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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
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.
Method
A twin convolutional neural network uses received pilot signals to estimate each user’s direct BS-user and cascaded BS-LIS-user channels.
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.
Takeaways & Limitations
The framework provides robust channel estimation for LIS-assisted massive MIMO under user-location changes and non-ideal LIS switching.
Abstract
from arXiv · showhide
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.
- Related work: Prior LIS channel-estimation methods include an OFDM transmission protocol, sparse matrix factorization, and dual-ascent estimation.
- 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.
- Evaluation: The network is trained on several channel realizations and evaluated on separately generated test data to assess robustness.
- Results: The proposed approach outperforms existing DL-based techniques and tolerates user-location changes up to 4 degrees without retraining.
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.
- 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.
- Signal model: Each user receives a direct BS-user component and an LIS-mediated component from the BS through the reflecting surface.
- 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.
- 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.
- 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.
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.
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.
- A. Labeling: 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.
- A. Labeling: 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.
- A. Labeling: 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.
- A. Labeling: 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.
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}.
- B. Input Design: Received Pilots: 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.
- B. Input Design: Received Pilots: 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.
- B. Input Design: Received Pilots: The cascaded-channel input XCC is defined as an L × M × 3 real-valued matrix.Its construction follows the same three-channel input design.
- B. Input Design: Received Pilots: 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.
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.
- C. Network Architectures and Training: 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.
- C. Network Architectures and Training: 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.
- C. Network Architectures and Training: 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.
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.
- SNR = {10, 20, 30} dB is used during training, with synthetic label noise at SNRh = SNRG = {20, 30} dB.
- 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.
- 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.
- At high SNR (> 20 dB), DL-based performance saturates; noisy training data are used to improve tolerance to corrupted or imperfect inputs.
- 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.
- ChannelNet outperforms the other algorithms and provides satisfactory performance up to 4° angular mismatch in test data.
- ϵ ≤ 5 × 10^-3 provides satisfactory NMSE performance under non-ideal LIS-element switching.
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.
- The proposed approach outperforms the other evaluated algorithms in channel estimation experiments.
- 4 degrees: user-location changes do not require re-training the proposed method.
- 0.5% amplitude error: reasonable performance is maintained under non-ideal LIS-element switching.