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Learning-based Predictive Beamforming for Integrated Sensing and Communication in Vehicular Networks

Chang Liu, Weijie Yuan, Shuangyang Li, Xuemeng Liu, Husheng Li, Derrick Wing Kwan Ng, Yonghui Li

arXiv:2108.11540v2eess.SP

TL;DR

The paper addresses predictive beamforming for ISAC-assisted V2I networks, where accurate channel tracking creates training overhead and computational burden. It formulates sensing-constrained sum-rate maximization with interference and develops an unsupervised DL framework realized by HCL-Net. Simulations show that the method satisfies sensing requirements and achieves a sum-rate close to the genie-aided upper bound.

  • Problem

    Accurate channel tracking for ISAC beamforming requires substantial training overhead and computational complexity, while practical design must account for sensing constraints and multiple access interference.

  • Method

    An unsupervised DL-based predictive beamforming framework uses penalty-based problem transformation and HCL-Net to learn spatial and temporal features from historical estimated channels.

  • Results

    The predictive method guarantees the required sensing performance and achieves an average sum-rate around 5 bits/s/Hz at Nt = Nr = 28, approximately 1.5 times the naive DL method.

  • Takeaways & Limitations

    Predicting the next-slot beamforming matrix from historical channels can provide satisfactory communication performance while meeting sensing-accuracy requirements without explicit channel tracking.

Abstract

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This paper investigates the integrated sensing and communication (ISAC) in vehicle-to-infrastructure (V2I) networks. To realize ISAC, an effective beamforming design is essential which however, highly depends on the availability of accurate channel tracking requiring large training overhead and computational complexity. Motivated by this, we adopt a deep learning (DL) approach to implicitly learn the features of historical channels and directly predict the beamforming matrix to be adopted for the next time slot to maximize the average achievable sum-rate of an ISAC system. The proposed method can bypass the need of explicit channel tracking process and reduce the signaling overhead significantly. To this end, a general sum-rate maximization problem with Cramer-Rao lower bounds (CRLBs)-based sensing constraints is first formulated for the considered ISAC system taking into account the multiple access interference. Then, by exploiting the penalty method, a versatile unsupervised DL-based predictive beamforming design framework is developed to address the formulated design problem. As a realization of the developed framework, a historical channels-based convolutional long short-term memory (LSTM) network (HCL-Net) is devised for predictive beamforming in the ISAC-based V2I network. Specifically, the convolution and LSTM modules are successively adopted in the proposed HCL-Net to exploit the spatial and temporal dependencies of communication channels to further improve the learning performance. Finally, simulation results show that the proposed predictive method not only guarantees the required sensing performance, but also achieves a satisfactory sum-rate that can approach the upper bound obtained by the genie-aided scheme with the perfect instantaneous channel state information available.

I. INTRODUCTION

The paper develops predictive beamforming for ISAC-assisted V2I networks to reduce channel-tracking overhead while jointly supporting communication and sensing. It formulates interference-aware sensing-constrained optimization and addresses it with an unsupervised DL framework instantiated as HCL-Net.

  • ISAC co-designs communication and sensing over shared frequency bands and hardware to improve spectral efficiency and reduce hardware cost.
  • Accurate channel or motion prediction for beam alignment can incur high computational complexity, motivating a data-driven predictive beamforming approach.
  • The formulated beamforming problem maximizes communication sum-rate under CRLB-based sensing constraints while accounting for multiple access interference.
  • The proposed unsupervised framework uses a penalty method to convert the constrained problem into an unconstrained one for data-driven optimization.
  • HCL-Net feeds historical estimated channels into successive convolutional and LSTM modules to exploit spatial and temporal channel features.
  • The predictive method guarantees harsh sensing-CRLB requirements, while its sum-rate approaches the genie-aided upper bound based on perfect instantaneous channel state information.

B. Vehicle Mobility and Observation Model

The vehicle model assumes motion parallel to the road and represents vehicle dynamics through velocity magnitude, while matched filtering estimates delay and Doppler observations. Beamforming affects sensing observation accuracy through the array response.

