The Effect of Interference in Vehicular Communications on Safety Factors

Transcription

1 The Effect of Intefeence in Vehicula Communications on Safety Factos Ali Rakhshan School of Electical and Compute Engineeing Johns Hopkins Univesity Baltimoe, Mayland s: axiv: v2 [cs.ni] 27 Jun 2017 Abstact This pape studies how the intefeence of vehicula communications affects the safety of vehicles in a vehicula ad hoc netwok. Diffeent signal popagation models with and without caie sensing ae consideed fo the dissemination of peiodic safety messages. Then, by employing the esults fo diffeent packet success pobability of the vehicles, we compae the expected collision pobability of vehicles fo diffeent signal fading models. Ou esults show how the collision pobabilities of vehicles in the netwok vay with espect to diffeent models and designs. Index Tems Vehicula Netwoks, Wieless Netwoks, Ad Hoc Netwoks, Intefeence, Safety, Caie Sensing. I. INTRODUCTION Despite the fact that new technologies ae incopoated into tanspotation systems evey day, the impovement of dives safety is not popotional to the apid ise of advanced technology. Statistics fom the National Highway Taffic Safety Administation (NHTSA in 2013 [1] epot ove five million cashes in the U.S., causing ove two million injuies and moe than 30,000 fatalities. NHTSA eseach poposes a way to impove the effectiveness of collision waning systems by employing Vehicula Ad Hoc Netwoks (VANETs [2]. VANETs povide on-boad units with two types of vehicula communications. These include the communication between vehicles in close poximity to each othe as well as communication between the infastuctue on the oad and the vehicle. The Fedeal Communications Commission has allocated 75 MHz of spectum in the 5.9 GHz band fo Dedicated Shot Range Communications (DSRC. To seve as the goundwok fo these communications, the IEEE p standad was published in the yea 2010 [3] fo Wieless Access in Vehicula Envionments (WAVE. Thee ae diffeent types of collisions that potentially happen on oadways. Of these, ea-end collisions epesent 28% of the cashes [2]. This type of collision symbolizes the most impotant line-of-sight envionment fo vehicula communications. Hence, the majoity of cashes actually occu in non-line-of-sight envionments. A numbe of models exist to descibe the statistics of the amplitude and the phase of multi-path fading signals. The Nakagami-m distibution has some advantages ove othe models like Rayleigh fading and Rician fading. Howeve, many papes have consideed the simple models to analyze the intefeence at the expense of losing the equied accuacy fo dives safety analysis. Caie sensing has also been a neglected facto in the safety packets delivey analysis. Ou main contibutions in this pape ae as follows: - We analytically study the success pobability of safety packets by taking the multi-use intefeence, path loss, and two diffeent types of signal fading models into account. - We also conside the scheme in which each node senses the channel at the beginning of each slot. - We compae the vehicle collision pobabilities of the netwok fo vaious discussed models. The emainde of this pape is oganized as follows. Section II eviews the past liteatue in the intefeence modeling of VANET. In section III and section IV, the assumptions and the analysis to chaacteize the intefeence ae pesented. Finally, the numeical esults ae illustated in section V. II. BACKGROUND AND LITERATURE REVIEW Ou goal is to examine how many tansmissions on aveage ae equied fo a vehicle to eceive the desied safety packet. Chang et al. defined a new metic named the pobability of eception failue (PRF fo a scheme in which nodes tansmit with a given pobability in each slot. Howeve, they neglected fading and only consideed the stongest intefee in thei analysis [4]. Gacia-Costa et al. poposed a stochastic model in which they obtained the aveage numbe of collisions in a chain of vehicles. Each vehicle was assumed to be equipped with a collision waning system; howeve, the distibution of the safety packets delivey was fixed and unealistic fo evey MAC scheme [5]. Cabaugh et al. also studied the ea-end collisions of automated and manual highway systems. Yet, they assumed a fixed communications delay (fixed packet success pobability of 300, 150, and 120 milliseconds fo autonomous, low-coopeative, and high-coopeative vehicles, espectively, an assumption which might not be ealistic [6]. Haas et al. simulated two vehicula safety applications and detemined the effect of vaious communication paametes on vehicle cash avoidance though taffic simulations [7]. Howeve, they did not develop any mathematical famewok fo the intefeence modelling of VANET. Finally, we studied the concept of diffeent channel access fo the vehicles in a

