A Beacon Transmission Power Control Algorithm Based on Wireless Channel Load Forecasting in VANETs

In a vehicular ad hoc network (VANET), the periodic exchange of single-hop status information broadcasts (beacon frames) produces channel loading, which causes channel congestion and induces information conflict problems. To guarantee fairness in beacon transmissions from each node and maximum network connectivity, adjustment of the beacon transmission power is an effective method for reducing and preventing channel congestion. In this study, the primary factors that influence wireless channel loading are selected to construct the KF-BCLF, which is a channel load forecasting algorithm based on a recursive Kalman filter and employs multiple regression equation. By pre-adjusting the transmission power based on the forecasted channel load, the channel load was kept within a predefined range; therefore, channel congestion was prevented. Based on this method, the CLF-BTPC, which is a transmission power control algorithm, is proposed. To verify KF-BCLF algorithm, a traffic survey method that involved the collection of floating car data along a major traffic road in Changchun City is employed. By comparing this forecast with the measured channel loads, the proposed KF-BCLF algorithm was proven to be effective. In addition, the CLF-BTPC algorithm is verified by simulating a section of eight-lane highway and a signal-controlled urban intersection. The results of the two verification process indicate that this distributed CLF-BTPC algorithm can effectively control channel load, prevent channel congestion, and enhance the stability and robustness of wireless beacon transmission in a vehicular network.


Introduction
In an "active safety" system of a vehicular ad hoc network (VANET), intelligent vehicles cooperate to avoid dangerous situations and traffic accidents. Vehicles (in the subsequent text, "vehicle" and "node" refer to the same concept in a VANET) establish mutual perceptions by periodically exchanging single-hop status information broadcasts, which include geographical location, speed, and driving direction [1,2]. Mutual perception between vehicles can be employed to detect dangerous traffic conditions, such as traffic jams and passing vehicles. This propose the CLF-BTPC algorithm. Section 5 verifies the CLF-BTPC algorithm by simulations. We present our conclusions in Section 6.

KF-BCLF Algorithm
The Federal Communications Commission (FCC) has allocated 75-MHz band at 5.9 GHz for VANETs. This band is divided into seven channels with 10-MHz width for each channel. One channel is reserved for safety-related information exchanges, whereas the remaining six channels are employed for non-safety-related applications (FCC 2004). IEEE 802.11p provides a data transmission speed range of 3-27 Mbps for the 10-MHz channel (2008).
In a VANET, the communication process for traveling vehicles forms a large-scale nonlinear system [26,27]; it is influenced by random factors, such as vehicle operating property, vehicle performance, traffic flow conditions, communication parameters, and the communication environment [28,29]. Periodic status information (source of beacon massages) produces channel loads. From the standpoint of the channel load surrounding each vehicle, this load is not only influenced by the expected periodical information generation rate, average message size, configured transmission power, and channel fading conditions but is also related to factors such as traffic flow, traffic density, and road incidents. Kalman filter theory employs a small number of parameters and is computationally convenient [30,31]. However, the conventional type of model that utilizes Kalman filtering is based on historical channel load data and does not consider many influential factors in a subsequent time period, which causes shortcomings in forecasting accuracy and self-adaptability. To improve the channel load forecasting accuracy, a multivariate relationship model must be constructed to evaluate the channel load based on the selection of possible influential factors.
This study combines the characteristics of Kalman filter, selects m factors that influence the channel load [32], and establishes a multiple regression-based KF-BCLF algorithm. The specific steps are as follows: Step 1: Construct multiple linear regression equations that reflect the relationship between the channel load and the influential factors: . .
Step 3: Initialize the filter variance matrix P(0) and the measured value X(0).
Step 7: Calculate the channel load forecast value using y(k) = A(k)•X(k).

Example of the KF-BCLF algorithm
To support active vehicle safety applications and to increase the accuracy required for safety applications, several location messages must be generated every second by a vehicle. In extremely urgent safety applications, such as collaborative front collision warning systems, the periodic rate can exceed 10-20 messages per second [33,34]. In a safety study, Maxim [35] noted that the size of a periodic status message ranges from 250 to 800 bytes for current digital signatures and certificates.
To verify the effectiveness of the KF-BCLF algorithm proposed in this paper, a traffic survey method was employed. The floating car was employed to collect data on a segment of Renmin Street (between Jiefang Road and Nanhu Road) in Changchun City. Once every 5 minutes, the floating car collected traffic data on the speed, number of vehicles within communication range, and traffic flow density around it. The data comprised 300 points; the last 24 points were employed to verify front sampling data. Using the channel load (CL) sequence {x(k)}(k = 1,2,. . .,300) as the subject of study, a short-term CL forecasting experiment was conducted by using KF-BCLF algorithm.
For computational convenience, the transmission power of each vehicle was assumed to be 10 dBm, the communication range was set to 500 m, the size of the periodic status messages size was 800 bytes, and the periodic messages were generated at a rate of 20 per second. The CL near the floating car was computed using the following equation, the result was applied as the measured CL.
In Eq (8), Measured_CL represents the measured CL and cars com distance is the number of vehicles within the communication range. To simplify the CL forecasting computation, this study selected the traffic density and floating car speed as the variable parameters in the CL regression equation to construct the CL forecasting model. The values of the regression parameters were determined using the method of least squares. The single-step CL forecasting value was obtained according to Kalman recursion model and the measured CL. To compare the results, a relative error indicator was introduced as follows: In Eq (9), rerr is the relative error, L pred (t) is the CL forecasting value, and L real (t) is the measured CL value. The results are shown in the following graph: A shown in Figs 1 and 2, KF-BCLF algorithm considered the factors that exhibited the greatest influence on the CL. The maximum forecasting error was 13% The forecasting accuracy was satisfactory, which indicates that this algorithm is effective for CL forecasting.

