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Deep Learning Coordinated Beamforming for Highly-Mobile Millimeter Wave Systems

Ahmed Alkhateeb, Sam Alex, Paul Varkey, Ying Li, Qi Qu, Djordje Tujkovic

arXiv:1804.10334v3cs.IT

TL;DR

Highly mobile mmWave systems face coverage, reliability, and handover challenges. The paper combines deep learning with coordinated beamforming, approaching genie-aided performance with negligible training overhead.

  • Problem

    Highly mobile mmWave systems face limited coverage and reliability plus frequent handovers, motivating solutions that reduce these deployment challenges.

  • Method

    The paper integrates deep learning with coordinated transmission from multiple distributed BSs to predict beamforming vectors from jointly received uplink pilot signatures.

  • Results

    The proposed strategy performs almost as well as a genie-aided solution that perfectly knows the optimal beamforming vectors, while requiring negligible training overhead.

  • Takeaways & Limitations

    Integrating deep learning with coordinated multi-BS transmission provides reliable coverage and low latency for highly mobile mmWave applications.

Abstract

from arXiv · show

Supporting high mobility in millimeter wave (mmWave) systems enables a wide range of important applications such as vehicular communications and wireless virtual/augmented reality. Realizing this in practice, though, requires overcoming several challenges. First, the use of narrow beams and the sensitivity of mmWave signals to blockage greatly impact the coverage and reliability of highly-mobile links. Second, highly-mobile users in dense mmWave deployments need to frequently hand-off between base stations (BSs), which is associated with critical control and latency overhead. Further, identifying the optimal beamforming vectors in large antenna array mmWave systems requires considerable training overhead, which significantly affects the efficiency of these mobile systems. In this paper, a novel integrated machine learning and coordinated beamforming solution is developed to overcome these challenges and enable highly-mobile mmWave applications. In the proposed solution, a number of distributed yet coordinating BSs simultaneously serve a mobile user. This user ideally needs to transmit only one uplink training pilot sequence that will be jointly received at the coordinating BSs using omni or quasi-omni beam patterns. These received signals draw a defining signature not only for the user location, but also for its interaction with the surrounding environment. The developed solution then leverages a deep learning model that learns how to use these signatures to predict the beamforming vectors at the BSs. This renders a comprehensive solution that supports highly-mobile mmWave applications with reliable coverage, low latency, and negligible training overhead. Simulation results show that the proposed deep-learning coordinated beamforming strategy approaches the achievable rate of the genie-aided solution that knows the optimal beamforming vectors with no training overhead.

I. INTRODUCTION · A. Prior Work · B. Contribution

The paper addresses reliability, handover latency, and training-overhead challenges in highly mobile mmWave systems through integrated deep learning and coordinated beamforming. Its proposed approach predicts coordinated BS beamforming from jointly received omni or quasi-omni uplink signals, achieving rates close to genie-aided performance.

  • I. INTRODUCTION: Highly-mobile mmWave applications face unreliable links from blockage and LOS/NLOS SNR differences, frequent BS handovers, and large-array beam-training overhead.These challenges affect coverage, latency, control overhead, and support for mobile users.
  • A. Prior Work: Prior coordinated-beamforming studies established coverage gains from simultaneous service by multiple BSs but did not address constructing coordinated beams with low overhead.The paper targets low-complexity coordination strategies that retain coverage and latency gains.
  • A. Prior Work: Existing beam-training, compressive-estimation, and location-aided methods reduce or manage training costs but retain overhead, scaling, sensor, or environment-dependence limitations.Compressive methods scale with antenna count, while location-only methods can fail with inaccurate or unavailable positioning and NLOS variation.
  • B. Contribution: The proposed system uses distributed coordinating BSs to simultaneously serve one mobile user and predicts their beamforming vectors from jointly received omni or quasi-omni signals.The received multipath signature reflects both user location and surrounding environment.
  • B. Contribution: Using uplink received signals instead of position information supports LOS and NLOS scenarios without special position-acquisition sensors.Only omni received pilots are needed, yielding negligible training overhead, and the model adapts to environments without pre-deployment training.
  • B. Contribution: The paper formulates RF and central-baseband beamforming design to maximize effective achievable rate, which accounts for training overhead and achievable rate.It also develops a training-based baseline whose RF beams come from a predefined codebook and whose baseband beams ensure coherent combining.
  • B. Contribution: The baseline obtains optimal achievable rates in special cases but requires high training overhead, motivating the integrated deep-learning strategy.The proposed method retains coordinated beamforming’s wide-coverage and low-latency gains with low coordination overhead.
  • B. Contribution: Simulations show that deep-learning coordinated beamforming approaches genie-aided effective achievable rate, improves over the baseline especially at high speed and with large arrays, adapts to time-varying environments, and may not require BS phase synchronization.The reported findings support efficient operation in highly-mobile large-array mmWave systems.