  • Vehicle velocity directions are assumed parallel to the road, enabling the mobility model to characterize motion through velocity magnitude.
  • The study considers only line-of-sight channels because occlusion, blocking, and non-line-of-sight echoes can hinder sensing and communication or mislead target localization.
  • The average vehicle velocity is modeled as uniformly distributed between minimum and maximum velocity magnitudes, with slot-wise velocity increments.
  • Matched filtering estimates each vehicle’s time-delay and Doppler frequency before ideal interference cancellation is applied to the received echoes.
  • Observation models represent delay and radial-velocity measurements with Gaussian estimation errors.
  • Sensing observation noise variances depend on the beamforming vector through |aH(θk,n)wk,n|, so beam adjustment can improve observation accuracy.

C. Communication Model

The communication model describes downlink reception, path loss, noise, and equivalent channels for vehicles. It explicitly includes multi-user interference in beamforming and sum-rate design.

  • Each vehicle receives a downlink signal from the RSU during a time slot.
  • The received signal model includes antenna gain, distance-dependent path loss, and complex Gaussian receiver noise.The path loss coefficient depends on reference loss, reference distance, and path loss exponent.
  • Interference from signals intended for other vehicles is included in the beamforming design to improve sum-rate performance.The multi-user interference component appears in both sensing and communication signal models.
  • The k-th vehicle’s received SINR is used to characterize its communication performance.
  • The equivalent channel vector combines path loss and the vehicle’s steering vector.

D. Proposed Protocol

The proposed protocol presets the next slot’s beamforming matrix from historical channels, avoiding real-time channel tracking and explicit prediction. Compared with beam training and two-stage prediction, it reduces complexity and signaling overhead while targeting communication and sensing objectives.

  • The protocol presets a predictive beamforming matrix for the next time slot using historical channel information.This bypasses real-time channel tracking or motion-parameter prediction.
  • Beam training requires downlink pilots and uplink feedback, creating substantial complexity and signaling overhead.
  • The two-stage beam prediction protocol avoids beam training but retains explicit channel prediction and considerable computational overhead.
  • The proposed protocol directly predicts the beamforming matrix from historical channels through a learning-based joint mechanism.It does not perform explicit channel prediction or beam training.
  • The design objective is to maximize average achievable downlink sum-rate while guaranteeing vehicle sensing performance.The formulation derives CRLBs of motion-parameter estimation to quantify sensing performance.

A. Cramer-Rao Lower Bound for Parameter Estimation

The paper derives CRLBs to quantify motion-parameter estimation accuracy from sensing observations. The analysis exposes a beamforming tradeoff: focusing beams for sensing can neglect multi-user interference relevant to communication.

  • The observation vector contains sensing outputs, while the motion-parameter vector contains angle, distance, and velocity.
  • The observation model assumes a complex Gaussian distribution whose mean depends on the motion parameters and whose covariance is specified by the noise model.
  • The Fisher information matrix is used within the CRLB theorem to characterize estimation accuracy.
  • The paper assumes uncorrelated noise terms, representing an unfavorable ISAC sensing scenario.Correlated noise could provide additional observation information, while the framework is positioned as a foundation for extensions.
  • The CRLB bounds the mean-squared-error matrix and yields lower bounds for estimating vehicle angle and distance.
  • Beam alignment toward each vehicle can improve desired sensing signal strength but ignores multiple access interference in downlink communication.

B. Problem Formulation

The problem formulation optimizes beamforming for ergodic communication and sensing performance using historical channel, angle, and distance information. It enforces power and CRLB constraints, while recognizing an inherent rate–sensing tradeoff and using a penalty method for deep learning.

