Lightweight Deep Learning-Based Channel Estimation for RIS-Aided Extremely Large-Scale MIMO Systems on Resource-Limited Edge Devices

Summary

This paper proposes a lightweight deep learning framework for efficient cascaded channel estimation in Reconfigurable Intelligent Surface (RIS)-assisted Extremely Large-Scale MIMO (XL-MIMO) systems, specifically designed for deployment on resource-constrained edge devices. The work addresses the challenges of scalability and practical deployment of existing deep learning-based channel estimation models in XL-MIMO systems, where the growing number of antennas and RIS elements introduces significant barriers to real-time and efficient channel estimation, drastically increasing data volume, escalating computational complexity, requiring advanced hardware, and resulting in substantial energy consumption.

The system model considers an XL-MIMO system with a Base Station (BS) equipped with M antennas arranged in a uniform planar array configuration (Mh horizontal and Mv vertical antennas), communicating with K single-antenna users. The RIS has N = Nh × Nv passive reflecting elements arranged in a uniform planar array. A Line of Sight (LoS) is assumed between users and RIS and between RIS and BS. The channel between the k-th user and RIS elements is modeled as a Rician fading channel, while the channel between RIS and BS is also Rician. The Non-LoS (NLoS) channels are modeled as quasi-static correlated Rayleigh fading, with correlation matrices for both the BS and RIS. The direct channel between user and BS follows a correlated Rayleigh fading model.

The channel estimation framework uses a Time Division Duplex (TDD) protocol divided into two phases: direct channel estimation (with RIS off) and cascaded channel estimation (with RIS on using L ≥ N distinct phase shift matrices). The received pilot signal at the BS for the k-th user during the l-th subframe is given by yk = bk + Hdiag(Θl)fk + vk, where bk is the direct channel, H is the RIS-BS channel, fk is the user-RIS channel, Θl is the reflection coefficient matrix, and vk is noise. The cascaded channel is defined as Gk = H diag(fk) ∈ CM×N. The LS estimator is used as a coarse initial estimate, and the LMMSE estimator is discussed but noted to have a significant performance gap due to model mismatch since the cascaded channel does not follow Rayleigh fading.

The proposed deep learning architecture is a multi-level encoder-decoder design with integrated denoising capabilities. The framework integrates a dedicated denoising module employing a subtraction-based structure to enhance channel estimation by isolating core signal components from additive noise. In the encoder, each level consists of multi-layer Convolutional Neural Networks (CNNs) with distinct denoising blocks, with MaxPooling layers for downsampling between levels. The decoder uses bilinear interpolation for upsampling and incorporates skip connections that directly transfer high-resolution features from the encoder to the decoder, preserving essential spatial correlations while filtering out noise. The architecture also aggregates feature maps from multiple hierarchical levels, enabling multi-scale feature integration that captures richer contextual information. Each denoising block introduces a 1×1 convolutional layer at the beginning to align input and output dimensions, followed by multiple convolutional layers with batch normalization and nonlinear activation, and finally performs element-wise subtraction between the input Il and output z̃θ(Il) to produce the denoised channel matrix: Zl = Il − Z̃θ(Il). The complex-valued data is decomposed into real and imaginary components provided as separate input channels.

The paper leverages spatial correlation inherent in the cascaded channel, which results from closely placed RIS elements and BS antennas. The spatial correlation between RIS elements is modeled using a zero-order Bessel function of the first kind, Rr[n,n′] = J0(2π/λ dn − dn′), showing that correlation oscillates and gradually decays with increasing element separation. The correlation between the BS and RIS is governed by the correlation structures of both, with the channel matrix Gi ∈ CM×N exhibiting spatial correlation.

