Channel Estimation

Accurate and low latency channel estimation is critical for modern MIMO systems, particularly under mobility, where channels exhibit structured sparsity and strong temporal correlation. This paper proposes a time-series conditioned diffusion framework for channel estimation that performs denoising in the angular domain. Starting from least squares (LS) observations, we train a diffusion denoiser whose conditioning information is encoded by a long short-term memory (LSTM) network over a short observation sequence, enabling the model to exploit temporal dynamics beyond per-snapshot estimation. To robustly balance observation fidelity and learned generative priors across a wide signal-to-noise ratio (SNR) range, we introduce a learnable SNR-gated late-fusion shortcut that injects the network input into the final decoding stage through a sigmoid gate with trainable center and scale. To reduce inference latency, we adopt deterministic denoising diffusion implicit model (DDIM) style reverse updates with SNR-adaptive truncation and step allocation, which significantly reduces the number of reverse diffusion steps at high SNR while maintaining strong performance in low SNR regimes. Simulations on time-evolving standardized channel models demonstrate that the proposed method achieves consistent performance gains over existing diffusion-based channel estimation baselines, while retaining low latency through SNR-adaptive inference.

In frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems, the uplink (UL)-to-downlink (DL) channel covariance matrix (CCM) conversion problem is studied to relieve the heavy burden of DL training and feedback required for channel estimation. Learning- based methods perform well up to a certain array size, but for a fixed dataset size their accuracy deteriorates with the number of antennas, to the point where simple model-based methods outperform them. This paper identifies a key cause of this behavior and addresses it. The mean angle of arrival (AoA) induces a phase ramp along the lags of the CCM. Since the oscillation rate of this ramp grows with the number of antennas, a dataset of fixed size becomes increasingly sparse relative to the variation that must be captured. We propose estimating the slope of this ramp from the UL CCM separately and mapping it to the DL band in closed form, leaving the learner with a residual that is largely insensitive to the mean AoA, which substantially reduces the performance degradation with an increasing number of antennas. The proposed scheme, termed deramping, is a combination of pre- and post-processing steps that applies to learning-based conversion methods without altering their internal structure, as demonstrated on three structurally different learners. Simulation results show that deramping reduces the covariance estimation error of all three learners under uniform, Laplacian, and Gaussian angular power spectra,keeps the interpolation-based learners ahead of a model-based benchmark at large array sizes, and improves downlink channel estimation.

Pilot-aided channel estimation is a decisive block in orthogonal frequency-division multiplexing (OFDM) receivers for both 5G New Radio (5G-NR) and Long-Term Evolution (LTE). A large body of estimators exists, from simple least-squares (LS) interpolation to statistically optimal linear minimum-mean-square-error (LMMSE) variants and, more recently, deep convolutional denoisers, yet no single estimator is uniformly best: the winner depends on the propagation scenario, the numerology, the operating signal-to-noise ratio (SNR), the mobility (Doppler), and the antenna configuration. In this paper, we quantify this fact through a unified study of eight literature estimators evaluated over the 3GPP TR~38.901 Urban-Macro (UMa), Urban-Micro (UMi), and Rural-Macro (RMa) channels generated with NVIDIA Sionna, for both 5G-NR and LTE numerologies, in single-input single-output (SISO) and $8\times2$ multiple-input multiple-output (MIMO) settings. We then propose a \emph{condition-adaptive multi-agent orchestrator} that treats each estimator as an independent agent and dispatches, per operating condition, to the agent that is best on a validation split without any genie knowledge. The orchestrator tracks the per-realization oracle to within $1.07$~dB and improves the normalized mean-square error (NMSE) over the best \emph{fixed} strategy by up to $3.6$~dB at high SNR, where the low-SNR champion is no longer optimal. Because the agents are independent, running them concurrently delivers this best-of-eight accuracy at essentially single-estimator latency: a data-parallel partition scales the wall-clock nearly as $1/K$ with $K$ workers (up to $6.9\times$), whereas naive by-algorithm partitioning is Amdahl-limited by the heaviest agent. The results substantiate multi-agent orchestration as a practical route to robust channel estimation across heterogeneous 5G-NR/LTE deployments.

