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Deep Denoising Neural Network Assisted Compressive Channel Estimation for mmWave Intelligent Reflecting Surfaces
Shicong Liu, Zhen Gao, Jun Zhang, Marco Di Renzo, Mohamed-Slim Alouini
TL;DR
The paper addresses the challenge of estimating high-dimensional mmWave IRS channels when passive elements make channel acquisition difficult. It combines a hybrid passive/active IRS and multi-carrier compressive sensing with angular-domain common sparsity and a complex-valued DnCNN. Simulations report improved NMSE, approximately 4 dB gain from CV-DnCNN refinement, and adaptation across mismatched SNR and multipath conditions.
Problem
Accurate IRS channel estimation with reduced overhead is challenging because cascaded channels are high-dimensional and passive elements complicate separate IRS–UE and IRS–BS estimation.
Method
The method uses a hybrid passive/active IRS, multi-carrier pilot transmission, compressive sensing that exploits common angular sparsity across subcarriers, and a complex-valued DnCNN.
Results
Approximately 4 dB performance gain is obtained over preliminary SOMP-based estimation, while CV-DnCNN also outperforms real-valued DnCNN and adapts to mismatched channel conditions.
Takeaways & Limitations
The proposed approach achieves considerable NMSE performance with few activated elements and supports offline pretraining for operation across different SNR scenarios without repetitive training.
Abstract
from arXiv · showhide
Integrating large intelligent reflecting surfaces (IRS) into millimeter-wave (mmWave) massive multi-input-multi-ouput (MIMO) has been a promising approach for improved coverage and throughput. Most existing work assumes the ideal channel estimation, which can be challenging due to the high-dimensional cascaded MIMO channels and passive reflecting elements. Therefore, this paper proposes a deep denoising neural network assisted compressive channel estimation for mmWave IRS systems to reduce the training overhead. Specifically, we first introduce a hybrid passive/active IRS architecture, where very few receive chains are employed to estimate the uplink user-to-IRS channels. At the channel training stage, only a small proportion of elements will be successively activated to sound the partial channels. Moreover, the complete channel matrix can be reconstructed from the limited measurements based on compressive sensing, whereby the common sparsity of angular domain mmWave MIMO channels among different subcarriers is leveraged for improved accuracy. Besides, a complex-valued denoising convolution neural network (CV-DnCNN) is further proposed for enhanced performance. Simulation results demonstrate the superiority of the proposed solution over state-of-the-art solutions.
I. INTRODUCTION
IRS-assisted mmWave massive MIMO can improve coverage and link quality, but channel estimation remains difficult because cascaded channels are high-dimensional and IRS elements are largely passive. The paper addresses this challenge with compressive sensing, a hybrid passive/active architecture, and a complex-valued denoising network.
- Motivation: IRS can serve users whose direct base-station links are blocked, improving mmWave coverage and reducing blockage probability.IRS elements apply independently controllable phase shifts with few RF chains and many near-passive elements.
- Motivation: Accurate channel estimation with low overhead is challenging because cascaded BS–IRS–UE channels are high-dimensional and passive elements hinder separate channel estimation.Prior work often assumes that the BS and IRS already know the channel state information.
- Proposed approach: The paper proposes deep denoising neural network assisted compressive sensing broadband channel estimation for mmWave IRS systems.The approach is designed to reduce training overhead.
- Proposed approach: A hybrid passive/active IRS architecture and multi-carrier pilot transmission scheme use few receive RF chains to estimate user-to-IRS channels.The architecture trades channel-estimation performance against power consumption and hardware complexity.
- Proposed approach: Compressive sensing exploits angular-domain common sparsity across subcarriers, while a redundant dictionary improves reconstruction accuracy.The contribution uses joint multi-subcarrier estimation under the multiple-measurement-vector structure.
- Proposed approach: A complex-valued DnCNN further enhances estimation accuracy and can operate across varying SNRs and numbers of multipath components after training at one condition.The paper also provides model-related notation for complex variables, matrix operations, and convolution.