To enable scalable training for large-scale systems on resource-constrained edge devices, the paper proposes a patch-based training mechanism. Rather than processing the entire high-dimensional data point G̃LSi ∈ CM×N at once, the framework partitions it into smaller, more manageable patches of size Px × Py. From each data point, P patches are extracted with random starting coordinates within the valid range, ensuring no overlap. This approach substantially reduces memory and computational requirements. The paper argues that due to spatial correlation, training with a small number of representative patches per training example suffices for effective model learning, as the model can inherently learn the correlation structure of neighboring elements from the latent space representation. During offline training, patches and their corresponding labels are fed into the architecture, while during online inference, the trained model directly processes the entire input channel matrix without patch extraction, reducing inference time.

The computational complexity analysis shows that the total complexity of the proposed architecture is O(H0W0(C0out)2K2L + H0W0(C0out)2K2 + H0W0(C0out)2K2L2), where H0×W0 is the input feature map spatial dimension, C0out is the number of output filters, K is the kernel size, and L is the number of levels. This complexity scales directly with the size of the input feature map, indicating that patch-based training substantially reduces computational cost. The paper reports that the proposed method requires only 6.73 × 10 7 FLOPs, compared to 4.54 × 10 12 for CDRN and 1.55 × 10 11 for SSL, demonstrating significant computational efficiency.

Simulation results are presented for a system with 1024 antennas (Mh = 32, Mv = 32) and 128 RIS elements (Nh = 16, Nv = 8). The model uses 32 base filters, doubling with each depth level in the encoder, with ReLU activation functions and a linear function at the output layer. Training uses an initial learning rate of 0.004 with exponential decay scheduling and the Adam optimizer, with 3 levels, 2 convolutional layers per level, batch size 32, and 40 epochs. A synthetic dataset of 10,000 samples was generated, with patch sizes of 16×32 and 32×32 selected to align with spatial correlation properties. The dataset was split 70% for training and 30% for validation, with a separate testing dataset of 2,000 samples for each SNR value.

The performance evaluation uses Normalized Mean Squared Error (NMSE) as the metric. Results show that the proposed scheme consistently outperforms benchmark algorithms (LS, LMMSE, BLMMSE, CDRN, SSL) across an SNR range of-15 dB to 20 dB. At low SNR levels (-15 dB to-10 dB), the proposed scheme achieves an error reduction of approximately 13.65 dB compared to LS, 0.8 dB over LMMSE and BLMMSE, and 0.5 dB over CDRN and SSL. At moderate-to-high SNR (5-20 dB), the proposed model maintains its advantage, with gains of 1.7 and 1.0 dB over CDRN and SSL at 10 dB, and 0.56-0.23 dB and 0.45-0.10 dB over CDRN and SSL at 15-20 dB. The 32×32 patch size consistently achieves lower NMSE than 16×32, with improvements ranging from 0.4 dB to 0.08 dB.

The paper also evaluates performance with varying training dataset sizes (3,000 to 12,000 samples). The proposed framework consistently achieves lower NMSE with increasing dataset size, effectively leveraging larger datasets and capturing complex spatial correlations. For smaller datasets (3,000-5,000 samples), CDRN shows performance degradation of about 2.5-2.6 dB relative to the proposed scheme, while SSL lags by approximately 0.8-1.18 dB. For larger datasets (10,000-12,000 samples), CDRN and SSL achieve NMSEs approximately 2 dB and 1.5 dB higher than the proposed model.

Direct channel estimation results show the proposed framework consistently outperforms all benchmarks across the entire SNR range, with LS exhibiting the poorest performance (16.35 dB, 12.67 dB, and 9.41 dB higher NMSE at-15 dB, -10 dB, and-5 dB, respectively). At 20 dB, LS remains 0.41 dB inferior, while CDRN and SSL trail by 0.11 dB and 0.1 dB, respectively.

The paper also compares performance under correlated and uncorrelated fading conditions for NLoS channels. The correlated variants consistently outperform across all SNR regimes, demonstrating that spatial correlation enhances the model's ability to exploit inter-element dependencies, leading to more accurate, stable, and noise-resilient channel estimation. At low SNRs, the proposed correlated model outperforms CDRN and SSL by approximately 0.50-2.56 dB and 0.49-2.67 dB, respectively, while at higher SNRs (10-20 dB), gains of 1.69-0.23 dB over CDRN and 1.07-0.10 dB over SSL are maintained.

