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Radar-assisted Predictive Beamforming for Vehicular Links: Communication Served by Sensing

Fan Liu, Weijie Yuan, Christos Masouros, Jinhong Yuan

arXiv:2001.09306v1eess.SP

TL;DR

The paper addresses vehicular V2I beam tracking that must support communication and sensing without the overhead of communication-only feedback. It uses DFRC downlink echoes with an EKF to track and predict vehicle kinematics, and a power allocation scheme for multiple vehicles. The reported results show improved tracking over feedback-based beam tracking and a sensing–communication performance trade-off under the proposed allocation.

  • Problem

    Vehicular V2I systems need low-latency communication and accurate localization, while conventional beam tracking relies on pilots and feedback that create overhead.

  • Method

    The paper combines DFRC downlink signaling, EKF tracking and prediction of vehicle kinematic parameters, and optimization-based power allocation for multiple vehicles.

  • Results

    The DFRC-based beam-tracking approach significantly outperforms communication-only feedback-based tracking, while the power allocation method provides a favorable sensing–communication trade-off.

  • Takeaways & Limitations

    RSU radar functionality can replace frequent beam-tracking feedback, while power allocation can improve sensing subject to a downlink sum-rate constraint.

Abstract

from arXiv · show

In vehicular networks of the future, sensing and communication functionalities will be intertwined. In this paper, we investigate a radar-assisted predictive beamforming design for vehicle-to-infrastructure (V2I) communication by exploiting the dual-functional radar-communication (DFRC) technique. Aiming for realizing joint sensing and communication functionalities at road side units (RSUs), we present a novel extended Kalman filtering (EKF) framework to track and predict kinematic parameters of each vehicle. By exploiting the radar functionality of the RSU we show that the communication beam tracking overheads can be drastically reduced. To improve the sensing accuracy while guaranteeing the downlink communication sum-rate, we further propose a power allocation scheme for multiple vehicles. Numerical results have shown that the proposed DFRC based beam tracking approach significantly outperforms the communication-only feedback based technique in the tracking performance. Furthermore, the designed power allocation method is able to achieve a favorable performance trade-off between sensing and communication.

I. INTRODUCTION

The paper addresses low-latency, high-rate vehicular communication and accurate localization by integrating sensing and communication at an RSU. It develops DFRC-based predictive beamforming with EKF tracking and power allocation to reduce beam-tracking overhead while balancing sensing and communication.

  • Motivation: V2X requires low-latency Gbps transmission alongside robust obstacle detection and centimeter-scale localization.
  • Motivation: mmWave mMIMO jointly supports high data rates, improved range resolution, and narrow beams with enhanced angular resolution.
  • Research gap: Communication-only mmWave beam tracking typically sends pilots, estimates angles, and feeds them back, while high mobility also requires beam prediction.
  • Proposed framework: The proposed DFRC framework uses downlink echoes for vehicle tracking and localization, eliminating downlink pilots and removing the beam-tracking feedback loop.
  • Proposed framework: An EKF tracks and predicts each vehicle’s angle, distance, and velocity, using angle information for beamforming and angle plus distance for localization.
  • Proposed framework: The multiple-vehicle power allocation scheme improves sensing while guaranteeing a downlink sum-rate, targeting a favorable sensing–communication trade-off.

B. Signal Model

The signal model describes DFRC downlink streams, radar echoes, and communication reception for a mmWave mMIMO RSU serving vehicles. Narrow beams separate vehicles, while matched filtering supplies angle, distance, and velocity measurements for tracking and communication beamforming.

  • Radar signal model: The RSU transmits K downlink DFRC streams through a beamforming matrix whose columns target one-step predicted vehicle angles.The resulting K beams point toward predicted directions for vehicle tracking.
  • Radar signal model: The radar echo model includes transmit power, array gain, noise, reflection coefficient, Doppler frequency, and time delay for each vehicle.The vehicle RCS is assumed constant during the observation period, corresponding to a Swerling I target.
  • Radar measurement model: Massive-MIMO steering vectors are asymptotically orthogonal, so reflected echoes from different vehicles do not interfere and can be processed individually.This follows from the narrow beams generated by the RSU array.
  • Radar measurement model: Matched filtering estimates delay and Doppler, after which the compensated echo yields measurement models for vehicle angle and reflection coefficient.The matched-filtering gain contributes to the measurement SNR.
  • Radar measurement model: Distance and velocity measurements are obtained from delay and Doppler, with Doppler determined by radial velocity vk,n cos θk,n.Measurement-noise variances are inversely proportional to the receive SNR.
  • Communication model: Each vehicle receives a DFRC stream using a receive beamformer, and inter-vehicle interference vanishes because of the narrow mMIMO beams.The receive beamformer uses two-step predicted angles because one-step predictions would be outdated at the vehicle.