II. SYSTEM AND CHANNEL MODELS · A. System Model

The paper models a frequency-selective coordinated mmWave system in which multiple connected BSs jointly serve one mobile station using analog beamforming. The model specifies the multi-carrier transmission, synchronization, channel, noise, and phase-shifter assumptions.

  • II. SYSTEM AND CHANNEL MODELS: The adopted framework is a frequency-selective coordinated mmWave system with explicit assumptions for its system and channel models.The models and their key assumptions are introduced together.
  • A. System Model: N BSs or APs simultaneously serve one mobile station, with each BS equipped with M antennas.This defines the coordinated multi-BS deployment and antenna configuration.
  • A. System Model: All BSs connect to a centralized/cloud processing unit, enabling coordinated transmission across the serving sites.The inter-BS connection is part of the system architecture.
  • A. System Model: Each BS uses one RF chain and analog-only beamforming implemented through phase-shifter networks.The stated architecture uses RF beamforming rather than a more sophisticated precoding structure.
  • A. System Model: The model assumes a single-antenna mobile user, while extending the algorithms and solutions to multi-antenna users remains possible.Hybrid precoding is identified as future research, and multi-antenna-user extensions are noted.
  • A. System Model: Downlink data symbols are transmitted over K subcarriers after centralized processing, time-domain conversion with N K-point IFFTs, and cyclic-prefix insertion of length D.The resulting blocks are sent to the BSs through error-negligible and delay-negligible wired channels.
  • A. System Model: Each BS applies a time-domain analog beamforming vector, with quantized phase-shifter entries defined by quantized angles.The formulation also adopts a per-subcarrier transmit-power constraint.
  • A. System Model: After perfect frequency and carrier-offset synchronization, the received signal is FFT-processed over K subcarriers through the M ×1 channel vector hk,n and receive noise vk ∼NC (0, σ2).The channel vector is defined between the user and the nth BS at subcarrier k.

B. Channel Model · III. PROBLEM FORMULATION · T k FRF

The paper models wideband mmWave channels geometrically and formulates coordinated beamforming as an effective-achievable-rate optimization under mobility, hardware, and training-overhead constraints. It motivates integrating machine learning with beam training to achieve very low overhead and near-optimal effective achievable rates for highly-mobile mmWave systems.

  • B. Channel Model: The wideband mmWave channel uses L clusters, each contributing one ray characterized by delay and azimuth/elevation angles of arrival.Path loss between the user and the n-th BS and pulse shaping for TS-spaced signaling are also included.
  • B. Channel Model: The model defines delay-domain and frequency-domain channel vectors between the user and each BS, including the channel vector at subcarrier k.The frequency-domain representation is based on the delay-d channel and array response at the corresponding angles of arrival.
  • III. PROBLEM FORMULATION: Coordinated transmission from multiple BSs targets high mobility and data rates while improving coverage, reliability, and latency through transmission diversity and blockage robustness.The central challenge is reducing the substantial training and beamforming-design overhead for highly-mobile users.
  • III. PROBLEM FORMULATION: The formulation seeks efficient channel-training and beamforming-design strategies that maximize the system effective achievable rate under quantized RF hardware constraints.RF beamforming vectors are selected from a finite-size codebook F_RF with cardinality |F_RF| = Ntr.
  • T k FRF: The optimal cloud baseband and terminal RF beamforming vectors define the optimal achievable rate R⋆ under the stated optimization problem.R⋆ assumes perfect channel knowledge at the cloud processing unit and RF terminals.
  • T k FRF: Effective achievable rate accounts for mobility by retraining and redesigning beamformers every beam coherence time TB, allocating Ttr to training and the remainder to data transmission.Higher mobility decreases TB and lowers the data rate for the same beamforming vectors and training overhead.
  • T k FRF: The paper seeks very low channel-training overhead while maximizing achievable rate, addressing the large overhead of compressed sensing and exhaustive or hierarchical beam training.Integrating machine learning with beam-training solutions is reported to yield very low training overhead and near-optimal effective achievable rates for highly-mobile mmWave systems.

