A Survey of Intelligent Methods Under Inadequate Pilots in 5G/6G MIMO Systems: Pilot-Domain Mitigation, Channel Estimation, and Receiver Processing

Abstract

In large-scale multiple-input multiple-output (MIMO) systems, inadequate pilots can necessitate pilot reuse, reducing channel-estimation accuracy, while too few received pilot observations can also lead to inaccurate interference-plus-noise covariance estimates. These estimation errors can further degrade the performance of downstream interference suppression and data detection. Learning-based methods have been developed for pilot assignment, channel estimation, and receiver processing, but these methods are often studied separately. This survey organizes recent studies according to where learning-based methods are applied in the signal-processing chain: pilot-domain mitigation, intelligent channel estimation with contaminated or limited pilots, and intelligent receiver processing with contaminated or limited pilots. We also classify the studies by learning method and compare them using the same set of evaluation criteria. Across the surveyed papers, performance is evaluated using different metrics. Many studies also lack evaluations under changing channel or system conditions and do not fully report implementation costs such as computational complexity, memory usage, and latency. Among the studies that satisfy our selection criteria, none directly investigates learning-based estimation of the interference-plus-noise covariance matrix for interference rejection combining (IRC) receivers when only limited pilot observations are available. Based on these findings, we propose a minimum set of benchmarking requirements and identify lightweight online adaptation, joint processing, learning-based covariance estimation for IRC receivers, and robust processing for large-array architectures as future research directions for emerging sixth-generation (6G) systems.

1. Introduction

1.1. Large-Scale MIMO Evolution and Pilot-Resource Challenges

The evolution from fifth-generation (5G) to sixth-generation (6G) communication systems calls for higher throughput, broader connectivity, greater reliability, and lower communication latency. The International Mobile Telecommunications 2030 (IMT-2030) vision further expands the capabilities of future mobile systems to include integrated sensing, artificial intelligence (AI) support, ubiquitous coverage, and sustainability [1,2,3,4]. To support these capabilities, multi-antenna architectures are evolving toward larger arrays and more distributed deployments, which increases the amount of channel state information (CSI) that must be reliably acquired within a finite coherence interval.

Massive multiple-input multiple-output (MIMO) and extremely large-scale MIMO (XL-MIMO) employ large antenna arrays to support more efficient spatial multiplexing and finer spatial resolution, while cell-free MIMO uses distributed access points to serve users cooperatively [5,6]. Figure 1 illustrates an XL-MIMO uplink with near- and far-field users, where individual near-field users may be visible to different portions of the large-aperture array. More generally, large-scale and distributed MIMO architectures increase the number of channel links to be estimated and the diversity of their spatial characteristics. However, the finite coherence interval limits the number of orthogonal pilots. As user density and network connectivity increase, assigning orthogonal pilots to all users becomes more difficult. Pilot reuse or nonorthogonal pilot allocation can therefore become necessary, making reliable channel acquisition more challenging and leading to the pilot-related impairments discussed next.

1.2. Pilot-Limited Channel and Receiver Impairments

In large-scale multi-cell MIMO systems, uplink pilots are commonly used for channel estimation under time-division duplexing (TDD), because channel reciprocity reduces the need for downlink training and feedback. However, a finite coherence interval limits the number of orthogonal pilots available to users. In dense networks, this limitation can lead to pilot reuse. When pilots reused across different cells are nonorthogonal, interfering channel components can remain in the resulting channel estimate, causing pilot contamination [7]. The resulting channel-estimation errors can degrade receive combining, beamforming, scheduling, and other operations that rely on channel state information (CSI) [8].

A second problem arises when the receiver estimates the interference-plus-noise covariance matrix from only a small number of received pilot samples. In this case, the covariance estimate can be inaccurate and can degrade receiver performance. Therefore, inadequate pilots can affect receiver processing through two different paths: nonorthogonal pilots can reduce channel-estimation accuracy, while too few received pilot samples can reduce covariance-estimation accuracy. These two problems can occur separately or simultaneously, and both can degrade downstream receiver processing.

