediate QoS specifications for CUDs and DUEs. A joint D2D association, power control optimization, and spectrum assignment problem have been formulated as
\begin{equation*}\max\limits_{\phi,X,P_{i,n}^{\max},P_{i,m}^{\max}}\sum\limits_{i\in I}\sum\limits_{\substack{n\in N,\\ m\in M}} \sum\limits_{k\in K}\sum\limits_{t\in T}\phi_{i,m}^{t}\cdot X_{i,m}^{t}\cdot W\log_{2}(1+\text{SINR}_{i,m,t,k}^{D})\tag{9}\end{equation*}\begin{align*}& \mathrm{C}1: \log_{2}(1+\text{SINR}_{m,t,k}^{C})\geqslant C_{th,i,k}^{t},\forall i,k,m,t;\\ & \mathrm{C}2: \sum\limits_{k\in K} \sum\limits_{m\in M}\phi_{i,m}^{t} \log_{2}(1+\text{SINR}_{m,t,k}^{D})\geqslant C_{th,i,k}^{t},\forall i,k,m,t;\\ & \mathrm{C}3: \sum\limits_{k\in K} \sum\limits_{m\in M}\phi_{i,k}^{t} X_{i,m}^{t}\in\{0,1\},\forall i,k,m,t;\\ & \mathrm{C}4: \sum\limits_{k\in K} \phi_{i,k}^{t}=1,\forall i,k,t;\\ & \mathrm{C}5: \sum\limits_{m\in M} X_{i,m}^{t}=1,\forall i,m,t;\\ & \mathrm{C}6: \sum\limits_{n\in N,k\in K} X_{i,k}^{t}\leqslant\frac{W}{n\cdot \beta_{o}},\forall i,k,t;\\ & \mathrm{C}7: 0\leqslant P_{i,m}^{t}\leqslant P_{i,m}^{\max},\forall m\in M;\\ & \mathrm{C}8: 0\leqslant P_{i,n}^{t}\leqslant P_{i,n}^{\max},\forall n\in N.\end{align*}
The binary variable
Tripartite Graph-Based Resource Allocation and Time Scaling Power Optimization Algorithm
In this section, we will discuss the solution of the formulated problem in Formula (9). The formulated problem is an MINLP problem, and there is no way to solve directly and it is hard to get the solution. Because D2D networks are often having a large number of connectives, employing an optimization strategy that operates for a short period may lead high amount of signalling overhead. Also, CSI gets affected due to perturbation. To overcome this issue, we propose a method that requires a low amount of signalling overhead, and the precise strategy involved in providing the optimize solution. In order to minimize the perturbation effect caused by D2D spectrum reuse, we achieve the overall throughput optimization problem by dividing the original problem into subproblems. To make this tractable, the problem is categorized into different sub-problems and can be solved in different stages. In the first stage, to increase the system sum throughput and signaling overhead reduction, a combined device association and a resource management plan are developed by using a tripartite matching-based resource allocation method. The second stage involves proposing an effective power control plan for each time slot to meet the users' immediate QoS requirements.
4.1 Tripartite Graph-Based Resource Allocation Strategy for Throughput Maximization
As we have seen in Fig. 2, the concept of the resource allocation model based on a tripartite graph takes into account the social relations between the various users of the IoT ecosystem. For instance, the cellular user provides the cache resources and the spectrum allocation. On the other hand, the D2D user provides the request for the link establishment phase.
In the first stage of the proposed solution, the concept of the tripartite matching theory as shown in Fig. 2 has been used. A direct link has been established between the D2D-SIoT system and the cellular users. We also address the related problems of the three-dimensional graph matching between cellular users and D2D users. As shown in Fig. 3, two algorithms are proposed to solve the problems in the various phases of the link establishment and spectrum allocation process. The first algorithm is a one-to-one stable matching method that utilizes the social D2D connection. The other is a channel-state approach. The channel-state algorithm is mainly used to ensure that the link between the various D2D users is close. The importance of social and mobile similarity is acknowledged to ensure that the information and content delivered to users are reliable and efficient. The channel-state algorithm takes into account the interference and fading issues to improve the transmission rate.