IV. BASELINE COORDINATED BEAMFORMING · A. Proposed Solution

The baseline coordinated beamforming solution separates RF and baseband design, replaces joint exhaustive search with simultaneous uplink beam training and disjoint RF selection, then enables coordinated downlink transmission.

  • IV. BASELINE COORDINATED BEAMFORMING: The baseline solution targets channel-training and beamforming design with low complexity and integration with the machine-learning model.It is also evaluated for achievable rate performance and mobility support.
  • A. Proposed Solution: For given RF beamforming vectors, optimal baseband beamformers are functions of the effective channel, making cloud baseband and terminal RF design separable.The design can therefore be solved in two stages for RF and baseband beamformers.
  • A. Proposed Solution: Exhaustive search over all BS beamforming combinations has high computational complexity, particularly for large antenna systems and codebooks.The proposed operation is introduced to obtain a lower-complexity solution.
  • A. Proposed Solution: All combined signals are fed back to the cloud processor, which calculates received power for each RF beamforming vector and selects each BS’s downlink vector separately.Disjoint selection avoids combinatorial optimization complexity and supports integration with machine learning.
  • A. Proposed Solution: Disjoint RF optimization can yield optimal achievable rate in important special cases for mmWave systems.After RF selection, cloud baseband beamforming vectors are constructed according to (10).
  • A. Proposed Solution: The designed cloud and RF beamforming vectors are used for downlink coordinated data transmission to achieve coverage, reliability, and latency gains.The baseline’s effective achievable rate RBL_eff is characterized using the beam-training pilot-sequence time Tp and RF vectors f BL_n given by (17).

B. Performance Analysis and Mobility Support · V. DEEP LEARNING COORDINATED BEAMFORMING

The baseline coordinated beamforming solution can approach the upper-bound rate in important mmWave cases, but exhaustive codebook training creates substantial mobility overhead. The paper therefore introduces machine learning for coordinated beamforming to reduce training overhead and enable highly mobile mmWave applications.

  • B. Performance Analysis and Mobility Support: The baseline solution’s achievable rate converges to the upper bound R⋆ in single-path channels and large-antenna regimes.This result holds despite the solution’s low complexity and disjoint RF beamforming design.
  • B. Performance Analysis and Mobility Support: For important special cases, disjoint RF beamforming across BSs achieves the same data rate as the upper bound R⋆, which requires combinatorial optimization.
  • B. Performance Analysis and Mobility Support: Effective achievable rate depends on both training and beamforming-design overhead and the rate achieved with the constructed beamforming vectors.
  • B. Performance Analysis and Mobility Support: The baseline exhaustively searches all Ntr codebook beamforming vectors, making it inefficient for applications requiring high throughput and mobility.
  • B. Performance Analysis and Mobility Support: ∼45% of the channel beam coherence time is consumed by training for 32 × 8 arrays, Ntr = 1024, Tp = 10 us, and v = 30 mph.The corresponding beam coherence time is around 23 ms.
  • B. Performance Analysis and Mobility Support: Machine learning is integrated with the baseline solution to dramatically reduce training overhead and enable highly mobile mmWave applications.
  • V. DEEP LEARNING COORDINATED BEAMFORMING: The paper introduces machine learning for mmWave coordinated beamforming and argues that it can provide performance gains difficult to attain with traditional communication systems.The section proceeds to explain the proposed coordinated deep learning solution, system operation, and machine learning modeling.

A. The Main Idea · B. System Operation

The proposed system integrates deep learning with coordinated beamforming to learn environment-dependent beam mappings from jointly received omni or quasi-omni uplink pilots. It operates through online learning and prediction phases, using the learned model to eliminate beam training while retaining effective rates and adapting to changing environments.

