Influence of Channel Fading and Capture for Performance Evaluation in Vehicular Communications

Autonomy and intelligent transportation systems (ITSs) have recently received increased interest for vehicular ad hoc networks (VANETs). In addition, the impending 5G and 6G technologies will result in substantial advancements for VANETs. The IEEE 802.11p summarizes specifications of physical (PHY) and medium access control (MAC) layers for VANETs. Although IEEE 802.11p MAC performance has been investigated, analytical methods need improvement. Bit error and channel capture influence the performance of vehicular communications in real-world transmission. These effects are investigated separately in previous works. In this article, an extensive study is provided that integrates these two major factors. In VANETs, the influence of channel fading and capture on IEEE 802.11p is investigated analytically using a Markov chain model. For Nakagami-m, Rayleigh, and Rician fading channels, performance-impacting factors are considered, and the relationships between parameters as well as performance metrics are derived. The probability of unsuccessful and successful transmission, outage probability, probability of frame capture, throughput, bit error rate (BER), and delay terms are attained. Moreover, simulation results are provided, which verify analytical studies.

Abstract-Autonomy and intelligent transportation systems (ITSs) have recently received increased interest for vehicular ad hoc networks (VANETs).In addition, the impending 5G and 6G technologies will result in substantial advancements for VANETs.The IEEE 802.11p summarizes specifications of physical (PHY) and medium access control (MAC) layers for VANETs.Although IEEE 802.11pMAC performance has been investigated, analytical methods need improvement.Bit error and channel capture influence the performance of vehicular communications in real-world transmission.These effects are investigated separately in previous works.In this article, an extensive study is provided that integrates these two major factors.In VANETs, the influence of channel fading and capture on IEEE 802.11p is investigated analytically using a Markov chain model.For Nakagami-m, Rayleigh, and Rician fading channels, performance-impacting factors are considered, and the relationships between parameters as well as performance metrics are derived.The probability of unsuccessful and successful transmission, outage probability, probability of frame capture, throughput, bit error rate (BER), and delay terms are attained.Moreover, simulation results are provided, which verify analytical studies.

I. INTRODUCTION
V EHICULAR ad hoc networks (VANETs) not only increase road safety and efficiency of transportation but also enable autonomous vehicles (AVs) to be implemented more rapidly and efficiently by reducing reliance on expensive sensor suites.VANETs support a lot of applications, some of which are classified as safety messages (sm) and others as nonsafety data (nsd).Lane-changing assistant, emergency alert, accident avoidance, warning for traffic sign or signal violation, indication of the emergency electronic brake light, road condition, and so on are sm.Map update, traffic information system, web browsing, weather information, gaming, location and price information of gas station or restaurant, content distribution, and so on are nsd.For safety or crucial communication, sm has priority over nsd.Sm is time-dependent and the packet size of sm is smaller than nsd, which is about 100-300 bytes [1].The IEEE 802.11p [2] summarizes specifications of physical (PHY) and medium access control (MAC) layers for VANETs.The MAC layer is the most crucial for any ad hoc network because fast and reliable transfer of data is completely dependent on the MAC layer [3].
The contributions of this article can be outlined as follows.This article presents an analytical model to study the influence of channel fading and capture on IEEE 802.11p in vehicular communications where both sm and nsd are considered.In practical transmission, two prime factors, which are channel capture and bit error, have an impact on the performance of VANETs.These effects are investigated separately in previous works.This work provides an in-depth analysis that incorporates these two key elements.Parameters that have an impact on performance are analyzed and relationships between parameters as well as performance metrics are extracted analytically using the Markov chain model.Rayleigh, Nakagami-m, and Rician fading channels are considered.The probability of collision and frame capture, probability of successful and unsuccessful transmission, outage probability, bit error rate (BER), throughput, and delay terms are derived.Moreover, simulation results validate the performance model and show the effect of channel fading as well as capture on IEEE 802.11pMAC in VANETs.Comparison among system using different fading channels is presented and new findings are summarized.