1.3. Motivation for Intelligent Processing

Conventional methods for pilot-contamination mitigation and receiver processing are mainly model-based and often rely on optimization algorithms [9,10]. These methods remain important, but inadequate pilots and time-varying channels can make it difficult for model-based approaches to adapt to changing conditions. Learning-based methods can learn nonlinear relationships and decision rules from training data and have been widely studied for physical-layer processing in 6G systems [11,12,13]. Recent 6G surveys also cover related applications such as AI-based waveform recognition and electromagnetic spectrum mapping [14,15].

Under inadequate pilot resources, learning-based methods can be applied to three main stages of the signal-processing chain: pilot assignment, channel estimation, and receiver processing. Most surveyed studies focus on only one of these stages, which makes comparison across different methods difficult. Accordingly, we classify the reviewed methods by where they operate in the pilot assignment–channel estimation–receiver processing chain. We also classify the studies by learning method to show how the algorithms are trained and adapted.

1.4. Survey Scope, Contributions, and Structure

This survey focuses on learning-based and learning-assisted methods for MIMO systems with inadequate pilot resources. The reviewed studies consider problems such as pilot reuse, nonorthogonal pilots, pilot contamination, and insufficient pilot observations for channel and interference-plus-noise covariance estimation. We classify the surveyed studies into three classes: Class I, intelligent pilot-domain mitigation, which covers learning-based pilot assignment and pilot-domain decisions; Class II, intelligent channel estimation with contaminated or limited pilots, which covers learning-based channel estimation from unreliable pilot observations; Class III, intelligent receiver processing with contaminated or limited pilots, which covers learning-based receiver-side suppression and detection.

This survey makes three contributions. First, we use the study selection procedure described in Section 2.3 to identify 24 studies for detailed analysis and organize them according to the signal-processing chain: 10 studies on pilot-domain mitigation, 9 on channel estimation, and 5 on receiver processing. Second, we compare the reviewed studies using the same set of evaluation criteria, including system and pilot settings, evaluation metrics, learning methods, training data, required information, computational complexity, deployment requirements, and robustness. Third, based on this comparison, we identify the main limitations of current studies and propose a minimum set of benchmarking requirements presented in Section 7.

Section 2 positions the survey and defines its scope and study selection procedure. Section 3 describes how inadequate pilot resources can affect channel estimation, covariance estimation, and receiver processing. Section 4, Section 5 and Section 6 review the three classes of learning-based methods. Section 7 provides a cross-class comparison and a minimum set of benchmarking requirements, Section 8 discusses future directions, and Section 9 concludes the survey.

2. Survey Positioning and Scope

2.1. Positioning Against Existing Surveys

Previous surveys have covered pilot-contamination mitigation, pilot assignment, cell-free massive MIMO, channel estimation, deep-learning-based pilot decontamination, and broader interference management [6,16,17,18,19,20,21,22].

Table 1. Comparison of representative surveys by scope, learning coverage, stage coverage, and overlap with the studies reviewed in this survey.

Survey	Main Scope	Learning Coverage	Class I	Class II	Class III	Overlap and Main Difference
Elijah et al. [16] (2016)	Pilot contamination; pilot-based and subspace-based mitigation.	No	Yes	Partly	No	Conventional pilot-contamination mitigation; no overlap.
Misso et al. [17] (2020)	Pilot assignment for pilot-contamination mitigation	Partly	Yes	No	No	Pilot assignment only; no overlap.
Saeed et al. [18] (2024)	Pilot assignment, signal processing, and channel estimation	Partly	Yes	Yes	Partly	Overlap: [23,24]; organized by mitigation method rather than processing stage.
Victor et al. [19] (2024)	Deep-learning-aided pilot decontamination	Yes	Yes	Yes	Partly	Overlap: [23,24]; receiver processing is not treated as a separate class.
Chen et al. [6] (2022)	User-centric cell-free massive MIMO: resource allocation and signal processing	Partly	Yes	Yes	Partly	Organized around the cell-free architecture rather than inadequate pilots; no overlap.
Ma et al. [20] (2025)	Channel estimation for massive MIMO	Yes	Partly	Yes	Partly	Overlap: [25]; focuses on channel estimation.
Tarafder et al. [21] (2025)	Channel estimation under pilot contamination and feedback overhead	Yes	Yes	Yes	Partly	Learning-based methods focus mainly on channel estimation; no overlap.
Trabelsi et al. [22] (2024)	Interference management in 5G and beyond networks	Partly	No	No	Partly	Broad interference-management focus with limited coverage of learning-based receiver processing; no overlap.
Present survey (2026)	Learning-based methods under inadequate pilot resources, organized by processing stage	Yes	Yes	Yes	Yes	Covers all three processing stages and treats receiver-side suppression and detection as a separate category.