  • A. The Main Idea: A. The Main Idea: Deep learning learns the implicit mapping from environment geometry and user location to beam training results.The environment includes user/BS locations and surrounding geometry, whose effects are difficult to characterize with closed-form equations.
  • A. The Main Idea: A. The Main Idea: Jointly received uplink pilots form an RF signature that captures user/BS locations and environmental propagation effects.The signature arises through propagation, reflection, and diffraction after pilots are received at multiple BSs using omni or quasi-omni patterns.
  • A. The Main Idea: A. The Main Idea: Using only omni-received pilots, the model predicts the best RF beamforming vectors and totally eliminates beam training.This avoids special learning resources such as GPS data and yields negligible training overhead for highly-mobile mmWave applications.
  • A. The Main Idea: A. The Main Idea: The approach supports LOS and NLOS scenarios, learns from experienced scenarios, and inherits coordinated beamforming gains in coverage, reliability, and latency.It can adapt to different environments and become more robust over time as it memorizes scenarios such as traffic patterns.
  • B. System Operation: B. System Operation: Online learning monitors baseline coordinated beamforming, combining codebook-beam and omni-pattern observations to train the neural network.The cloud receives omni signals and beam-specific achievable rates while the baseline operation supplies training outcomes.
  • B. System Operation: B. System Operation: In prediction, the model uses only omni-received signals to select each BS’s RF beamforming vector and estimate effective channels.The predicted vectors are then used by BS terminals for pilot combining and construction of cloud baseband beamformers.
  • B. System Operation: B. System Operation: Predicting NB candidate beams instead of one beam gives training overhead (NB + 1)Tp, still much smaller than baseline overhead when NB is much smaller than Ntr.The model can refine a small candidate set through uplink training rather than directly selecting one beam.
  • B. System Operation: B. System Operation: The system switches to prediction when its estimated effective rate exceeds the baseline rate, and should periodically return to online learning as the environment changes.Optimizing this mixed operation for time-varying environments is identified as future research.

C. Machine Learning Modeling

The model uses jointly collected OFDM omni-received sequences from N base stations to predict beamforming performance, with separate per-base-station outputs and a regression objective. It adopts dataset-level input normalization and a simple fully connected ReLU/dropout architecture, while offering no optimality guarantees.

  • Loss function and learning model: This machine-learning model is one possible integrated-system design and has no optimality guarantees for performance or complexity.Developing higher-performance, lower-complexity models is identified as future research.
  • Input representation and normalization: The neural-network inputs are raw OFDM omni-received sequences romni k,n from the N BSs, retaining real and imaginary signal components.The total input dimension is 2KDLN.
  • Input representation and normalization: Per-dataset normalization is adopted because per-carrier, per-BS, and per-sample normalization can discard correlations encoding frequency, base-station, and location information.A simple implementation divides all inputs by a constant scaler Δnorm.
  • Output representation and normalization: N independent deep-learning models predict the RF beamforming performance for the N BSs using the omni-received sequences from all BSs.Each model has Ntr = |F RF| outputs, one predicted rate for each RF beamforming codeword.
  • Neural network architecture: The adopted architecture has MLayer fully connected layers with MNodes nodes, ReLU activations, and dropout after each layer for regularization.Optimizing the neural-network architecture is outside the paper’s scope.
  • Loss function and learning model: Regression training minimizes mean-squared error between predicted and desired normalized rates, enabling prediction of the best, second-best, third-best, or generally the best NB RF beams.The outputs represent achievable rates for candidate RF beamforming vectors rather than only a single selected beam.

D. Effective Achievable Rate and Mobility Support

The baseline coordinated beamforming solution can approach the optimal bound in important cases, but exhaustive beam training substantially reduces effective achievable rate. The deep-learning solution uses only two training resources, making overhead almost negligible while approaching the optimal effective achievable rate R⋆ for highly-mobile mmWave applications.

  • The baseline coordinated beamforming solution approaches the optimal bound in some special yet important cases.
  • Exhaustive beam training consumes substantial resources and significantly reduces the baseline solution’s effective achievable rate.
  • The learning model is trained to approach the baseline solution’s achievable rate, which is optimal in some cases.
  • Two training resources for omni-pattern and predicted-beam training make the proposed solution’s training overhead almost negligible.
  • When efficiently trained, the proposed solution can approach the optimal effective achievable rate, R⋆, and support highly-mobile mmWave applications.

VI. SIMULATION RESULTS · A. Simulation Setup

The simulations evaluate coordinated deep-learning beamforming for highly mobile mmWave applications using realistic vehicular LOS and NLOS channel scenarios. The setup models four coordinated 60 GHz BSs, ray-traced channels, user mobility, baseline beam training, and neural-network beam prediction.

