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Federated Learning for Channel Estimation in Conventional and RIS-Assisted Massive MIMO

Ahmet M. Elbir, Sinem Coleri

arXiv:2008.10846v2eess.SPcs.ITcs.LG

TL;DR

The paper addresses the high communication overhead of centralized learning for ML-based channel estimation. It trains a CNN through federated learning on local user datasets for conventional and RIS-assisted massive MIMO, achieving approximately 16 times lower overhead than centralized learning while maintaining satisfactory performance close to it.

  • Problem

    Centralized channel-estimation training collects complete user datasets at the base station, creating substantial communication overhead.

  • Method

    A CNN is trained with federated learning on local user datasets for conventional and RIS-assisted massive MIMO, using one architecture for both scenarios.

  • Results

    The proposed approach provides approximately 16 times lower communication overhead than centralized learning while maintaining satisfactory channel-estimation performance close to centralized learning.

  • Takeaways & Limitations

    Federated CNN training supports channel estimation in both conventional and RIS-assisted massive MIMO without transmitting complete local datasets to the base station.

Abstract

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Machine learning (ML) has attracted a great research interest for physical layer design problems, such as channel estimation, thanks to its low complexity and robustness. Channel estimation via ML requires model training on a dataset, which usually includes the received pilot signals as input and channel data as output. In previous works, model training is mostly done via centralized learning (CL), where the whole training dataset is collected from the users at the base station (BS). This approach introduces huge communication overhead for data collection. In this paper, to address this challenge, we propose a federated learning (FL) framework for channel estimation. We design a convolutional neural network (CNN) trained on the local datasets of the users without sending them to the BS. We develop FL-based channel estimation schemes for both conventional and RIS (intelligent reflecting surface) assisted massive MIMO (multiple-input multiple-output) systems, where a single CNN is trained for two different datasets for both scenarios. We evaluate the performance for noisy and quantized model transmission and show that the proposed approach provides approximately 16 times lower overhead than CL, while maintaining satisfactory performance close to CL. Furthermore, the proposed architecture exhibits lower estimation error than the state-of-the-art ML-based schemes.

I. INTRODUCTION

The paper motivates federated learning for channel estimation in conventional and RIS-assisted massive MIMO, where centralized training creates substantial data-transfer overhead. It proposes decentralized CNN training while retaining channel-estimation performance close to centralized learning.

  • Millimeter-wave massive MIMO relies on large antenna arrays to compensate for severe scattering, penetration losses, and path loss.
  • RISs use passive reconfigurable elements to manipulate incident signals, improving received energy and expanding base-station coverage.
  • Accurate instantaneous CSI is important for designing beamformers and RIS-element phase shifts in dynamic massive-MIMO channels.
  • Centralized learning transfers complete user datasets to the base station, creating huge communication overhead because datasets can contain hundreds of thousands of symbols.
  • Federated learning exchanges model updates instead of complete datasets, motivating its use for channel estimation where prior FL studies largely assumed perfect CSI.
  • The proposed framework trains a CNN on local user datasets for conventional and RIS-assisted systems, using one architecture for direct and cascaded channel estimation.

B. Problem Description

The problem is to estimate each user's channel matrix from received pilot signals using a federated ChannelNet trained on local input-output datasets. ChannelNet learns a nonlinear mapping from pilots to channel labels.

  • The global ChannelNet at the base station is trained through federated learning on users' local datasets.
  • Each local dataset contains input-output pairs, with received pilot signals as inputs and channel matrices as output labels.
  • For each pair (X, Y), ChannelNet constructs the nonlinear relationship f(X|θ) = Y using learnable parameters θ.

III. FEDERATED LEARNING FOR CHANNEL ESTIMATION

The proposed framework collects training data locally, trains the channel-estimation model through federated learning, and performs prediction at users without sending local datasets to the BS. It addresses noisy gradient transmission with regularized training and establishes an O(1/t) convergence rate.