Notes: Class I–III indicate coverage of the corresponding processing stages. “Yes”, “Partly”, and “No” denote substantive, limited, and no substantive coverage, respectively. Overlap is counted only when a retained study is substantively discussed rather than merely cited. Class I: intelligent pilot-domain mitigation; Class II: intelligent channel estimation with contaminated or limited pilots; Class III: intelligent receiver processing with contaminated or limited pilots. 5G: fifth-generation; MIMO: multiple-input multiple-output.

compares these surveys in terms of their main topics, coverage of machine-learning (ML) methods, coverage of the three classes considered in this survey, and overlap with the studies reviewed in this paper.

Saeed et al. [18] mainly focus on pilot-contamination mitigation, while Victor et al. [19] review deep-learning methods for pilot decontamination. Neither treats learning-based receiver-side suppression as a separate category. Chen et al. [6] organize their review around user-centric cell-free massive MIMO and its resource-allocation and signal-processing problems, whereas Ma et al. [20] and Tarafder et al. [21] focus mainly on channel estimation. In contrast, this survey uses limited pilot resources as the common problem setting and organizes learning-based methods according to three stages of the processing chain: pilot-domain mitigation, channel estimation, and receiver processing.

Table 1 also shows the overlap between previous surveys and the studies reviewed in this work. Compared with these reviews, the present survey applies a common limited-pilot criterion across the three processing stages and treats receiver-side suppression and detection as a separate category.

2.2. Scope of Learning-Based Methods

This survey includes learning-based methods that directly address problems caused by inadequate pilots, including pilot reuse, nonorthogonal pilots, pilot contamination, and insufficient received pilot samples. Following the classification introduced in Section 1.4, we group these methods into Classes I–III according to whether they address pilot-domain mitigation, channel estimation, or receiver processing.

This classification does not depend on the type of learning algorithm. Supervised and unsupervised learning, reinforcement learning, untrained priors, and model–data hybrid methods can therefore appear in different classes depending on where they are applied in the processing chain. In this survey, we mainly focus on studies that either employ learning-based methods directly or use machine learning to assist conventional algorithms in addressing limited-pilot problems. Purely model-based methods, general channel or covariance estimation methods, and general interference management methods are included only when they provide relevant background or serve as useful benchmarks.

2.3. Literature Search and Study Selection

We conducted literature searches in IEEE Xplore, Scopus, and Web of Science. A common query structure was used in each database, combining keyword modules for large-scale MIMO systems, inadequate-pilot conditions, intelligent methods, and a task-specific module. The task-specific modules covered pilot-domain mitigation, pilot-limited estimation and reconstruction, and receiver-side suppression and detection. The complete search queries for each database are provided in Appendix A.

We considered peer-reviewed journal articles, conference papers, and early access articles that met the scope defined in Section 2.2. Studies that only mentioned machine learning in the background, as well as studies that focused on general power control, beamforming, precoding, user association, or resource allocation without addressing a pilot-limited problem were excluded.

We identified 460 publications through the initial searches: 182 from IEEE Xplore, 148 from Scopus, and 130 from Web of Science. After removing duplicates based on digital object identifier (DOI) and title, 166 unique records remained. We then evaluated these publications based on their titles, abstracts, and full texts and identified 72 studies that met the inclusion criteria. For the final detailed review, we mainly selected studies published between 2023 and 2026, while also including earlier studies that were highly cited or introduced methods not adequately covered by more recent work. For Class III, we extended the publication range back to 2021 because relatively few recent studies directly addressed receiver-side processing under limited pilot resources. The final set contains 24 studies: 10 in Class I, 9 in Class II, and 5 in Class III. Figure 2 summarizes the search and selection process.

