Accurate wireless channel estimation is critical for next-generation wireless systems, enabling precise precoding for effective user separation, reduced interference across cells, and high-resolution sensing, among other benefits. Traditional model-based channel estimation methods suffer, however, from performance degradation in complex environments with a limited number of pilots, while purely data-driven approaches lack physical interpretability, require extensive data collection, and are usually site-specific. This paper presents a novel physics-informed neural network (PINN) framework that synergistically combines model-based channel estimation with a deep network to exploit prior information about environmental propagation characteristics and achieve superior performance under pilot-constrained scenarios. The proposed approach employs an enhanced U-Net architecture with transformer modules and cross-attention mechanisms to fuse initial channel estimates with RSS maps to provide refined channel estimates. Comprehensive evaluation using realistic ray-tracing data from urban environments demonstrates significant performance improvements, achieving over 5 dB gain in NMSE compared to state-of-the-art methods, with particularly strong performance in pilot-limited scenarios and robustness across different frequencies and environments with only minimal fine-tuning. We further extend the decoder for multi-step temporal prediction, enabling accurate forecasting of several future channel snapshots from a single estimate, useful for proactive beamforming and scheduling in mobile scenarios. The proposed framework maintains practical computational complexity, making it viable for massive MIMO systems in upper-mid band frequencies. Unlike black-box neural approaches, the physics-informed design provides a more interpretable channel estimation method.
Figures & tables
Figure 1: Block diagram of the proposed PINN-based channel estimation approach.
Method
Complexity
LS + linear interp.
O(DNr(Np+Nt))
LS + DFT denoising
O(DNrNtlogNt)
LS-OFDM (freq.-dom.)
O(DNrNtlogNFFT+NrNtNFFT)
Table I : Computational complexity of initial channel estimation methods
Figure 2: physics-informed neural network structure for channel estimation.
Figure 3: Multi-step temporal channel estimation architecture. The decoder generates L consecutive future channel snapshots in parallel from the current channel estimate and RSS map.
Parameter
Value
Map scale ( m2 )
350×450
Cropped map scale ( m2 )
10×10
Carrier frequency (GHz)
15 and 8
Bandwidth (MHz)
400 and 200
Number of samples
9877
Table III : System parameters in Boston map
Figure 4: RSS map for the Boston environment with PT=50 dBm and fc=15 GHz.
Figure 5: Urban canyon environment with fc=15 GHz. The multipath components with gains above −120 dBm are plotted.
FLOPs
Latency [ms]
Parameters
(Nt,Nr,D)
(576,4,16)
(576,4,16)
(576,4,16)
PINN
70.85G
11.12
3.5×108
DM
130.15G
50.30
5.5×104
Table VII : Complexity, latency, and parameters comparison
Figure 6: Ablation study of weight for physical component in loss function.
Figure 7: Log–scale comparison of training loss for the selected models.
Figure 8: NMSE performance of channel estimation using less complex initial estimation
Np
512
256
128
64
32
16
8
4
2
Initial LS-OFDM
-14.40
-11.23
-8.25
-5.49
-3.32
-1.33
0.28
1.98
3.01
Refined LS-OFDM
-19.21
-17.40
-16.20
-16.00
-13.87
-13.85
-12.87
-12.89
-12.35
Improvement
4.81
6.17
7.95
10.51
10.55
12.52
13.15
14.87
15.36
Table VIII : NMSE performance of channel estimation with varying Np at SNR=0 dB.
Figure 9: NMSE comparison across varying SNRs and pilot counts.
Figure 10: Transfer learning performance: NMSE vs. dataset for 20 and 100 epoch fine-tuning using Np=4 and SNR=0 .
Figure 11: NMSE performance as a function of prediction horizon L for multi-step temporal channel estimation in Boston and urban canyon environments at 0 dB SNR with Np=4 pilots.
Figure 12: NMSE performance versus SNR for different prediction horizons ( L=3,4,5 ) in the urban canyon environment with average velocity of 35 km/h and Np=16 pilots.
