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Integrated Sensing and Communications for V2I Networks: Dynamic Predictive Beamforming for Extended Vehicle Targets

Zhen Du, Fan Liu, Weijie Yuan, Christos Masouros, Zenghui Zhang, Shuqiang Xia, Giuseppe Caire

arXiv:2111.10152v2eess.SP

TL;DR

The paper addresses high-data-traffic and localization challenges in V2I networks by proposing sensing-assisted predictive beam tracking and an optimized two-stage time allocation strategy. The proposed schemes provide gains in sensing and communications and outperform state-of-the-art beam tracking approaches.

  • Problem

    DSRC cannot meet high data traffic demands, while existing localization services offer only 10m accuracy and 1s latency.

  • Method

    The paper proposes sensing-assisted predictive beam tracking with EKF beam prediction and convex-optimization-based time allocation between two transmission stages.

  • Results

    The proposed schemes provide significant gains in sensing and communications and show remarkable superiority over state-of-the-art beam tracking approaches.

  • Takeaways & Limitations

    ISAC-based beam tracking for extended target vehicles can improve both sensing and communication performance within the evaluated setting.

Abstract

from arXiv · show

We investigate sensing-assisted predictive beamforming schemes for vehicle-to-infrastructure (V2I) communication by exploiting the integrated sensing and communication (ISAC) functionalities at the roadside unit (RSU). The RSU deploys a massive multi-input-multi-output (mMIMO) array and operates at millimeter wave (mmWave) frequencies. The pencil-sharp mMIMO beams and fine range resolution achieved at mmWave, implicates that the point target assumption is impractical in such V2I networks, as the volume and shape of the vehicles become essential for beamforming. Simply pointing a beam to the vehicle may result in the communication receiver (CR) never lying in the beam, even when the vehicle's trajectory is accurately tracked. To tackle this problem, we consider the extended vehicle target with two novel beam tracking schemes. For the first scheme, the beamwidth is adjusted in real-time to cover the entire vehicle, followed by an extended Kalman filtering (EKF) algorithm to predict and track the position of CR according to the resolved high-resolution scatterers. An upgraded scheme is further proposed by splitting each transmission block into two stages. The first stage is exploited for ISAC transmission, where a wide beam is adopted for both communication and sensing. Based on the sensed results at the first stage, the second stage is dedicated to communication by adopting a pencil-sharp beam, yielding a significant improvement of the achievable rate. We further reveal the inherent tradeoff between the two stages in terms of their durations, and develop an optimal time allocation strategy that maximizes the average achievable rate. Finally, numerical results are provided to verify the superiorities of proposed schemes over the state-of-the-art methods.

I. INTRODUCTION

The paper motivates sensing-assisted predictive beam tracking for extended vehicle targets in mmWave V2I networks, where point-target models can misalign beams with the communication receiver. It proposes dynamic-beam and alternating wide/narrow-beam schemes to improve reliable alignment and achievable rate.

  • Motivation: mmWave mMIMO improves beam, angular, communication-rate, and ranging resolution, supporting integrated sensing and communication in V2X networks.The setting also benefits from sparse mmWave channels and fewer non-line-of-sight components for vehicle localization.
  • Problem: Existing sensing-assisted methods model vehicles as point-like targets, although practical vehicles extend across both range and angle.This mismatch is important because the communication receiver’s precise position within the vehicle matters for beam tracking.
  • Problem: A narrow beam can miss the communication receiver despite accurate vehicle tracking, causing beam misalignment and link outages.A 128-antenna array can produce a beamwidth on the order of 1°–2°, making complete vehicle illumination difficult, especially nearby.
  • Problem: High-resolution sensing can distribute the vehicle across multiple range cells, while point-target modeling may select the wrong cell and produce tracking errors.For B = 500MHz, the stated range resolution is 30cm.
  • Proposed schemes: ISAC-DB infers the communication receiver from resolvable scatterers and adjusts beamwidth in real time using predicted receiver distance and angle.A tailored EKF supports beam alignment while the beam covers the entire extended vehicle.
  • Proposed schemes: ISAC-AB divides each transmission block into ISAC and communication stages, using wide and pencil-sharp beams respectively, with optimized time allocation for average rate.Numerical results report effective alignment, more stable and reliable transmission, and excellent achievable rate over conventional methods.

II. SYSTEM MODELING

The system models a full-duplex mmWave RSU with a variable-size uniform linear array serving an extended vehicle target on a parallel straight road. Vehicle motion is represented by angle, distance, and velocity over discretized tracking epochs.