2 highway scenaio, but we only analyzed a specific scenaio [11] [13], [18]. Thee ae majo diffeences between this pape and othes. Fist, most of the studies which examine diffeent intefeence models ae only simulation-based (e.g. [9] and [10]. Howeve, we want to find insights though the analysis on how diffeent paametes can actually change the delivey of packets and thus the vehicle collision pobability. Clealy, the esults obtained fom both diffeent simulatos and analysis ae only an appoximation of eality. Second, we will demonstate the effect of caie sensing (o non-independent channel access of vehicles on the packet success pobability which is usually neglected in the analysis. Thid, the channel access is assumed to be equal fo diffeent vehicles in the analysis. Although this assumption seems ealistic based on the cuent vehicles equipped with DSRC antennas, in the nea futue this assumption may need to be elaxed. In othe wods, the channel access of diffeent dives may depend on the safety of thei vehicles in futue designs. Hence, we assume the vehicles can tansmit at diffeent ates. III. ASSUMPTIONS Communications between vehicles can help dives eact popely to deceleation events, especially when a dive cannot eithe obseve o peceive the deceleation of othe vehicles due to low visibility, high unexpectedness of the incident, defected bake lights, o many of the othe distactions that nowadays exist on the oads. Howeve, we need to know the communication intefeence of othe vehicles signals in ode to find any othe impotant safety factos in ou design, such as packet delivey success pobability and vehicle collision pobability. It has been shown that the Nakagami fading model descibes the intefeence moe accuately than othe wellknown elatively simple models fo vehicula ad hoc scenaios [9], [10]. Othe papes examine this intefeence only though simulations, but we study it analytically to find citical factos in dives safety. It is notewothy that due to both the shot length of packets and the boadcast natue of communications, the 4- way handshake anticipated by the standad is not efficient fo the dissemination of peiodic safety messages. RTS/CTS and ACK message exchanges wosen the hidden node poblem thus leading to highe pobability of packet collisions [17]. Futhemoe, only the potocols which do not need a detailed desciption of the netwok topology to schedule packet tansmissions ae effective because the topology of VANETs is immensely dynamic. Repetition-based potocols not only eveal this popety, but also fight packet collisions due to the poblem of hidden nodes. A simila appoach has been used in othe papes, e.g. in [16] and [17]. In the next section, fist we employ epetition-based potocols fo the dissemination of peiodic safety messages. Second, we conside the Slotted Asynchonous P-pesistent with caie sensing (SAP/CS scheme. Heeafte, we do not estict ou analysis to any specific geomety unless explicitly stated othewise. IV. ANALYSIS We need to know the communication intefeence of othe vehicles signals in ode to find any othe impotant safety factos in ou design, such as packet delivey success pobability and vehicle collision pobability. Path loss and Nakagami-m fading ae taken into account fo fomalizing the signal popagation chaacteistics. If the nodes tansmit with unit powe, the eceived powe at distance is h whee (> 1 is the path loss exponent and h is the fading coefficient. We assume that the magnitude of the signal that has passed though the tansmission medium will vay andomly accoding to the Nakagami-m distibution. This is a valid assumption because the sum of multiple independent and identically distibuted (i.i.d. Rayleigh-fading signals, which have a Nakagami distibuted signal amplitude, have been shown to be an efficient intefeence model fo multiple souces [8]. Since the amplitude of the eceived signal is a Nakagami-m distibuted andom vaiable, h has gamma distibution with mean λ: f H (h = 1 ( m m h m 1 e mh λ h 0 λ whee is the gamma function fo intege shape facto m. Assuming that a vehicle tansmits a packet, the pe-hop tansmission success pobability can be calculated as follows (E(h i = λ = 1: ( S P S = P I > β (1 ( h P S = P n b ih i > β i = P (h > β I I = i f I (idi [ = E I 1 1 ] γ(m, mβ I = 1 1 mm = 1 1 (2 ( m k β k+m k!