The remaining sections of this article are structured as follows.Section II confers related works.Section III sketches an analytical study using the Markov chain model.In Section IV, error rate analysis is presented.The throughput analysis is provided in Section V. Delay study is carried out in Section VI.The analytical and simulation results are exhibited in Section VII.Finally, this article draws a conclusion in Section VIII.

II. RELATED WORKS
The performance of IEEE 802.11p for vehicular communications is scrutinized in [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], and [14].In [4], an analytical study is provided to show the effect of IEEE 802.11p in VANETs, and an optimization mechanism is presented.In [5], the Markov chain model-based theoretical study is outlined where delay expression is derived.In [6], the influence of IEEE 802.11p in VANETs for various traffic densities is investigated.In [7], a systematic study by means of Markov chain is given where throughput and delay expressions are carried out.Backoff is frozen when the channel being busy is not considered in [7].Various contention window sizes are examined in [8] to see how well the system performs.In [9], the performance is investigated based on the vehicle's number and contention window sizes.In [10], the influence of IEEE 802.11p in the delivery of sm is investigated.The throughput analysis is not presented in [5], [8], [9], and [10].Moreover, only sm is considered in [4], [5], [6], [7], [8], [9], and [10].To evaluate the efficiency of IEEE 801.11p for VANETs, an analytical study is provided in [11] and an optimization mechanism is presented in [12].In [13], the performance was assessed using a stochastic vehicular traffic model.Throughput and delay are optimized based on transmission range and contention window size in [13].Nevertheless, only nsd is considered in [11], [12], and [13].In [14], both sm and nsd are considered in performance analysis.However, ideal channel is assumed in [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], and [14].These studies assumed that transmission of a packet is successful if there is no collision and that transmission is unsuccessful if there is a collision.In reality, the opposite can happen in both cases.It is common for a transmitted signal to have different power levels when it arrives at the receiver as a result of shadowing, fading, and multipath propagation.The transmission of a packet may fail due to decoding error under these conditions, even if no collision occurs.Alternatively, because of the capture effect, even if a packet transmission collides, it may still be effectively received at the receiver.The packet with the greatest power may be efficiently captured by the receiver after concurrent transmissions.The impact of capture and channel fading is not considered in [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], and [14].
Only the decoding error is considered in [15], [16], [17], [18], [27], [28], and [29], and only the capture effect is considered in [21], [22], [23], [24], [25], and [26].In [27], a Markov chain is built to simulate the behavior of a VANET cluster in terms of congestion, and the probability that a link could fail as a result of wireless channel fading is estimated.The propagation effects, such as shadowing, path loss, and multipath fading, are considered in [28].To assess whether a packet is lost due to a collision or not, the received signal strength of interfering packets is considered.In [19] and [20], the analysis is provided based on Rayleigh fading channel only and decoding error analysis is not presented.In [25], Rayleigh and Rician fading channels are considered.In VANETs, the capture effect for Rayleigh faded channel is presented in [21] and [26].In [27], the decoding error analysis for the Rayleigh fading channel is studied for VANETs.In [29], the influence of IEEE 802.11p is explored in VANETs only for sm where the Nakagami fading model is used, but the capture effect is not considered.
Bit error and channel capture should be addressed while investigating the efficiency of IEEE 802.11pMAC in vehicular communications in real transmission [30].This study presents a comprehensive analysis that incorporates these two major factors.Moreover, Nakagami, Rayleigh, and Rician fading channels are considered.BER for M-ary phase shift keying (M-PSK) modulation as well as M-ary quadrature amplitude modulation (M-QAM) modulation are presented.Furthermore, both sm and nsd are considered in performance analysis.

III. MODELING AND PERFORMANCE ANALYSIS
A saturated condition is assumed.A VANET is studied where the distribution of V vehicles is random and moving on a multilane street.Fig. 1 shows the system model.Fig. 2 shows the block diagram of the proposed system model for the methodology of 802.11pVANET.Let s l be the length of street segment.The number of vehicles (V ) is a Poisson process over s l .Therefore, the probability mass function (pmf) of V along s l can be defined as follows: where which is the number of vehicles per unit distance in each lane (l) along s l , and V d l expresses the traffic density of lane l.