  • System setting: The RSU supports simultaneous sensing and downlink data transmission using a mmWave mMIMO uniform linear array.The array has N_t,n transmit and N_r receive antennas, with N_t,n varying across epochs because of dynamic beamwidth.
  • Target and geometry: The vehicle moves along a straight road parallel to the array and is modeled as an extended target with a single-antenna communication receiver.Resolvable scatterers are uniformly distributed within the vehicle geometry.
  • Position inference: Localizing the scatterers enables recovery of the vehicle centroid and, using known relative receiver coordinates, inference of the communication receiver position.This geometric relation supplies the basis for extended-target beam tracking.
  • Motion model: The receiver’s angle, distance, and velocity relative to the RSU array are denoted by φ(t), d(t), and v(t), then sampled at discrete epochs.The tracking interval T is divided into time slots of duration ΔT.
  • Sampling constraint: The stop-go radar model requires v_nΔT ≤ Δr = c/(2B), ensuring no range migration within a tracking interval.With 500MHz bandwidth and 20m/s vehicle speed, the example parameterizes ΔT < 0.015s.

A. Radar Signal Model

The radar model represents each vehicle as K resolved scatterers and uses matched-filtering measurements of their delay, Doppler, and angle to localize and track the vehicle and predict the CR angle. Dynamic beamforming adapts the transmit array size and beam vector to the predicted CR angle.

  • Signal and array model: At each epoch, the RSU receives echoes from the vehicle’s K resolved scatterers using transmit and receive ULA steering vectors.The model includes transmitted ISAC signals, additive Gaussian noise, scatterer Doppler, reflection coefficient, and round-trip delay.
  • Signal and array model: The transmit steering vector and beamforming vector are dynamic because the adjustable transmit-array size depends on the resolved scatterers and predicted CR angle.The beamforming vector is designed using the predicted CR angle from the previous measurement.
  • Vehicle state estimation: The model estimates and predicts the CR angle rather than only the vehicle centroid angle, using the CR’s known offset from the centroid.The offset is assumed known from initial beam training, and ISAC-DB uses prediction while ISAC-AB uses both estimation and prediction.
  • Scatterer resolution: Matched-filtering resolves scatterers in delay and Doppler, with high range resolution associated with a narrow time-delay mainlobe.The matched-filtering process also provides a gain G that improves sensing receive SNR.
  • Measurement uncertainty: The separation analysis assumes negligible matched-filter sidelobes; their effect on perfect scatterer separation is not considered.This assumption limits the direct applicability of the ideal separation result.
  • Vehicle state estimation: The measured scatterer delays and angles localize the vehicle centroid, while the Doppler measurements are used to estimate its velocity.The resulting centroid and velocity estimates support the radar measurement model used for CR-angle prediction.
  • Measurement uncertainty: Measurement noises are modeled explicitly, but their variances are unknown in practice, so approximate variance counterparts are developed.The derivations for these approximations are provided in the Appendix.

C. Communication Receiver Model

The communication receiver model uses the ISAC signal for simultaneous vehicle tracking and communication, with the achievable rate depending on the CR’s predicted-angle beamforming gain and line-of-sight path loss. The rate expression is an upper bound on the practical communication rate.

  • Receiver signal model: The same ISAC signal is used for both vehicle tracking and communication throughout the transmission block.
  • Channel model: The line-of-sight channel coefficient is determined by distance-based path loss, so estimating the coefficient is equivalent to estimating the CR distance.The reference path loss is measured at d0 = 1m.
  • Beamforming and rate: The achievable rate is formulated from the communication receiver’s SNR and incorporates the transmission-block beamforming and channel model.
  • Beamforming and rate: The beamforming gain has modulus 1 under perfect predicted-angle matching and is less than 1 otherwise.Thus, CR-angle prediction accuracy directly affects the communication SNR.
  • Beamforming and rate: The reported achievable rate is an upper bound on the practical communication rate, while synchronization can be achieved with pilots at the frame beginning.

III. ISAC-BASED PREDICTIVE BEAM TRACKING SCHEMES FOR V2I LINKING

The ISAC-DB scheme dynamically adjusts beamwidth to cover the extended vehicle and uses EKF-based prediction to track the communication receiver from resolved scatterers.

