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Analytical Models of the Performance of C-V2X Mode 4 Vehicular Communications

Manuel Gonzalez-Martin, Miguel Sepulcre, Rafael Molina-Masegosa, Javier Gozalvez

arXiv:1807.06508v3cs.NI

TL;DR

C-V2X Mode 4 supports infrastructure-independent V2V safety communication, but its communication performance requires analytical evaluation across operating conditions. This paper develops models for PDR and four transmission errors, then validates them against Veins-based simulation, finding close agreement across broad parameter and density ranges.

  • Problem

    Analytical models were needed to evaluate C-V2X Mode 4 communication performance across a wide range of parameters and conditions, complementing computationally expensive simulations.

  • Method

    The paper develops analytical models for distance-dependent average PDR and four transmission-error types, implementing and validating them against a C-V2X Mode 4 simulator over Veins.

  • Results

    PDR estimates differed on average by less than 2.5% from simulation, while close agreement persisted across traffic densities and operating conditions, except for 6.5% mean absolute deviation at CBR 0.85.

  • Takeaways & Limitations

    The models accurately represent C-V2X Mode 4 communications across a wide range of transmission parameters and traffic densities.

  • Takeaways & Limitations

    C-V2X Mode 4 has unspecified standard parameter values requiring configuration analysis, and semi-persistent scheduling can lose efficiency for nonperiodic transmissions or underused reservations.

Abstract

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The C-V2X or LTE-V standard has been designed to support V2X (Vehicle to Everything) communications. The standard is an evolution of LTE, and it has been published by the 3GPP in Release 14. This new standard introduces the C-V2X or LTE-V Mode 4 that is specifically designed for V2V communications using the PC5 sidelink interface without any cellular infrastructure support. In Mode 4, vehicles autonomously select and manage their radio resources. Mode 4 is highly relevant since V2V safety applications cannot depend on the availability of infrastructure-based cellular coverage. This paper presents the first analytical models of the communication performance of C-V2X or LTE-V Mode 4. In particular, the paper presents analytical models for the average PDR (Packet Delivery Ratio) as a function of the distance between transmitter and receiver, and for the four different types of transmission errors that can be encountered in C-V2X Mode 4. The models are validated for a wide range of transmission parameters and traffic densities. To this aim, this study compares the results obtained with the analytical models to those obtained with a C-V2X Mode 4 simulator implemented over Veins.

I. INTRODUCTION

C-V2X Mode 4 enables infrastructure-free V2V communication through autonomous resource selection, but its analytical performance had not previously been modeled. This paper introduces models for PDR and four transmission-error types, using sensing-based SPS.

  • I. INTRODUCTION: Mode 4 lets vehicles autonomously select and manage radio resources without cellular infrastructure support.It uses the sensing-based Semi-Persistent Scheduling scheme defined in Release 14.
  • I. INTRODUCTION: Prior C-V2X Mode 4 studies relied on network simulations, while existing analytical models focused on infrastructure-managed Mode 3.The paper identifies this as the gap addressed by its analytical models.
  • I. INTRODUCTION: The paper presents analytical models for average PDR versus transmitter–receiver distance and four mutually exclusive transmission errors.The errors are half-duplex, below-threshold received power, propagation, and packet collisions.
  • B. Sensing-based Semi-Persistent Scheduling: Sensing-based SPS uses a Selection Window, excludes resources using received SCI and RSRP criteria, then selects the lowest-RSSI candidate resources.The candidate list contains 20% of resources identified in the Selection Window.
  • I. INTRODUCTION: The four modeled errors distinguish half-duplex reception failures, insufficient sensing power, propagation-related failures, and collisions.The propagation definition excludes half-duplex and sensing-threshold errors, while the listed error types are mutually exclusive.

IV. ANALYTICAL MODELS

The analytical framework models PDR from four mutually exclusive packet-loss mechanisms in a multi-lane highway scenario with periodic transmissions and autonomous Mode 4 resource selection.

  • IV. ANALYTICAL MODELS: The model considers vehicles separated by 1/β meters, transmitting λ packets per second on a shared 10MHz channel at power Pt.The transmitter and receiver are separated by distance dt,r.
  • IV. ANALYTICAL MODELS: Because the error types are exclusive, correct reception is defined as the absence of all four errors.The normalized PDR is expressed as 1 minus the four normalized error probabilities.
  • IV. ANALYTICAL MODELS: The framework quantifies half-duplex, sensing-threshold, propagation, and collision errors using separate variables and equation groups.Table I maps HD, SEN, PRO, and COL to their corresponding analytical sections.
  • IV. ANALYTICAL MODELS: The model tracks channel and resource-selection quantities including β, CBR, α, N, NA, and NC.α weights the influence of sensing-based Steps 2 and 3 in candidate-resource selection.

