Abstract
This paper addresses the problem of adaptive power control based on outage probability minimization in Vehicular Ad Hoc Networks (VANETs), called a Power Control Algorithm Based on Outage Probability Awareness (PCOPA). Unlike most of the existing works, our power control method aims at minimizing the outage probability and then is subject to the density of nodes in certain area. To fulfill power control, cumulative interference is assumed to be available at the transmitter of each terminal. The transmitters sent data by maximum power and then get the cumulative interferenceaware outage probability. Furthermore, we build the interference model by stochastic geometric theory and then derive the expression between outage probability and cumulative interference. According to the expression, we adjust the transmitter power and optimize the outage probability. Simulation results are provided to demonstrate the effectiveness of the proposed power control strategies. It is shown that the PCOPA can achieve a significant performance gain in terms of the outage probability and throughputs. Comparing MPC (Maximum Power Control algorithm) and WFPC (WaterFilled Power Control algorithm), the proposed PCOPA decreased by 23% in terms of the outage probability and increased by 25% in terms of throughputs.
1. Introduction
Vehicular Ad Hoc Networks (VANETs) are a promising intelligent transportation system technology that offers many applications such as traffic and congestion control, safety assistance, and autodriving, all of which will drastically change and provide tremendous benefits to our lives [1–5]. The key technologies for VANETs, called VehicletoVehicle (V2V) communication, involve the networking of vehicles and other communication devices, e.g., roadside units (RSUs). Power control is the key to maintain the better connectivity of networks among devices, which is used for VANETs. However, unlike the current mobile ad hoc networks, VANETs have a lot of characteristics, such as broadcasting, random node mobility, timespace uncertainty transmission, and interference [6–8]; this makes VANETs more challenging. For example, when the transmitter with the maximum power control sends the data, in certain area big density of nodes brings more interference to the receiver, which results in high outage probability. Addressing this issue, a Power Control Algorithm Based on Outage Probability Awareness, simply named PCOPA, is proposed.
In VANETs, traffic congestion is easy to happen [9–11]. When congestion happens, more density of nodes results in more interference, which leads to high outage probably. Furthermore, the retransmission results in more consumption, which leads to the poor connectivity in VANETs. If the high channel capacity is pursued, the probability of collision is greater. Therefore, compared to traditional power control algorithm, the PCOPA aims at the optimal outage probability regardless of the optimal channel capacity. In [12], Power Control based on Broadcasting Messages (PCBM) algorithm is proposed, in which the transmission power is adjusted according to the distance of the nodes. Further, the broadcasting area of nodes is restricted, which reduces the interference among nodes. However, the constant position in nodes is hard to get due to the random mobility in nodes. Therefore, PCBM algorithm has rarely considered the random mobility in reality environment. In [13], in highway scene, Power Control based on Roadside Unit (PSRSU) algorithm is proposed, in which the aim is to be sure of connectivity in nodes of one side. However, Roadside Unit (RSU) costs more. When the congestion happens, PCRSU algorithm is not good to solve the question of more interference because of the more density. In [14], Power Control based on Beacon (PCB) algorithm is proposed, in which action time of driver and access collision in nodes are considered. In long distance communication, the peak power control algorithm based on L beacon is used to obtain the SINR, whereas in short distance communication the minimum power control algorithm based on S beacon is used to satisfy the SINR. According to the communication distance, in PCB algorithm, difference beacon is selected to be adaptive to VANET. Therefore, PCB algorithm is widely used. However, when the speed of a vehicle is very fast, the power in transmitter is used more, which leads to more communication areas. Further, multiuser interference is serious due to more high density in nodes, which leads to high outage probability. At present for more interference of multiusers few powers control algorithm is considered.
In this paper, the performance of improvement of the proposed power control algorithm is achieved in terms of reducing cumulative interference of multiusers. Based on the stochasticgeometry theory in receiver the spatial user interference model is built. Further, the expression of outage probability is deduced. After the outage probability awareness, the transmitter adjusts the power. At last, PCOPA is subject to obtaining the optimal outage probability and good throughput.
