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Delay and Doppler Spreads of Non-Stationary Vehicular Channels for Safety Relevant Scenarios

Laura Bernadó, Thomas Zemen, Fredrik Tufvesson, Andreas F. Molisch, Christoph F. Mecklenbräuker

arXiv:1305.3376v1cs.NI

TL;DR

Vehicular channels are non-stationary because propagation conditions change rapidly, motivating time-frequency-local characterization for safety-relevant scenarios. The paper estimates LSFs from DRIVEWAY’09 measurements, derives time-varying PDP, DSD, and RMS spreads, and finds bi-modal distributions, with high delay spreads linked to rich scattering and high Doppler spreads to drive-by scenarios.

  • Problem

    Safety-relevant vehicular scenarios require characterization beyond conventional stationary channel assumptions and generic cellular-based scenario descriptions.

  • Method

    The paper estimates time-frequency-varying LSFs from DRIVEWAY’09 measurements, derives PDP and DSD projections, and calculates RMS delay and Doppler spreads.

  • Results

    The RMS delay and Doppler spread distributions are adequately modeled by a bi-modal Gaussian mixture, with high delay spreads in rich-scattering situations and high Doppler spreads in drive-by scenarios.

  • Takeaways & Limitations

    High RMS delay spreads are associated with large reflecting structures or strong LOS obstruction, while high RMS Doppler spreads occur when late Doppler components are significant.

Abstract

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Vehicular communication channels are characterized by a non-stationary time- and frequency-selective fading process due to rapid changes in the environment. The non-stationary fading process can be characterized by assuming local stationarity for a region with finite extent in time and frequency. For this finite region the wide-sense stationarity and uncorrelated-scattering (WSSUS) assumption holds approximately and we are able to calculate a time and frequency dependent local scattering function (LSF). In this paper, we estimate the LSF from a large set of measurements collected in the DRIVEWAY'09 measurement campaign, which focuses on scenarios for intelligent transportation systems. We then obtain the time-frequency-varying power delay profile (PDP) and the time-frequency-varying Doppler power spectral density (DSD) from the LSF. Based on the PDP and the DSD, we analyze the time-frequency-varying root mean square (RMS) delay spread and the RMS Doppler spread. We show that the distribution of these channel parameters follows a bi-modal Gaussian mixture distribution. High RMS delay spread values are observed in situations with rich scattering, while high RMS Doppler spreads are obtained in drive-by scenarios.

I. INTRODUCTION

Vehicular channels change rapidly because both vehicles and scattering environments are mobile, making realistic, safety-relevant channel characterization necessary. This paper addresses that need with time-frequency-varying spread measures and a bi-modal statistical model.

  • Realistic channel models require measurements that extract fading parameters for evaluating vehicular communication systems.
  • Rapidly changing propagation conditions make vehicular channels non-stationary and unlike cellular wireless channels.Both transmitter and receiver are mobile, while the scattering environment can also change rapidly.
  • Existing literature does not analyze the time-variability of statistical properties in non-stationary vehicular fading channels.Prior work commonly uses cellular-style highway, rural, suburban, and urban scenario descriptions that are not well matched to safety-relevant ITS scenarios.
  • Local stationarity over finite time-frequency regions enables approximate WSSUS modeling and calculation of a time- and frequency-dependent LSF.
  • The paper characterizes RMS delay and Doppler spreads for safety-related scenarios and models their distributions with a bi-modal Gaussian mixture.These parameters are obtained from the time-frequency-varying second central moments in the delay and Doppler domains.

Organization of the Paper:

The paper analyzes DRIVEWAY’09 measurements collected with a multi-antenna vehicle-to-vehicle channel sounder. Its setup measures 16 links over 240 MHz at 5.6 GHz while incorporating antenna and vehicle effects into the channel.

  • DRIVEWAY’09 uses passenger vehicles carrying the channel sounder and batteries in the trunks of the TX and RX vehicles.
  • The RUSK-Lund sounder uses switched multi-carrier sounding to obtain time-variant frequency-domain channel estimates.Each vehicle uses a four-element roof-top antenna array connected through a high-speed switch.
  • The antenna arrays contain four circular patch antennas separated by λ/2 and mounted perpendicular to the driving direction for directional analysis.
  • Antenna and metallic vehicle-hull effects are treated as part of the measured channel because directionally separating them is infeasible for rapidly non-stationary channels.
  • The measurements comprise 16 links at a 5.6 GHz carrier frequency, close to the 5.9 GHz ITS band.
  • The setup measures 240 MHz bandwidth with 307.2 µs snapshot repetition and resolves Doppler shifts up to 1.6 kHz.The minimum delay resolution is 4.17 ns.