Let r t be transmission range, which is the maximum distance a vehicle can transmit its data.The mean value of V within r t can be expressed as follows: Let λ vehicle be the average arrival rate of vehicles in r t and s be the vehicle speed.The distribution of s is uniform between the minimum (s min ) and maximum (s max ) values.λ vehicle and s are linearly associated, which can be expressed as follows [31]: where l t indicates the total number of lanes on the road.The vehicle density (V d ) also depends on vehicle's flow, which can be stopped because of traffic jam or can be free flow if there is no traffic jam.Since s and V d vary linearly, V d can also be written based on vehicle's flow as follows: where J T denotes the traffic jam density at which flow of vehicles halts and s f is the speed of vehicle at free flow.When a node in VANET has an sm, the sm will be broadcast across the network.If a node wants to exchange nsd, WAVE service advertisement (WSA) is broadcast in the network.Node intended to the offered service receives nsd by shifting into channel frequency.A vehicle starts to listen to the channel when there is a packet to transmit.The vehicle transmits if the channel is listened idle and retains idle for difs that is the interval of distributed coordination function (DCF) interframe space (DIFS).Otherwise, the vehicle starts an arbitrary backoff to minimize collisions since any of the remaining vehicles may be transmitting a packet.
Let u(t) be the random process, which denotes backoff timer for a node at time t, where u b is the backoff counter value.If ψ represents the contention window size, then u(t) ∈ {0, 1, . . ., ψ − 1} and u b ∈ (0, ψ − 1).Compared to IEEE 802.11, broadcast is not acknowledged in IEEE 802.11p.Thus, ψ is always minimum ψ.For the backoff process, a Markov chain model is outlined in Fig. 3 where the Markov state u b ∈ [0, ψ − 1] is the value of the backoff timer.The first value of u b is uniformly chosen from [0, ψ − 1].u b is decremented by 1 if the channel is idle in a slot duration, put on hold when the channel becomes busy, and recommenced to decrease when the channel becomes idle again for longer than difs .The packet will be sent when u b expires.Let P cb and P c be the probability of channel busy and collision, respectively.
From the Markov chain, the probability of transitions can be written as follows: where u b is reduced by 1 since the channel remains idle in (5.1), u b is stopped at the current value because the channel is busy (5.2), and prompt transmission of the packet will be done when u b is zero (5.Markov chain, the following expression can be achieved Since the summation of all probable states is one Therefore, Let τ represent the probability that a particular vehicle will transmit a packet at a specific time slot, which can be shown as follows: If any vehicle sends a packet, the channel becomes busy, and P cb can be given as follows: Collision happens if any of the remaining V − 1 nodes is sending a packet, and thus, P c can be defined as follows: Interference is due to simultaneous transmission (collision).Signal-to-interference-plus-noise ratio (SINR) at the receiver can be given as follows: where σ R , σ N , and σ (i) R represent the transmission power at the receiver (R), background noise, and ith interfering transmissions at R, respectively.The channel fading coefficient, denoted by h, is between the transmitter (S) antenna and the receiver (R) antenna.At the ith interferer, g i is the channel fading coefficient between the interferer's antenna and the receiver's antenna.When there is no collision, i.e., k = 0, the total is null.From (12), the SINR can be given by the following equation: where The capture probability may be expressed as follows [32], [33] if there are i interfering frames and power-controlled nodes are operating in the infrastructure mode where z o indicates the capture ratio and p(C sf ) is the processing gain of correlation receiver.The cumulative distribution function (cdf) of SINR at R is F γ R (•).Having an 11-chip spreading factor (C sf = 11) in direct sequence spread spectrum (DSSS), p(C sf ) can be given as follows [23]: P Ri is the probability that there will be i interfering frames generated from V contending senders within a time slot that can be calculated as follows: P cap is the probability of frame capture that can be expressed as follows: Therefore, P cap can be obtained using (14) to get the value of P pc (z o p(C sf )|i).P s is the probability that a packet is conveyed successfully after transmission that can be defined as follows: P us is the probability of unsuccessful transmission.Collision at the MAC layer and/or an errored frame due to channel fading and/or noise at the PHY layer might cause a delivery failure.Let P ef be the probability of errored frame.P us can be expressed as follows: Let a vehicle's expected time in each Markov state be denoted by e that can be given as follows: e = (1 − P cb ) slot + P cb P s (1 − P ef ) s + P cb (1 − P s ) c + P cb P s P ef ef (20) where slot , s , c , and ef are the span of a slot, successful transmission, collision, and transmission of errored frame, respectively.The type of communication for sm is broadcast, whereas the mode of communication for nsd is unicast.s , c , and ef can be written for sm and nsd as follows: where is the packet size, h symbolizes the MAC and PHY header lengths, sifs specifies the period of short interframe space (SIFS), T R and T C denote the transmission rate and transmission rate control packet, respectively, del represents the propagation delay, and WSA is wireless access in vehicular environments (WAVE) service advertisement.