  • Framework stages: The framework has three stages: local training-data collection, federated model training, and channel prediction with the trained model.Users collect received pilots and estimated channel data, then use the trained neural network for local channel estimation.
  • Training objective: The received pilot signals are used as inputs, while channel data serve as labels and the training loss is the mean-squared error between labels and predictions.The local and centralized objectives are optimized iteratively using gradient descent.
  • Federated training: Unlike CL, FL preserves each local dataset at the user and transmits model updates to the BS for aggregation.CL collects the whole dataset at the BS, whereas FL solves local training problems and iteratively aggregates updates.
  • Communication efficiency: Gradient transmission reduces communication and energy costs because it sends updates rather than already known model information.The paper contrasts gradient transmission with direct model-parameter transmission and centralized dataset collection.
  • Noisy transmission: Noisy model and gradient transmission is modeled through additive noise, motivating a regularized loss function for FL training.The paper states that noisy gradients slow convergence compared with the noiseless objective.
  • Convergence and limitations: O(1/t) convergence is established for the FL-based model training, while wireless packet errors and changing channel statistics can slow practical convergence.The analysis differs from prior gradient-transmission results that rely on gradient sparsity.

C. FL for Channel Estimation in Massive MIMO

For conventional massive MIMO, ChannelNet maps received pilot signals to the channel matrix. Its real-valued CNN input contains real, imaginary, and phase information from the processed received pilots.

  • Input formation: ChannelNet receives pilot signals acquired during the preamble and processed through the users’ transmit and receive beamformers.The channel acquisition process uses MBS⌈MMS/NRF⌉ channel uses under the stated single-RF-chain assumption.
  • Input formation: The received pilot data are represented as three input channels containing their real part, imaginary part, and angle.This construction enables ChannelNet to accept real-valued data.
  • Output formation: ChannelNet outputs a real-valued vector formed from the vectorized real and imaginary parts of the channel matrix.The output dimension is 2NBSNMS × 1.
  • Channel estimation: The resulting mapping estimates the channel matrix Hk[m] directly from the received pilot signals Gk[m].

D. FL for Channel Estimation in RIS-Assisted Massive MIMO

The RIS-assisted scheme models and estimates both direct BS-user and cascaded BS-RIS-user channels. A single ChannelNet input-output construction jointly represents these channels for federated training.

  • Channel model: RIS-assisted channel estimation considers both direct BS-user and cascaded BS-RIS-user channels in the received-signal model.The direct and cascaded estimates are sufficient for beamformer design.
  • RIS representation: The RIS reflecting vector encodes each element’s on/off state and phase shift, while the cascaded channel represents the BS-RIS-user link.Practical RIS elements may have insertion loss when switched on or off.
  • Channel acquisition: The direct channel is estimated with all RIS elements off, whereas cascaded-channel estimation activates RIS elements one at a time.The resulting measurements are used to estimate the direct channel and cascaded channel matrix.
  • Training data: ChannelNet is trained with direct-channel pairs {yB,k, hB,k} and cascaded-channel pairs {YC,k, Vk}, then combines them into one input-output pair.
  • ChannelNet representation: The RIS-assisted input uses three real-valued channels from Υk, and the output concatenates hB,k and Vk.The stated input and output sizes are (NRIS + 1) × MBS × 3 and 2NBS(NRIS + 1) × 1.

E. Neural Network Architecture and Training

ChannelNet is a single CNN used for both conventional and RIS-assisted massive MIMO datasets. Its layered design includes convolution, normalization, feature mapping, dropout, and regression components, and FL iteratively aggregates user updates.

  • Architecture: A single 10-layer ChannelNet is trained on two datasets covering conventional and RIS-assisted massive MIMO.
  • Architecture: The CNN uses three convolutional layers with 128 filters and 3 × 3 kernels, followed by normalization layers for spatial feature extraction.The convolutional layers are the second, fourth, and sixth layers.
  • Architecture: A 1024-unit fully connected layer performs feature mapping, followed by dropout with κ = 1/2 before output regression.Dropout randomly selects weights in the fully connected layer during FL training.
  • Communication design: Dropout reduces the transmitted model-update size by reducing the active parameter and gradient vectors.
  • Training procedure: During FL, users transmit model updates, the BS aggregates them, and the aggregated parameters are broadcast for the next communication round until convergence.

A. Communication Overhead

The paper compares communication overhead and computational complexity for FL-based ChannelNet against CL and conventional channel-estimation methods.

