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Deep Channel Learning For Large Intelligent Surfaces Aided mm-Wave Massive MIMO Systems

Ahmet M. Elbir, A Papazafeiropoulos, P. Kourtessis, S. Chatzinotas

arXiv:2001.11085v3eess.SPcs.ITcs.LG

TL;DR

LIS-assisted massive MIMO reduces hardware complexity but requires estimating both direct and cascaded channels, with complexity growing with the number of LIS elements. The paper proposes a twin-CNN framework that uses received pilots for per-user channel estimation. Experiments report superior performance to existing DL-based techniques, robustness to user-location changes up to 4 degrees, and reasonable performance with 0.5% switching amplitude error.

  • Problem

    LIS-assisted systems involve both direct and cascaded wireless channels, while channel-estimation complexity is high because of the large number of LIS elements.

    Source: §I · p. 1

  • Method

    A twin convolutional neural network uses received pilot signals to estimate each user’s direct BS-user and cascaded BS-LIS-user channels.

    Source: §I · p. 1, A. Labeling · p. 2, C. Network Architectures and Training · p. 3

  • Results

    The proposed approach outperforms other algorithms, requires no retraining for user-location changes up to 4 degrees, and provides reasonable performance up to 0.5% switching amplitude error.

    Source: §I · p. 1, §V · p. 5

  • Takeaways & Limitations

    The framework provides robust channel estimation for LIS-assisted massive MIMO under user-location changes and non-ideal LIS switching.

    Source: §I · p. 1, §IV · p. 5, §V · p. 5

Abstract

from arXiv · show

This letter presents the first work introducing a deep learning (DL) framework for channel estimation in large intelligent surface (LIS) assisted massive MIMO (multiple-input multiple-output) systems. A twin convolutional neural network (CNN) architecture is designed and it is fed with the received pilot signals to estimate both direct and cascaded channels. In a multi-user scenario, each user has access to the CNN to estimate its own channel. The performance of the proposed DL approach is evaluated and compared with state-of-the-art DL-based techniques and its superior performance is demonstrated.

I. INTRODUCTION

The paper addresses high-complexity channel estimation in LIS-assisted mm-Wave massive MIMO by proposing a DL framework that estimates direct and cascaded channels. Its twin-CNN approach is reported to outperform existing DL-based techniques and remain robust to user-location changes up to 4 degrees.

Motivation

  • LIS introduces both direct and cascaded BS-user channels, making channel estimation complex because of the large number of reflecting elements.DL techniques are proposed as a way to lower this complexity.Source: §I · p. 1

Related work

  • Prior LIS channel-estimation methods include an OFDM transmission protocol, sparse matrix factorization, and dual-ascent estimation.Source: §I · p. 1

Proposed approach

  • The proposed framework uses a twin CNN to estimate direct BS-user and cascaded BS-LIS-user channels from received pilot signals.Each user accesses the deep network to estimate its own channel.Source: §I · p. 1

Evaluation

  • The network is trained on several channel realizations and evaluated on separately generated test data to assess robustness.Source: §I · p. 1

Results

  • The proposed approach outperforms existing DL-based techniques and tolerates user-location changes up to 4 degrees without retraining.Source: §I · p. 1

II. SYSTEM MODEL AND PROBLEM FORMULATION

The system comprises a BS serving single-antenna users through an LIS with passive reflecting elements, producing direct and LIS-mediated channel components. The estimation objective is to recover each user’s direct and cascaded channels from downlink pilot observations.

System model

  • The modeled system has a BS with M antennas, K single-antenna users, and an LIS containing L passive reflecting elements.Source: §II · p. 1

LIS operation

  • The LIS elements apply controllable phase shifts to incident signals through PIN diodes connected to an LIS controller over a BS backhaul link.Source: §II · p. 2

Signal model

  • Each user receives a direct BS-user component and an LIS-mediated component from the BS through the reflecting surface.Source: §II · p. 2

LIS model

  • The LIS reflection matrix is diagonal, with each element specified by an on/off amplitude state β_l and phase shift φ_l.The ideal states are β_l ∈ {0, 1}, while practical switching may introduce errors.Source: §II · p. 2

Channel model

  • The mm-Wave channels use a Saleh-Valenzuela geometric model with limited scattering and path contributions for the direct, LIS-user, and BS-LIS links.Source: §II · p. 2

Problem formulation

  • The estimation target is each user’s direct channel hD,k and cascaded channel matrix Gk in downlink transmission.Each user feeds received pilot signals to ChannelNet for its own channel estimation.Source: §II · p. 2

III. CHANNEL ESTIMATION VIA DEEP LEARNING

The proposed channel-estimation framework uses received pilot signals as inputs to estimate both direct and cascaded channels.

Channel estimation

  • Received pilot signals are provided as inputs to the deep-learning framework for estimating the direct and cascaded channels.Source: §III · p. 2

A. Labeling

The labeling procedure separates direct-channel estimation from cascaded-channel estimation, using pilot configurations and generated input-output pairs for the deep network. Two cascaded-channel approaches are described, with correlated or corrupted pilots favoring the formulation involving less-corrupted X.