In the presence of path loss, the average value of SINR γ R at distance d can be given as follows [34]: where G r = G t = 4π/λ 2 denotes the gain of antenna for R and S. λ = c/ f , which is the wavelength of the signal.α is the path loss exponent.Block fading patterns, in which a packet to be delivered is divided into H blocks, are considered in order to account for the effect of fading (or coherence time).The H value is influenced by the vehicle's velocity.H is significant when the velocity is raised and the coherence period is shortened.H is also influenced by , which is expressed as follows: where the SINR threshold value is γ th , and the coherence time is coh which can be given as follows: where f dop is the Doppler shift, which can be given as follows: In this case, c represents the speed at which light is moving in the direction of the transmitter, f stands for the carrier frequency, and θ denotes the angle that exists between the signal that was received and the direction that the vehicle is moving.

A. Nakagami-m Fading Channel
The Nakagami-m fading is a channel model that describes fast fading over large distances and has a more wide distribution than the Rayleigh as well as Rician fading system.Since the |h| and |g i | Nakagami-m distribution, the probability density function (pdf) and cdf of Z in (13) can be derived as follows [34]: where (•) expresses the Gamma function and the parameter defining the form of the distribution is denoted by m. (.,.,.) represents the generalized regularized incomplete Gamma function and For pdf of Y in ( 13), Nakagami-m expressions can be obtained as [34] f Y (y) = where ]/σ N .The cdf of γ R in ( 13) can be calculated as follows [34]: where .,. (•) indicates the Meijer-G function.
It converges to the AWGN channel when the Nakagami-m fading parameter is set to a value that is excessively big (m → ∞).When m is equal to one, the Rayleigh distribution is obtained.
P out is the outage probability that occurs when the received signal's SINR (γ R ) is lower than the specified threshold (γ th ).P out can be obtained as follows: A packet is partitioned into H blocks, and therefore, P ef may be expressed as follows:

B. Rayleigh Fading Channel
When there is no line of sight (LoS) between S and R, communication is only possible via reflection, refraction, and scattering of signals as they travel from S to R. A signal's envelope is distributed according to the Rayleigh distribution if its constituent parts are zero-averaged random variables with the identical variance, which is one of the channel types that owns the poorest impact on the system's error performance.The receiver's cdf of SINR with Rayleigh fading channel may be calculated when m = 1 in (32).
P out of the system in the Rayleigh fading model can be attained from (33) by using m = 1.Now, P ef can be obtained as follows: Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

C. Rician Fading Channel
The fading coefficients seem to follow a Rician distribution when there is an LoS between S and R or if one transmission line is more dominant than the others.Although the Gaussian processes used to create this channel model have the same variances, their means might vary from zero.The mean power of a direct transmission path, or the main transmission path, is here determined by the nonzero means of Gaussian processes.The pdf and cdf of Z in (13) for the Rician fading channel system can be given as follows [35]: where W denotes the ratio of power in the LoS path to power in the dispersed multipath components.The Rician distribution will converge to the AWGN channel when W = ∞ and the Rayleigh channel if W = 0. Q 1 (.,.) represents the Marcum-Q function.I 0 (•) denotes the zero-order Bessel function.
