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Bayesian Predictive Beamforming for Vehicular Networks: A Low-overhead Joint Radar-Communication Approach
Weijie Yuan, Fan Liu, Christos Masouros, Jinhong Yuan, Derrick Wing Kwan Ng, Nuria Gonzalez-Prelcic
TL;DR
Vehicular networks need joint sensing and communication with low-overhead beam tracking. The paper develops DFRC predictive beamforming that estimates motion from radar echoes, applies factor-graph message passing, and designs beams from predicted angles. Simulations show improved estimation and communication performance over feedback-based schemes, while the proposed low-complexity algorithm performs similarly to particle-based methods.
Problem
Vehicular networks require localization, tracking, and communication, but feedback-based beam tracking incurs signaling overhead and separate radar resources consume spectrum.
Method
The paper uses DFRC radar echoes, Bayesian factor-graph message passing with closed-form approximations, and predicted vehicle angles to design communication beamformers.
Results
The proposed DFRC beamforming scheme outperforms feedback-based approaches in estimation and communication performance, while its message passing algorithm achieves similar performance to high-complexity particle-based methods.
Takeaways & Limitations
DFRC predictive beamforming provides zero signaling overhead for beam tracking and a low-complexity solution for vehicular beam alignment.
Abstract
from arXiv · showhide
The development of dual-functional radar-communication (DFRC) systems, where vehicle localization and tracking can be combined with vehicular communication, will lead to more efficient future vehicular networks. In this paper, we develop a predictive beamforming scheme in the context of DFRC systems. We consider a system model where the road-side units estimates and predicts the motion parameters of vehicles based on the echoes of the DFRC signal. Compared to the conventional feedback-based beam tracking approaches, the proposed method can reduce the signaling overhead and improve the accuracy. To accurately estimate the motion parameters of vehicles in real-time, we propose a novel message passing algorithm based on factor graph, which yields near optimal solution to the maximum a posteriori estimation. The beamformers are then designed based on the predicted angles for establishing the communication links.}With the employment of appropriate approximations, all messages on the factor graph can be derived in a closed-form, thus reduce the complexity. Simulation results show that the proposed DFRC based beamforming scheme is superior to the feedback-based approach in terms of both estimation and communication performance. Moreover, the proposed message passing algorithm achieves a similar performance of the high-complexity particle-based methods.
I. INTRODUCTION
DFRC combines vehicular sensing and communication to address spectral-efficiency and beam-tracking challenges in high-mobility V2X networks. This paper proposes predictive beamforming using radar echoes, factor-graph message passing, and angle prediction to reduce signaling overhead and improve estimation and communication performance.
- DFRC jointly performs radar sensing and communication with one transmission, reducing hardware cost and increasing overall system throughput.
- High-mobility V2X scenarios require fast beam tracking, but feedback-based alignment sends pilots and returns estimated relative angles to the roadside unit.
- The proposed V2I scheme estimates vehicle beam directions and motion parameters from radar echoes, avoiding vehicle feedback and using the whole downlink block as data symbols and sensing pilots.
- The scheme predicts vehicle angles for beamformer design, reducing latency while achieving better estimation performance and higher spectral efficiency than conventional feedback-based schemes.
- A factor-graph framework and message passing algorithm track and predict vehicle motion parameters, with closed-form messages derived through mean-field message passing and Taylor expansion.
- The system model uses a roadside unit with separate transmit and receive arrays to receive vehicle echoes while maintaining uninterrupted downlink transmission.
B. Observation Model
The observation model uses radar-matched-filter outputs to estimate vehicle delay and Doppler, then models received antenna samples for angle and reflection-coefficient estimation.
- Radar matched filtering estimates delay and Doppler, which correspond to vehicle range and speed.The measurement model assumes Gaussian observation noise.
- Single-time-slot observations make vehicle-speed estimation challenging because the Doppler phase shift is not significant.The paper suggests accumulating Doppler shifts over multiple time slots.
- The received signal samples across receive antennas support estimation of the vehicle angle and reflection coefficient after delay and Doppler filtering.The model includes receive-antenna noise samples and a transmit beamformer based on the predicted angle.
