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

Motivation

• V2X requires low-latency Gbps transmission alongside robust obstacle detection and centimeter-scale localization.Source: §I · p. 1
• mmWave mMIMO jointly supports high data rates, improved range resolution, and narrow beams with enhanced angular resolution.Source: §I · p. 1

Research gap

• Communication-only mmWave beam tracking typically sends pilots, estimates angles, and feeds them back, while high mobility also requires beam prediction.Source: §I · p. 2, A. The General Framework · p. 3

Proposed framework

• The proposed DFRC framework uses downlink echoes for vehicle tracking and localization, eliminating downlink pilots and removing the beam-tracking feedback loop.Source: §I · p. 2
• An EKF tracks and predicts each vehicle’s angle, distance, and velocity, using angle information for beamforming and angle plus distance for localization.Source: §I · p. 2
• The multiple-vehicle power allocation scheme improves sensing while guaranteeing a downlink sum-rate, targeting a favorable sensing–communication trade-off.Source: §I · p. 2

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.Source: B. Signal Model · p. 4
• 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.Source: B. Signal Model · p. 4

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.Source: B. Signal Model · p. 4
• 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.Source: B. Signal Model · p. 4
• 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.Source: B. Signal Model · p. 4

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.Source: B. Signal Model · p. 5

• The tracked vehicle state comprises angle, distance, velocity, and reflection coefficient parameters.Source: C. State Evolution Model · p. 5
• 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.Source: C. State Evolution Model · pp. 5–6
• The angle approximation uses sin ∆θ ≈∆θ, while the distance approximation neglects terms involving the squared displacement.Source: C. State Evolution Model · p. 6
• 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.Source: C. State Evolution Model · p. 6
• With v = 54 km/h, ∆T = 100 ms, and ∆d = 1.5 m, the approximation errors are generally negligible over 20 time slots.Source: C. State Evolution Model · p. 6

• The proposed EKF tracks and predicts the state x = [θ, d, v, β]^T from measured signal vectors.Source: A. Extended Kalman Filtering · p. 6
• The nonlinear state-evolution and measurement models are represented compactly by functions g(·) and h(·), respectively.Source: A. Extended Kalman Filtering · p. 6
• The EKF locally linearizes both models by computing their Jacobian matrices.Source: A. Extended Kalman Filtering · pp. 6–7
• The filtering procedure follows the standard Kalman prediction and tracking sequence.Source: A. Extended Kalman Filtering · p. 7

• The RSU uses predicted angles for transmit beamforming and sends the next predicted angle to each vehicle for receive beamforming.Source: 6) MSE Matrix Update · p. 7
• Radar echoes refine the predicted state at each epoch, enabling iterative sensing and communication.Source: 6) MSE Matrix Update · p. 7
• Vehicle angle estimates are associated across epochs by matching each current state to the previous state with minimum Euclidean distance.Source: B. Beam Association for Multiple… · p. 7
• 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.Source: B. Beam Association for Multiple… · p. 7
• The multi-beam allocation design minimizes angle and distance estimation errors while guaranteeing the V2I downlink sum-rate.Source: §IV · p. 8
• Water-filling maximizes the sum-rate under the RSU power budget but does not minimize vehicle-parameter estimation errors.Source: A. Water-filling Power Allocation: A… · p. 8

• The CRB provides a lower bound on the variances of unbiased parameter estimators.Source: B. Posterior Cram´er-Rao Bound for… · p. 8
• The joint state-measurement density is decomposed into the measurement likelihood and the prior state density using Bayes’ theorem.Source: B. Posterior Cram´er-Rao Bound for… · p. 8
• Because the state evolution is nonlinear, the prior state distribution is obtained through EKF-style linearization.Source: B. Posterior Cram´er-Rao Bound for… · p. 8
• The posterior Fisher information combines information from the measurement and the state-evolution prior.Source: B. Posterior Cram´er-Rao Bound for… · p. 8
• More accurate state models and previous estimates provide more Fisher information about the current state.Source: B. Posterior Cram´er-Rao Bound for… · p. 8
• The inverse Fisher information matrix bounds the state MSE matrix, including the angle and distance MSEs.Source: B. Posterior Cram´er-Rao Bound for… · pp. 8–9

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.Source: C. Problem Formulation and Analysis · p. 9
• 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.Source: C. Problem Formulation and Analysis · p. 9
• 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.Source: C. Problem Formulation and Analysis · p. 9
• 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.Source: C. Problem Formulation and Analysis · p. 9
• 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.Source: C. Problem Formulation and Analysis · p. 9, + PCRB · p. 9

+ 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.Source: + PCRB · pp. 9–10
• 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.Source: + PCRB · pp. 9–10
• 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.Source: + PCRB · p. 10

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.Source: §V · p. 10
• 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.Source: §V · p. 10
• 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.Source: §V · p. 10

• 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.Source: A. Performance for Tracking A Single… · p. 10
• 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.Source: A. Performance for Tracking A Single… · p. 10
• 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.Source: B. Performance Comparison for DFRC and… · pp. 11–12
• 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.Source: B. Performance Comparison for DFRC and… · p. 12
• 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.Source: B. Performance Comparison for DFRC and… · p. 12, Figure 8 · p. 12

• 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.Source: C. Performance for Tracking Multiple… · p. 13, Figure 10 · p. 13
• 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.Source: C. Performance for Tracking Multiple… · p. 13
• 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.Source: C. Performance for Tracking Multiple… · pp. 13–14
• 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.Source: C. Performance for Tracking Multiple… · p. 14
• 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.Source: C. Performance for Tracking Multiple… · pp. 12–13, §VI · p. 14