In sub-terahertz (sub-THz) communications, the coupling of ultra-wide bandwidth and severe phase noise (PN) impairments renders conventional joint channel and PN estimation highly complex and computationally prohibitive. To address this, we propose CRFCAN, a complex-valued residual FFT convolutional attention network designed for joint channel and PN estimation. Unlike existing deep learning schemes that rely on cascaded networks or hybrid frameworks combining neural networks with conventional iterative estimators, CRFCAN performs joint recovery in a truly end-to-end fashion through a physics-inspired cross-domain structure. Specifically, Fast Fourier Transform (FFT) and inverse FFT modules are embedded within residual groups to enable iterative feature interaction across the time and frequency domains, thereby capturing both frequency-selective fading and time-varying phase distortions. In addition, two dedicated residual blocks are introduced for complex feature extraction and multiplicative phase-distortion modeling, respectively. A physics-aware PN output tail with soft normalization is further employed to improve estimation stability while preserving the physical characteristics of the effective PN process. Simulation results demonstrate that CRFCAN significantly outperforms conventional algorithms and state-of-the-art deep learning models in terms of normalized mean square error (NMSE) and bit error rate (BER). Notably, CRFCAN achieves superior performance with single-shot, fixed-complexity inference and generalizes well to unseen PN models without fine-tuning, highlighting its robustness and practicality for sub-THz receivers.

Deep learning models, notably Long Short-Term Memory (LSTM), have demonstrated promising performance in channel estimation for high-mobility vehicular environments. However, their black-box nature and architectural overhead limit trustworthiness and efficiency. Classical explainable AI (XAI) methods rely on costly iterative processes, offering only input-level filtering without addressing architectural fine-tuning. To overcome these limitations, this paper proposes the XAI-assisted Recurrent neural network Attribution for Channel Estimation (X-RACE) framework. X-RACE uses a low-complexity, one-shot dual-optimization strategy to simultaneously evaluate and prune irrelevant input subcarriers and internal hidden units. Furthermore, we propose novel temporal XAI metrics: Saturation Time, Importance Drift, and Relevance Contrast to characterize the LSTM's learning dynamics and memory convergence. Extensive simulations demonstrate that X-RACE reduces inference complexity by at least 44.1% while improving or preserving Bit Error Rate (BER) performance, outperforming classical XAI schemes.

Recent advances in machine learning have enabled training of wireless foundation models, which aim to support tasks such as channel estimation, beam prediction, and localization based on wireless signals. Existing wireless foundation models typically pretrain on channel tensors using masked reconstruction over subcarriers, antennas, or time but ignore the physical characteristics of wireless propagation. In this work, we propose to instead use multipath propagation as the fundamental pretraining object. We present MultiPathFormer, an autoregressive foundation model that represents each transmitter-receiver link as an ordered sequence of continuous-valued path tokens and pretrains with next-path prediction. We introduce an Environmental RAG (retrieval-augmented generation) mechanism and a first-path codebook on top of the transformer backbone, leveraging environment knowledge to improve path statistics estimation like delay and power by up to 59%. MultiPathFormer pretrained on 27 environments transfers to unseen users and, after scenario-specific fine-tuning, outperforms training the corresponding models from scratch in new environments. Across downstream tasks, it outperforms SOTA channel-based foundation models, achieving 5.57 m mean localization error, 0.914 top-3 beam accuracy, 0.994 line-of-sight classification accuracy, and 0.561 channel estimation NMSE. These results show that path-level pretraining can learn reusable representations of wireless propagation.

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.

Extremely large-scale reconfigurable intelligent surface (XL-RIS)-assisted communication is regarded as a key enabling technology for future 6G networks. However, hybrid-field channel estimation for XL-RIS-assisted systems is challenging due to the high-dimensional cascaded channel and the coexistence of far-field and near-field propagation. In this case, traditional full-dimensional sparse recovery methods require a large cascaded dictionary and suffer from severe computational and storage burdens. To address these challenges, we develop a double-timescale channel estimation framework that decouples sparse dictionary representation and recovery. Then, by exploiting the quasi-static property of the channel at the base station (BS) and RIS side, we propose a Dirichlet kernel-based off-grid dictionary compression (DK-ODC) scheme for sparse representation, which reduces the dimension of the corresponding dictionary as well as mitigates BS-side angular off-grid error. Furthermore, for the dynamic channel at the user equipment (UE) and RIS side, we propose a subspace-aware incremental variational Bayesian learning (SI-VBL) algorithm, which enables incremental learning of sparse channels by exploiting the identified low-dimensional subspace and pruning threshold. Analysis and simulation results confirm that the proposed framework avoids full-dimensional Bayesian recovery and achieves a favorable tradeoff among estimation accuracy, computational complexity, and storage overhead.