In addition, the results of the tripartite matching algorithm[42] are proposed to improve the D2D throughput of SIoT services. This method can be performed simultaneously with global optimization.
Based on the stability model, a one-to-one framework for connecting social D2D users has been developed. This framework provides a link between the two users that is necessary for their activities. D2D users will benefit from having a shared data kink, as it allows them to successfully download the desired data while maintaining their QoS. Thus, the user reassociation ratio is
\begin{align*}& A_{j,m}^{D}= \frac{\phi_{j,m} \xi_{\text{th}}}{\alpha T_{j,m}^{D}}\tag{10}\\ & \alpha=1-\mathrm{e}^{-\frac{\chi\cdot^{l}{}_{j}}{d_{j,m}}}\tag{11}\end{align*}\begin{equation*}\chi=\begin{cases}
1,\mathrm{D}2\mathrm{D}\ \text{relationship with SIoT};\\ 1/2,\mathrm{D}2\mathrm{D}\ \text{with CUE}.\end{cases}\end{equation*}
Flow chart of the two-stage resource allocation and power optimization for throughput maximization.
The channel state information of the D2D link multiplexing system leads to a one-to-one matching model[17] between the link multiplexing and the allocation of the social IoT link spectrum. This model ensures that the link multiplexes the allocated downlink spectrum for communication. Suppose that a total of
One-to-one matching can be performed in the allocation process by mapping the cellular user, D2D user, and SIoT user. This can be done by satisfying the following cases. Such that,
Case 1. If
Case 2. If
If the D2D-SIoT link in D2D resources does not match any
Case 3. If
The channel must be considered when multiplexing the downlink spectrum. It should be regarded as the interference of the D2D transmitter to the receiver of the D2D device and the SIoT receiver when the link is multiplexed. The link between the D2D devices and the SIoT network should be considered as a means to meet the service requirements of the users. Therefore, the objective function is defined as
\begin{align*}T(\mathrm{D}2\mathrm{D},\mathrm{Q})= & \log_{2}\left(1+ P_{i,n}^{D} h_{i,n}^{D}\left(\sigma_{o}^{2}+ \sum\limits_{i=1}^{N-1} \sum\limits_{j=1}^{M-1} A_{i,j} P_{i,n}^{D} h_{D_{i,n}}^{B}+\right.\right.\\ &\left.\left. \sum\limits_{i=1}^{N-1} \sum\limits_{j=1}^{M-1} A_{i,j} P_{i,j}^{D} h_{D_{i,j}}^{S}+ \sum\limits_{i=1}^{N-1} \sum\limits_{j=1}^{M-1} A_{i,j} P_{i,j}^{D} h_{D_{i}}^{C}\right)^{-1}\right)\tag{12}\\ T (C,Q) = & \log_{2}\left(1+\frac{P_{i,m}^{C} h_{i,B}^{C}}{\sigma_{o}^{2}+ \sum\limits_{i=1}^{N-1} \sum\limits_{j=1}^{M-1} A_{i,j} P_{t}^{C} h_{D_{i}}^{C}}\right)\tag{13}\end{align*}
When the time comes to choosing the optimal solution, make sure that the D2D and SIoT links are allocated to the appropriate resources. This can be done through a tripartite matching model.