C. State Evolution Model
The state evolution model derives vehicle motion transitions from kinematic geometry and approximates them to obtain tractable updates over short time intervals.
- Vehicle range, angle, speed, and reflection coefficient evolve according to kinematic equations based on consecutive states.The transition noises are modeled as zero-mean Gaussian variables.
- For short intervals with small positional variation, the angular transition is approximated using sin(∆θk,n) ≈ ∆θk,n.This approximation converts the nonlinear geometric relation into a tractable expression.
- The range transition is simplified by treating consecutive ranges as approximately equal and omitting a negligible quadratic variation term.
- The model further uses the reflection-coefficient model and assumes the vehicle speed is approximately constant.
- Estimated previous states replace coupled variables so each motion-parameter evolution depends only on its own previous state.
D. Communication Model
The communication model forms the vehicle’s received signal using transmit and receive beamformers, with beam directions selected from predicted vehicle angles.
- Vehicle k receives the RSU transmission through a receive beamformer, with the received signal determined by the vehicle channel and steering vector.
- The receive beamformer is designed from the vehicle’s predicted angle relative to the RSU at time n.
- The RSU’s beamforming update at time n uses an estimate from time n−2 conveyed in the DFRC signal at time n−1.
- Achievable sum-rate depends on the transmit and receive beamformers, and perfect angle prediction yields maximum received SNR and maximum achievable sum-rate.
- The channel pathloss coefficient can be estimated from the vehicle range.
III. FACTOR GRAPH MODEL
The factor-graph model represents the Bayesian estimation problem through state transitions and observation likelihoods, enabling message passing instead of prohibitively costly direct marginalization.
- The goal is to estimate vehicle range, speed, angle, and path loss using the state-evolution and observation models through MAP estimation.
- Direct marginalization of the joint posterior has prohibitively high complexity because it requires multidimensional integrations.
- The joint posterior is factorized into likelihood and prior terms using Bayes’ theorem and conditional independence.
- Initial vehicle parameters are obtained with an omnidirectional probing waveform and modeled with Gaussian initial distributions.
- An auxiliary variable is introduced because each received-sample factor contains Nt components, making inference difficult.
- The factor graph separates state-evolution and observation-model factors, allowing message passing to compute approximate marginals, or beliefs, of unknown variables.
IV. THE PROPOSED MESSAGE PASSING APPROACH
The paper introduces conventional belief propagation message updates between factor and variable vertices, then obtains approximate variable marginals from incoming messages.
- Factor-to-variable messages are denoted by −→ µ f(x), while variable-to-factor messages are denoted by ←−ν f(x).
- Belief propagation (BP) passes messages in both directions between factor vertices and variable vertices.The paper distinguishes factor-to-variable messages from variable-to-factor messages.
- The message-update rules use the variables in a function and the factor vertices connected to a variable.
- After receiving messages from connected factors, the belief of a variable is computed as its approximate marginal.
B. Vehicle State Prediction
The RSU predicts current and future vehicle angles from previously estimated motion parameters and state-evolution messages, then uses those predictions for beamforming.
- The RSU predicts angle θn from motion-parameter estimates at time n−1 using the state-evolution model.
- The predicted angle is sent to vehicles in the DFRC signal for receive-beam steering at the next time instant.
- Accurate prediction aligns RSU transmit beams with vehicle receive beams, improving communication performance.
- Gaussian state-evolution messages provide prediction means and variances based on the previous marginal distribution.For vehicle speed, the predicted mean equals the previous mean and the variance adds process uncertainty.
- The RSU further predicts the relative angle at time n+1 from the estimated angle and predicted motion parameters.
C. Vehicle State Tracking
At each epoch, vehicles receive predicted angles while the RSU uses reflected echoes to update motion states through factor-graph message passing and Gaussian approximations.
- Vehicles decode data and receive next-epoch angle predictions, while the RSU refines current motion estimates from vehicle echoes.
- The causal model lets messages depend only on past states and propagate forward along time.
- Range beliefs are Gaussian, so the range estimate is the belief mean and feeds the next state-evolution model.