In multiple-input multiple-output (MIMO) semantic communication, imperfect channel state information (CSI) and equalization mismatch can seriously degrade semantic reconstruction quality. To address this issue, we propose a unified restoration flow matching (RFM)-based framework for channel refinement and equalization correction. Specifically, the channel RFM (CRFM) module is developed to refine the coarse channel, thereby improving channel estimation accuracy. Based on the refined channel, the developed semantic RFM (SRFM) module is employed to correct the residual distortions in the post-equalization latent space. The key idea is to formulate the two cascaded inverse problems of channel estimation and equalization as the unified conditional restoration task, in which the learned conditional velocity field guides the perturbed distribution towards the target distribution. To enhance the robustness of these two modules under various distortion conditions, we develop a dual-anchor perturbation training strategy that jointly learns near-manifold refinement and large-error correction, and implement inference through a few-step deterministic ordinary differential equation (ODE) solver. Extensive experiments on MIMO channels and visual semantic transmission tasks demonstrate that the proposed scheme improves key metrics for channel estimation and semantic reconstruction quality. Moreover, compared with representative diffusion-based generative baselines, the proposed method requires fewer sampling steps.

Hardware impairments in massive multiple-input multiple-output (MIMO) receivers introduce inter-symbol memory and inter-element coupling, severely degrading channel estimation. This paper employs a residual recurrent gated unit (RGRU) to model the intra-slot memory of the hardware impairments and proposes a message-passing-based two-timescale Bayesian deep learning (MP-TTBDL) framework for joint channel and impairment tracking. Owing to small-scale fading, the wireless channel varies rapidly across slots, whereas hardware impairments drift slowly due to hardware aging and environmental variations. To capture these distinct physical timescales, a fastvarying Markov prior and a slow-varying Gaussian Markov prior are assigned to the sparse channel and the network parameters, respectively. Based on a multi-slot factor graph formulation, a message-passing algorithm is developed. Specifically, the inter-slot messages admit closed-form updates, while the intra-slot factor graph, due to its complex recurrent structure, is partitioned into a channel tracking module and an impairments calibration module. The channel tracking module performs sparse channel estimation via turbo orthogonal approximate message passing (Turbo-OAMP), and the impairments calibration module updates the impairment parameters via a specially designed deep approximate message passing (DAMP) procedure, with the two modules iteratively exchanging extrinsic information through expectation propagation (EP) until convergence. Simulation results show that the proposed framework robustly achieves lower channel estimation error than conventional compensators followed by channel estimation across different online impairment scenarios and signal-to-noise ratio (SNR) conditions.

In next-generation wireless networks, the growing density of devices and limited spectrum resources pose severe jamming challenges to fragile legitimate communication links in the wireless electromagnetic environment. Crucially, when jamming overlaps with pilot and data symbols in both time and frequency domains, it inflicts a severe bottleneck on receiver-side joint estimation and detection. Existing schemes often lack an effective framework to combat such jamming contamination, thereby failing to guarantee reliable transmission. To address this issue, we propose a Brownian bridge diffusion-based joint channel estimation and data detection framework (BBD-JCED) for jamming-resilient receivers. Specifically, the proposed framework comprises two core modules: the first extracts jamming features in the short-time Fourier transform (STFT) domain and suppresses jamming samples, thereby improving the signal-to-jamming-plus-noise ratio (SJNR) of the received signal; the second introduces a Brownian bridge diffusion (BBD) process to model the evolution of the suppressed signal and the encoded bits in the presence of channel estimation errors, thereby enabling enhanced joint channel estimation and data detection. To alleviate the computational burden of the BBD process in the second module, we further derive a fast ordinary differential equation (ODE) solver that enables its low-complexity iterative evolution. Finally, we design a multi-module training algorithm to improve the data recovery capability of the proposed framework. Simulation results demonstrate that the proposed framework achieves superior bit recovery performance compared with baseline schemes while maintaining a lower number of model parameters and competitive computational complexity.