4.2 Time Scale Optimization Approach To Minimize Signaling Overhead
The optimization strategy ensures that users' average QoS needs are met. The system sum throughput may, however, be significantly reduced if the instantaneous QoS requirements of delay-sensitive services are not met, leading to additional signaling overhead. This problem has a proposed solution, where a power control technique that among other things, maximizes the sum throughput of DUEs at each time slot. As a consequence of this, the optimal issue for each time slot is formulated as follows:
\begin{gather*}\mathrm{P}1: \max\limits_{P_{m^{\prime}}^{i,t}} f(P_{i,n,t}^{D})\\ \mathrm{s}.\mathrm{t}.\qquad \mathrm{C}1, \mathrm{C}2,\ \text{and}\ \mathrm{C}6\ \text{in Formula} (9).\tag{14}\end{gather*}
Analysis shows that the objective function \begin{equation*}f(P_{i,n,t}^{D})= \frac{1}{\ln 2}\sum\limits_{i\in I}\sum\limits_{n\in N}\sum\limits_{k\in K}(-\ln\delta+P_{i,n}^{D}+\ln(h_{D_{i,n,k}}^{t}))\tag{15}\end{equation*}
Problem P1 will be solved using Lagrange dual decomposition[43], [44]. Here define
Translating \begin{equation*}P_{t}^{D\ast}= \max\left\{\frac{1+\mu_{k}}{\sum\limits_{m\in M}\sum\limits_{k\in K}\sum\limits_{i\in I,j\neq i}y+(\gamma_{k}h_{i,m}^{t}+w_{k})\ln(2)},0\right\}\tag{16}\end{equation*}
Lagrange multipliers in \begin{gather*}
\gamma_{t}^{(1+l)}= \gamma_{t}^{l}-\alpha\left(\frac{P_{t,m}^{C} h_{B,0}^{0}}{C_{k,th}^{i,t}}- \sigma_{o}^{2}- \sum\limits_{m\in M} P_{t,m}^{C} h_{B,i}^{t}\right)\tag{17}\\ \gamma_{t}^{(1+l)}= \gamma_{t}^{l}+\beta(C_{k,th}^{i,t}- \log_{2}(1+\text{SINR}_{i,m,k,t}^{D}))\tag{18}\\ w_{t}^{(1+l)}= W_{t}^{l}+\eta(P_{t,i,m}^{D}- P_{t,i,m}^{\max})\tag{19}
\end{gather*}
The suggested solution can be formulated using a multi-slotted time-scale analysis method if the statistical data on CSI is available. The suggested strategy can also be affected by how fast the channel's behavioral changes. CSI's statistical behavior may change slowly, which can result in a reduction in complexity while increasing it with diminished mobility. Formula (9) can be rewritten as
\begin{equation*}\max\limits_{a,b,c}T(P_{\max}^{D},\tau,\xi,\delta)\tag{20}\end{equation*}
Due to the existence of multiple D2D users and the non-linear nature of objective function, the solution of the formulated problem is complex. The problem mentioned in Formula (20) can be solved by offloads the delay and time scaling concept for the optimization of transmission power level. Device power gets distributed at different time slot. Based on the requirement of the power by the distance dependent users, power will be utilized. With the help of lemma 1, we will study the impact of threshold SINR and maximum transmission power constraints C7 and C8 given in Formula (9).
Lemma 1
Let
Proof
Lemma 1 indicates the log-sum exponential procedure can be utilized to approximate the maximum functions, which are both tractable and varied, where \begin{gather*}f(x)\leqslant f_{m}(x)\tag{21}\\ \lim\limits_{m\rightarrow+\infty} f_{m}(x)=f(x)\tag{22}\end{gather*}
When
Lemma 1 is important for analyzing the complex problems in the network, particularly constraints such as threshold SINR and maximum transmission power, as seen in constraints C7 and C8 of Formula (9). The lemma introduced an approximation of mathematical expression where the max function, difficult to optimize due to its non-differentiable behavior, which is replaced by the log-sum-exponential function. This approximation transforms the original problem into a easier and more tractable form, making it amenable to gradient-based optimization techniques. The log-sum-exponential function is particularly advantageous because it closely approximates the maximum function as the maximum transmission power parameter increases, ensures that the solution maintains reliability while benefiting from enhanced throughput. Lemma 1 allows for a more flexible and reliable approach to handle randomness and variability in channel conditions, enabling more effective analysis and optimization of the system performance under varying channel conditions. This is crucial and important to help in the proof of Theorem 1 to optimize the problem that can robustly meet SINR thresholds and maximum transmission power constraints, ensures reliable and efficient communication in challenging environments.