  • B. Problem Formulation: The optimization maximizes average achievable sum-rate subject to the RSU’s transmit-power constraint and CRLB sensing constraints.
  • B. Problem Formulation: The objective includes log2(1 + SINR_k,n(h_k,n, w_k,n)) for each vehicle.
  • B. Problem Formulation: W_n is the beamforming matrix and h_k,n is the channel vector used in the communication objective.
  • B. Problem Formulation: The communication objective averages over current channels conditioned on historical estimated channels.
  • B. Problem Formulation: The sensing objective averages over current angles and distances conditioned on their respective historical estimates.
  • B. Problem Formulation: Only historical channel information from the preceding τ time slots is available when designing the beamforming matrix for slot n.
  • B. Problem Formulation: The CRLB thresholds γθ and γd constrain sensing performance, while P specifies the RSU power budget per time slot.
  • B. Problem Formulation: Communication and sensing objectives require a tradeoff because sum-rate favors balanced vehicle SINRs whereas CRLB minimization favors balanced sensing SNRs.The resulting problem lacks tractable closed-form solutions, motivating the penalty method’s transformation of constrained optimization into an unconstrained problem for deep learning.

A. DL-based Predictive Beamforming Framework for ISAC

The framework converts constrained ISAC beamforming into an unconstrained objective and solves it with unsupervised deep learning. Its generality permits different neural architectures, including the HCL-Net realization.

  • Problem transformation: The penalty method transforms the constrained beamforming problem into an equivalent unconstrained optimization problem.A fixed penalty parameter is adopted for implementation simplicity.
  • DL-based problem solving: The framework uses Monte-Carlo samples to approximate the statistical expectation in the unconstrained objective.The approximation becomes valid when the number of experiments is sufficiently large.
  • DL-based problem solving: A DNN maps available historical-channel inputs to predictive beamforming matrices while optimizing the resulting cost function.The optimized matrix is obtained by updating network parameters during training.
  • Framework versatility: The framework can use different neural-network architectures, such as CNNs, dense networks, and residual networks.The penalty stage handles non-convex constraints, while the DNN stage is architecture-agnostic.
  • HCL-Net realization: HCL-Net realizes the framework with successive convolutional and LSTM modules to exploit spatial and temporal channel dependencies.The architecture is designed for predictive beamforming in ISAC-based V2I networks.

1) Input Layer:

HCL-Net processes historical complex channel inputs through parallel CNN modules, concatenation, an LSTM, and a fully connected output layer. This design combines spatial and temporal feature extraction for predictive beamforming.

  • Input representation: The complex input is divided into real and imaginary parts before neural-network processing.The mapping function converts the input into a real-valued tensor representation.
  • CNN feature extraction: K identical CNN modules independently extract spatial features from the channel inputs of the K vehicles at each time slot.Each module includes input, convolution, pooling, and flatten layers, with four 3 × 3 × 2 filters in the convolutional layer.
  • Feature aggregation: A concatenate layer combines the extracted features from all vehicles for subsequent temporal processing.Its output contains channel features for every vehicle at each time slot.
  • Temporal feature extraction: An LSTM recurrently processes the past τ time slots to capture temporal correlations among historical channel vectors.The output at the final time step represents temporal dependencies across all past steps.
  • Output generation: A fully connected layer with linear activation converts the LSTM features into the desired beamforming output.The resulting mapping generates a complex-valued beamforming matrix.
  • Architecture rationale: The HCL-Net architecture balances learning performance and neural-network complexity while remaining scalable across system deployments.Its input and output sizes can be altered for different vehicle and antenna counts.

1) Offline Training:

Offline training learns HCL-Net parameters from unlabeled channel data by minimizing the penalty-based unsupervised cost function. After training, the network produces predictive beamforming matrices for test sequences.

  • Offline Training: The algorithm performs unsupervised offline training using a channel training set and randomly initialized network parameters.Backpropagation updates the parameters to minimize the HCL-Net cost function.
  • Offline Training: The training cost incorporates communication and sensing objectives through the penalty-based formulation.The CRLB terms are defined within the predictive beamforming objective.
  • Offline Training: After convergence, the trained HCL-Net is represented by h_ς*(·), whose output is the optimized predictive beamforming matrix.The matrix is generated from the trained network parameters.
  • Offline Training: Algorithm 1 separates offline training from online beamforming design.Offline training iteratively updates the network, while online design applies the trained model to test data.