Driven by their remarkable success in computer vision and inverse problem solving, score-based models are increasingly applied to wireless communications, where they show promise across a range of physical-layer tasks. However, despite this growing interest, the current literature often lacks a rigorous analysis of when score-matching offers a tangible advantage over traditional discriminative learning. This paper aims to address this gap through the use-case of channel estimation, a fundamental inverse problem in wireless systems. We present a theoretically grounded interpretation of score-based channel estimation through the lens of the perception-distortion tradeoff, identifying the conditions where score matching excels as well as its key limitations. In particular, by modeling downstream wireless tasks (e.g., capacity maximization) as functionals of the channel estimation process, we quantify the excess risk incurred by standard distortion-minimization approaches. Extensive numerical results show that under high predictive uncertainty, the large excess risk gap can be offset by score-based estimation, enabling near Bayesian-optimal precoding via the learned posterior, whereas in the low predictive uncertainty regime, discriminative distortion-minimization approaches are preferable due to lower complexity and more efficient use of model capacity.

Wireless foundation models offer a path toward reusable channel state information (CSI) intelligence for sixth-generation (6G) systems. However, existing generic-backbone adaptation and CSI pretraining methods often treat CSI as task tensors rather than propagation-conditioned channel responses, thereby failing to capture the intrinsic time-frequency-spatial geometry of wireless environments. This paper presents a channel-adaptive roadmap toward CSI-native foundation models, proposing a unified framework that aligns pretraining, positional modeling, and attention control with three channel requirements: scale-aware heterogeneous exposure, physical time-frequency-antenna coordinates, and correlation-bounded token interaction. Extensive experiments demonstrate the superiority of the proposed framework across three dimensions: zero-shot generalization, reducing NMSE by more than 4 dB across spatial-temporal-frequency tasks; scale extrapolation, yielding up to a 5.4 dB gain under 8 times unseen antenna scaling; and inference efficiency, accelerating mobility-aware processing by up to 18.8%. A system-level evaluation with Sionna SYS further shows that the proposed framework uses only 7.01% of dense-pilot overhead, reaches -18.64 dB average NMSE, and improves average net spectral efficiency by 36.6% over dense LMMSE and 15.5% over WiFo, indicating that CSI-native representation learning can support pilot-efficient radio access.

Multi-channel mixed-SNR training improves out-of-distribution (OOD) generalisation of deep learning channel estimators for IEEE 802.11p vehicular communications, yet the internal mechanism responsible for this remains unexplained. This work presents REACH (Relevance-based Explanation and Architectural Compression for cHannel estimators), a gradient-based interpretability framework that operates at two levels. Input-level attribution identifies a subset of time-frequency features consistently relevant across all evaluated channel conditions, enabling input dimensionality reduction with minimal performance loss. Filter-level attribution reveals a near-universal internal representation, providing a representational account of the observed OOD generalisation. Guided by the resulting filter taxonomy, relevance-guided architecture compression substantially reduces both the number of parameters and the number of floating-point operations (FLOPs) with sub-1 dB normalised mean square error (NMSE) degradation, and OOD generalisation degrades more slowly than within-distribution accuracy under increasing compression.

This letter studies CSI denoising for MIMO--OFDM with variable NR resource block (RB) allocations. ReFLEX is a length-generalizable Transformer whose frequency attention uses a relative-frequency position bias (RFPB) generated from subcarrier offsets. A single checkpoint handles unseen RB lengths and can be applied to sparse DM-RS observations in the tested RB5/RB10 PUSCH setup without retraining. In a 3GPPTR38.901 UMa NLOS channel, ReFLEX achieves about $-9.6$dB NMSE on unseen RB lengths. In NR PUSCH/UL-SCH simulations, ReFLEX denoising followed by time-frequency interpolation reduces the 10% BLER threshold by about 2--3dB.

Non-terrestrial networks (NTNs) are expected to play a pivotal role in sixth-generation (6G) systems by enabling ubiquitous connectivity and massive communication. In this context, channel prediction emerges as a key technique to improve the spectrum utilization efficiency by limiting the pilot overhead. However, many proposed predictors based on artificial intelligence (AI) are characterized by high inference complexity, posing challenges to onboard implementation. In this paper, we address the challenge of designing accurate yet computationally efficient channel prediction techniques tailored to low Earth orbit (LEO) NTNs, where strict power constraints limit model complexity, to enable spectral efficiency gains. We propose an iterative joint channel estimation and prediction framework in the context of 6G NTNs that significantly reduces pilot overhead by transmitting pilots only in the initial slot and relying on data-driven processing for subsequent slots. We introduce Data-driven Refinement and Iterative Forecast for wireless channel Tracking (DRIFT), a lightweight architecture that refines data-aided channel estimates and predicts future channel frequency responses with low computational cost and reduced error propagation. Two predictor variants based on convolutional and long short-term memory layers are investigated. Simulation results in an end-to-end simulation of an uplink LEO NTN scenario show that the proposed approach achieves up to 12% spectral efficiency gain compared to conventional pilot-based systems, with robustness to training-test mismatches and consistent performance across different channel models. Moreover, DRIFT requires fewer than 200k multiply-accumulate operations, making it suitable for on-board satellite implementation under stringent power constraints.