Accurate multipath parameter estimation is critical for modern wireless communication systems, particularly in challenging low-SNR environments. Traditional Maximum Likelihood Estimation algorithms, such as CLEAN, provide high-resolution parameter extraction but suffer from prohibitive computational complexity due to exhaustive grid search. Conversely, purely data-driven deep learning approaches lack physical grounding and struggle to generalize across variable multipath densities and off-grid parameters. To address these limitations, this paper proposes Neural Network-Assisted CLEAN (NN-CLEAN), a hybrid framework that embeds a multi-head residual network directly into the iterative CLEAN extraction loop. By replacing the exhaustive grid search with rapid, parallelizable forward passes while delegating residual subtraction to exact mathematical models, NN-CLEAN isolates physical multipath parameters without accumulating non- physical errors. Extensive Monte Carlo simulations demonstrate that NN-CLEAN achieves estimation accuracy exceeding 96% at 5 dB SNR, matching the traditional Grid-Search CLEAN (GS- CLEAN) baseline, while providing a massive reduction in computational complexity and substantially outperforming subspace methods and standalone one-shot neural networks. Crucially, NN-CLEAN exhibits a near-flat scaling in execution runtime and memory consumption as batch sizes increase. This highly efficient parallelization establishes NN-CLEAN as a robust, real- time solution for channel estimation in MIMO systems.
Chaofan Deng, Linyu Sun, Jaeho Lee +1
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, USA
Intelligent Reflecting Surfaces (IRSs) are a promising technology for enhancing the spectral and energy efficiency of millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems. In these systems, accurate channel estimation remains challenging due to the passive nature of IRS elements and the high pilot overhead in large-scale deployments. This paper presents a deep learning-based Multi-Block Attention (MBA) framework for efficient cascaded channel estimation in IRS-assisted mmWave MIMO systems that utilize orthogonal frequency division multiplexing (OFDM). First, we show the optimality of the discrete Fourier transform (DFT) and Hadamard matrices as phase configurations for least squares (LS) estimation. To reduce training overhead, we selectively deactivate IRS elements and compensate for induced feature loss using a two-stage architecture: (i) a Convolutional Attention Network (CAN) for spatial correlation recovery and (ii) a Complex Multi-Convolutional Network (CMN) for noise suppression. The MBA architecture mitigates error propagation through attention-guided feature refinement and denoising. Simulation results indicate that the MBA method reduces pilot overhead by up to 87% compared to the LS estimator. Additionally, at signal-to-noise ratios of 10 dB, our proposed method achieves approximately 51% lower normalized mean squared error (NMSE) than leading methods. It also maintains low computational complexity and adapts effectively to various propagation environments.
School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran · Department of Computer Engineering, Sharif University of Technology, Tehran, Iran
Deep generative models offer a powerful alternative to conventional channel estimation by learning complex channel distributions. By integrating the rich environmental information available in modern sensing-aided networks, this paper proposes MultiCE-Flow, a multimodal channel estimation framework based on flow matching and diffusion transformer (DiT). We design a specialized multimodal perception module that fuses LiDAR, camera, and location data into a semantic condition, while treating sparse pilots as a structural condition. These conditions guide a DiT backbone to reconstruct high-fidelity channels. Unlike standard diffusion models, we employ flow matching to learn a linear trajectory from noise to data, enabling efficient one-step sampling. By leveraging environmental semantics, our method mitigates the ill-posed nature of estimation with sparse pilots. Extensive experiments demonstrate that MultiCE-Flow consistently outperforms traditional baselines and existing generative models. Notably, it exhibits superior robustness to out-of-distribution scenarios and varying pilot densities, making it suitable for environment-aware communication systems.
Xiaotian Fan, Xingyu Zhou, Le Liang +2
School of Information Science and Engineering, Southeast University, Nanjing 210096, China · Purple Mountain Laboratories, Nanjing 211111, China