  • VI. SIMULATION RESULTS: The simulation study evaluates coordinated deep-learning beamforming for highly-mobile mmWave applications, including beam-direction prediction, achievable-rate performance, parameter impacts, environmental adaptation, synchronization, and untrained scenarios.The study is organized across Sections VI-A through VI-F.
  • A. Simulation Setup: The setup focuses on vehicular communications and models four BSs simultaneously serving one mobile user over the 60 GHz band.The BSs are positioned on four lamp posts in a street-level environment.
  • A. Simulation Setup: The four lamp posts form a rectangle with 60m spacing along the street and 50m spacing across it.The environment uses a street-level geometry for the vehicular scenario.
  • A. Simulation Setup: The baseline selects each BS’s best RF beam through uplink beam training, whereas the deep-learning method uses omni-received sequences to predict the best RF beamforming vector.The omni-received sequences and corresponding rates form machine-learning data points, and performance is evaluated through effective achievable rate.

B. Does the System Learn How to Beamform?

The deep-learning model learns to map jointly received multi-path signatures to RF beamforming vectors, achieving effective rates that approach the optimal upper bound as training data increases. It succeeds in both LOS and NLOS settings while outperforming baseline coordinated beamforming and avoiding reliance on user coordinates alone.

  • LOS evaluation: As the training dataset grows, the proposed deep-learning coordinated beamforming approaches the optimal effective achievable rate R⋆ in the LOS scenario.The LOS setup uses 4 BSs with 32 × 8 UPAs serving a vehicle moving at 30 mph.
  • Beam prediction: The model predicts the best RF beamforming vector out of 1024 candidate beams for every BS using multi-path signatures received with a single antenna or omni-pattern.This demonstrates beam selection without narrow-beam training during inference.
  • Performance comparison: Deep learning achieves considerable data rate gains over baseline coordinated beamforming and performs nearly as well as the upper bound for large arrays and highly-mobile users.The model in the large-array and mobility comparison was trained with a LOS dataset of size 20k samples.
  • NLOS evaluation: The deep-learning strategy learns both LOS and best NLOS beamforming vectors from joint multi-path signatures, with effective achievable rate approaching the upper bound for larger training datasets.The NLOS evaluation includes NB = 1 and NB = 4, the baseline coordinated beamforming solution, and the upper bound R⋆.
  • Signature-based learning: The key advantage is learning from multi-path signatures rather than user coordinates, which cannot efficiently determine NLOS beams when identical locations correspond to different environments.Different NLOS setups at the same user location can require different beamforming vectors.

C. Impact of Communication System Parameters

The section evaluates how user speed, BS antenna count, uplink transmit power, and normalization affect coordinated beamforming. Deep learning remains near the upper bound across mobility and array sizes, but requires sufficient omni-received SNR.

  • Impact of User Speed and Number of BS antennas: Baseline coordinated beamforming faces a beamforming-gain versus training-overhead trade-off, with performance degrading as BS antennas or user speed increase.This produces an optimal antenna count for each user speed or beam coherence time.
  • Impact of User Speed and Number of BS antennas: The deep-learning strategy, trained on 20k samples, achieves almost the upper-bound performance across user speeds and BS antenna counts with negligible omni-pattern training overhead.Larger arrays may require bigger datasets during online learning, but prediction-phase uplink overhead remains antenna-independent.
  • Impact of Uplink Transmit Power and Omni Training Pattern: In the NLOS normalization comparison, per-dataset input normalization with per-BS output normalization achieves higher effective rates than the other candidate strategies.The comparison uses a deep learning model trained with a 20k samples dataset.
  • Impact of Uplink Transmit Power and Omni Training Pattern: The proposed system avoids estimating directional information such as arrival and departure angles by predicting it from signals captured at multiple distributed BSs.This supports beamforming from omni or quasi-omni reception rather than conventional directional training or channel estimation.

D. Impact of Machine Learning Parameters · E. System Adaptability and Robustness

The section examines how normalization and neural-network architecture affect effective rates, then shows that the coordinated beamforming system adapts over time to changing LOS and NLOS environments. Per-dataset and output normalization preserve useful learning information, while a lower-complexity CNN achieves comparable performance and later generalizes across scenarios.