The rest of this paper is organized as follows. Section 2 discussed the related work on the system model, as well as its usage in the analysis of VANETs characteristics. Section 3 describes the mechanism of PCOPA. Simulation results and the validation of the proposed matching mechanism are presented in Section 4. Finally, concluding remarks are given in Section 5.
2. System Model
VANETs have the obvious characteristics such as randomness and dynamics which makes interference of multiuser difficult to find. Therefore, multiuser’s interference in power control of VANETs is rarely considered. Addressing this issue, the expression about interference is needed to describe the relationship between interference and outage probability, which is the theoretical support for power control algorithm. Therefore, according to the randomness, stochasticgeometry theory is applied to build the system model and then deduce the expression [15, 16]. In Figure 1, we present the model of urban road system.
Due to the fact that characteristics of VANETs are randomness and dynamic, multiple user interference model is established that node random arrived at some region, which can be regarded as stochastic point process. Using identical probability , any nodes are joined by edges among nodes. The total of edges is random variable and average value of edges is . When , we consider a set of transmitting nodes with locations specified by a homogeneous Poisson Point Process (PPP) [17], , of transmitting nodes on the infinite twodimensional plane. The nodes of random walk obey independent and uniform distribution and have the mobility and substitutable. Let and denote the random walk between two adjacent vehicles. Let and denote the speed of and . Therefore, the probability density of TX within communication coverage area is
Within communication coverage area of , multiple user interference increased with density and mobility of nodes and then the information may not be decoded properly in target node, while outage probability increased significantly. We assume that network tends to be infinity, of Palm distribution [18] and Slivnyak theorem [19]; according to the requirement, the interference of receiver is analyzed by conditional distribution of TX and follows a homogeneous Poisson Point Process, where Poisson Point Process is moved. The signaltointerferenceandnoise radio seen at the RX_{0} iswhere , denoted by multiple user interference; therefore,where is background noise, is transmission power, is transmission power of other users, is channel gain, and is propagation distance. Therefore, the reference node has effects on background noise and on interference of other users. In Figure 2, we present the relationship between receiver and interference.
According to stochastic geometry, we consider a Vehicular Ad Hoc network that has the following key properties.
Transmitter node locations are modeled by a homogeneous spatial Poisson Point Process. The number of random nodes in twodimensional arbitrary finite area is limited, which is called local finiteness of Poisson Point Process, and then any nodes' locations are nonoverlapping.
Suppose that bounded A and B are disjoint areas, where , and and are independent random variables, where denotes the set of Poisson Point Process in plane.
The density of bounded disjoint area is superposition; in other words, aiming at characteristics of random mobility in VANETs, and random process is assumed to be a homogeneous Poisson Point Process.
According to theorem of Slivnyak, when moving and removing of nodes, the distribution of homogeneous Poisson Point Process will not be affected.
In short, we introduce theories and properties of random geometric, by space accumulated interference model building in VANETs; it is seen that accumulated interference and outage probability increased with density of nodes, which lead to the network throughput decreasing significantly.
3. The Mechanism of Power Control Algorithm Based on Outage Probability Awareness
In this section, we consider a power control algorithm that sends data with a maximum power to make a deduction of the formula of outage probability and then adjusts transmission power on the basis of outage probability information of awareness [21]. Finally, optimal outage probability and network throughput were obtained by PCOPA.
3.1. Sending Data with a Maximum Power
SINR is shown as follows:where , if , the thesis holds that network transmission is interrupted. In accordance with statistical law, stochastic node sets distributed in space are called Poisson Point Processes. Suppose satisfies , and have the same distribution, and then is homogeneous Poisson Point Processes. Therefore, obeys the Poisson distribution in a bounded domain of B, and the bounded function is a measurement.where is Lebesgue measure, namely, area of B. is intensity or average density of unit space. It is based on such an assumption that location of interference sources obeys the Poisson Point distribution and interference power is function of power law decay of transmission distance. The accumulated interference signal in receiver constitutes the shot noise in twodimensional space ; we obtain thatwhere is small scale power fading factor.
