Game-Theoretical Data Offloading for NOMA-Enabled Urban Internet of Things

Urban Internet of Things (IoT) plays an extremely important role in our daily life by deploying smart cities and urban brains. Orthogonal multiple access (OMA) technology has been a commonly used communication method in recent years, but nonorthogonal multiple access (NOMA) attracts the attention of many researchers due to its superiority of successive interference cancellation (SIC) technology. We consider adding the base station (BS) and unmanned aerial vehicle (UAV) to perform collaborative data o ﬄ oading services with urban IoT devices and introduce the NOMA technology to improve o ﬄ oading e ﬃ ciency. In order to solve the data unloading problem in this model cost-e ﬀ ectively, we formulate the model as a game model based on noncooperative competition and propose the iterative game-based data o ﬄ oading algorithm (GDOA) to obtain the Nash equilibrium (NE) solution. Finally, we use the simulation data to conduct parametric analysis experiments and comparison experiments on GDOA to evaluate its real performance.


Introduction
With the advancement of mobile communication technology, the urban IoT will play an increasingly important role in our daily life [1]. Different from ordinary IoT, urban IoT focuses on intelligent communication and smart city [2][3][4]. At the same time, the massive data generated by various sensors in the urban IoT puts enormous pressure to the IoT services, mainly including high communication delay, nonnegligible energy consumption, and quality of experience for urban IoT devices [5,6]. In order to improve the quality of urban IoT communication services, it is essential to establish a reasonable framework, such as an efficient data offloading model [7][8][9]. Among them, the devices in the urban IoT can request services with the neighboring BS through wireless transmission, so as to determine the way of data offloading, i.e., the devices upload its data to be calculated in the server through the wireless link [10,11]. However, since the data transmission in most urban IoT systems adopts the OMA technology, each device will be subject to a lot of intracell interference, which causes the delay and energy consumption of the device to become extremely high [12,13]. In addition, the UAV is often used to assist the BS to perform data offloading services with devices, which reduces the computational pressure of the BS to a certain extent [14].
Nevertheless, due to the increasing data transmission and service requests in the urban IoT, the OMA technology is gradually unable to meet the services with a very large number of devices [15,16]. Therefore, the NOMA technology that effectively reduces the intracell interference in the multirequest low-latency problem has been widely used [17,18]. The main idea of NOMA is to send the nonorthogonal data from the transmitter and eliminate the interference at the receiver, and then, the realization of the whole process depends on the SIC technology [19][20][21]. The process of SIC can be expressed as follows: the receiving end judges the signals of the device one by one according to the descending order of channel gain, subtracts the signals of other devices whose channel gain is higher than that of the device from the interference, and finally loops the above operation until the successive interference of all devices is eliminated [22][23][24]. Because most of the interference is eliminated, NOMA greatly improves the efficiency of data offloading from devices in the urban IoT system.
In this paper, the scenario we consider is an urban IoT data offloading system that supports NOMA, the data offloading problem in this system is solved by the potential game method in game theory [25], and we add UAVs to assist the BS with the devices to communicate. Our optimization goal is to minimize the energy consumption cost of all urban IoT devices. According to the limited resource competition between devices, we formulate this model into a noncooperative competitive game model and propose a game-based data offloading algorithm (GDOA) based on the iterative update process, which can obtain the device strategy profile in NE state after a finite number of iterations [26]. Finally, a series of simulation performance evaluations are carried out for our proposed GDOA, including parameter analysis experiments and comparison experiments. The main contributions in our study include the following: (i) We study a NOMA-enabled urban IoT data offloading model, while incorporating server-loaded UAVs to assist the BS in wireless communication with devices. There are three ways to offload data from devices: local computing, data offloading by the BS, or data offloading by the UAVs. Our overall optimization goal is to minimize the sum of the energy consumption costs of all urban IoT devices (ii) We formulate this urban IoT data offloading model as a game model based on noncooperative competi-tion between devices. The potential function in game theory is proposed, and it is proved that our game model is a generalized ordinal potential game. And we propose a game-based iterative algorithm GDOA, which can obtain the NE strategy profile after a finite number of iterations (iii) We evaluate the simulation performance of this model, including many parameter analysis experiments of GDOA and several comparison experiments between GDOA and other excellent algorithms The rest of this paper is organized as follows. The system model and problem formulation are introduced in Section 2. We describe the game-based data offloading for urban IoT in Section 3, including game-based offloading model and offloading algorithm design. And several parametric analysis experiments and comparison experiments are conducted in Section 4 to evaluate the performance of this model. Section 5 describes the related work. Finally, we summarize this study in Section 6.