By resorting to lemma 1 and the fact that \begin{align*}\tau & (P_{\max}^{D},\tau,\xi,\delta) > \bar{T}(P_{\max},\tau,\xi,\delta)\ {\buildrel\triangle\over=}\\ &\quad\ \ \phi\log(1+\text{SINR}_{i,j}^{D}(P_{\max}^{D},\tau,\delta))-\\ &\quad\ \ \frac{1}{P_{m}}\beta\log(1+\text{SINR}_{i,j}^{C}(P_{\max}^{D},\tau,\delta))\tag{23}\end{align*}
The problem in Formula (9) can be transformed into
\begin{equation*}\max\limits_{P_{t}^{D},P_{t}^{C}} T(P_{\max}^{D},\tau,\delta)\tag{24}\end{equation*}
The transmit power and link data issue in Equation (16) and Formula (24) can be considered as an approximation of the problem given in the equation. If the issue is not finite, then the solution becomes comparable. The challenge arises since the short-term and long-term variables,
The channel realization is related to one interval of time and can be solved in different available slotted times. Here,
We observe that \begin{equation*}P_{i,n,t}^{D}=\begin{cases}
P^{n}(i), & 0 < P^{n}(i) < P_{\max};\\ P_{\max}, & P^{n}(i)\geqslant P_{\max}\end{cases}\tag{25}\end{equation*}
The above Eq. (25) is applied to satisfy the constraints of Formula (9), that is, C7 and C8.
4.2.1 Minimal Delay Strategy Based on User Reassociation and Resource Allocation Ratio
The first step is to fix the resource computations and get the optimal amount of offloading traffic in D2D-enabled SIoT network. This will transform the issue into a system delay minimization problem.
Total delay minimization can be expressed as
\begin{gather*}\tau_{k}^{D}=\frac{\xi_{k}^{D}(\delta)}{CT_{k}^{D}}\tag{26}\\ \tau_{k}^{C}=\frac{B \xi_{k}^{C}(\delta)}{\alpha_{m,n} T_{k}^{C}}\tag{27}\end{gather*}
Now, the latency minimization problem P2.1 can be formulated as
\begin{align*}& \mathbf{P}\mathbf{2.1}:\\ & \min\limits_{\text{SINR}_{\text{th}}, C_{\text{th}}}\left\{\max\limits_{P_{\max}^{D},P_{\max}^{D}}\left\{\tau_{k}^{D}, \tau_{k}^{C}\right\}\right\}=\\ & \min\limits_{\text{SINR}_{\text{th}}, C_{\text{th}}}\left\{\max\limits_{P_{\max}^{D},P_{\max}^{D}}\left\{\frac{\xi_{k}^{D}(\delta)}{CT_{k}^{D}}, \frac{B \xi_{k}^{C}(\delta)}{\alpha_{m,k}^{C} T_{k}^{C}}\right\}, \frac{\left(1-\sum \beta\right) \xi_{k}^{T}}{\alpha_{n,k}^{D} T_{k}^{D}}\right\}\tag{28}\end{align*}
The reduction of the overall delay can be achieved through jointly optimizing the reassociation and resource allocation ratios.
\begin{align*}& \min\limits_{\text{SINR}_{\text{th}}, C_{\text{th}}} \{\tau\}=\\ & \min\limits_{\text{SINR}_{\text{th}}, C_{\text{th}}}\left\{\frac{1}{N+2}\left(\sum\limits_{n=0}^{N}\left(\frac{B \xi_{k}^{C}(\delta)}{\alpha_{m,k}^{C} T_{k}^{C}}+\frac{\xi_{k}^{D}(\delta)}{CT_{k}^{D}}\right)\right), \frac{\left(1-\sum \beta\right) \xi_{k}^{T}}{\alpha_{n,k}^{D} T_{k}^{D}}\right\}\tag{29}\end{align*}
From the above Eq. (27), it can be assumed that the total delay
The total delay is inversely proportional to the resource allocation ratio
The reassociation ratio beta's negative correlation with the local processing latency can prevent us from achieving a resource allocation ratio with this method. The optimization of the resource allocation and user reassignment ratios is carried out through the use of the gradient descent method.