3. Pilot-Limited Estimation Errors and Problem Formulation

This section describes two ways in which inadequate pilots can reduce estimation accuracy and receiver performance. First, when the number of available orthogonal pilots is insufficient, pilot reuse or nonorthogonal pilot allocation may be required. If pilots used in different cells are nonorthogonal, interfering channel terms remain in the channel estimate and cause pilot contamination. Second, when only a small number of received pilot samples are available, the interference-plus-noise covariance matrix may be estimated inaccurately. These two problems can both degrade receiver performance.

To describe these effects, we consider a multi-cell time-division duplexing (TDD) uplink system that exploits channel reciprocity. Each cell serves K single-antenna users, and each base station has M antennas. For simplicity, all cells are assumed to use the same values of K and M. The channels remain constant within a coherence block that contains both pilot and data transmission, and we do not assume a specific small-scale fading model. Pilot transmissions are assumed to be synchronized at the symbol level. We do not consider timing or carrier-frequency offsets, hardware impairments, or channel aging within the coherence block. We also assume that the interference-plus-noise covariance remains constant over the estimation period and the corresponding receiver processing interval.

3.1. Limited Pilots, Pilot Reuse, and Nonorthogonality

Within a finite coherence interval, the available pilot length may be too short to assign orthogonal pilots to all users across all cells [7]. Figure 3 illustrates this multi-cell setting.

Consider L cells, each serving K single-antenna users with an M-antenna base station. Let ${\mathit{\varphi }}_{l,k}\in {\mathbb{C}}^{\tau \times 1}$ denote the pilot transmitted by user k in cell l, where $\tau$ is the pilot length. If all pilots are orthogonal across the network,

$${\mathit{\varphi }}_{l,k}^H{\mathit{\varphi }}_{i,m}=\left\{\begin{array}{cc}\tau ,\hfill & (l,k)=(i,m),\hfill \\ 0,\hfill & (l,k)\ne (i,m).\hfill \end{array}\right.$$

(1)

Assigning an orthogonal pilot to every user in all L cells requires at least $LK$ pilot dimensions, i.e.,

$$\tau \ge LK.$$

(2)

A common case with limited pilots is

$$K\le \tau <LK.$$

(3)

In this case, each cell can still assign orthogonal pilots to its K users, but orthogonality cannot be maintained across all cells. Let ${\mathbf{\Phi }}_l\in {\mathbb{C}}^{\tau \times K}$ denote the pilots in cell l. The pilots within each cell satisfy

$${\mathbf{\Phi }}_l^H{\mathbf{\Phi }}_l=\tau {\mathbf{I}}_K.$$

(4)

Across different cells, some pilots may be nonorthogonal, such that

$${\mathbf{\Phi }}_l^H{\mathbf{\Phi }}_j\ne {\mathbf{0}}_{K\times K},l\ne j.$$

(5)

When $\tau <LK$, cross-cell pilot reuse or nonorthogonal pilot assignment becomes necessary. Pilot contamination occurs when these nonorthogonal pilot signals are received together at the base station. The received pilot matrix at base station j is

$${\mathbf{Y}}_j=\sqrt{{\rho }_p}{\displaystyle \sum _{l=1}^L}{\mathbf{H}}_{j,l}{\mathbf{\Phi }}_l^H+{\mathbf{N}}_j,$$

(6)

where ${\mathbf{H}}_{j,l}\in {\mathbb{C}}^{M\times K}$ is the channel from the users in cell l to base station j, and ${\mathbf{N}}_j\in {\mathbb{C}}^{M\times \tau }$ denotes the noise during pilot transmission. The noise terms in the pilot and data phases are modeled as independent zero-mean circularly symmetric complex Gaussian variables.