CLF-BTPC algorithm
In mobile network transmission power control algorithm, the goals for overall system capacity maximization, energy consumption, or point-to-point communication connectivity are typically established [36][37][38]. Because the inter-vehicular communication mode in a VANET environment is generally one-to-many [39][40][41], energy consumption is generally not an issue; therefore, existing studies are not applicable for a VANET.
Using higher transmission power may produce longer transmission distance and increase the robustness of message transmission but will cause channel saturation and a greater message conflict ratio [42,43]. In a safety application, fairness in the communication must be considered [44,45]. Because a VANET does not have a central communications coordinator, a distributed algorithm must be employed to optimize the beacon message transmission power and ensure fairness among all nodes; otherwise, dangerous conditions may be created for surrounding nodes [46,47]. When designing and optimizing an algorithm to control transmission power, the transmission power of each node within the communication range must be fairly assigned in a way that satisfies the safety requirements for the purpose of each individual node increasing their total packet transmission efficiency.
We consider a scenario in which a set of vehicles (also referred to as nodes) is moving along a road. The nodes periodically send beacon messages to inform the nodes in the vicinity of their current position, direction, and velocity. We assume that the beaconing frequency is identical for all nodes. However, the power for transmitting beacon messages can be adjusted to control the channel load. A short version of the statement and definitions, which is required to prove Theorem 1, is presented as follows: Assumption 2: Node u i 2N periodically transmits beacon messages to other nodes u j 2N, j6 ¼i with the constant frequency f. The initial beacon transmission power is P ini 2[0,P max ], where p max is the maximum allowable transmission power.
The following terms can be defined:  on the CLF under the premise that the real CL of each node is controlled within an allowable range.
If the PA of a beacon message is increased, the robustness to power fluctuation and interference also increases, which indicates that the message can be transmitted over a longer distance. If the PAs of all nodes in the network simultaneously increases, then the CSR and the number of channel-sharing nodes of each vehicle also increases, which decreases the spatial multiplexing rate. According to a study by Torrent [48], under highway conditions, when the beacon communication distance is 300 m, if the transmission power is increased from 10 dBm to 20 dBm, the wireless CL of the emitting end increases from 2.58 Mbps to 18.5 Mbps, which reduces the beacon receiving ratio at the receiving end from 0.6 to 0.1. Therefore, when assigning the beacon transmission power, a suitable balance should be achieved to determine the optimal operating strategy.
The objective of this CLF-BTPC algorithm is to fairly assign the PA (assigned power) to every vehicle in a distributed manner while satisfying the condition that the CL around each vehicle is guaranteed to be within the predefined threshold range. The beacon transmission power of each vehicle is maximized; therefore, the connectivity of the mobile network is also maximized. CLF-BTPC algorithm is as follows: while (max_CL(PA) max_adjust_load) do 5.
end for

Algorithm 1 CLF-BTPC algorithm
In Algorithm 1, forecast_load is the channel load forecast value, the max_adjust_load is the maximum allowable channel load, the min_adjust_load is the minimum allowable channel load, PA is the beacon's assigned power, and ε is the step size for power adjustments.
Theorem 1: The value of the obtained PA using the CLF-BTPC algorithm is the optimal solution to the TPAP.
Proof: The transmission power that corresponds to the transmission power assignment PA from algorithm 1 is p max . If 9PA'>PA is the maximum assigned transmission power, then the corresponding transmission power is P', and p'>p max . According to Definition 4, CL(PA',i)<max_CL(PA) 8i21,. . .,n, i.e., p'<p max , which conflicts with a known condition. Therefore, PA is the maximum transmission power assigned to the node. The PA value obtained from CLF-BTPC algorithm is the optimal solution to the TPAP. QED.
The workflow of the CLF-BTPC algorithm is as follows: all nodes in the network transmit periodic beacon messages with the initial transmission power p ini , and the target node forecasts the CL once in each time interval. If the CL-forecasted value of the target node is less than the lower bound of the predefined CL range, then all nodes within the CSR of this target node increase their transmission power by kε (k is the number of steps) until max_CL(PA) is less than the upper boundary of the predefined range. If the CL of the target node is higher than the upper bound of the predefined range, then all nodes within the CSR of this target node decrease their transmission power by kε (k is the number of steps) until min_CL(PA) is greater than the lower bound of the predefined range.