III. SAFETY-RELATED MEASUREMENT SCENARIOS

DRIVEWAY’09 organizes measurements around safety-related ITS scenarios rather than generic cellular environment categories. The campaign covers crossings, highway obstruction, merging, congestion, tunnels, and bridges with varied mobility and scattering conditions.

  • The campaign defines application-specific scenarios based on the ETSI basic ITS application set.
  • Road-crossing measurements cover rural, suburban, and urban environments with perpendicular vehicle approaches at 10–50 km/h.Four configurations vary traffic and urban lane structure, affecting line-of-sight availability.
  • Highway LOS-obstruction measurements use vehicles traveling in the same direction at 70–110 km/h while large trucks intermittently block the direct path.
  • The campaign also includes rural merging lanes and traffic congestion involving vehicles traveling together or approaching stopped traffic.
  • Tunnel and bridge scenarios measure same-direction vehicles at highway speeds, including a bridge with large, regularly spaced metallic structures.Bridge measurements used vehicle separations of about 150 m and 3–15 runs per scenario.
  • Two illustrative examples are urban single-lane street crossing and general highway LOS obstruction.

B. Locally Defined Power Spectral Density

The paper estimates local scattering functions from sampled time-varying frequency responses by applying orthogonal two-dimensional tapers within finite stationarity regions. The resulting LSF supports time-varying delay and Doppler analysis.

  • Fast-changing vehicular propagation is approximated as locally stationary within finite time-frequency regions.
  • Orthogonal windowed spectra provide multiple spectral estimates from one measurement set, which are averaged into the total estimated power spectrum.
  • The multitaper estimator uses I orthogonal time-domain tapers and J orthogonal frequency-domain tapers, producing IJ two-dimensional tapering functions.
  • Consecutive M × N sample regions are processed, with each LSF indexed at the center of its time-frequency stationarity region.
  • The delay index n and Doppler index p identify the LSF coordinates in the delay-Doppler domain.
  • The selected stationarity region is M = 128 and N = 128, corresponding to 39.32 ms in time and 39.95 MHz in frequency.The earlier minimum stationarity dimensions were 40 ms and 40 MHz.

2) Power Delay Profile and Doppler Power Spectral Density:

The paper derives time-varying PDPs and DSDs from local scattering functions and illustrates how propagation scenarios shape their observed components.

  • The PDP is the LSF projection onto delay, while the DSD is its projection onto Doppler.
  • Road crossing - urban single lane: For the urban road crossing, weak signal components appear before the vehicles reach the crossing because reflections sustain communication without line of sight.
  • Road crossing - urban single lane: Between 7 and 10 seconds in the urban crossing, strong LOS and multipath components coexist in the more open area.
  • General LOS obstruction - highway: In the highway convoy, a truck initially obstructs LOS, then changes lanes, while same- and opposite-direction vehicles create visible multipath components.
  • General LOS obstruction - highway: The strongest highway component remains at 0 Hz Doppler and constant delay because the relative TX-RX speed does not change.

V. TIME-FREQUENCY-VARYING RMS DELAY SPREAD AND RMS DOPPLER SPREAD

Because vehicular channels are non-stationary but locally stationary over finite time-frequency regions, their RMS delay and Doppler spreads should be characterized as time-frequency-varying parameters.

  • Vehicular channels have rapidly changing fading, so local stationarity within finite regions motivates time-frequency-varying RMS delay and Doppler spreads.

A. Definition

The paper defines RMS delay and Doppler spreads from estimated PDPs and DSDs, while noting that delay spread varies across time and frequency.

  • The second central moments of the PDP and DSD describe the fading process and relate directly to coherence bandwidth and coherence time.
  • The time-frequency-varying RMS delay spread and RMS Doppler spread are calculated from the estimated PDP and DSD, respectively.
  • Noise-power thresholding removes components that could be mistaken for multipath components, using a threshold 5 dB above the noise floor.The threshold is applied separately for each stationarity region and averages around −85 dBm.
  • Figure 3 shows notable time and frequency variability in RMS delay spread for a highway convoy with LOS obstruction.
  • The subsequent analysis selects the 5480 −5520 MHz stationarity frequency region and focuses on time variability.