According to the above properties, when data is sent with a maximum power, outage probability is as follows:where denotes accumulated interference with area of radius a; from the definition of (7), we obtain
is success probability:and , denote the success probabilities taking into account only noise and interference, respectively. Since , the Laplace transform of the accumulated interference of is
Applying here with , :Outage probability in a closedform expression is as follows:with
We define as outage probability. Now consider network throughput of success delivery with constrained outage probability.
where B is bandwidth.
3.2. Adjusting Transmission Power
Adjust transmission power based on channel state information, where is chosen in . Clearly, if , implies maximum transmission power; whereas , is channel inversion.
From function (10), we have that
Adjusting transmission power, we obtain
Then, the outage probability in a closedform expression is as follows:
From (19), is the accumulated interference of channel fading. It can be verified that outage probability decreased with power control exponent since transmission power is adjusted. In order to improve the network throughput, after derivation calculus to (19), we can get optimal solution of power control exponent .
3.3. Adjusting behind Transmission Power of Outage Probability
Adjust behind transmission power of outage probability to judge whether there is maximum value. If is not maximum value, outage probability information is obtained with feedback CSI in sender. If is maximum value, outage probability minimum is obtained with adjusting behind transmission power. Since , is convex function:
Taking logarithm on (20),
By Holder’s inequality,
Applying here with and , ,
Calculating the derivatives of (22),
Function (20) is lowest when . The results show that transmission power is adjusted at ; the outage probability has minimum value.
4. Simulation and Results
Here, we present some numerical results to evaluate the performance our proposed PCOPA strategies. We compared the outage performance of the proposed strategies with that of WFPC (WaterFilled Power Control Algorithm) and NPC (NonPower Control algorithm). Assume that simulation area is 2000 m2000m; the numbers of nodes vary from 0 to 160. The simulation parameters are shown in Table 1.
In Figure 3 we present relationship between outage probability and power control exponent. Path loss exponents for different environments are shown in Table 2. Figure 3 is for the case of , where four different values of α, i.e., , , , and are assumed. Different parameters represent the different environments for wireless channel. As is shown, the PCOPA is more effective and achieves the minimization of the outage probability. represents maximum transmission power, whereas is channel inversion. Clearly, achieves a significant performance gain in terms of the outage probability regardless of the radio environment, whereas and are seen to be essentially equivalent, which is high cumulative interference and outage probability in receiver. This simulation is provided to demonstrate the effectiveness of the proposed power control strategies.
Figure 4 is for the case of , where three different values of α, i.e., , , and , are assumed. We plot the outage probability as absorption factor for the proposed PCOPA strategy. Clearly, when the absorption factor varies from 5 to 50 dB/km, the outage probabilities reduce. The reason is that the accumulated interference declines as absorption factor grows. Few accumulated interferences make it easy to be adaptive to the SINR of the receiver. Therefore, in different radio environment, the proposed PCOPA is subjected to the minimization of outage probability according to the distribution of absorption factor.
Figure 5 shows that the optimized outage probability is a function of density of nodes for the proposed PCOPA strategy. Clearly, as the density of nodes grows, the outage probability grows. The reason is that the more the number of the nodes is, the more accumulated the interference is. Then a lot of accumulated interference leads to more outages. Therefore, to reduce accumulated interference between multiusers, the density of nodes is limited in a certain area. According to the feedback of channel fading distribution, the transmitter adjusted the power to reduce the accumulated interference. The simulation results show that the proposed PCOPA strategy achieves the optimum outage probability in different environment, in which the aim is to achieve the optimal outage probability by reducing accumulated interference.