The pdf of Y in ( 13) can be presented as follows [34]: The cdf of γ R in (13) under the Rician fading channel can be shown as follows: P out can be defined as follows: P ef can be given as follows: IV. ERROR RATE ANALYSIS Bit error due to interference and noise is considered in this study.The definition for average symbol error rate (SER) mathematically can be given by utilizing the expression of Here, the Gaussian Q-function is represented by Q(•).For the M-PSK modulation, φ = 2 and χ = sin 2 (π/M) where modulation order is denoted by M.
The average SER can be obtained as follows [35]: When applied to SINR at R, the moment generation function (MGF) can be given as follows: In the case of M-QAM modulation, χ = 3/(2(M − 1)) and φ = ( Therefore, for M-QAM modulation, the average SER can be given as follows [35]: The average BER ( Pber ) can be obtained using the average SER, which can be given as follows [35]: V. THROUGHPUT ANALYSIS Let represent the system throughput, which is the ratio of data transmitted and average period of slot time and can be written as follows: If the average packet data size is , then the mean amount of data transmitted successfully in a slot time is P s P cb (1 − P ef ) because the probability of occurring a successful transmission in a slot time is P s P cb (1 − P ef ).The mean duration of a slot time is readily attained, considering that the probability of empty slot duration is (1 − P cb ); the probability of containing a successful transmission is P cb P s (1 − P ef ); the probability of containing a collision is P cb (1 − P s ); and with probability P cb P s P ef , it contains an errored frame transmission.Therefore, (46) becomes for sm and nsd as follows ( 47) and (48), as shown at the bottom of the next page.

VI. DELAY ANALYSIS
The delay is the period from the creation of a frame to its effective delivery [41], and [42].Let ℵ be the delay that can be given as follows: where E[a fc ] denotes the average number of frame collisions before successful delivery, E[ϖ ] represents the backoff delay that is a vehicle's backoff until the channel is accessed, and v is a vehicle's waiting period after a collision to listen the channel again.v can be expressed as follows: E[a fc ] can be derived from P s .As for a successful delivery, the mean number of retransmission is E[ϖ ] depends on the backoff counter value and counter pause period while the channel is busy.Without considering counter pause, if u b slot times are expected for the backoff counter at u ub to reach 0, then the average of the duration can be given as follows: Let E[Sa fc ] be the average period of counter freezes for a vehicle, E[V Sa fc ] be the average duration until the backoff counter becomes 0 and a vehicle detects transmission from other nodes, and E[ϕ] be the mean number of consecutive idle times until a transmission happens.The association can be shown as follows: By utilizing (52) to (55), E[ϖ ] can be obtained as follows: s and c can be obtained by utilizing (21) to (23).Thus, by substituting (50), (51), and (56) into (49), ℵ can be derived.

VII. ANALYTICAL AND SIMULATION RESULTS
In this section, the influence of channel fading and capture on IEEE 802.11p in VANETs is examined, and the accuracy of the analytical analysis is confirmed using Monte Carlo simulations.MATLAB is used to obtain the outcomes of simulations.Results of simulation are obtained by 1000 Monte Carlo iterations.We simulate a two-lane road with almost similar vehicle speeds.Table I lists the value of parameters utilized in simulation results.Assume that the average signalto-noise ratio (SNR) is Throughput is shown against the number of vehicles (V ) in Fig. 4. Up to a certain point, throughput grows with V , since as V decreases, collisions become less likely.The competition for transmission among additive packets, which increases channel busy probability and hence collision probability, will cause throughput to decrease as V is increased further.Fig. 4 shows that throughput is greater for sm than nsd since sm is transmitted immediately without the need of extra control messages and nsd is delivered after the broadcast of WSA.A system with capture has a throughput that is much greater than a system without capture.Due to the capture effect, the probability of successful transmission is increased in the event of concurrent transmission.Because capture enhances the likelihood that a transmission will succeed, it also boosts throughput.Furthermore, if the capture threshold is low, throughput increases.Since capture probability decreases at high capture thresholds, throughput is greater for 6 dB than 24 dB.In [24], from the same 45-dB SNR, throughput is obtained greater for the capture threshold of 6 dB than 24 dB.