Based on the allocation ratio for each resource, when \begin{equation*}\beta_{k}=\frac{1}{\left(\frac{1}{\alpha_{k}T_{k}^{D}}+\frac{k}{T_{k}^{D}}\right)\left(\sum\limits_{k=0}^{K}\left(\frac{1}{\alpha_{k}T_{k}^{C}}+\frac{k}{T_{k}^{C}}\right)+\frac{1}{k/T_{k}}\right)}\tag{30}\end{equation*}
The minimum throughput of a system \begin{align*}L(\alpha,\gamma)= & \frac{1}{K+2}\left(\sum\limits_{k=0}^{K}\frac{\beta_{k} \xi_{k}^{D}}{\alpha_{k} T_{k}^{D}}+\frac{\beta_{k} \xi_{k}^{C}}{T_{k}^{C}}\right)+\\ & \frac{\left(1-\sum \beta_{k} \xi_{k}^{C}\right)}{T_{k}^{C}}+\gamma\left(\sum\limits_{k=0}^{K} \alpha_{k}-1\right)\tag{31}\end{align*}
The KKT provides a relaxation condition that can be used as a factor that influences the allocation of certain resources. It can be expressed as
\begin{equation*}\gamma\left(\sum\limits_{k=0}^{K}\alpha_{k}-1\right)=0\tag{32}\end{equation*}
We are going to discuss these two cases.
Case 1:
When
$\gamma > 0, \sum\limits_{k=0}^{K}\alpha_{k}-1=0$ $\frac{\partial L(\alpha,\gamma)}{\partial\alpha_{k}}=0$ $\alpha_{k}=\sqrt{\frac{\beta_{k}\xi_{k}^{C}}{\gamma T_{k}^{C}}}$ Case 2:
When
$\gamma=0$ $\sum\limits_{k=0}\alpha_{k}-1 < 0$ $\sum\limits_{k=0}^{K}\alpha_{k}-1=0$
When \begin{equation*}\alpha_{k}=\sqrt{\frac{\beta_{k}\xi_{k}^{C}}{\gamma T_{k}^{C}}}\tag{33}\end{equation*}
Equation (33) indicates that the optimal expression can be obtained in a closed-form equation by merging \begin{equation*}\gamma=\xi_{k}\left(\sum\limits_{k=0}^{K}\sqrt{\frac{\beta_{k}}{T_{k}}}\right)^{2}\tag{34}\end{equation*}
Equation (34) refers to the Lagrange multiplier used to minimize or offloads the delay by improving the user re-association and resource allocation ratio.
4.2.2 Power Optimization Strategy To Improve Quality of Service
To optimize the transmission power by satisfying the QoS of the D2D-enabled SIoT devices, throughput maximization of the network can be reformulated as
\begin{align*}& T\left(P_{\max}^{D},\tau,\xi,\delta\right)=\\ & \max\limits_{P_{\max }^{D}, P_{\max}^{C}}\left(\sum\limits_{k=1}^{K} \phi_{k} \log_{2}(1+\text{SINR}_{n}^{D}(P_{\max}^{D},\tau,\delta))\right)\tag{35}\\ &\qquad\qquad \mathbf{P}\mathbf{2.2}: \max\limits_{P_{\max}^{D},\tau, \xi,\delta} T\left(P_{\max}^{D},\tau,\xi,\delta\right)\end{align*}
The optimal solution for addressing the transmission power issue to maximize throughput is not feasible since it is related to the algorithm's objective.