(k + m E[ I] (k+m (3 ( 1 k β k k!(m + k[(m 1!] k ( k (m + k k 1, k 2,, k i 1! n k 1+k 2+ +k n=k ( ki E. (4 j=1 j The definitions of the vaiables ae given in Table I. A fixed coding scheme is consideed in Equation 1 that equies the SIR at the eceive to be geate than some theshold which is chosen based on IEEE p tables [3] (e.g. Table II. S denotes the powe of the main signal which faces intefeence

3 TABLE I DEFINITIONS OF THE VARIABLES IN EQUATIONS 1, 2, 3, 4 S I β b i i n h i Desied signal powe Intefeence powe at the eceive Path loss exponent SIR decoding theshold Tansmission pobability of node i Benoulli andom vaiable with pobability Distance fom the intefee i to the eceive Distance between the tansmitte and the eceive Numbe of vehicles Fading coefficient of intefee i fom the othe vehicles with the accumulative powe of I. Equation 2 is then obtained by substituting the definitions of the tansmitte signal stength and the intefeence signal stength in Equation 1. Each of the vehicles is eithe in the tansmitting mode with pobability o in the eceiving mode with pobability 1. A Benoulli andom vaiable, b i, epesents the state of the tansmitte vehicle i. Equation 3 is esulted by employing the following convegent seies of the incomplete gamma function to cancel h: γ (m, mβ I = 1 ( mβ I k k!(m + k. Finally, the multinomial expansion and chaacteistic functions of fading andom vaiables leads us to Equation 4. The obtained packet success pobability equation clealy holds fo all the possible geometies. Fo m = 1, Equation 3 will be equal to: P S = 1 + ( 1 + β i. (5 which is the packet success pobability equation when the Rayleigh fading model is employed [11]. If the time slots in which nodes tansmit ae not synchonized, this scheme is named Slotted Asynchonous P-pesistent (SAP. In this case, an intefee can potentially intefee with at most two time slots of anothe tansmission. Hence, the tansmission pobability fo the intefees is: p i = + 2. (6 Since the pobabilities ae small, this appoximation is close to the eal value. Up to this point, we have assumed that each vehicle tansmits independently of all othe vehicles. Howeve, in ode to educe the pobability of packet collisions, we study a scheme in which each vehicle tansmits only if it finds the channel idle (sensing. Ou goal is to find the packet success pobability unde the Nakagami-m fading model by employing the SAP/CS scheme. To make the analysis feasible, we stat Fig. 1. A chain of vehicles which employ SAP/CS MAC scheme. T, R, CS, I epesent the tansmitte vehicle, the eceive vehicle, the caie sensing distance, and the distance in which the vehicles can cause intefeence at the eceive vehicle, espectively. with: P s = P t P s t. P t epesents the pobability that node T accesses the channel, i.e. finds it idle and tansmits. P s t is the packet success pobability at vehicle R, given that vehicle T accesses the channel (Fig. 1. We define the caie sensing distance as CS. A vehicle can tansmit if and only if no othe vehicle tansmits within CS distance of it. The numbe of vehicles within this adius is called n CS : CS P t p T (1. (7 in which p T epesents the channel access pobability of the tansmitte vehicle. The appoximation is sufficiently tight because tansmission pobabilities ae small despite the tansmissions not being independent. If the pobabilities ae not small, Equation 7 denotes an uppebound fo P t. Next, we need to find the adius of a disk centeed at R in which any active node can cause intefeence at R. Accoding to the SIR-based eception model, thee must be h > β whee h and h h i i ae the espective Nakagami-m i fading components of the intefeence model, and and i ae the distance between the tansmitte and the eceive and the distance between the intefee i and the eceive. Theefoe, we have: [ ] ] I β 1 E h 1 E [h 1 i. By employing the concept of factional moments, we obtain: I β 1 = β 1 Γ(m + 1 Γ(m 1. π Γ 2 (m csc( π.