Throughput is shown versus the probability of errored frame (P er ) in Fig. 5. Since the probability of a failed transmission increases as P er rises, throughput decreases.For both capture thresholds and without capture, the throughput of sm is higher sm = P cb P s (   than nsd.Throughput is increased through capture by increasing the probability of successful transmission.In addition, throughput is high at lower capture threshold values due to increased capture.The outage probability (P out ) against distance for various fading channel models is shown in Fig. 6 where m = 2 for the Nakagami fading-m channel.The P out rises with increasing distance.If the distance is short, the Nakagami fading-m channel achieves the smallest P out , while the Rayleigh fading channel (W = 2) has a larger P out than the Rician fading channel (W = 2).The Nakagami fading-m channel attains the greatest P out when the distance is lengthy, more than 350 m, while the Rician fading channel (W = 2) obtains a little lower P out than the Nakagami fading-m channel.
The outage probability is shown versus SNR in Fig. 7 where m = 2 for the Nakagami fading-m channel.Outage probability falls with increasing SNR for all fading channels.Since SNR increases with signal intensity, the probability of an outage falls.In outage probability versus SNR is shown only for the Rayleigh fading which provides the same results.The model employing Rician fading channel with W = 2 achieves the smallest P out , whereas the one having Rayleigh fading channel faces the utmost outage probability.The Nakagami-m fading channel achieves a little larger P out than the Rician fading channel with W = 2, which has a slightly lower P out .
Vehicle velocity is shown against packet error frame probability in Fig. 8. P ef increases as speed rises.When a vehicle's speed rises, the network topology quickly changes, causing communication to become unstable and a rise in the probability of packet error frames.The model utilizing Rayleigh fading channel suffers from the utmost P ef , while the one having Nakagami-m fading channel attains the smallest Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.(m 2).When the vehicle velocity is modest, the model employing Rician fading channel (W = 2) obtains a somewhat lower P ef than the one applying the Rayleigh fading channel.However, Rician fading (W = 2) and Rayleigh fading channels attain almost identical P ef when the velocity is high (s > 50).
The average BER versus SNR is shown in Fig. 9.As SNR rises, system performance rises as well.The BER therefore decreases.The performance of a model utilizing the Nakagami-m fading channel is superior to that of a system utilizing the Rayleigh and Rician fading channel types for each modulation technique.Rician fading channels perform better than Rayleigh fading channels in terms of system performance.For each modulation method, the Rayleigh fading channel achieves the greatest BER whereas The BER versus SNR for the Nakagami-m fading channel is the lowest.BER versus SNR for every system is 64 QAM > 16 QAM > QPSK > BPSK.Performance declines as modulation order M is increased due to an increase in BER.Fig. 10 plots the probability of an unsuccessful transmission against V where m = 2 for the Nakagami For all fading channels, the risk of an unsuccessful transmission rises as V grows.With an increase in V , more packets will contend for transmission, increasing the probability of a collision.The probability of an unsuccessful transmission grows along with the probability of a collision.The system having the Rayleigh fading channel attains the highest probability of a failed transmission, while the system having the Nakagami fading-m takes the lowest probability.The probability of an unsuccessful transmission is smaller in the Rician fading channel (W = 2) system than in the Rayleigh fading channel system.When is low, the difference between various fading channels for failed transmission probability is significant, but when V is big, the difference between various fading channels for unsuccessful transmission probability small.Fig. 11 shows throughput against V for various channel types.a rise in V , throughput declines for all fading channels.More packets come more cars as V rises, increasing the number of packets competing for transmission.Additional packet transmission with a larger V will result in a higher likelihood of collisions, which will reduce throughput.Maximum throughput is achieved with the Nakagami fading-m channel (m = 2) system, while minimum is achieved with the Rayleigh fading channel system.In comparison to Rayleigh fading channel system, the Rician fading channel system (W = 2) has a better throughput.