The objective function in Formula (9) can be equivalently written with the help of the Lagrange dual transform is
\begin{equation*}\sum\limits_{k=1}^{K}A_{k}\log_{2}(1+Z_{k})-\sum\limits_{k=1}^{K}A_{k}Z_{k}+\sum\limits_{n=1}^{N}\sum\limits_{k=1}^{K}\frac{(1+Z_{k})A_{k}\text{SINR}_{n}^{D}}{1+\text{SINR}_{n}^{D}}\tag{36}\end{equation*}
The optimal
Then, for the fixed optimal \begin{align*}\mathbf{P}\mathbf{3}: & \\ &\qquad \mathrm{P}3: \max\limits_{P_{t}^{D}}\sum\limits_{k=1}^{K}\frac{(1+ Z_{k})A_{k}\sum\limits_{r=1}^{R} P_{r} G_{r}}{\sum\limits_{l=1}^{L} \sum\limits_{r=1}^{R} P_{r} G_{r}+ N_{o}}\tag{37}\\ \end{align*}
The Quadratic transform can be used to solve the above-formulated problem in Eq. (26) by resorting to the following theorem with the help of Lemma 1, and Formula (23) and (24).
Theorem 1
Let's introduce some auxiliary variables, such as
Then the following problem:
\begin{equation*}\min\limits_{w,x,y,z,P_{t}}\left(ze(w,x,P)-\log(z)+\frac{1}{\alpha}xe\left(w,P_{t}^{D}\right)-\frac{1}{\alpha}\log(x)\right)\tag{38}\end{equation*}
Proof
According to Lemma 1 and the statement of Theorem 1, optimizing
To proceed further, we introduce a set of auxiliary variables the problem in Eq. (13) can be equivalently transformed into the following problem:
\begin{align*}& \min\limits_{w,x,y,z, P_{t}}\left(ze(w,x,P)-\log(z)+\right.\\ &\qquad\left. \frac{1}{\alpha}x\left(\sum 1+\text{SINR}_{\text{th}}\right)-\frac{1}{\alpha}\log(x)\right),\\ & \mathrm{s}.\mathrm{t}.\ \text{SINR}_{n}^{D}(w,x,P)\leqslant \text{SINR}_{\text{th}}\tag{39}\end{align*}
The equivalence between Formula (37) and (38) can be easily verified as the optimal SINR* of Formula (41) must be satisfied.
\begin{equation*}\text{SINR}_{n}^{\ast}=\zeta_{n}^{\ast}=\text{SINR}_{n}^{D}(w,x,P)\tag{40}\end{equation*}
If the problem defined in Formulas (39) does not satisfy the SINR, then it will automatically reduce the objective value by minimizing it without affecting the constraints. This method can lead to the optimal solution of Formula (38). We present a method that can solve the problem defined in Formula (39) by considering the auxiliary variables in the gradient descent procedure. We must first recognize that the constraints related to power consumption and the SINR threshold are difficult to handle. To solve these problems, we have introduced the upper bounds for Maximum Transmission power and SINR.
\begin{equation*}\text{SINR}_{n,ij}^{D}\leqslant\frac{P_{n,t}^{D}h_{ij}^{D}}{P_{m,t}^{C}h_{ij}^{D}+2R\sum\limits_{n=m=1}^{N,M}P_{m,t}^{C}h_{B,0}^{0}+\sigma_{o}^{2}}\tag{41}\end{equation*}
The problem in Formula (41) can be rewritten as
\begin{align*}& \min\limits_{w,x,y,z, P_{t}}\left(ze(w,x,P)-\log(z)+\right.\\ &\qquad\left. \frac{1}{\alpha}x\left(\sum 1+\text{SINR}_{\text{th}}\right)-\frac{1}{\alpha}\log(x)\right)\tag{42}\end{align*}\begin{align*}& \mathrm{C}1: \frac{P_{n,t}^{D} h_{ij}^{D}}{P_{m,t}^{C} h_{ij}^{D}+2R \sum\limits_{m=1}^{C} P_{m,t}^{C} h_{B,0}^{0}+ \sigma_{o}^{2}}\leqslant \text{SINR}_{\text{th}},\\ & \mathrm{C}2: -P \cdot h-P\cdot w+2R\left\{\sum\limits_{m=1}^{M} P_{t,m}^{C} h_{B,0}^{0}+ \sigma_{o}^{2}\right\}\geqslant y_{m},\end{align*}
With fixed one variable (auxiliary)
With fixed variable { \begin{equation*}x= \frac{P_{t}^{D}h_{t}^{D}}{P_{t}^{C}h_{io}^{C}+\sum P_{t}^{D}h_{ij}^{D}+\sigma_{o}^{2}}\tag{43}\end{equation*}
By solving the problem formulated in Formula (42) with the help of Eq. (43), we have calculated the optimal SINR* of Eq. (40). Then, sum throughput gets calculated and maximized through efficient resource allocation and achieved low latency with low power consumption in D2D based Social IoT Networks from Eq. (35). Impact of perturbation in CSI gets minimized with the help of proposed approach for Social IoT Applications. Pseudo code of the proposed method is given in Algorithm 1.