System Model and Problem Formulation
2.1. System Model for Urban Internet of Things. As shown in Figure 1, we study a NOMA-based data offloading system for urban IoT, which consists of a single base station (BS), multiple UAVs, and multiple urban mobile devices. In this system, we consider n densely distributed urban mobile devices, and the set of all devices is U = fu 1 , u 2 , ⋯, u n g.   Wireless Communications and Mobile Computing There are x clusters covering y devices; the set of these clusters is expressed as W = fw 1 , w 2 , ⋯, w x g. And we represent each cluster as w j = fu 1 , u 2 , ⋯, u y g; thus, the set of all n devices can also be denoted by U = w 1 ∪ w 2 ⋯ ∪w x . There is a single base station S in our system; the devices of any cluster are within the coverage of this base station. The set of all UAVs is denoted as V = fv 1 , v 2 , ⋯, v x g, and one UAV v j is arranged in each cluster w j . The main notations and their definitions of this paper are given in Table 1.
The computing power of each device u i when computing locally is f i , which is related to device u i 's chip architecture. In addition, the transmit power of each device u i is p i , the bandwidth of the BS's channel and the UAV's channel is B, and the channel gain in data transmission for device u i is g i . We assume that device u i will choose a data offloading approach (local computing, BS or UAV) based on its own resource requirements and possible cost.
To simplify the data transmission and computation of the device, each device u i has a computation task K i ≜ ðD i , X i Þ, where D i represents the amount of intensive data when transmitting the task and X i represents the number of CPU cycles required to compute the task [27].
Definition 1 (data offloading strategy). Each device u i in this system needs to make a data offloading strategy a i = f0, 1, 2g, a i = 0 means that u i chooses completing its computation task locally, a i = 1 denotes that u i chooses offloading the data of its computation task by BS, and a i = 2 represents that u i chooses offloading the data of its computation task by UAV.  Each cluster w j shares one channel of the BS, and the set of devices sharing the same channel of the BS is denoted by And each cluster w j shares one channel of the UAV; the set of devices sharing the same channel of the UAV is expressed as The strategy profile of all the devices is a = fa 1 , a 2 , ⋯, a n g, and a −i = fa 1 , ⋯, a i−1 , a i+1 , ⋯, a n g represents the strategy profile of all devices except device u i .

NOMA-Enabled Transmission
Model. In our system, the geographic positions of devices, BS, and UAVs are represented by three-dimensional coordinates, the position of device u i is denoted by L i = ðx i , y i , 0Þ, the position of BS's server is represented by H m = ðx m , y m , z m Þ, and UAV v j server's position is expressed as Q j = ðx j , y j , z j Þ. The distance between the device and the server can be calculated through their coordinates, and we can get the channel gain when device u i chooses UAV v j to offload its data, which is expressed as where We represent θ as the channel fading factor obeying the Rayleigh distribution, similar to the channel gain g i,j ; the channel gain when device u i chooses BS S to offload its data is denoted by Therefore, we can get the channel gain of device u i in two cases, which can be expressed as Taking the BS server as an example, on the basis of the definition for NOMA at the transmitter, NOMA can broadcast the signal q i of each device u i ∈ S j on the same channel, and the server of the BS receives a superposition-coded signal q bs j mixed with these signals, which can be expressed as Similarly, the superposition-coded signal q uav j received by the UAV server can be denoted by Then, we will introduce successive interference cancellation (SIC) technology in this NOMA-enabled data offloading system. SIC is a signal decoding method; its basic principle is to gradually subtract the interference of the device who possesses the maximum signal power. During this process, the SIC detector makes data judgments for multiple devices one by one in the received signal, and when a device is judged, the multiple access interference caused by the device's signal is subtracted at the same time, and the operation is performed in the order of signal power, and the signal with higher power is operated first. The operation is repeated until all the multiple access interference are eliminated [28]. In this order, any device u i can correctly decode the superimposed signals of other devices whose channel gain is greater than g i in the same channel, so as to eliminate successive interference in u i 's received signal.
Given the BS selection set S j and UAV selection set V j , all devices on the same channel are sorted based on their channel gains, and the devices with higher channel gains are ranked ahead of the devices with lower channel gains. Thus, we can get the sorted sequence of all devices on the same channel of BS S: u 1 , u 2 , ⋯, u jS j j , where jS j j is the number of devices in S j , device u 1 and, the channel gain g 1 of device u 1 is the maximum value, the channel gain g jS j j of device u jS j j is the minimum value. And we can also obtain the sorted sequence of all devices on the same channel of UAV v j : u 1 , u 2 , ⋯, u jV j j , where jV j j is the number of devices in V j , device u 1 and, the channel gain g 1 of device u 1 is the maximum value, the channel gain g jV j j of device u jV j j is the minimum value [29,30].
We next investigate the SIC process between the device and the UAV server when the device selects the UAV to offload data. For two devices u i , u b ∈ V j , suppose u b 's channel condition is better than u i , i.e., g b < g i . In order to use SIC reasonably, the data rate of device u b for decoding device u i 's received signal cannot be lower than device u i 's data rate for decoding device u i 's received signal, and r uav bji ≥ r uav iji . If the above condition cannot be satisfied, device u i 's data rate will reduce because its received inside interference is not eliminated. On the contrary, device u i 's data rate can be denoted by where r uav b|i denotes device u b 's data rate for decoding device u i 's signal, which can be expressed as