A. Half-duplex errors

The half-duplex model captures packet losses when a receiver transmits in the same sub-frame as the incoming packet. This loss is local and depends on packet frequency, not distance or channel occupancy.

  • A. Half-duplex errors: Half-duplex loss occurs when a receiving vehicle transmits its own packet in the same sub-frame.The radio is half-duplex, so simultaneous transmission prevents reception.
  • A. Half-duplex errors: Half-duplex loss does not depend on transmitter–receiver distance, the SPS scheme, or channel occupancy.It depends on the probability that two vehicles select the same sub-frame.
  • A. Half-duplex errors: The half-duplex error probability is δHD = λ/1000 for 1ms sub-frames.λ is the number of packets transmitted per vehicle per second.
  • A. Half-duplex errors: The effect is local: vehicles transmitting in other sub-frames can still receive the packet.

B. Errors due to a received signal power below the sensing power threshold

The sensing-threshold model estimates losses when received power falls below PSEN, combining distance-dependent pathloss with log-normal shadowing.

  • B. Errors due to a received signal power below the sensing power threshold: Received power is modeled as transmission power minus distance-dependent pathloss and shadowing.Pt, PL(dt,r), and Pr are expressed in dB; shadowing has a log-normal distribution with zero mean and variance σ.
  • B. Errors due to a received signal power below the sensing power threshold: A sensing-threshold error occurs when received signal power is below PSEN and the packet therefore cannot be decoded.This error is distinguished from half-duplex losses.
  • B. Errors due to a received signal power below the sensing power threshold: The sensing-threshold loss probability is obtained by integrating the received-power PDF below PSEN.The PDF is derived from the log-normal shadowing model.
  • B. Errors due to a received signal power below the sensing power threshold: The complementary quantity 1−δSEN is the Packet Sensing Ratio, generalized to compute PSR at any distance d.The expression uses the error function erf.

C. Error due to propagation

The propagation-error model derives packet-loss probability from the receiver’s SNR distribution and PHY-layer BLER, while excluding packets already counted as below the sensing threshold.

  • Propagation-error model: Propagation losses depend on PHY-layer receiver performance modeled through BLER look-up tables.The tables provide BLER as a function of SNR, packet size, MCS, scenario, and relative speed.
  • Propagation-error model: SNR is modeled as a random variable whose mean is determined by transmit power, path loss, and noise power.At a fixed transmitter–receiver distance, path loss is constant, so SNR follows the shadowing distribution shifted by Pt - PL - N0.
  • Probability calculation: The propagation-error probability integrates BLER over SNR values for which received power exceeds the sensing threshold.This restricts δPRO to packets not already classified under δSEN.
  • Probability calculation: The conditional SNR density is normalized by 1-δSEN so the resulting propagation-error probability remains between 0 and 1.The normalization removes packets whose received power is below PSEN.

D. Errors due to packet collisions

Packet-collision losses occur when a transmitting vehicle and an interferer use the same resource and the resulting interference prevents correct reception.

  • Collision conditions: A collision requires simultaneous use of the same sub-frame and sub-channel by the transmitter and an interfering vehicle.The interference must also be sufficient to prevent packet reception at the receiver.
  • Collision conditions: The collision probability depends on link-level performance, sensing-based SPS scheduling, scenario, and distances among transmitter, receiver, and interferer.These factors jointly determine whether resource overlap produces packet loss.
  • Analytical formulation: For each interferer, collision loss is modeled as the product of same-resource transmission probability and interference-exceedance probability.The overall collision probability is then computed from the individual interferer contributions.
  • Analytical formulation: Figure 2 summarizes the main steps used to calculate the packet-loss probability due to collisions.

D1. Probability pINT(dt,r,di,r) that interference is higher than threshold

The model separates interference strength from resource overlap: pINT captures whether an interferer exceeds the reception threshold, while pSIM captures simultaneous use of the same resource under sensing-based SPS.

  • Interference probability: Interference is modeled as additional noise, yielding an SINR distribution formed from received-signal and interference power distributions.The resulting SINR distribution is used with BLER look-up tables to estimate interference-related loss.
  • Resource overlap: pSIM represents the probability that vt and vi transmit simultaneously using the same sub-channel and sub-frame.Its calculation follows the sensing-based SPS resource-selection process.
  • Resource overlap: The resource-selection model distinguishes excluded, assignable, and candidate resources, with NC equal to 20% of N.NA counts resources remaining after Step 2, while NC counts resources available after Steps 2 and 3.
  • SPS operating regimes: Step 3 has limited effect at high channel load, whereas Step 2 has limited effect at low channel load.At intermediate loads, both steps are combined using a weighting factor α in pSIM = α·pSIM,Step2 + (1-α)·pSIM,Step3.
  • SPS operating regimes: The weighting factor α is derived as a function of CBR using simulation values and a linear approximation.α=1 when only Step 2 influences selection at high load, and α=0 when only Step 3 is needed at low load.
  • Step 3 adjustment: When only Step 3 is executed, previously excluded resources may be reintroduced by increasing the sensing threshold until the candidate set reaches 0.2·N.The model finds the minimum threshold increment needed to reduce exclusions below 0.8·N.