II. SYSTEM MODEL
The system model considers an IRS-assisted mmWave massive MIMO link with blocked direct BS–UE paths and OFDM across multiple subcarriers. A hybrid IRS combines many passive reflecting elements with a small number of active elements connected through an antenna-switch network.
- System configuration: OFDM with K subcarriers is used to address time-dispersive channels, while the IRS reflects incident signals with controllable phases.The modeled users have direct links to the mmWave base station completely blocked by obstacles.
- Hybrid IRS architecture: The hybrid IRS architecture combines many passive elements with very few active elements connected through an antenna-switch network.Passive elements only impose phase shifts and reflect signals, whereas active elements can be sequentially connected to RF chains.
- System configuration: The system notation distinguishes antennas, RF chains, and data streams at the BS and UEs for the hybrid MIMO transceiver.The described scenario assumes a single user, with extension to multiple users through mutually orthogonal pilot resources.
- System configuration: The IRS serves users in coverage dead zones where no direct BS–UE link exists.This deployment targets users whose direct paths are blocked by obstacles such as buildings.
III. PROPOSED CHANNEL ESTIMATION TECHNIQUE
The proposed technique estimates user-to-IRS channels with reduced training overhead by combining a hybrid passive/active IRS, multi-carrier pilots, compressive sensing, and deep learning reconstruction. Limited measurements are used to reconstruct high-dimensional channels with improved accuracy.
- Architecture and training: A hybrid passive/active IRS and uplink multi-carrier pilot scheme collect measurements for user-to-IRS channel estimation.Only a small number of active elements and receive RF chains are required during training.
- Channel reconstruction: Compressive sensing and deep learning reconstruct high-dimensional user-to-IRS channels from the few measurements collected at the IRS.The method combines sparse reconstruction with a denoising neural network for improved estimation accuracy.
A. Pilot Training with Hybrid Passive/Active IRS Architecture
The proposed pilot-training architecture uses very few active IRS elements and receive RF chains to collect partial uplink channel measurements, trading hardware and power costs against training overhead. Measurements are gathered across OFDM pilot slots and assembled for channel reconstruction.
- A. Pilot Training with Hybrid Passive/Active IRS Architecture: The IRS combines many passive elements with very few active elements connected through an antenna switching network.Passive elements apply controllable phase shifts, while active elements are sequentially connected to receive RF chains during training.
- A. Pilot Training with Hybrid Passive/Active IRS Architecture: The uplink pilot phase uses B time slots, with active elements sequentially activated to collect IRS measurements for each subcarrier.During data transmission, the active elements operate as passive elements.
- A. Pilot Training with Hybrid Passive/Active IRS Architecture: The channel is represented using array steering vectors for IRS and UE angles within a geometric multipath model over the OFDM subcarriers.The model includes multipath components, path gains, delays, and azimuth and elevation angles.
- A. Pilot Training with Hybrid Passive/Active IRS Architecture: Each time slot produces a number of measurements equal to the number of IRS receive RF chains, so total measurements satisfy M = B N_RF^IRS.Increasing the number of RF chains can reduce the required training overhead B, but increases power consumption and hardware requirements.
- A. Pilot Training with Hybrid Passive/Active IRS Architecture: The received pilot observations are modeled with frequency-flat precoding, antenna selection, vectorized channels, and stacked noise across the training slots.The frequency-flat assumption simplifies calculation but may increase peak-to-average-power ratio; scrambling can relax it.
- A. Pilot Training with Hybrid Passive/Active IRS Architecture: Using only one RF chain is an energy-saving and low-cost option, requiring successive activation of N_RF^IRS active elements across the training slots.The architecture explicitly trades channel-estimation performance against power consumption and hardware complexity.
B. CS-Based UE-IRS Channel Reconstruction
The reconstruction stage exploits angular-domain sparsity and shared scatterers across subcarriers to recover high-dimensional UE-IRS channels from limited measurements. A redundant dictionary mitigates angular-grid leakage, while SOMP jointly estimates multiple subcarrier channels.
- B. CS-Based UE-IRS Channel Reconstruction: Compressive sensing reconstructs high-dimensional channels from limited pilot measurements by exploiting angular-domain sparsity in mmWave MIMO channels.The reconstruction targets the vectorized channel representation associated with the UE-IRS links.