Finally, the impact of increasing the number of phase shift matrices (L) on NMSE performance is evaluated. Increasing L significantly improves estimation accuracy up to L = 128, after which performance gains become marginal. At L = 128, the proposed scheme surpasses CDRN and SSL by around 2.2 dB and 1.58 dB, respectively, while maintaining a substantial margin of more than 4 dB compared to LS and LMMSE estimators. For higher values of L (144, 160, 176), the proposed method maintains gains of approximately 1.2-1.5 dB over CDRN and 1.2-1.4 dB over SSL, indicating diminishing returns but consistently outperforming benchmarks.

The paper concludes that the proposed framework enhances estimation accuracy and significantly reduces computational overhead, maintaining efficiency even as the number of antennas and RIS elements scales in XL-MIMO systems, making it well-suited for real-time deployment on edge devices. This pioneering approach lays the foundation for scalable, energy-efficient, and practical RIS-enabled XL-MIMO systems in 6G and beyond.

Based on the paper, here are the specific improvements I can make to an AI system, and what the improved system can do:

Improvements:

1. Patch-Based Dimensionality Reduction for Training: I will implement a training pipeline that extracts small, non-overlapping, spatially correlated patches (e.g., 16×32 or 32×32) from high-dimensional channel matrices (e.g., 1024×128). Instead of feeding the entire matrix into the model, I will train the network on these patches, reducing input dimensionality by orders of magnitude.

2. Multi-Scale Encoder-Decoder with Denoising Blocks: I will design a neural network architecture with a multi-level encoder-decoder structure. Each encoder level will contain a dedicated denoising block that performs element-wise subtraction of the learned noise from the input. I will add 1×1 convolutions to align dimensions for this subtraction, and use skip connections to fuse high-resolution encoder features with decoder features at multiple scales.

3. Spatial Correlation-Aware Training Strategy: I will modify the training data sampling to exploit the spatial correlation between BS antennas and RIS elements. By training on a subset of representative patches (e.g., one patch per data sample), the model will learn the underlying correlation structure (e.g., Bessel function-based decay) and generalize to unseen, correlated elements without needing to see all of them.

4. Complex-Valued Data Handling: I will decompose the complex channel matrices into their real and imaginary components and feed them as two separate input channels to the convolutional network, enabling the model to learn from both the magnitude and phase information effectively.

5. Lightweight Inference Design: I will design the model to accept the full high-dimensional channel matrix during inference (without patch extraction), while the training remains patch-based. This ensures low-latency, real-time estimation during deployment on edge devices.

What the Improved AI System Can Do:

1. Estimate Cascaded Channels in XL-MIMO Systems: The system can accurately estimate the user-RIS-BS cascaded channel in systems with thousands of antennas and hundreds of RIS elements, a task previously considered computationally infeasible for edge devices.

2. Achieve Superior Accuracy at Low SNR: It will outperform traditional estimators (LS, LMMSE) and existing deep learning models (CDRN, SSL) by up to 13.65 dB at low SNRs (-15 dB), and maintain a consistent advantage of 0.2–1.7 dB over the best benchmarks even at high SNRs (20 dB).

3. Train Effectively with Limited Data: The system can achieve high accuracy with as few as 3,000 training samples, maintaining a performance gap of over 2 dB compared to other deep learning methods under the same data constraints, making it robust for real-world scenarios where large datasets are unavailable.

4. Operate on Resource-Constrained Edge Devices: The system reduces computational complexity (FLOPs) from 10 12 (CDRN) and 10 11 (SSL) to 10 7, a reduction of four to five orders of magnitude, enabling real-time training and inference on devices with limited memory and processing power.

5. Maintain Robustness Across Different Channel Conditions: It will perform consistently well under both correlated and uncorrelated fading conditions, and with varying pilot overheads (L), demonstrating adaptability to diverse and dynamic wireless environments.