  • D. Impact of Machine Learning Parameters: Per-dataset normalization achieves the highest effective achievable rate among the four candidate input-normalization strategies.The comparison considers per-dataset, per-sample, per-basestation, and per-element normalization in an NLOS scenario with 16×8 UPAs and a 20k-samples training dataset.
  • D. Impact of Machine Learning Parameters: Per-dataset normalization preserves correlations across subcarriers, BSs, and user locations, enabling the model to exploit training-dataset information for beam prediction.These correlations can encode distances, multipath signatures, and mappings between received signals and beamforming beams.
  • D. Impact of Machine Learning Parameters: Output normalization is required to achieve good data rates because otherwise large LOS rate differences dominate training and the model learns to beamform only for LOS links.The explanation is based on the NLOS scenario, where NLOS achievable rates are much smaller than LOS rates.
  • D. Impact of Machine Learning Parameters: The fully-connected and CNN architectures achieve almost the same effective data rates despite the potential complexity reduction in the CNN model.The comparison uses an LOS scenario with BSs employing 32 × 8 UPAs.
  • D. Impact of Machine Learning Parameters: The CNN-based architecture uses ∼754k parameters versus ∼1048k parameters in the fully-connected architecture while achieving almost the same effective spectral efficiency.Its filters can capture correlations between adjacent OFDM samples, extracting valuable information with lower complexity.
  • E. System Adaptability and Robustness: At dataset size 18k samples, performance recovered to the first-stage level, and at dataset size 26k samples it remained effective after the bus arrived again.The results show that the model generalized its learning to both LOS and NLOS scenarios, becoming more robust over time.
  • E. System Adaptability and Robustness: The coordinated beamforming system became more robust over time and adapted to perform well in both LOS and NLOS scenarios.The paper describes eventual coverage of previously unseen conditions such as cars, pedestrians, and trees blocking signals.

F. Does the System Require Phase Synchronization to Learn? · VII. CONCLUSION

The study finds that coordinated beamforming can be learned without phase synchronization, particularly with sufficient training data, while downlink coherent transmission may still require synchronization. Overall, the integrated deep-learning strategy enables low-overhead, reliable, and low-latency highly-mobile mmWave communication.

  • F. Does the System Require Phase Synchronization to Learn?: The evaluation compares perfect synchronization, no synchronization with random per-BS phase offsets, and RSSI-only inputs in a four-BS LOS scenario.RSSI-only inputs provide only the amplitude of the omni-received sequence to the neural network.
  • F. Does the System Require Phase Synchronization to Learn?: The deep-learning solution maintains good gain over the baseline even when only received signal strength indicators are used.The RSSI setting supplies no phase information to the machine learning model.
  • F. Does the System Require Phase Synchronization to Learn?: With more neural-network training or larger datasets, unsynchronized coordinated beamforming approaches the performance achieved with perfect phase synchronization.This indicates that phase synchronization may not be needed to learn coordinated beamforming when datasets are sufficiently large.
  • F. Does the System Require Phase Synchronization to Learn?: RSSI-based deep-learning coordinated beamforming still achieves a reasonable gain over the baseline coordinated beamforming solution.This approach does not require any phase information during learning.
  • F. Does the System Require Phase Synchronization to Learn?: Phase synchronization remains necessary during downlink transmission when signals from four BSs must add coherently at the mobile user antenna.The requirement can be relaxed by coordinating learning across four BSs while allowing only one BS to beamform to the user at a time.
  • VII. CONCLUSION: The paper develops an integrated machine-learning and coordinated-beamforming strategy that maps omni-received uplink pilots and beam-training results to beamforming vectors.Joint signals from distributed BSs provide an RF signature of user location and environmental interaction.
  • VII. CONCLUSION: The proposed solution requires negligible training overhead and performs almost as good as the genie-aided solution that perfectly knows the optimal beamforming vectors.Coordinated transmission from multiple BSs supports reliable coverage and low latency for highly-mobile mmWave applications.
  • VII. CONCLUSION: Accurate-ray-tracing simulations across LOS and NLOS environments show high data-rate gains over non-machine-learning coordinated beamforming, robust adaptation, and no need for BS phase synchronization during learning.Future directions include multi-user systems, time-varying scenarios, and more sophisticated machine-learning models.
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