  • ISAC-DB Method: ISAC-DB adjusts beamwidth in real time according to the vehicle trajectory so the beam covers the vehicle and its resolved scatterers.This supports refining the vehicle centroid and tracking the CR.
  • ISAC-DB Method: The transmit antenna number is updated from predicted distance and angle while remaining bounded by the system maximum Nt,max.The cited implementation example gives Nt,max = 128.
  • ISAC-DB Method: The scheme infers the CR coordinates from measured state vectors associated with multiple resolvable vehicle scatterers.
  • ISAC-DB Method: Because the state evolution is nonlinear, ISAC-DB uses an EKF that linearizes the model and updates state predictions with measurements.The tracked state comprises the CR angle, distance, and velocity.
  • ISAC-DB Method: The EKF procedure is initialized through conventional beam training with limited pilots at the beginning of the frame.

B. ISAC-AB Method

ISAC-AB splits each transmission block between wide-beam ISAC and narrow-beam communication, then optimizes the split to balance tracking reliability and rate.

  • ISAC-AB Method: ISAC-AB divides each block into wide-beam ISAC transmission followed by narrow-beam communication.The wide beam supports sensing and communication, while the narrow beam is used for the communication stage.
  • ISAC-AB Method: The time-splitting factor ρ is optimized to maximize the average achievable rate in each block.Only the first part is used for sensing, so ρ controls the sensing-stage duration.
  • ISAC-AB Method: A smaller ρ gives the narrow beam more time and higher array gain, but excessive reduction can cause tracking failure and narrow-beam misalignment.
  • ISAC-AB Method: The proposed wide beam varies to cover the vehicle, whereas the narrow beam is aligned using the angle estimated during the wide-beam stage.
  • ISAC-AB Method: The relaxed optimization solution is suboptimal because the original problem depends on quantities unavailable before optimization.
  • ISAC-AB Method: The optimization model is convex, and its optimum ρopt can be obtained from the stationary-point condition or a grid search.The objective curves are described as concave over 0 < ρ ≤ 1.

IV. SIMULATIONS

The simulations evaluate the proposed V2I beam-tracking schemes using resolved vehicle scatterers, specified channel parameters, and averages over 500 runs.

  • IV. SIMULATIONS: The simulation section evaluates the proposed V2I beam-tracking schemes using parameters from Table I.
  • IV. SIMULATIONS: The modeled vehicle contains resolved scatterers uniformly distributed over its spatial geometry.
  • IV. SIMULATIONS: Scatterer RCS values are generated from a zero-mean, unit-variance complex Gaussian distribution with slow fluctuations.
  • IV. SIMULATIONS: The vehicle moves along the negative x-axis, and all reported results are averaged over 500 runs.

A. Performance Evaluation of ISAC-DB Method

ISAC-DB achieves accurate CR tracking, but its achievable rate can decline as the vehicle approaches the RSU because dynamic coverage reduces the antenna count and array gain.

  • Performance Evaluation: The achievable rate increases with transmit SNR, while approximated variances have only a tiny effect relative to real variances.This supports the effectiveness of the variance approximations used by ISAC-DB.
  • Performance Evaluation: The achievable rate deteriorates as the vehicle approaches the RSU because the receive SNR reduces.
  • Performance Evaluation: As the vehicle approaches the RSU, fewer transmit antennas are needed to cover it, and the resulting power attenuation dominates the approaching-range gain.
  • Performance Evaluation: When the vehicle drives away near t = 8s, the antenna count reaches the system limit Nt,max = 128.
  • Performance Evaluation: Predicted and real CR trajectories generally coincide well, although prediction error increases near the RSU as array gain declines.
  • Performance Evaluation: The angle RMSE increases near the RSU, distance RMSE does not show the same pattern, and velocity RMSE has a peak caused by small measured radial velocity.
  • Performance Evaluation: Overall, the prediction procedure exhibits high accuracy, and simulations verify the superiority of the proposed schemes over state-of-the-art methods.

B. Performance Evaluation of ISAC-AB Method

The ISAC-AB evaluation examines optimized time allocation, variance approximations, and achievable-rate behavior under vehicle motion. Approximated variances closely match measured distributions and cause only slight rate loss, while approach-dependent beam allocation improves communication performance.