In Figures 6, 7, and 8, we plot the outage probability as some parameters for the proposed the power control strategies, such as PPC (Peak Power Control), PCOPA, and WFPC (WaterFilled Power Control). Considering above the parameters, we can see that outage probability increased with the density of nodes. As is shown, the PCOPA strategy achieves the minimization of the outage probability. In the case of the same density, outage probabilities of PCOPA, WFPC, and MPC are, respectively, 0.63, 0.75, and 0.86. The outage probability is significantly decreased by the PCOPA compared with that by MPC, which is decreased by 23%. The MPC algorithm uses the maximum power to send the data. When the channel deteriorates beyond some point, transmissions are made in vain. The WFPC algorithm is greedy. However, the WFPC algorithm aims at achieving the optimal capacity regardless of the outage probability. More outage probability leads to deterioration of the network connectivity and brings more retransmission probability. Therefore, in this paper, the optimal outage probability algorithm is proposed. The PCOPA achieves the optimal outage probability under multiusers.
In Figure 7, we plot the outage probability as a function of the distance from 0 to 250 m. The outage probability varies with the distances. It should be noted that the expression in (14) is for the case of channel fading. The method of PCOPA provides channel fading variations for different distance and adaptively adjusts the transmission power according to the time varying characteristic of wireless channel; thus the outage probability of PCOPA is lower compared to WFPC and MPC.
In Figure 8, we plot the outage probability as a function of the density of nodes for the three power control algorithms. As is shown in reality environment, there is serious Doppler frequency. When the density and the Doppler frequency increase, the accumulated interference in the receiver grows more. In certain area the density of nodes trends very fast to the saturation, which leads to the outage probability attaining to the maximum very fast. Therefore, the density of nodes is closer to the outage probability. The simulation results in Jack channel model show that when vehicle speed is equal to , the Doppler frequency is given for . Compared with Figure 4, outage probability increased with the number of nodes for the same density. In the case of Doppler frequency, the outage probabilities of PCOPA, WFPC, and MPC are, respectively, 0.83, 0.92, and 0.98. The outage probability is significantly decreased by the PCOPA compared with that by MPC, which is decreased by 9%. The simulation results demonstrate that the reality of PCOPA is better. The reason is that, considering the multiuser interference and joint with the feedback of CSI, the PCOPA achieves the optimal outage probability.
The outage probability awareness algorithm is shown in Algorithm 1. Figure 9 shows that the throughput is varying as the node densities. With the increasing of the density nodes, the throughput grows more. Clearly, MPC is very fast trending to the saturation, and then WFPC is second. The PCOPA achieves the most throughputs among the three algorithms. In the case of the same density of nodes, the network throughput of PCOPA was significantly higher than that of WFPC and MPC, and then success delivery rate of PCOPA is 600. The high delivery rate makes more throughputs, but results in more cumulative interference. As is shown, the PCOPA can adjust the transmitter power according to CSI, in which the aim is to optimize the outage probability. Therefore, among three power control algorithms, the PCOPA achieves the optimal outage probability and then achieves the most throughput.

5. Conclusion
In this paper, to address these issues, such as random mobility of nodes, interference in multiusers, and high outage probability, we proposed a power control algorithm, called simply PCOPA. The PCOPA analyzes the situation of multiple user interference through stochastic geometry and then establishes relationship between outage probability and channel accumulated interference. At last, the aim of the PCOPA is to minimize the outage probability. Further, the throughputs increase, while the outage probability declines. Our simulation results validated the derived expression and confirmed the feasibility of the proposed PCOPA. It is shown that, in general, not all the terminals need to use their maximum power consumption to achieve the best outage probability. If all the terminals use their maximum power consumption, it is easy to increase cumulative interference. Therefore, based on CSI, the PCOPA in this paper is proposed. The simulation results show that the outage probability of the PCOPA decreased by 23% and the throughput is increased by 25%, compared to MPC and WFPC.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported in part by the following projects: the National Natural Science Foundation of China through Grant 61571318, Guangxi Science and Technology Project (AC16380094, 159800829, and AA17204086), the Guangxi Nature Science Fund (2016GXNSFAA380226), Guangxi Nature Science Fund Key Project (2016 GXNSFDA380031), and Guangxi University Science Research Project (ZD 2014146).