C. State Evolution Model

The vehicle state evolves through nonlinear kinematic relationships, which are approximated over short intervals to obtain a tractable model. The resulting state evolution includes Gaussian approximation and systematic-error noises, with simulations indicating negligible approximation error under the tested conditions.

  • The tracked vehicle state comprises angle, distance, velocity, and reflection coefficient parameters.
  • Short-interval motion permits approximating the nonlinear distance and angle evolution because vehicle displacement is small relative to the RSU distance.At 15 m/s over 10 ms, the displacement is 0.15 m, negligible relative to distances of tens or hundreds of meters.
  • The angle approximation uses sin ∆θ ≈∆θ, while the distance approximation neglects terms involving the squared displacement.
  • The state evolution model includes zero-mean Gaussian noises for angle, distance, velocity, and reflection coefficient.These noises represent approximation and systematic errors rather than measurement SNR.
  • With v = 54 km/h, ∆T = 100 ms, and ∆d = 1.5 m, the approximation errors are generally negligible over 20 time slots.

A. Extended Kalman Filtering

The paper uses an extended Kalman filter because the vehicle state-evolution and measurement models are nonlinear. Local linearization through Jacobian matrices enables recursive prediction and tracking of the vehicle state.

  • The proposed EKF tracks and predicts the state x = [θ, d, v, β]^T from measured signal vectors.
  • The nonlinear state-evolution and measurement models are represented compactly by functions g(·) and h(·), respectively.
  • The EKF locally linearizes both models by computing their Jacobian matrices.
  • The filtering procedure follows the standard Kalman prediction and tracking sequence.

3) MSE Matrix Prediction:

The beam-tracking procedure predicts vehicle states for transmit and receive beamforming, then refines those predictions using radar echoes. For multiple vehicles, angle estimates are associated across epochs and power is allocated to balance sensing accuracy with communication rate.

  • The RSU uses predicted angles for transmit beamforming and sends the next predicted angle to each vehicle for receive beamforming.
  • Radar echoes refine the predicted state at each epoch, enabling iterative sensing and communication.
  • Vehicle angle estimates are associated across epochs by matching each current state to the previous state with minimum Euclidean distance.
  • At 15 m/s and ∆T = 10 ms, the inter-epoch distance change is at most 0.15 m, which supports the association rule given vehicle size and safety distance.
  • The multi-beam allocation design minimizes angle and distance estimation errors while guaranteeing the V2I downlink sum-rate.
  • Water-filling maximizes the sum-rate under the RSU power budget but does not minimize vehicle-parameter estimation errors.

B. Posterior Cram´er-Rao Bound for Parameter Estimation

The posterior Cramér–Rao bound combines measurement information with prior information from the state-evolution model. It provides lower bounds on state-estimation errors, including angle and distance MSEs.

  • The CRB provides a lower bound on the variances of unbiased parameter estimators.
  • The joint state-measurement density is decomposed into the measurement likelihood and the prior state density using Bayes’ theorem.
  • Because the state evolution is nonlinear, the prior state distribution is obtained through EKF-style linearization.
  • The posterior Fisher information combines information from the measurement and the state-evolution prior.
  • More accurate state models and previous estimates provide more Fisher information about the current state.
  • The inverse Fisher information matrix bounds the state MSE matrix, including the angle and distance MSEs.

C. Problem Formulation and Analysis

The paper formulates predicted PCRB-based sensing optimization for multiple vehicles, subject to a required downlink sum-rate, and shows the resulting power-allocation problem is convex.