2) Online Optimization:

Online optimization feeds a test sequence of historical channels into the trained HCL-Net to obtain the next predictive beamforming matrix. The algorithm’s complexity is analyzed through its CNN and LSTM computations.

  • Online Optimization: Online beamforming applies the trained HCL-Net to test data and outputs an optimized predictive beamforming matrix.The trained mapping is used directly after offline parameter optimization.
  • Complexity Analysis: The neural-network computation comprises CNN processing across vehicles and time steps together with recurrent LSTM processing.The CNN modules independently handle the K vehicle inputs over τ time steps.
  • Complexity Analysis: Offline-training complexity depends on the maximum iteration number and the number of training examples.The analysis explicitly identifies It and Ne as the relevant training-scale factors.

V. NUMERICAL RESULTS

Simulations evaluate predictive beamforming for communication performance across system, vehicle, and algorithm parameters. HCL-Net consistently outperforms naive and random beamforming and approaches the genie-aided upper bound.

  • Simulation Setup: The simulations use an mmWave V2I network with one 32-antenna RSU serving three single-antenna vehicles unless otherwise specified.Results average 2,000 Monte Carlo realizations, using 2,000 training and test examples and six training epochs.
  • Power Variation: The proposed method significantly outperforms naive and random beamforming as transmit power increases, because outdated or random beams poorly align with rapidly varying vehicle channels.The naive method uses only the previous-slot estimated channel, whereas the proposed method predicts the next-slot beamforming matrix.
  • Network Architecture: HCL-Net achieves the best sum-rate among the tested neural architectures by jointly exploiting spatial and temporal channel features through CNN and LSTM modules.This performance comes with greater computational complexity than standalone LSTM or CNN structures.
  • Antenna Scaling: At Nt = Nr = 28, the proposed method reaches around 5 bits/s/Hz, 1.5 times higher than naive DL beamforming and near the upper-bound performance.Increasing the RSU antenna count improves the proposed method’s performance and scalability.
  • Vehicle Parameters: The proposed method remains near the upper bound across vehicle velocities from 10 km/h to 60 km/h and with varying vehicle counts.Its scalable network design exploits temporal prediction and multiuser diversity as vehicle conditions change.
  • Algorithm Parameters: Increasing historical time steps benefits the proposed method, while the other benchmarks remain nearly constant because they do not exploit temporal channel dependencies.The study also varies penalty parameters to assess algorithmic sensitivity.

B. Sensing Performance

The proposed predictive beamforming method satisfies the sensing constraints while maintaining strong communication performance. Estimation accuracy improves with transmit power and antenna count, and both sensing metrics converge within six epochs.

  • Sensing Metric: The square root of the CRLB is used as the RMSE lower bound to characterize angle and distance estimation performance.The sensing constraints set γθ = 0.01 rad2 and γd = 0.01 m2.
  • Angle Estimation: Angle-estimation CRLB values remain around 10^-3 rad to 10^-2 rad, below the constrained thresholds.This indicates satisfactory tracking accuracy under the evaluated transmit powers and antenna counts.
  • Angle Estimation: For Nt = Nr = 48, increasing transmit power from 10 dBm to 15 dBm reduces the angle-estimation CRLB from 10^-2 rad to 10^-3 rad.Higher transmit power improves received echo SNR and reduces the relative impact of noise.
  • System Scaling: Increasing transmit power or antenna count improves received signal strength and enhances sensing and communication performance simultaneously.The antenna-array gain contributes to lower angle-estimation CRLB values.
  • Distance Estimation: With Nt = Nr = 48, the proposed method achieves a distance-estimation CRLB of 10^-4 m, sufficient for accurately tracking high-speed vehicles.This result supports the method’s sensing performance in the evaluated V2I setting.
  • Training Convergence: Both angle and distance estimation performances converge within six training epochs.The convergence result is presented alongside testing sum-rate behavior across training epochs.
  • Sensing-Communication Tradeoff: The achievable sum-rate increases as the maximum tolerable CRLB threshold γ loosens and saturates when γ ≥ 9 × 10^-3.The results expose a sensing-communication tradeoff because beamformers optimized for communication and sensing constraints differ.
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