Numerical Result and Discussion
In this section, numerical results are provided to evaluate the performance of the proposed tripartite graph-based resource allocation and time scale optimization algorithm. Figure 4 illustrates the deployment of users in a cellular cell. The coordinates of D2D users, cellular users and base station have been observed to reflect the real ground truth of the users in the network. All users are distributed in a cellular cell within a radius of 500 m. The simulation parameters are set with a BS at the centre of the area under consideration and the number of RSUs spaced apart by 150 m. The typical distance between devices is 50 m, while the distance from a cellular user to the base station is 150 m. We also set the following values: maximum D2D power set as
Tripartite graph-based resource allocation and time scaling power optimization algorithm
Initialization: Set the initial value of the system parameters and then create directed edges for each D2D node. Then, label the edges to indicate the current state of the system. Initialize variables such as transmission power, the distance between users, resource block, path loss exponent, etc. to a feasible value and set the iteration index
Stage 1: Initialize and establish a connected tripartite graph for the allocation of resources.
Arbitrarily assign a sub-carrier to the node's location of the DUE and CUD.
Link establishment phase.
From Eq. (18), to establish the initial stable link, obtain the resource matching, update the edges, and call Theorem 1.
Spectrum sharing edges.
From Theorem 1, to allocate the spectrum, repeat line 5.
Stage 2a: A time-scale optimization algorithm based on Stochastic and maximum-spanning tree
for
for
Select the edges in the D2D users from
if there is a node
Change the location of the edges of the D2D users into set L
else
Repeat lines 2 and 3 until there is a node
end if
end for
end for
Repeat lines 2-4 until there is no blockage in the resource allocation and low latency in the network.
Stage 2b: Evaluation of throughput
for
do device re-association, power control, and spectrum assignment
for
Determine the throughput
end for
end for
Output: Obtain the enhanced throughput and optimal power consumption with low latency.
Results from simulations demonstrate that how the system's performance in terms of sum-rate is influenced by the quantity of DUE and the length of the time slot, probability of satisfying the QoS requirements will meet across all users and signaling overhead. We determine the signaling overhead of the system by the calculation of the ratio of D2D user reassociation and reassignment of resources, which is denoted by the notation
Figures 5 and 6 demonstrate the impact of varying the number of D2D pairs and the variation in the length of the time slot affect the performance of the sum throughput. In Fig. 5, as we increase the number of D2D users, sum throughput also increases. Performance gain of the proposed approach compared to other standard approaches ranges anywhere from 17% to 66.67%. The sum throughput is affected by the number of pairs of D2D. This is due to the interference between cellular and D2D users. The proposed method performed better than the baselines in the sum throughput category. In Fig. 6, as the duration of the time increases, the D2D user's sum rate decreases. The proposed algorithm's performance is better compared to other standard methods would range from a low of 21% to a high of 93%. In general, it performs better when compared to the other benchmark algorithms.
Figures 7 and 8 illustrates the instant requirement of QoS may be satisfied based on the provided strategy; nevertheless, the baselines cannot guarantee that the users will not exceed their instantaneous QoS constraints. According to Fig. 7, when the recommended proposed approach is compared to other algorithms, it has the lowest signaling overhead across all of the simulated schemes. On the other hand, the random algorithm has the highest signaling overhead of all of the methods. This is a result of the fact that random guarantees quality of service criteria and improves the performance of the network by increasing the sum throughput, both of which lead to a considerable increase in signaling overhead. In Fig. 8, as the value of the time slot is increased using various techniques, the probability of satisfying the requirement of QoS decreases.