  • C. Problem Formulation and Analysis: Predicted PCRBs are computed from predicted vehicle angles and distances because their real values are unknown at the RSU.The predicted parameters are substituted into the Fisher information and PCRB expressions.
  • C. Problem Formulation and Analysis: The predicted PCRB matrix equals the updated MSE matrix in the EKF iteration.This equivalence follows from the EKF identity and evaluating the Jacobian at the predicted state.
  • C. Problem Formulation and Analysis: These PCRBs remain approximated bounds because both the EKF MSE matrix and PCRB rely on linearization.They should not be interpreted as the exact real MSE values.
  • C. Problem Formulation and Analysis: For K vehicles, the joint PCRB is formed by summing the individual angle and distance estimation bounds.The formulation uses independence between the estimations of each vehicle’s angle and distance.
  • C. Problem Formulation and Analysis: The design objective allocates transmit power among multiple beams to minimize the joint PCRB while satisfying a required sum-rate.The optimization uses the RSU transmit-power budget and predicted vehicle parameters.
  • + PCRB: The power-allocation formulation can be recast using coefficients and eigenvalues evaluated at the predicted vehicle state.The time index is omitted when optimizing power independently at each epoch.
  • + PCRB: The optimal allocation fully uses the RSU power budget because increasing unused power reduces the objective and increases the sum-rate.The formulation’s constraints include the required sum-rate and the RSU transmit-power budget.
  • + PCRB: The power-allocation problem is convex and can therefore be solved efficiently with numerical tools such as CVX.Convexity follows from the concave sum-rate constraint, linear power constraints, and convex objective terms.

V. NUMERICAL RESULTS

The numerical evaluation uses a 30 GHz RSU–vehicle system with short 0.02 s blocks and specified noise and state-evolution parameters. The state-noise variances are treated as model-approximation errors rather than actual SNR terms.

  • V. NUMERICAL RESULTS: The simulations use carrier frequency fc = 30 GHz and block duration ΔT = 0.02s for both RSU and vehicles.Radar and communication noise variances are set to σ2_C = 1, with reference communication channel coefficient α̃ = 1.
  • V. NUMERICAL RESULTS: The state-evolution parameters are σθ = 0.02°, σd = 0.2m, σv = 0.5m/s, and σβ = 0.1.These settings represent approximation errors in the state-evolution models.
  • V. NUMERICAL RESULTS: The state-evolution variances are small because they model evolution-model approximation errors and short-duration state changes, not actual SNR.The paper notes that adjacent states differ only slightly over the short block duration.

A. Performance for Tracking A Single Vehicle

For a single vehicle, the DFRC-based scheme tracks angle variation more accurately than communication-only feedback while maintaining achievable-rate performance. Tracking errors increase when the vehicle moves away or when angular variation becomes too rapid for the EKF.

  • Achievable rates rise with RSU transmit and receive antenna numbers because of improved array gain.Rates increase initially and then decrease as the vehicle passes the RSU, peaking when the vehicle is closest.
  • Angle and distance RMSEs generally decrease as the vehicle approaches and increase as it drives away.The angle changes too quickly for EKF tracking around θ ≈90° during 1200–1400 ms, producing angle-estimation spikes.
  • The DFRC-based scheme accurately tracks vehicle-angle variation, whereas feedback-based tracking shows larger errors.Matched-filtering preserves angular information, while receive-beamformer processing projects pilots into a lower-dimensional space.
  • Larger antenna arrays increase feedback-based tracking error because narrower beams make the added SNR gain insufficient.This effect is reported for the comparison between 64- and 128-antenna cases.
  • Feedback-based rates match DFRC when angle variation is slow but decrease drastically during rapid vehicle approach.For 64 antennas, feedback rates catch up while the vehicle drives away; for 128 antennas, narrower beams and higher misalignment probability prevent recovery.

C. Performance for Tracking Multiple Vehicles

For multiple vehicles, the proposed power allocation scheme balances sensing accuracy and communication-rate constraints. Compared with water-filling, it improves fairness and low-SNR tracking while sometimes sacrificing rate for estimation accuracy.

  • The proposed allocation improves rate fairness by ensuring a minimum achievable rate, whereas water-filling may produce a higher sum-rate.CDF crossovers occur at 1bps/Hz for SNR = −3dB and 3.5bps/Hz in the other reported SNR regime.
  • At low SNR, the proposed power allocation considerably outperforms water-filling in both angle and distance tracking.At high SNR, the two methods show similar sensing performance because both tend toward uniform power allocation.
  • The proposed power allocation achieves a sensing–communication trade-off rather than maximizing communication sum-rate alone.Its design prioritizes minimizing summed PCRB subject to the rate constraint, while water-filling is optimized for sum-rate.
  • The proposed allocation reduces angle RMSE to 0.01° but may sacrifice SNR for vehicles with good channel conditions.Water-filling can yield larger angle-estimation errors while allocating more power to favorable channels.
  • The proposed power allocation minimizes joint angle- and distance-estimation PCRB while guaranteeing a downlink sum-rate threshold and power budget.The multi-vehicle evaluation uses five vehicles, Nt = Nr = 128, M = 32, and Rt = 0.9Rmax.
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