- The nonlinear cosine relation is reconstructed with an auxiliary cosine variable because direct message computation lacks a closed-form Gaussian representation.
- Trigonometric nonlinearities are handled through Gaussian moment calculations and second-order Taylor approximations of inverse functions.The inverse-cosine approximation is arccos ϑ ≈π/2 −ϑ −ϑ^3/6.
- Observation messages update angular and motion-variable beliefs, including contributions from the receive antennas.
- The cyclic κq subgraph requires several message-passing iterations, with inverse trigonometric transformations reconstructed through auxiliary processing.
- The resulting angle belief supplies the next prediction and the state-transition model, while estimated angles support reliable data links.
D. Beam Misalignment Analysis
The analysis models beam alignment probabilistically under narrow beams, using predicted-angle uncertainty to characterize misalignment and examining beamwidth as a key factor.
- The vehicle and RSU use predictions from different time instants, with Gaussian uncertainty associated with the vehicle’s next-epoch steering direction.
- Beam alignment requires the vehicle’s predicted direction to remain within δ of the actual angle, where δ = π/Nantenna.The beamwidth is defined as ∆ = 2δ.
- The misalignment probability pmis is obtained from cumulative distributions of the predicted-angle variables.
- Misalignment probability depends on beamwidth, motivating future beamwidth optimization to minimize pmis.
E. Computational Complexity and Signaling Overhead
The proposed message passing algorithm has closed-form message calculations, yielding low complexity and lower overhead than feedback-based beam tracking.
- O(4K) complexity results from closed-form message calculations using appropriate approximations and message-updating rules.The calculations require only addition and multiplication operations.
- The particle-filter-based algorithm has O(4KR) complexity because it represents nonlinear functions with R particles.A sufficiently large R is generally needed for reasonably good estimation performance.
- The extended Kalman filter has O((4K)3) complexity because it requires matrix inversion.
- The proposed approach provides zero signaling overhead for beam tracking, unlike feedback-based approaches that usually use one or two pilot symbols.
V. SIMULATION RESULTS
Simulations evaluate motion-parameter tracking, comparisons with feedback-based and benchmark methods, communication rates, and beam misalignment under varying vehicle speeds and beamwidths.
- Tracking performance: The proposed approach tracks range and angle parameters across four antenna deployments and four vehicles in the simulation setup.The setup uses vehicles with randomly generated initial speeds and evaluates averaged tracking results.
- Tracking performance: 10−2 rad is the reported error level for angle estimation, with larger antenna arrays providing higher array gain and more observations.
- Comparison with benchmarks: The proposed parametric message passing method attains the performance of the PF-based method with significantly reduced complexity.The comparison uses the velocity-estimation error at the last time instant with M = Nt = Nr = 64 antennas.
- Comparison with benchmarks: The proposed approach significantly outperforms feedback-based schemes using 1 and 2 pilots because of its higher SNR gain.
- Communication performance: The feedback scheme degrades with more antennas because one pilot cannot sufficiently track angular variation in narrower beams.The degradation is more significant with 128 antennas.
- Communication performance: The proposed scheme achieves rates higher than 4 bps/Hz at SNR 10 dB, whereas the feedback-based scheme achieves much lower rates.The rate degradation is attributed to angle-estimation error causing beam misalignment and reduced received SNR.
- Beam misalignment: Low-speed vehicles have lower misalignment probability than high-speed vehicles, while high-speed vehicles are more sensitive to beamwidth.The high-speed case shows a significant rise in misalignment probability at δ = π/128.
VI. CONCLUSIONS
The paper proposes Bayesian DFRC predictive beamforming using factor-graph message passing and angle prediction to reduce beam-tracking overhead and latency. Simulations show superiority over conventional feedback-based beam tracking.
- The scheme estimates vehicle motion parameters from RSU echo signals using a factor graph representing a factorized joint a posteriori distribution.
- Second-order Taylor expansion produces closed-form factor-graph messages and a low-complexity beam-tracking solution.
- A two-step angle prediction is transmitted through DFRC signals to reduce beam-alignment latency.
- The proposed approach provides zero signaling overhead for beam tracking and outperforms the conventional feedback-based scheme in simulations.