Simulation verifications of the CLF-BTPC algorithm
In this study, a basic section of eight-lane highway and a signal-controlled urban intersection were selected to examine the changes of the CL produced by periodic beacon messages before and after the CLF-BTPC algorithm was applied in high-density wireless communication environment. Paramics was selected as the traffic simulation tool. In reference to the requirements for the periodic beacon message generation rate and the packet size for mobile safety applications in the literature [48], the beacon message size was set to 800 bytes, and the generation rate was set to 15 messages per second, i.e., beacon message generation rate is 96 Kbps per vehicle. The initial communication range was 250 m, and the initial CSR was 500 m. The maximum communication range was 500 m, and the maximum CSR was 1000 m. The minimum CL threshold was 3 Mbps, the maximum CL threshold was 6 Mbps, the power adjustment step size was 0.01, and the CL forecasting interval was 1 min.

Signalized urban intersection
The traffic simulation parameters for a signalized urban intersection are listed in Table 1.
According to the traffic simulation parameters in Table 1, the average vehicle headway is 15 m. Near the intersection, the average CL produced by periodic beacon messages is

Eight-lane highway basic section
The traffic simulation parameters for an eight-lane highway basic section are listed in Table 2. Based on the traffic simulation parameters in Table 2, when the average headway of the vehicles is 20 m, for a given road section, the average CL produced by periodic beacon messages is The average CLs before and after the CLF-BTPC algorithm was applied are shown in Figs 5 and 6.   Fig 4, when vehicles approach the intersection, the CL increases with an increase in speed. At 600 m, the maximum vehicle speed is attained. The maximum CL is attained near the intersection, and the CL value is less than 6 Mbps after the CLF-BTPC algorithm is applied. The results indicate that the CLF-BTPC algorithm is more effective for frequent changes in vehicle speeds (e.g., near the intersection).
doi:10.1371/journal.pone.0142775.g004 The maximum and minimum power assignments PA can be calculated using the following equations: In Eqs (10) and (11), PA min is the minimum PA, PA max is the maximum PA value, CSR max is the maximum CSR, CSR min is the minimum CSR, Vehicle_Density is the traffic flow density, Load vehicle is the periodic beacon generation rate, Min_Adjust_Load is the minimum allowed CL, and Max_Adjust_Load is the maximum allowed CL. Substituting the communication and traffic parameters in this paper into Eqs (10) and (11) yields the following minimum and maximum PA values: The PA is shown in Fig 7:   Fig 6. CL in different traffic flows in on highway. According to CLF-BTPC, as the beacon message transmission power changed, the CSR and number of shared nodes in a channel for each vehicle also changed; therefore, the wireless spatial multiplexing rate changed. When the transmission power changed by kε, the CSR was adjusted to (1±kε)ÁCSR ini , where CSR ini is the initial CSR. The target node sends beacon messages at its highest transmission power, assuming that the CL fell within the predefined range. As shown in Fig 6, the CL is decreased to predefined threshold range of 3-6 Mbps after a period of oscillation. The simulation results show that CLF-BTPC algorithm sufficiently solves the CL congestion control problem in a VANET. doi:10.1371/journal.pone.0142775.g006

Conclusion
In a VANET, designs for algorithm that control wireless channel loading under the premise of satisfactory vehicle safety are required. When the size and generation rate of periodic beacon messages have been reduced to minimum values, the transmission power of periodic beacon messages must be adjusted to effectively decrease the wireless channel load, prevent channel congestion, and guarantee maximal network connectivity. (1) In this study, the primary factors that influence channel load were selected, regression equations were constructed and Kalman filter-based recursion was performed. The actual road experimental results show that the KF-BCLF algorithm has a relatively high adaptability and forecasting accuracy. (2) According to a comparison of the channel load that was obtained from the KF-BCLF algorithm and the predefined maximum and minimum threshold values, the beacon transmission power is adjusted when the fairness is satisfactory. The simulation results show that the CLF-BTPC algorithm can respond to the dynamic topological structure of a mobile network, which enables beacon messages to be sent at the maximum transmission power and causes the channel load to rapidly converge to a value within a reasonable range. The selection of additional parameters that influence a load may increase the accuracy of the KF-BCLF algorithm; however, the computational intensity and storage space requirements also increase. The impact of a wireless transmission environment was not included in the CLF-BTPC algorithm. For different channel fading conditions, the performance gain provided by controlling the transmission power generally produces different success rates for decoding beacon messages, which impacts the probability of successfully receiving a beacon message.
Supporting Information S1 Data. There are two sheets (floating car and traffic simulation) in the file . The sheet of floating car contains the traffic survey data collected by floating car, which is employed to verify the effectiveness of KF-BCLF. The sheet of traffic simulation contains the traffic simulation data from Paramics, which is employed to verify the effectiveness of CLF-BTPC. (XLSX)