- B. CS-Based UE-IRS Channel Reconstruction: After compressive-sensing estimation, the CV-DnCNN jointly processes the real and imaginary channel parts and outputs residual noise for denoising.The network treats the complex channel matrix as a two-channel noisy image in the angular-delay domain.
- B. CS-Based UE-IRS Channel Reconstruction: The redundant-dictionary formulation models the channel as an approximately sparse vector plus effective noise that combines quantization error and measurement noise.The effective noise is n_E = Φvec(N̄) + n_k.
- B. CS-Based UE-IRS Channel Reconstruction: Channels on different subcarriers share similar scatterers because spatial propagation characteristics remain nearly unchanged within the system bandwidth.This shared structure provides common angular-domain sparsity across subcarriers.
- B. CS-Based UE-IRS Channel Reconstruction: The simultaneous orthogonal match pursuit algorithm jointly acquires multiple sparse channel vectors at different subcarriers.SOMP is used to solve the stated compressive-sensing optimization problem.
C. DL-Assisted Estimation Enhancement Architecture
The architecture treats the angular-delay channel as a two-channel noisy image and uses a complex-valued denoiser to remove estimation errors from CS-reconstructed channels.
- The channel matrix is represented by its real and imaginary parts as a two-channel noisy image for denoising.This representation exploits their correlation in the angular-delay domain.
- The CV-DnCNN jointly processes real and imaginary channel components using complex signal-processing modules.It integrates complex building blocks into a DnCNN architecture rather than processing the two parts independently.
- The CV-DnCNN uses complex weights and a complex ReLU activation while retaining the DnCNN-style MSE training objective.The network architecture contains repeated convolutional layers with batch normalization between convolution and ReLU in the repeated layers.
- The denoiser learns a residual mapping from the noisy estimated channel Ĝ to the overall estimation error E.The enhanced estimate is obtained after predicting the error from the preliminary estimate.
- The final spatial-frequency channel is reconstructed from the denoised angular-delay representation using the DFT matrix.The transformation is expressed as Ĥ = G e^T.
IV. SIMULATION RESULTS
Simulations evaluate the CS estimator and CV-DnCNN across measurement counts, SNRs, multipath conditions, and processing time, showing improved accuracy, robustness, and fast inference.
- Simulation setup: The simulations use a 28GHz carrier, 100MHz bandwidth, 256 OFDM subcarriers, and an IRS with 16 × 16 elements and 64 active antennas.The default channel setting is L = 6 multipath components, with SOMP oversampling rate β = 4.
- Preliminary CS estimation: Increasing the number of measurements M improves preliminary SOMP estimation, while M—not the active-element proportion—primarily determines performance.With fixed L and M, NMSE degrades only slightly as the IRS grows; M = 64 is selected for subsequent simulations as a complexity-performance trade-off.
- CV-DnCNN enhancement: The CV-DnCNN improves preliminary SOMP estimation by around 4dB and outperforms the real-valued DnCNN.This enhancement is evaluated after preliminary estimation with β = 4.
- Robustness and generalization: A CV-DnCNN trained at SNR = 10dB remains robust when tested across SNRs from −10 ∼20dB.The robustness is evaluated using a channel dataset whose parameters differ from those used for training.
- Robustness and generalization: A model pretrained at SNR = 10dB with L = 6 adapts to channels with different MPC counts with almost the same performance as matched training.The paper therefore reports negligible performance loss when offline-pretrained on simulated channels and applied to practical scenarios.
- Computational cost: CV-DnCNN processes each preliminary channel estimate in less than 1 × 10^-5s on an i7-8700 processor with an NVIDIA 1060ti GPU.
V. CONCLUSION
The paper combines a few-RF-chain passive/active IRS, CS-based broadband estimation, and complex-valued denoising for low-overhead mmWave IRS channel estimation.
- The method achieves considerable NMSE performance with a small number of activated elements and further improves estimation through a fast deep-learning step.
- The CV-DnCNN provides superior performance to real-valued networks and supports operation across different SNR scenarios without repetitive training.