Wireless Communications and Mobile Computing
In other words, we can deduce that the data rate of device u i is lower than the devices ranked after device u i .
Through the above description, the decoding order of these devices derived from the channel gain is very important and directly affects the data rate of each device [31]. Therefore, how to get a reasonable order is essential when optimizing the data rate of all devices in this model. According to (8) and (9), we can obtain the available data rate r uav i of device u i : where M i is denoted by In order to ensure that all devices can accept the data rate under the same transmit power, we should determine the decoding order according to the channel gain and the received intracell interference of the device which can be expressed as If all devices assigned to the UAV server follow the order in (12), the SIC process is successfully completed. When the order of these devices follows this decoding order, the data rate r uav i of device u i can be denoted by In the same way, we represent r bs i as the data rate of device u i when u i chooses to offload data by the BS, and r bs i is also denoted by Combining SIC technology and the data rate of device, the upper bound Q i of intracell interference received by device u i can be represented by where z represents the total number of devices on the channel selected by device u i .

Data Offloading
We denote ε as the energy consumption factor when computing locally; the size of which is determined by the device's own chip architecture. The energy consumption generated by the computing task K i is expressed as 2.3.2. Offloading Data by BS. When u i chooses offloading its data by BS, the delay generated by the task transmission can be expressed as and the energy consumption of the task transmission is represented by 2.3.3. Offloading Data by UAV. When u i chooses offloading its data by UAV, the delay generated by the task transmission can be expressed as and the energy consumption of the task transmission is represented by 2.4. Problem Formulation. Through the above description, we take the energy consumption of the device as the main influence part of its cost function. Assuming that the strategies a −i of other devices remain unchanged, the cost generated by strategy a i of device u i can be expressed as where λ is the varying parameter of device's cost function.
When the intracell interference of device u i reaches the upper bound Q i , the energy consumption of the device will reach the maximum value E max i . Due to the instability and weak computing power of the device, we believe that the local computing energy consumption should meet

Wireless Communications and Mobile Computing
In this data offloading system for NOMA-enabled urban IoT, in order to reduce costs and improve efficiency, we aim to minimize the overall cost, namely, where (8) is the NOMA-enabled data rate constraint of device u i , (15) is u i 's received intracell interference constraint, and (23) denotes u i 's energy consumption constraint.
3. Game-Based Data Offloading for Urban Internet of Things 3.1. Game Model for Data Offloading. In our system, each device wants to minimize its own cost, which is not only determined by the decisions it makes but also affected by the decisions of other devices. Based on the competition (each device is aimed at minimizing its own cost) among the devices in our system and the resource constraints of the whole system, this problem cannot be solved with the common methods in reality [2,32]. Potential game, a game-theoretical tool to solve the competition between devices when there are multiple constraints, is suitable for solving competition problems and minimizing the overall cost for this system. We can formulate this model as a game model of noncooperative competition among devices, defined as where n represents the number of all devices in this system, a i is the data offloading strategy of device u i , and C a −i ða i Þ denotes the cost resulted by strategy a i when other devices' strategies are given. In model G, due to the principle of individual rationality of devices, each device tends to reduce its own cost when the system resources are limited, and our system will reach the NE state after multiple iterations. In this state, any device unilaterally changing its own strategy (the strategies of other devices remain unchanged) will not reduce its own cost.
Definition 2 (Nash equilibrium). In this noncooperative competition game model G, in case there is a strategy profile a * = fa * 1 , a * 2 , ⋯, a * n g for all devices, each device does not want to change its strategy to reduce the cost; it can also be expressed as The Nash equilibrium (NE) solution is the combination of all strategies, i.e., the stable strategies of all game players (devices) [33]. At this point, any device will not reduce its cost by changing strategy, but the existence of NE needs to be proven. There must be the NE in potential game due to potential game's Finite Improvement Property (FIP), so we need to prove that G is a potential game to ensure the existence of NE in our model. Definition 3 (potential game). ∀a i , a i ′ ∈ a, given the other devices' strategies a −i except u i 's strategy a i , a game G is an generalized ordinal potential game if there is a function Following the above, we need to testify that our game model G is a potential game through the potential game theorem, i.e., satisfying Definition 2. Before introducing this theorem, we need to define a conditional judgment variable I f⋯g = f0, 1g. Taking I fa t =a i g as an example, I fa t =a i g = 1 when device u t 's strategy a t and device u i 's strategy a i are the same, and I fa t =a i g = 0 when a t is different from a i [23].