  • Time allocation: ISAC-AB allocates longer duration to prediction when the vehicle approaches the RSU because the dynamic beam has smaller array gain.The optimized allocation is obtained by solving (40).
  • Time allocation: ρopt ≈1 near t = 8s because the antenna number reaches Nt,max = 128, making both transmission parts use the same antenna number.The matched-filtering gain cannot increase further, producing small fluctuations near this epoch.
  • Achievable rate: ISAC-AB significantly outperforms ISAC-DB because its rate is principally contributed by the second-stage narrow beam with high array gain.ISAC-DB degrades near the RSU because of array-gain loss, whereas ISAC-AB overcomes this dilemma through its second part.
  • Variance approximation: Gaussian fittings using approximated variances well match angle and distance histograms, supporting the Gaussian assumptions and variance approximations.Angle estimation exhibits spikes near t = 3s because scatterer angles change rapidly, but these spikes do not seriously affect achievable rate.
  • Variance approximation: Approximation errors produce slight achievable-rate loss relative to known variances, while the optimized objective with approximated variances can exceed that with true variances.The latter occurs when the estimated angle is slightly smaller than the true value.

C. Performance Comparison Among the Proposed Schemes and State-of-The-Art Methods

The proposed ISAC-AB and ISAC-DB schemes are compared with ABP and EKF-Point Target across achievable rate, tracking error, and outage behavior. ISAC-AB is strongest in high-mobility conditions, whereas ABP can lead when angular variation remains within its search range.

  • Achievable-rate comparison: ISAC-AB achieves better performance than EKF-Point Target but is inferior to ABP during t ∈[0s, 2.6s].ABP uses a fixed 128-antenna narrow beam with the highest array gain, provided tracking succeeds.
  • Achievable-rate comparison: When the vehicle approaches the RSU, ABP tracking fails because angular variation becomes too large for its searching range.The resulting lost trajectory causes beam-tracking failure.
  • Achievable-rate comparison: EKF-Point Target is inferior to ISAC-AB because a narrow beam aligned to a tracked scatterer may not simultaneously cover the CR.This beam misalignment becomes more likely as the extended vehicle approaches the RSU.
  • High-mobility tracking: ISAC-AB, ISAC-DB, and ABP have worse RMSE tracking results as velocity increases because vehicle movement within each epoch interval becomes nonnegligible.ABP is especially sensitive to velocity and rapidly breaks down above 12.875m/s.
  • Velocity effects: At v = 20m/s, ISAC-AB achieves higher rates than ISAC-DB, ABP, and EKF-Point Target, whereas at v = 10m/s, ABP outperforms the other methods.At lower mobility, ABP benefits from angular variation remaining within its search range and maintains its narrow beam throughout each block.
  • Outage performance: ISAC-AB outperforms the other methods in outage-probability performance under high-mobility scenarios.The proposed methods and ABP generally achieve better communication transmission at lower velocity, while ABP remains velocity-sensitive.

V. CONCLUSION

The conclusion presents sensing-assisted mMIMO beam tracking for extended vehicle targets through variable beamwidth EKF prediction and optimized beam tracking. Numerical results verify the feasibility, effectiveness, and state-of-the-art superiority of the proposed optimization scheme.

  • V. CONCLUSION: The paper proposes sensing-assisted mMIMO beam tracking schemes specifically for extended target vehicles.The schemes exploit ISAC to obtain gains in both sensing and communications.
  • V. CONCLUSION: The proposed EKF beam prediction approaches exploit varying beamwidths to focus beam tracking on the CR.This design follows from the extended-target modeling used in the paper.
  • V. CONCLUSION: Numerical results verify the feasibility and effectiveness of the proposed optimization scheme, with remarkable superiority over state-of-the-art beam tracking approaches.The conclusion reports these findings without specifying a single aggregate metric.

APPENDIX

The appendix derives approximations for angle and distance measurement variances using first-order Taylor expansions. It also notes the limitations of the approximation and reports little beam-tracking impact from a coarse approximation.

  • APPENDIX: The appendix identifies intractable variance expressions and addresses them with first-order Taylor expansion around the estimated scatterer state.The state vector contains scatterer angles and distances, and the expansion uses the corresponding Jacobian.
  • APPENDIX: The resulting derivations provide approximations for the CR's angle and distance variances from the transformed scatterer measurements.The distance derivation uses a Jacobian analogous to the angle-variance derivation.
  • APPENDIX: The Gaussian approximation relies on Gaussian variables and independence among the elements of the scatterer-state vector.These assumptions are stated for the variables and elements used in the approximation.
  • APPENDIX: The first-order Taylor approximation cannot be conducted in one case because it assumes known θn.This marks a scope boundary of the variance-approximation derivation.
  • APPENDIX: The coarse approximation is acceptable for beam tracking because its variance component has little impact on performance.The appendix therefore permits replacing the more detailed approximation with a coarser form.
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