4 TABLE II IEEE P DATA RATES AND CORRESPONDING SIR DECODING THRESHOLDS TABLE III SIMULATION PARAMETERS. DATA RATE AND SIR DECODING THRESHOLD ARE CHOSEN BASED ON [16] R (Mbps β (db Vehicle Distibution Velocity Equal Distance 20 m s Fo the Rayleigh fading scenaio, I β 1 π csc( π. In the absence of fading, I β 1. Fo usual values of, the I is geate than when thee is no fading. When vehicle T tansmits, only the hidden nodes whose activities ae not sensed by node T can cause outage at node R (see Fig. 1. If thee ae x hidden nodes and N i epesents the event that the ith hidden node does not tansmit, then P s t is equal to ( x P s t = P N i = 1 P = 1 ( x N c i x P(Ni c. (8 The last equality is tue when N c i N c j = Ø. This condition holds tue since the MAC scheme does not allow the hidden nodes to tansmit simultaneously fo the pactical values of CS and I. Fo a one lane case, the packet success pobability of the tansmitte T at the eceive R can be appoximated as: [ ncs p T (1 1 N(+ I CS max ( I, + I 2 CS < + I P s p i ncs p T (1 CS + I (9 N( + I CS epesents the numbe of hidden nodes in the hidden aea ( + I CS. The optimal caie sensing distance is CS + I. Hee, I CS epesents the scenaio in which thee is no hidden node to the left of node + T (in Fig. 1. In ode fo Equation 8 to hold, I 2, which is the maximum distance between the hidden nodes, must be less than CS to foce the vehicles not to be active togethe. If the time slots ae not synchonized, the intefees can cause outage ove two consecutive time slots with the pobability obtained by Equation 6. V. NUMERICAL RESULTS In this section, we want to compae the pefomance of diffeent designs in a highway scenaio consideing both discussed cases, with and without caie sensing. Table III shows all the values assigned to diffeent paametes. In a chain of vehicles, we assume tansmissions acoss the chain ] Deceleation ate [ 6, 9] m s 2 Total numbe of selected vehicles 25 SIR decoding theshold 8 db R=Data ate 6 Mbps Numbe of Obstuctive Vehicles 4 L=Packet length 250 Bytes Reaction times of dives lnn(0.17, 0.44 Distance between neighbos 25m Fig. 2. The aveage collision pobability of vehicles in the netwok vesus channel access pobability. ae patially obstucted by some vehicles that ae chosen unifomly in ou Monte Calo simulations. In othe wods, the selected vehicles disupt the line-of-sight envionment fo the specific scenaio and divide the chain into smalle chains. The collision pobability is calculated based on the equations of motion. The dives can eact to the deceleation of thei leading ca with eaction time chosen andomly fom the lognomal distibution with paametes µ = 0.17 and σ = 0.44 (see [15]. The vehicles tansmit with equal channel access pobability and the distance between neighbo vehicles equals to 25m (see [14]. Theefoe, the packet success pobability is obtained by employing Equations 9, 5, and 4. Also, each vehicle deceleates as soon as it is infomed with a ate chosen unifomly at andom fom the inteval [ 6, 9] m s. 2 We need to compute the time it takes fo a message to be eceived by vehicle i in the pat of the chain that doesn t include any obstuctive vehicles. As a esult, the successful eception at vehicle V i has a geometic distibution with paamete P s (i p t (1. Hee, p t,, and P s (i epesent the channel access pobability of the tansmitte, the channel access pobability of the desied eceive (i th vehicle, and the packet success pobability at the desied eceive, espectively. Let s assume a chain of vehicles is moving in a cetain diection on a highway. We name the fist vehicle in the chain V 0 and the following vehicles V 1, V 2,... espectively. Clealy, it takes longe time fo the vehicles fa away fom V 0 to eceive