  • Communication Overhead: FL overhead includes uplink gradient and downlink model transmissions across T training rounds, whereas CL transmits the full training dataset to the BS.The dominant overhead terms are D, the number of training data pairs, and P, the number of neural-network parameters.
  • Communication Overhead: 600,192 parameters are used in ChannelNet, and because training datasets usually contain more samples than model parameters, the paper expects TFL < TCL.The model uses three convolutional layers and three spatial channels.
  • Computational Complexity: ChannelNet has higher complexity than LS, while MMSE becomes more complex than ChannelNet at approximately NMSNBS ≥720.The comparison is made with respect to the product of the numbers of antennas at users and the BS.
  • Computational Complexity: ChannelNet can run efficiently on parallel processors such as GPUs, whereas GPU implementation is not straightforward for the other algorithms.The paper notes that other algorithms require algorithm-dependent processor configuration for GPU implementation.

V. NUMERICAL SIMULATIONS

The simulations evaluate FL-based channel estimation against ML-based, MMSE, and LS baselines under varying noise, user counts, and quantization conditions. They examine training RMSE and channel-estimation NMSE in massive MIMO settings.

  • Evaluation Setup: The simulations compare the proposed FL approach with SF-CNN, MLP, MMSE, and LS using channel-estimation NMSE and validation RMSE.Validation data comprise 20% of the whole dataset, and NMSE is evaluated over 100 Monte Carlo trials.
  • Simulation Parameters: The experiments use K = 8 users, NBS = 128 and NMS = 32 for massive MIMO, and NBS = NRIS = 64 for RIS-assisted systems.Each user's local dataset contains 100 channel realizations.

A. Channel Estimation in Massive MIMO

The proposed FL channel-estimation approach is evaluated in conventional and RIS-assisted massive MIMO under user variation, noisy or quantized transmission, information loss, and imperfect labels. It achieves satisfactory estimation performance while substantially reducing communication overhead relative to CL.

  • User variation: The proposed FL approach improves toward CL as the number of users increases, because aggregated model updates become more robust against noise.With fewer users, training-data diversity increases corruption during model aggregation.
  • Transmission impairments: At most 5% parameter loss during transmission is required for reliable channel estimation, because model-data loss significantly affects training and accuracy.The result concerns impulsive noise that completely removes portions of gradient or model data.
  • Transmission impairments: At least 5-bit quantization is required for reasonable channel-estimation performance, while quantization affects accuracy more than SNRθ.The quantization study reports improving performance with larger B and greater influence than SNRθ.
  • Massive MIMO comparison: FL and CL achieve similar NMSE for SNR≤25 dB, although CL performs better overall and FL saturates at high SNR.Imperfect labels slightly degrade performance but still outperform SF-CNN and MLP; the proposed CNN also reports lower NMSE than state-of-the-art NN architectures.
  • Communication overhead: 16 times lower communication overhead is achieved by FL than CL, requiring approximately 1×10^6 versus 16×10^6 data blocks.The corresponding overhead estimates are approximately 960×10^6 and 16×10^9 transmitted symbols for FL and CL, respectively.
  • RIS-assisted massive MIMO: In RIS-assisted massive MIMO, training diverges when SNRθ≤5 dB, while satisfactory channel estimation requires SNR≥15 dB and at least B≥5 bits at large SNRs.The RIS results combine direct and cascaded channel NMSE in a single plot.

APPENDIX A PROOF OF THEOREM 1

The appendix proves a convergence result for the averaged objective by assuming convexity, Lipschitz continuity, and smoothness, then bounding gradient-descent updates and objective decrease.

  • Assumptions: The proof assumes that the loss function is convex, L-Lipschitz, and β-smooth.These assumptions provide the regularity conditions used throughout the convergence argument.
  • Smoothness lemma: The averaged objective is established as β̄-smooth, with its gradient variation bounded by β̄||θ−θ′||.The proof derives this using the stated assumptions and a Hessian bound.
  • Descent argument: Gradient-descent substitution yields an upper bound relating the updated objective to the current objective through the averaged gradient.The proof then relates the updated objective to the optimal objective value using convexity.
  • Telescoping argument: Summing the per-iteration inequalities telescopes because consecutive terms cancel, while monotonic decrease of the averaged objective completes the bound.The argument replaces the generic update with θ_i and sums over iterations before invoking objective decrease.
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