Wideband channel estimation (CE) in high-mobility scenarios remains challenging because channel responses vary rapidly, while practical systems can allocate only sparse pilots to accommodate dense users. Fortunately, many high-mobility environments, such as high-speed railways, exhibit scheduled trajectories, predictable velocities, and a limited number of dominant propagation paths. These properties induce a delay--beam power spectrum that is more stable than the instantaneous complex channel frequency response (CFR), less sensitive to the random phase coherence, and rich in geometric information. To exploit such environmental properties, we propose GeoGS-CE, a two-stage channel estimation framework for sparse-pilot high-mobility scenarios. In the offline stage, GeoGS-CE jointly models: 1) a scene-level 3D Gaussian representation that captures the non-line-of-sight (NLoS) geometric scattering support, and 2) a leakage-aware differentiable wireless rendering process that maps the NLoS Gaussians, together with an explicit virtual line-of-sight (LoS) component, to the measured delay--beam power spectrum, while accounting for practical OFDM delay and array leakage effects. In the online stage, the delay--beam power spectrum is predicted for each user location and used as a strong covariance prior, enabling accurate full-band and full-array CFR reconstruction and tracking through a linear MMSE estimator. Simulations based on channels generated from a segment of the Guangshen high-speed railway show that the proposed geometric prior substantially improves CFR reconstruction over pilot-only and non-geometric baselines.

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.

The integration of terahertz communications and ultra-massive multiple-input multiple-output (UM-MIMO) systems in 6G networks is motivated by their ability to enable unprecedented data rates, mitigate spectrum congestion, and enhance overall network performance. However, the enlarged antenna apertures and higher carrier frequencies in these systems increase the Rayleigh distance, causing users to span both the near-field and conventional far-field regions. Accurate spatial precoding thus requires exact channel estimation at the base station - a task made more challenging by the hybrid coexistence of near- and far-field effects and the limited number of digital chains available in hybrid beamforming architectures. In this paper, we propose a block recurrent transformer model to address this challenge. We demonstrate that a single transformer block equipped with state memory can be trained once and then iteratively applied for hybrid-field channel estimation. Furthermore, we train the model such that it generalizes to wireless channels with varying scatterer distances, different numbers of propagation paths, and wideband operation. Simulation results show that the proposed method achieves performance gains of approximately 5 dB and 7.5 dB in normalized mean squared error (NMSE) over state-of-the-art solutions in narrowband and wideband scenarios, respectively.

Channel estimation is crucial in 5G communication networks for optimizing transmission parameters and ensuring reliable, high-speed communication. However, the use of multiple-input and multiple-output (MIMO) and millimeter-wave (mmWave) in 5G networks presents challenges in achieving accurate estimation under strict latency requirements on resource-limited hardware platforms. To address these challenges, we propose SwiftChannel, an algorithm-hardware co-design framework that integrates a hardware-friendly deep learning-based channel estimator with a dedicated accelerator. Our approach employs a convolutional neural network enhanced with a parameter-free attention mechanism, which effectively reconstructs full-resolution spatial-frequency domain channel matrices from low-resolution least squares (LS) estimates. We further develop a multi-stage model compression pipeline combining knowledge distillation, convolution re-parameterization, and quantization-aware training, resulting in substantial model size reduction with negligible accuracy loss. The hardware accelerator, implementing the compressed model and the LS estimator on FPGA platforms using High-level Synthesis (HLS), features a fine-grained pipeline architecture and optimized dataflow strategies. Tested on a Zynq UltraScale+ RFSoC, the accelerator achieves sub-millisecond latency, providing up to 24x speed-up and over 33x improvement in energy efficiency compared to GPU-based solutions. Extensive evaluations demonstrate that the proposed design generalizes not only across various noise levels and user mobilities, but also to a variety of unseen channel profiles, outperforming state-of-the-art baselines. By unifying algorithmic innovation with hardware-aware design, our work presents a future-proof channel estimation solution for 5G MIMO systems.