A. Framework and Simulation Environment

The analytical models are implemented in Matlab and validated against a Veins-based C-V2X Mode 4 simulator using realistic mobility, complete MAC behavior, and varied transmission settings.

  • Framework: The models are implemented in Matlab and compared against a C-V2X Mode 4 simulator developed over Veins.The simulator serves as the benchmark because the authors report no other open-source Mode 4 implementation or analytical models.
  • Simulation environment: The simulator combines OMNeT++ wireless-network simulation with SUMO vehicle mobility modeling.Vehicle mobility uses the Krauss car-following model in the highway scenario.
  • Simulation environment: The simulated protocol includes the complete C-V2X Mode 4 MAC, sensing-based SPS, and the Winner+ B1 propagation model.
  • Validation: The principal validation setting uses λ=10Hz, Pt=20dBm, QPSK, coding rate 0.7, 10 RBs per packet, and four sub-channels per sub-frame.Additional validation covers other power levels, packet frequencies, and QPSK with coding rate 0.5.
  • Validation: Validation compares analytical and simulated PDR and transmission errors using Mean Absolute Deviation.MAD expresses the average percentage difference between the analytical and simulation result vectors.

B. Validation

The analytical models closely match simulator results across transmission powers, traffic densities, packet frequencies, modulation and coding settings, and channel loads, with reduced accuracy at very high CBR. They also capture the distinct error mechanisms affecting C-V2X Mode 4 packet delivery.

  • PDR validation: The analytical PDR closely matches simulation across low and high traffic densities and corresponding channel loads.For β=0.1 veh/m, the estimated CBR is approximately 0.23; for β=0.3 veh/m, it is approximately 0.62.
  • PDR validation: The model remains consistent with simulation when transmission power increases from 20 dBm to 23 dBm.At 23 dBm, analytical CBR ranges from 0.27 to 0.69 across the reported traffic densities.
  • PDR validation: At λ=20 Hz and β=0.3 veh/m, the model shows a 6.5% mean absolute deviation under an analytical CBR of 0.85.The passage identifies this as a high-load condition that would compromise system stability and scalability and should be avoided through congestion control.
  • PDR validation: The models remain valid with QPSK coding rate 0.5 and two sub-channels per sub-frame across traffic densities producing CBR levels of 0.44, 0.74, and 0.86.This extends validation beyond the QPSK 0.7, four-sub-channel configuration.
  • Error validation: Collision-loss probability is accurately modeled across traffic densities, peaking around 350–400 m where hidden-node effects cause greater degradation.The analytical collision-error curves closely match simulation results.
  • Overall accuracy: Analytical PDR differs from simulation by less than 2.5% in all scenarios with CBR below 0.8, and often by less than 1%.The MAD analysis covers PDR and the four transmission-error types across transmission powers, traffic densities, packet frequencies, and sub-channel or MCS settings.

VI. CONCLUSIONS

The paper presents and validates analytical models for C-V2X Mode 4 communication performance across transmission parameters and traffic densities. The models closely match Veins-based simulation results while highlighting configuration boundaries for future work.

  • Contributions: The models represent average PDR as a function of transmitter–receiver distance and quantify four C-V2X Mode 4 transmission-error types.The four errors include half-duplex, sensing-threshold, propagation, and collision errors.
  • Validation: Validation covers transmission power, packet transmission frequency, MCS, and traffic densities using a simulator implemented over Veins.
  • Validation: Mean absolute deviation is generally below 2.5% between analytical-model and simulation results.
  • Implications: The models provide a tool for evaluating and gaining insights into C-V2X Mode 4 performance across a wide range of parameters.
  • Future work: C-V2X Mode 4 still requires further analysis because some operational and configuration parameters lack concrete 3GPP values.ETSI is defining default configurations, and optimum Mode 4 configuration needs detailed study before future deployment.
  • Future work: Semi-persistent scheduling can lose efficiency for non-periodic transmissions when vehicles frequently reselect resources or underuse reserved resources.

APPENDIX A

The appendix derives the PDR expression by substituting normalized error probabilities and factoring terms associated with the modeled transmission errors. The derivation connects the expanded expression back to the main PDR equation.

  • PDR derivation: Equation (5) expresses PDR using the different error probabilities, while Equation (6) uses normalized probabilities whose sum is at most 1.
  • PDR derivation: Substituting the normalized error-probability expressions expands the PDR formulation into terms associated with the modeled error components.
  • Algebraic simplification: The appendix factors out (1-δSEN), (1-δCOL), and (1-δHD) in successive algebraic steps.
  • PDR derivation: The resulting factored expression is identified as equivalent to Equation (5).
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