5 the packets due to delay. The fa vehicles on the highway (fo example V j eceive the messages about the deceleation of V 0 fom the vehicles V 1 V j 2 as well. V j 1 is not included since V j can see the bake lights of V j 1 with no need fo vehicle-to-vehicle communication. Taking all of the above into account, the aveage delay of eception at vehicle V i is: L 1 D(i = min( min (j 1,,i 2 R P s (jp 0 (1 p j + τ j + L 1 R P s (ip j (1, L 1 R P s (ip 0 (1, L 1 R P s (i 1p 0 (1 1 + τ i 1 i > 2. (10 R epesents the data ate which is chosen fom TABLE II while L denotes the packet length. In addition, τ j denotes the eaction time of the j th dive in the chain. Each vehicle can etansmit the tansmitte s safety packet afte its coesponding dive applies the bake. Theefoe, the communication delay is actually the minimum of thee pats. The fist pat of Equation 10 symbolizes the etansmission of the safe packets by the middle vehicles while the second pat epesents the diect communication between the tansmitte and the desied eceive. The last pat assumes the vehicle in font of the eceive eceives the safety packet and the dive of the desied eceive can see the bakes lights of the vehicle. The allowable numbe of tansmission oppotunities within the toleable delay peiod is: D = T (ir L. T (i denotes the maximum toleable delay to infom vehicle V i in a chain of vehicles. The aveage collision pobability of vehicles in the netwok is illustated in Fig. 2. When the channel access pobability is aound 0.04, the communication with caie sensing is almost the same as the scenaio without caie sensing. Also, fo lage channel access the diffeence between the schemes with and without caie sensing shinks. In these two anges of channel access, thee is less than 10% impovement in the collision pobability. Since Equation 7 epesents an uppebound fo the success pobability, the esulting eduction achieved by employing the caie sensing is the maximum possible diffeence between the two cuves. Theefoe, it confims that caie sensing could be noticeably beneficial only in a specific ange. Futhemoe, the minimum collision pobability can be achieved at lowe channel access fo the vehicles when caie sensing design is employed compaed to when it is not. Fig. 2 also depicts that employing the moe accuate model (Nakagami-3 esults in lowe collision pobability especially when caie sensing is used. VI. CONCLUSION In this pape, we studied the effect of the vehicula communications intefeence on the delivey of safety packets in vehicula ad hoc netwoks. We deived the appoximated packet success pobability fo diffeent scenaios. Ou esults illustated that the diffeence between the aveage collision pobability in the netwok fo two scenaios with and without caie sensing is minimized almost at the minimum point of the latte scenaio. The diffeence eaches local maxima when the channel access value inceases o deceases compaed to the minimum point. REFERENCES [1] National Highway Taffic Safety Administation, 2013 Moto Vehicle Cashes: Oveview, [2] United States Depatment of Tanspotation, National Highway Taffic Safety Administation, Ealy Estimate of Moto Vehicle Taffic Fatalities in 2011, Washington D.C., [3] IEEE Standad fo Infomation Technology - Telecommunications and Infomation Exchange Between Systems - Local and Metopolitan Aea Netwoks - Specific Requiements pat 11: Wieless LAN Medium Access Contol (MAC and Physical Laye (PHY Specifications Amendment 6: Wieless Access in Vehicula Envionments, IEEE Std p-2010, pp. 1-51, [4] Y. Chang, C. Lee, and J. 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