For several channel fading models, throughput is shown versus vehicle velocity in Fig. 12 where W = 2 for the Rician fading channel.As vehicle speed increases, throughput declines.Vehicle mobility results in quick topological changes and frequent connection breaks, which renders communications unstable due to collisions and packet loss.Nakagami-m fading channels provide the maximum throughput.When the speed is more than 20 km/h, both the Rician fading channel and the Rayleigh fading channel achieve similar throughput.The model utilizing the Rician fading channel achieves a greater throughput when the speed is less than 20 km/h than the model having the Rayleigh fading channel.The average delay is shown against the number of vehicles in Fig. 13.With more vehicles, there will be greater packet congestion since more packets would be available for transmission.As more packets contend for the same space on the channel, the likelihood a collision will rise.As a result, delay increases as V .sm has a shorter delay than nsd.When z o is lesser, the delay is smaller, and when z o is higher, the delay is greater since a lower z o improves the probability of successful transmission.Delay is thus smaller for both sm and nsd when the capture threshold is 6 dB than when it is 24 dB.Compared to nsd, sm is crucial and time-sensitive.Sm has 100-ms strict delay requirement [37], [38], [39], [40].In ideal channel conditions, the strict delay requirement is not satisfied, but the delay constraint is satisfied with the capture effect.
New findings based on considering bit error and channel capture are given as follows.
1) Without capture effect and bit error, throughput is derived in ideal channel conditions.
13. Average delay versus number of vehicles.
only the capture effect is considered, throughput is higher than ideal channel condition throughput.Packet transmission is unsuccessful if a collision occurs in ideal channel conditions.Alternatively, a collided packet can be successfully received because of the capture effect.Therefore, throughput is increased.
3) If only bit error is considered, throughput is lower than the ideal channel condition.In ideal channel conditions, packet transmission is successful when no collision occurs.However, a packet transmission may fail even when no collision occurs due to bit error.Therefore, throughput is decreased.4) Scenarios 1-3 are not practical.In practice, reception is subject to both bit error and channel capture.Bit error decreases throughput, but channel capture increases throughput.Therefore, real throughput can be obtained when both bit error and capture effect are considered.

VIII. CONCLUSION AND FUTURE WORKS
This article provides an analytical model to investigate the influence of channel fading and capture on IEEE 802.11p in vehicular communications.An analytical study using Markov chain model is carried out.Nakagami, Rayleigh, and Rician fading channels are considered.Parameters that have an impact on performance are considered and the relationships between parameters as well as performance metrics are obtained.Collision probability, unsuccessful transmission probability, probability of successful transmission, outage probability, probability of frame capture, BER, throughput, and delay terms are determined.To understand the impact channel fading as well as capture effect, simulation results are presented.Due to the increased probability of successful transmission, the throughput of a system with capture is substantially higher than without capture at all times.Alternatively, because of increased unsuccessful transmission probability, throughput decreases with increasing probability of errored frame.In future studies, co-channel interference will be considered and a guideline about how many vehicles should be connected to reduce the packet error frame for the different channel fading models will be provided.
3).Let u u b = lim t→∞ P{u(t) = u b }, which represents the Markov chain's stationary distribution.With the use of a Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE I VALUE
OF PARAMETERS UTILIZED IN SIMULATION 1 − P ef ) (1 − P cb ) slot + P cb P s (1 − P ef ) s−sm + P cb (1 − P s ) c + P cb P s P ef ef (47) P cb P s (1 − P ef ) (1 − P cb ) slot + P cb P s (1 − P ef ) s−nsd + P cb (1 − P s ) c + P cb P s P ef ef (48) nsd =Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.