D2D user reassociation and reallocation with respect to variation in number of D2D pairs.
Figures 9 and 10 illustrates the graph plotted for user re-association and resource re-allocation ratio versus variation in D2D connected pairs and time slot length. As D2D pairs increase, it becomes hard to satisfy the instant QoS needs with an increasing number of D2D pairs. In Fig. 9, resource re-allocation and user re-allocation has been performed, which significantly raises the signaling overhead. The simulation results validate the impact of the time slot duration and variant number of D2D users on user re-allocation and resource re-allocation ratio as shown in Fig. 10. Also, the ratio of D2D users re association and reassignment of resources increases. As we know the fact that, extending a time slot makes it challenging to meet immediate QoS requirements, which declines the D2D network's sum-rate performance and forces resource reallocation. Finally, there will be an increase in signal overhead as a result of this.
D2D user reassociation and reallocation with respect to variation in the length of the time slot.
Figure 11 shows the graph of time computation vs. different numbers of DUEs. The Hungarian algorithm shows a linear increase in computing time, while the other methods maintained little change in their initial performance even as the data increased. The proposed method maintains the same amount of computing time for each data type. The graph shows the trend in the time spent performing computation since various benchmark algorithms use a combination of factors and direct proportion increases in DUEs.
The power consumption of various subchannels is shown in Fig. 12. This is to show the efficiency of optimizing the number of channels. Up to 8% of the total power consumptions have been saved by minimizing the interference due to reuse the allocated resources. These results indicate that the power requirements for downlink transmission increase with number of users. This is due to the rise in delay requirements.
D2D user reassociation and reallocation with respect to different power levels vs. length of the time slot.
In Fig. 13, the impact of variation of maximum transmission power
Figure 14 depicts the impact of variations in the SINR threshold on throughput and the compared with the benchmark algorithms. The proposed algorithm enhancement is visible once the SINR value surpasses the threshold. The increase in throughput becomes apparent as D2D users get access to higher numbers. The impact of SINR on throughput is evaluated by varying the threshold value of SINR. Higher the value of SINR, throughput gets better because we are increasing the signal strength. For instance, the sum throughput of the proposed scheme improved by 10.57%,17.12%,20.12%, and 27.29% than that of the benchmark schemes.
Conclusion
This paper investigates the challenges in D2D-based Social IoT Networks. One of the most significant challenges is the dynamic behavior of channel state conditions, which leads to substantial perturbation. A perturbation-based interference model is considered within the Social IoT framework. The problem is formulated with a focus on minimizing signaling overhead and maximizing sum-throughput for reliable D2D communication. The objective is to maximize sum throughput while mitigating the effects of perturbation in channel conditions. The perturbation impacts various parameters that are analyzed in this work. The formulated problem is an MINLP problem, which is non-convex in nature, making it challenging to solve directly. Therefore, the problem is addressed in two stages by decomposing it into subproblems: a tripartite graph-based resource allocation strategy is proposed in the first stage, followed by a time scaling-based power optimization approach in the next stage to maximize the network's sum throughput. The Lagrangian dual method is employed for optimal power consumption with minimal delay. Simulation results demonstrate that the proposed method effectively enhances the system's sum throughput while minimizing signaling overhead. A comprehensive theoretical analysis of various aspects of our proposed algorithms is conducted, thoroughly evaluating their advantages against state-of-the-art schemes. For algorithm validation, sum throughput is measured and found to improve by 21% to 93%, depending on variations in the length of the time slot, and by 17% to 66.67% with varying numbers of D2D users, compared to state-of-the-art schemes. The proposed approach may have applications in SIoT contexts such as home automation, smart classrooms, smart city, and intelligent transportation systems. Future work may involve developing models for social relationships with automated Internet of Vehicular Things (IoVT), aiming to minimize the Age of Information (AoI) to timely updates on the freshness of information of devices.