An evolution of Wireless Communications towards 5G and beyond provides improved user experience in terms of quality of services. Understanding and estimating Channel information plays crucial role in providing better user experience. Traditional methods of channel estimation involves periodically sending pilots (known signals), estimating channel and send back estimated channel information to the BS which increases computational complexity and communication complexity. Hence, we focus on data driven approach for channel estimation. In this work, we explore a channel estimation mechanism at 7GHz frequency band for a given user location. This work involves data generation using Ray tracing mechanism and Machine learning model training that contains feature variables such as transmitter location, user location and target variable as channel coefficient . We explored Support Vector Regression, K-nearest neighbor (KNN), Random Forest, XGBoost and MLP. We found via simulations that XG Boost and proposed MLP performs better than Support Vector Regression, KNN and Random forest regression.

Accurate yet low-latency channel state information (CSI) acquisition is essential for multiple-input multiple-output (MIMO) communication systems. While advanced deep generative models, such as score-based and diffusion models, enable high-fidelity CSI reconstruction from limited pilot observations, they often suffer from high inference latency. To achieve accurate CSI estimation under stringent latency constraints, this paper proposes a null-space flow matching (FM) framework that decomposes pilot-limited MIMO channel estimation into a range-space reconstruction problem and a null-space generation problem. Specifically, the range-space component of the channel is directly recovered from noisy pilot observations, while only the ambiguous null-space component is iteratively refined using an FM-based generative prior. To further improve the robustness of the proposed framework, we introduce a power-law time schedule to better allocate the limited number of refinement steps, along with a noise-aware adaptive correction strategy to suppress channel noise on the refinement trajectory. Experimental results demonstrate that our method achieves a competitive normalized mean square error (NMSE) even under a strict latency budget of around 3 ms, while delivering superior estimation accuracy and faster inference than both model-based and generative baselines.

Machine learning has greatly advanced data-driven channel modeling and resource optimization. However, most existing methods require accurately location-labeled datasets, which are costly to collect and maintain in dynamic environments. This paper develops a self-localizing multiple-input multiple-output (MIMO) beam map framework that constructs a hierarchical wireless memory from highly sparse channel state information (CSI) measurements without explicit location labels. To reduce acquisition and processing overhead, we use beamdomain received signal strength (RSS) as compact inputs and theoretically show that they enable asymptotically unbiased spatial signature estimation. A dual-scale extractor captures intrasnapshot angular dependencies and inter-sample correlations for incomplete observations, and a hybrid temporal encoder is designed to consolidate recent CSI into stable short-term context for physical anchor inference. The inferred anchors spatially index a physically structured radio map embedding that stores long-term channel knowledge, which conditions a diffusion decoder for location-consistent full CSI reconstruction. Such a radio map embedding provides a persistent wireless knowledge representation that can be continuously updated and reused without full CSI acquisition. Experiments show that the proposed framework improves physical-anchor recovery accuracy by over 30% under sparse measurements and achieves more than 20% channel-capacity gain in non-line-of-sight (NLOS) beam tracking over Kalman-filter-based methods.

In general, reliable communication via multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) requires accurate channel estimation at the receiver. The existing literature largely focuses on denoising methods for channel estimation that depend on either (i) channel analysis in the time-domain with prior channel knowledge or (ii) supervised learning techniques which require large pre-labeled datasets for training. To address these limitations, we present a frequency-domain denoising method based on a reinforcement learning framework that does not need a priori channel knowledge and pre-labeled data. Our methodology includes a new successive channel denoising process based on channel curvature computation, for which we obtain a channel curvature magnitude threshold to identify unreliable channel estimates. Based on this process, we formulate the denoising mechanism as a Markov decision process, where we define the actions through a geometry-based channel estimation update, and the reward function based on a policy that reduces mean squared error (MSE). We then resort to Q-learning to update the channel estimates. Numerical results verify that our denoising algorithm can successfully mitigate noise in channel estimates. In particular, our algorithm provides a significant improvement over the practical least squares (LS) estimation method and provides performance that approaches that of the ideal linear minimum mean square error (LMMSE) estimation with perfect knowledge of channel statistics.