Theorem 4. G is a generalized ordinal potential game; its potential function
Proof. If we assume C a −i ða i Þ > C a −i ða i ′ Þ, the possible strategies of device u i are divided into four cases: Case 1: a i = 0, a i ′ = 1; Case 2: a i = 0, a i ′ = 2; Case 3: a i = 1, a i ′ = 2; Case 4: a i = 2, a i ′ = 1.
According to equation (23), we can get Wireless Communications and Mobile Computing The potential function's difference between a i and a i ′ is Case 2.
Similar to Case 1, it is easy to know The potential function's difference between a i and a i ′ is Case 3.
The potential function's difference between a i and a i ′ is Case 4.
The potential function's difference between a i and a i ′ is According to the above description, Theorem 4 is proved.

Game-Based Offloading Algorithm Design.
To solve the problem of device data offloading (which offloading method to choose), we propose a game-based data offloading algorithm (GDOA) to minimize the total cost of this system [34,35]. In our algorithm, the necessary experimental parameters are first given, and all devices undergo a limited number of iterations, in which each device updates its strategy based on its own minimum cost, until no device is willing to update its own strategy to change the cost, i.e., the NE state is reached [36]. Our proposed algorithm is shown in Algorithm 1, and the main steps are as follows: (1) Environment initialization: given the required experimental parameters, we initialize the strategy a i of each device u i to a i = −1 (2) Iterative process: as shown on lines 3-14, in each iteration, we first need to calculate the cost of the system in the current state and then formulate the strategy for each device u i ∈ U. Given three data offloading approaches: local computing, base station data offloading, and UAV data offloading, before updating each device's strategy, we need to calculate the total system cost caused by these possible cases (assuming this device's strategy is one of them) and find the lowest total cost for device u i . Then, we find the lowest cost device among all devices and update the corresponding strategy for that device (3) End of iteration: no device is willing to update its own strategy and finally returns the strategy profile of all devices

Experimental Settings.
In order to correctly evaluate the simulation performance of the model, we need to give the important parameters involved in the experiment, as shown in Table 2. Besides, the coordinates of all devices need to be given, and the channel gain between the device and the BS or UAV can be calculated [37].

Parameter Analysis.
In this section, we will carry out a series of parameter analysis experiments to evaluate the performance of our model, i.e., setting different parameters to obtain the experimental results. As shown in Figure 2, it describes the effect of different values of channel fading factor on the system cost, and the independent variable is the number of devices in each cluster. It is obvious that the system cost (cost of all devices) increases as the number of devices in each cluster increases, regardless of the channel fading factor. The increase of devices in each cluster will lead to greater interference among all devices, and the sum of the costs of all devices will definitely increase when the system resources remain unchanged. When the number of devices in each cluster is determined, the channel fading factor increases from 3 to 5, and the average data rate decreases with it. In other words, as the channel fading factor becomes larger, the interference received by the device during the data transmission process is reduced, and the total system cost is reduced. Figure 3 shows the effect of different channel fading factors on the average data rate of all devices, where the independent variable of the experiment is the number of devices in each cluster. Regardless of the value of the channel fading factor, as the number of devices in each cluster increases, the average data rate of all devices decreases. The increase in the number of devices in each cluster will lead to increased interference, and by Shannon's theorem, the average data rate of all devices will decrease. When the number of devices in each cluster is determined, the channel fading factor increases from 3 to 5, and the average data rate decreases due to the smaller signal-to-noise ratio. Figure 4 denotes the effect of different values of the channel fading factor on the system cost, and the independent variable is the height of the UAV in each cluster. Regardless of the channel fading factor, the system cost increases as the height of the UAV in each cluster increases. The increase in the height of the drone will result in increased interference between all devices and an overall increase in cost. When the UAV height of each cluster is determined, the channel fading factor is increased from 3 to 5, and the system cost is reduced due to the smaller signal-to-noise ratio. Figure 5 represents the relationship between different channel fading factors and the average data rate of all devices, with the independent variable being the height of the UAV in each cluster. Obviously, the average data rate decreases as the UAV's altitude increases, because the increased altitude causes greater interference between all devices, which also affects the average data rate. And when the UAV's height of each cluster is determined, if the channel fading factor increases from 3 to 5, the average data rate decreases due to the increase of the overall interference.
The influence of different values of the channel fading factor on the data offloading ratio of the device can be obtained intuitively from Figure 6. With the increase of the channel fading factor, the proportion of the number of devices offloading locally to the total number of devices gradually decreases to zero, the number of devices offloading by the BS to the total number of devices gradually increases, and the proportion of the number of devices offloading by the UAV to the total number of devices remains unchanged. The reason is that after the channel fading factor is increased to 4, the channel gain of UAV offloading has nothing to do with the channel fading factor, and the cost of selecting BS offloading for any device is significantly lower than selecting local computing.