3.2. Pilot Contamination and Channel-Estimation Error

The effect of pilot contamination can be seen by projecting the received pilot signal onto the pilot matrix used in cell j. A least-squares (LS) channel estimate is

$${\widehat{\mathbf{H}}}_{j,j}^{\mathrm{LS}}={\displaystyle \frac{1}{\sqrt{{\rho }_p}\tau }}{\mathbf{Y}}_j{\mathbf{\Phi }}_j={\mathbf{H}}_{j,j}+{\displaystyle \sum _{\begin{array}{c}l=1\\ l\ne j\end{array}}^L}{\mathbf{H}}_{j,l}{\mathbf{C}}_{l,j}+{\displaystyle \frac{1}{\sqrt{{\rho }_p}\tau }}{\mathbf{N}}_j{\mathbf{\Phi }}_j,$$

(7)

where

$${\mathbf{C}}_{l,j}={\displaystyle \frac{1}{\tau }}{\mathbf{\Phi }}_l^H{\mathbf{\Phi }}_j\in {\mathbb{C}}^{K\times K}$$

(8)

is the normalized pilot-correlation matrix between cells l and j. Its $(k,m)$th entry represents the normalized correlation between the pilot of user k in cell l and that of user m in cell j. When ${\mathbf{C}}_{l,j}$ contains nonzero entries, the corresponding interfering channel components remain in the LS channel estimate.

We define the channel-estimation error as

$${\tilde{\mathbf{H}}}_{j,j}={\mathbf{H}}_{j,j}-{\widehat{\mathbf{H}}}_{j,j}^{\mathrm{LS}}.$$

(9)

Using Equation (9), the estimation error becomes

$${\tilde{\mathbf{H}}}_{j,j}=-{\displaystyle \sum _{\begin{array}{c}l=1\\ l\ne j\end{array}}^L}{\mathbf{H}}_{j,l}{\mathbf{C}}_{l,j}-{\displaystyle \frac{1}{\sqrt{{\rho }_p}\tau }}{\mathbf{N}}_j{\mathbf{\Phi }}_j.$$

(10)

The estimation error therefore contains two parts: interference from users in other cells due to nonorthogonal pilots and noise during pilot transmission. For simplicity, we drop the superscript "LS" in the following sections and write

$${\mathbf{H}}_{j,j}={\widehat{\mathbf{H}}}_{j,j}+{\tilde{\mathbf{H}}}_{j,j}.$$

(11)

Equations (7)–(11) show how nonorthogonal pilots introduce interfering channel components into the channel estimate and provide the channel-estimation model used in the following receiver analysis.

3.3. Finite-Sample Covariance Estimation and Receiver-Performance Degradation

A second source of estimation error arises when only a limited number of pilot samples are available to estimate the interference-plus-noise covariance matrix. Let ${\mathbf{R}}_{u,j}\in {\mathbb{C}}^{M\times M}$ denote the true interference-plus-noise covariance and ${\widehat{\mathbf{R}}}_{u,j}$ its estimate,

$${\widehat{\mathbf{R}}}_{u,j}={\mathbf{R}}_{u,j}+{\mathbf{E}}_{R,j},$$

(12)

where ${\mathbf{E}}_{R,j}$ denotes the covariance-estimation error. Let $N_R$ denote the number of effective observations used to estimate ${\mathbf{R}}_{u,j}$. In general, $N_R$ and the pilot length $\tau$ represent different quantities. They are equal when the covariance is estimated from the $\tau$ pilot-domain samples. If $N_R<M$, an $M\times M$ sample covariance matrix may be rank deficient [26]. In addition, if the covariance matrix is estimated from samples obtained after removing the desired-signal component from the received pilot observations, errors in the channel estimate can also affect the covariance estimate.

During uplink data transmission, the received signal at base station j is

$${\mathbf{y}}_j={\mathbf{H}}_{j,j}{\mathbf{x}}_j+{\displaystyle \sum _{\begin{array}{c}l=1\\ l\ne j\end{array}}^L}{\mathbf{H}}_{j,l}{\mathbf{x}}_l+{\mathbf{n}}_j,$$

(13)

where ${\mathbf{x}}_j\in {\mathbb{C}}^{K\times 1}$ and ${\mathbf{x}}_l\in {\mathbb{C}}^{K\times 1}$ denote the desired and interfering data vectors, respectively. To show how channel and covariance estimation errors affect receiver processing, consider the following interference rejection combining (IRC)-type linear combiner

$${\mathbf{W}}_j={\left({\widehat{\mathbf{H}}}_{j,j}{\widehat{\mathbf{H}}}_{j,j}^H+{\widehat{\mathbf{R}}}_{u,j}+\alpha {\mathbf{I}}_M\right)}^{-1}{\widehat{\mathbf{H}}}_{j,j},$$

(14)

where ${\mathbf{W}}_j\in {\mathbb{C}}^{M\times K}$ and $\alpha \ge 0$ is a regularization parameter. Equation (14) shows that both the channel estimate ${\widehat{\mathbf{H}}}_{j,j}$ and the interference-plus-noise covariance estimate ${\widehat{\mathbf{R}}}_{u,j}$ affect the combining filter.