A. Labeling

  • Training uses two phases: direct-channel estimation with LIS elements off, followed by cascaded-channel estimation.The direct channel hD,k is labeled first; the cascaded channel Gk is then estimated using one of two approaches.Source: A. Labeling · p. 2
  • The first cascaded-channel approach turns on one LIS element at a time and estimates each corresponding channel column using P = M pilots.The estimated columns are assembled into the cascaded matrix ˆGk.Source: A. Labeling · pp. 2–3
  • The second approach turns on all LIS elements and jointly estimates the L columns using an ML × ML pilot matrix.The reflect beamforming vector is set to an L×1 all-ones vector.Source: A. Labeling · p. 3
  • Perfectly orthogonal pilots make the two cascaded-channel estimates equivalent, whereas correlated or corrupted pilots make (6) perform better because X contains less corruption.The comparison is referenced to Fig. 4.Source: A. Labeling · p. 3
  • Algorithm 1 generates training datasets by iterating over channel realizations and user-related indices, producing datasets for direct and cascaded channels.The stated dataset length is T = UVK.Source: A. Labeling · p. 3

B. Input Design: Received Pilots

The input design converts received pilot signals into real-valued, three-channel matrices for direct and cascaded channel estimation. The network outputs vectorized channel representations derived from corresponding input-output training pairs.

B. Input Design: Received Pilots

  • The deep network receives pilot signals as inputs and pairs them with direct-channel or cascaded-channel labels.The corresponding pairs are {yD,k, hD,k} and {yC,k, gk,l}.Source: B. Input Design: Received Pilots · p. 3
  • Each received-signal entry is represented by its real part, imaginary part, and absolute value.The paper describes this as a real-valued “three-channel” representation.Source: B. Input Design: Received Pilots · p. 3
  • For direct-channel estimation, yD,k is partitioned into M columns to construct XDC for two-dimensional convolutional filters.XDC is formed as a ˜MטM×3 matrix.Source: B. Input Design: Received Pilots · p. 3
  • The cascaded-channel input XCC is defined as an L × M × 3 real-valued matrix.Its construction follows the same three-channel input design.Source: B. Input Design: Received Pilots · p. 3
  • The network outputs vectorized channel matrices, with zDC and zCC formed from real and imaginary components of the direct and cascaded channels.The stated output dimensions are 2M×1 and 2ML × 1, respectively.Source: B. Input Design: Received Pilots · p. 3

C. Network Architectures and Training

ChannelNet uses two identical CNN branches for direct and cascaded channel estimation, with input sizes adapted to each task. Training includes dropout, mini-batches, and validation-based stopping, while performance is examined against SNR using channel-estimation NMSE.

C. Network Architectures and Training

  • ChannelNet is composed of two identical nine-layer CNNs for direct- and cascaded-channel estimation.The shared architecture accepts different input sizes for the two channel-estimation tasks.Source: C. Network Architectures and Training · p. 3
  • The architecture includes three convolutional layers with 256 3 × 3 filters and fully connected layers with 1024 and 2048 units.A 50% dropout layer follows each fully connected layer.Source: C. Network Architectures and Training · p. 3
  • Figure 3 evaluates direct and cascaded channel-estimation NMSE with respect to SNR.The figure’s caption identifies channel-estimation NMSE and SNR as the plotted quantities.Source: Figure 3 · p. 4
  • A mini-batch size of 128 samples is used, and training stops when validation accuracy fails to improve for three consecutive epochs.The stopping criterion is validation-based.Source: C. Network Architectures and Training · p. 4

IV. NUMERICAL SIMULATIONS

The simulations evaluate ChannelNet against MLP, SF-CNN, and LS under pilot corruption, angle mismatch, and non-ideal LIS switching. ChannelNet generally provides the strongest reported performance and remains satisfactory under several test changes.

  • P = M = 64, L = 100, and K = 8 are used with ND = NA = NH = 10 paths in the simulation environment.Source: §IV · p. 4
  • SNR = {10, 20, 30} dB is used during training, with synthetic label noise at SNRh = SNRG = {20, 30} dB.Source: §IV · p. 4
  • 40 minutes are required for training, while online deployment takes 0.004 seconds; evaluation uses J = 100 Monte Carlo experiments on separately generated test data.Source: §IV · p. 4
  • ChannelNet has superior performance among the DL-based methods because it jointly uses convolutional and fully connected layers, while MLP and SF-CNN use only one of these structures.Source: §IV · p. 4
  • At high SNR (> 20 dB), DL-based performance saturates; noisy training data are used to improve tolerance to corrupted or imperfect inputs.Source: §IV · p. 4
  • SNRX ≥ 20 dB is required for reasonable NMSE under corrupted pilots, with ChannelNet performing best and the first cascaded-estimation method more robust than the second.Source: §IV · p. 4
  • ChannelNet outperforms the other algorithms and provides satisfactory performance up to 4° angular mismatch in test data.Source: §IV · p. 4, Figure 5 · p. 5
  • ϵ ≤ 5 × 10^-3 provides satisfactory NMSE performance under non-ideal LIS-element switching.Source: §IV · p. 5, Figure 6 · p. 5

V. SUMMARY

The proposed deep-learning method uses identical user-side networks to estimate direct and cascaded channels, outperforming other algorithms while remaining robust to location changes and switching errors.

  • Each user uses an identical deep network fed by received pilot signals to estimate direct and cascaded channels.Source: §V · p. 5
  • The proposed approach outperforms the other evaluated algorithms in channel estimation experiments.Source: §V · p. 5
  • 4 degrees: user-location changes do not require re-training the proposed method.Source: §V · p. 5
  • 0.5% amplitude error: reasonable performance is maintained under non-ideal LIS-element switching.Source: §V · p. 5

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