Comparison Experiments.
In order to demonstrate the superiority of Algorithm 1 in both simulated data and the real world, our algorithm are supposed to be compared with a benchmark algorithm and several advanced algorithms. These algorithms are as follows: (i) Random: in this algorithm, each device randomly selects an offloading way (local computing, by the     The height of UAV in each cluster (m) = 3 = 4 = 5 Figure 5: Effect of channel fading factor on average data rate. 10 Wireless Communications and Mobile Computing BS or by the UAV) as its strategy and then calculates the total cost of all devices. After repeating the above process hundreds of times, the average state is the final state (ii) OMA-DOA: a data offloading algorithm based on OMA, i.e., the calculation of intracell interference is different from NOMA. Similar to Algorithm 1, the idea of OMA-DOA is also an iterative process for each device to select the strategy that leads to the lowest system cost (iii) ICSOC19 [38]: regardless of the minimization of system cost, each device chooses the current offloading strategy that can bring the lowest cost in each iteration As shown in Figure 7, what can be known is the effect of the number of devices in each cluster on the system cost in different algorithms. As the number of devices increases, the system cost in all four algorithms increases. When the number of devices in each cluster increases from 3 to 5, the system cost of Random algorithm is the highest, the system cost of OMA-DOA algorithm is much higher than that of ICSOC19 algorithm, and the system cost of GDOA is the lowest. The reason is that the number of devices is not enough, and the interference in the OMA-DOA algorithm is not large enough, so the unstable Random algorithm has the highest system cost, and the GDOA is better than the local optimum of ICSOC19 algorithm due to its iterative update (reaching the global optimum). When the number of devices in each cluster increases from 6 to 8, the system cost of the OMA-DOA algorithm is the highest, the system cost of Random algorithm is much higher than that of ICSOC19 algorithm, and the system cost of the GDOA is the lowest. Similar to when the number of devices increases from 6 to 8, the gradient remains the same, when the number of devices per cluster increases from 8 to 10, but the cost gap between the algorithms becomes larger. The cause is that the increase in the number of devices leads to more and more interference in OMA-DOA algorithm, and the system cost caused by GDOA that is aimed at the overall optimal is the smallest.
What can be known in Figure 8 is the influence of the channel fading factor on the system cost in different algorithms. As the channel fading factor increases, the system cost in all four algorithms decreases. Among them, the decreasing trend of system cost of OMA-DOA algorithm is not obvious, and the decreasing trend of system cost of GDOA is the fastest. When the value of the channel fading factor is determined, the system cost of OMA-DOA algorithm is the highest, the system cost of Random algorithm is higher than that of ICSOC19 algorithm, and the system cost of GDOA is the lowest. The reason is that the larger channel fading factor will basically not affect the interference received by the equipment in OMA-DOA algorithm, which is of great help to GDOA and ICSOC19 algorithms based on SIC technology. And the iterative update property of GDOA (reaching the global optimum) is better than the local optimum of ICSOC19 algorithm.

Related Work
There is an increasing amount of work on data offloading in Internet of Things systems. The authors of [39] studied the problem of computation offloading based on age of informa-tion, while considering the energy control of its system. But this paper did not consider the complex data access of multiple BSs. In [40], the authors proposed an intelligent video application based on interference-aware data offloading, which can be combined with real-time traffic monitoring