Using Equation (11), the signal after combining is

$${\mathbf{r}}_j={\mathbf{W}}_j^H{\mathbf{y}}_j={\mathbf{W}}_j^H{\widehat{\mathbf{H}}}_{j,j}{\mathbf{x}}_j+{\mathbf{W}}_j^H{\tilde{\mathbf{H}}}_{j,j}{\mathbf{x}}_j+{\mathbf{W}}_j^H{\displaystyle \sum _{\begin{array}{c}l=1\\ l\ne j\end{array}}^L}{\mathbf{H}}_{j,l}{\mathbf{x}}_l+{\mathbf{W}}_j^H{\mathbf{n}}_j.$$

(15)

The second term represents the error introduced by imperfect channel estimation. Covariance-estimation error does not appear as a separate term in Equation (15), but it affects ${\mathbf{W}}_j$ through ${\widehat{\mathbf{R}}}_{u,j}$. Errors in either the channel estimate or the covariance estimate can therefore change the combining weights, reducing interference suppression and detection performance.

The equations above consider a multi-cell system in which each base station processes its received signals locally. In cell-free MIMO, multiple distributed access points (APs) jointly serve users, and the received signals can be processed locally at the APs. In XL-MIMO, near-field propagation, wide bandwidth, spatial non-stationarity, and visibility regions can lead to different channel and covariance structures. These architectures require different system models, but the main effect remains the same: inaccurate channel or covariance estimates can reduce receiver performance. This problem formulation provides the basis for the three classes of methods reviewed in Section 4, Section 5 and Section 6.

4. Intelligent Pilot-Domain Mitigation

The Class I studies mitigate pilot contamination by optimizing the pilot assignment and reuse strategy under limited pilots. Based on their primary pilot-assignment mechanisms, these studies can be categorized into three groups: learning-based pilot-reuse and reassignment strategies, graph- and clustering-assisted pilot assignment, and multi-agent or distributed pilot-assignment approaches. Figure 4 summarizes the problem and the three groups.

4.1. Learning-Based Pilot-Reuse and Reassignment Strategies

Masood [27] and Li et al. [28] both learn whether two users can reuse the same pilot, but they differ in their input features and training labels. Reference [27] employs a supervised convolutional neural network (CNN) that takes the channel vectors of a user pair as input, whereas [28] adopts a naive Bayes classifier using large-scale fading coefficients and the overlap between the users’ channel angle-of-arrival (AoA) intervals as input features. The training labels in [28] are derived from the results of an exhaustive search over pilot assignments, where all candidate pilot assignments are evaluated to identify the one that maximizes the average achievable capacity per terminal. The two studies also differ in how their model outputs are used for pilot assignment. Reference [27] uses the CNN outputs to group users that can reuse the same pilot, whereas [28] uses the classifier outputs to construct a binary connectivity model that guides pilot assignment. In contrast, Omid et al. [23] employ deep Q-learning to iteratively reassign pilots. The state of the Q-learning framework comprises the current pilot assignment and the contamination costs derived from AoA and large-scale fading, whereas the reward is determined by the contamination cost, the change in contamination cost after reassignment, and a penalty associated with reassignment actions.

The main distinction among these studies lies in the learning objective. The supervised approaches in [27,28] learn whether a pair of users can reuse the same pilot, whereas [23] employs reinforcement learning to learn pilot-reassignment actions based on a contamination-related reward.