B. Empirical Results

Time-varying PDPs, DSDs, and RMS spreads reveal distinct channel behavior across highway and street-crossing measurements. Across the dataset, a bi-modal Gaussian mixture provides the statistical characterization of these parameters.

  • Empirical channel behavior: Urban street-crossing measurements show stronger diffuse components, late reflections, and more pronounced channel time variability than the urban scenario examined.These features are visible in the time-varying PDP and DSD analysis.
  • Empirical channel behavior: The RMS delay spread oscillates around 50 ns in the obstructed-LOS highway scenario and decreases when late MPCs become insignificant.This decrease occurs between 1 and 4 s in the illustrative measurement.
  • Empirical channel behavior: Street-crossing RMS delay spread increases toward the measurement end when many MPCs are present, peaking just before 5 s because of a strong late contribution.The peak corresponds to a late component observed in the PDP.
  • Empirical channel behavior: The obstructed-LOS convoy has an approximately constant RMS Doppler spread of 33 Hz, with increases when strong new MPCs appear.The convoy vehicles travel in the same direction at approximately constant speed, producing a constant Doppler component at 0 Hz.
  • Statistical characterization: The analysis covers every measurement run, scenario, and six 40 MHz stationarity regions spanning the 240 MHz measurement bandwidth.The resulting empirical distributions are fitted using a bi-modal Gaussian mixture and compared with empirical CDFs.
  • Statistical characterization: A goodness-of-fit value GoF ≤ 0.11 indicates a good fit under the reported Kolmogorov-Smirnov criterion.The test compares the empirical and analytical CDFs using their maximum absolute difference.
  • Statistical characterization: The Gaussian-mixture means represent LOS and non-LOS channel-parameter means, while larger standard deviations indicate greater non-stationarity.Mixture weights indicate the relative frequency of the two situations; values near 0 or 1 imply low transition probability.

B. Discussion of Statistical Results

Statistical conclusions are based on mean values across processed measurement runs, while extreme maxima are reported separately because individual instants can depart from the mean trends.

  • Interpretation and scope: The reported scenario trends describe mean behavior, but individual RMS delay and Doppler values may depart from those trends at particular times.Extreme maxima are therefore displayed separately because they are critical for communication-system assessment.
  • RMS delay spread: Mean RMS delay spreads are around 30 ns in highway traffic-congestion environments, where nearby vehicles are relatively weak scatterers.More relevant multipath components arise from large scattering objects such as trucks or metallic structures.

1) RMS delay spread

RMS delay spread is higher when large reflecting objects or nearby metallic structures enrich multipath, while rural merging-lane conditions produce small values. The fitted parameter distributions require care because the bi-modal Gaussian mixture is truncated at observed bounds.

  • In-tunnel measurements yield the highest mean RMS delay spreads, attributed to nearby metallic ventilation structures.
  • Street-crossing situations show slightly higher mean RMS delay spreads, with values between 40 and 50 ns.
  • Rural merging-lane conditions produce small RMS delay spreads because few nearby scattering objects and little traffic are present.
  • Interpretation of the bi-modal Gaussian mixture requires care because it is truncated at zero and at the maximum observed spread.
  • General LOS-obstruction measurements show RMS delay spreads mainly determined by large objects beside the TX-RX link, with maxima below 1 µs.The reported maximum values range from 200 to 900 ns.

2) RMS Doppler spread

RMS Doppler spread is elevated in drive-by and reflection-rich scenarios but remains low when vehicles travel together at the same speed and direction. Reported maxima are generally hundreds of hertz, reaching 933.70 Hz.

  • RMS Doppler spreads are generally larger in street-crossing scenarios because the main Doppler component changes rapidly from positive to negative.
  • In-tunnel and on-bridge scenarios also show high RMS Doppler spreads because strong late multipath components reflect from metallic surfaces.
  • Same-direction measurements at equal vehicle speeds maintain low, nearly constant RMS Doppler spreads when multipath components are weak.The most relevant Doppler component remains around 0 Hz throughout these runs.
  • Maximum RMS Doppler spread values are mostly between 400 and 600 Hz, with a maximum of 933.70 Hz.
  • The study derives RMS Doppler spread from the time-frequency-varying DSD obtained from measured LSFs and fits its empirical distribution with a bi-modal Gaussian model.
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