4.2. Graph- and Clustering-Aided Pilot Assignment

The second group leverages graph-based and clustering methods for user equipment (UE) grouping in pilot assignment. Zhao et al. [29] cluster UEs based on their pairwise Euclidean distances and assign orthogonal pilots to users within each cluster. Ribeiro et al. [30] and Shaikh et al. [31] both exploit channel charting, but in different ways. Reference [30] constructs a low-dimensional channel chart from differences between users’ channel covariance matrices and then performs pilot assignment using a nearest-neighbor greedy strategy. In contrast, [31] predicts missing path-loss, angle-of-arrival (AoA), covariance, or channel-chart information and uses the predicted information to facilitate pilot assignment via weighted graph coloring. Rehman et al. [32] form initial user clusters based on inter-user distances and large-scale interference, and then iteratively refine the pilot assignment using Tabu Search through pairwise pilot swaps between UEs. A multilayer perceptron (MLP) is further employed to predict which user pairs are likely to yield beneficial swaps, thereby reducing the number of candidate swaps that need to be evaluated during the Tabu Search. Zhao et al. [33] construct a pilot-contamination (PC) graph, with edge weights determined by the potential level of PC between user pairs. A graph neural network (GNN) autoencoder is then employed to learn node embeddings from the PC graph, followed by unsupervised GNN-based clustering to generate the final user-clustering matrix for pilot assignment.

When angular information is used for pilot assignment, its estimation accuracy should also be taken into account. For example, Wen et al. [34] show that unknown gain and phase errors at antenna elements can degrade the accuracy of direction-of-departure (DOD) and direction-of-arrival (DOA) estimation in massive MIMO arrays.

4.3. Multi-Agent and Distributed Pilot Assignment

The third group uses multi-agent learning for coordinated pilot assignment, although the two studies [35,36] differ in how the agents are defined. Rahmani et al. [35] formulate pilot assignment as a multi-agent game where each pilot corresponds to an agent consisting of the UEs currently sharing that pilot. At each iteration, a pretrained deep neural network (DNN) first selects, from each agent, the UE that causes the most severe pilot contamination for reassignment. A multi-agent DQN with centralized training and decentralized execution (CTDE) then assigns a new pilot to each selected UE. Oh et al. [36], in contrast, associate each deep Q-network (DQN) agent with an Open Radio Access Network (O-RAN) Distributed Unit (O-DU). Each agent performs pilot assignment based on local observations supplemented by inter-DU message passing, with an additional codebook search step to further improve the assignment. The method in [36] does not require prior knowledge of channel statistics. Pilot assignments are updated in the near-real-time (near-RT) loop, while the DQN parameters are trained in the non-real-time (non-RT) loop.

Therefore, the key distinction is that [35] associates each agent with a pilot-based UE group, whereas [36] associates each agent with an O-DU.

4.4. Cross-Study Comparison and Pilot-Domain Limitations

Table 2. System and evaluation settings of the ten Class I studies.

Study	Architecture/ Link	System Scale	Pilot Setting	Channel/ Dynamics	Baselines	Metrics/Level	Representative Result
Masood [27]	Multi-cell uplink (UL) mMIMO	8 cells, 10 users/cell; BS antennas varied	At most 10 orthogonal pilots; cross-cell reuse	5-path block-fading channel; $10°$ angular spread	N/R	Co-pilot correlation (P)	Co-pilot correlation plateaus near the 0.2 labeling threshold; no E/L/N metric is reported.
Li et al. [28]	3-cell UL mMIMO	3 cells, 10 users/cell; BS antennas varied	10 orthogonal pilots reused across cells	Large-scale fading, AoA intervals	Time-shifted, coloring, covariance/ location-based PA	Capacity per terminal (N)	At 128 BS antennas, capacity is about 0.27 bit/s/Hz higher than the location-based method.
Omid et al. [23]	7-cell uplink massive MIMO	100 BS antennas, 4 users/cell	4 orthogonal pilots reused across cells	50-path channel; time-varying AoA intervals and large-scale fading	Exhaustive, random, soft pilot reuse	Minimum rate (N)	Approaches exhaustive search; soft pilot reuse requires 2.5× as many orthogonal pilots.
Zhao et al. [29]	Cell-free (CF) massive MIMO; downlink data	100 single-antenna access points (APs); 20 or 40 users	10 pilot symbols in a 200-symbol coherence block	Independent Rayleigh fading	K-means, user grouping	Channel-estimation accuracy (E); SE (N); runtime	Per-user SE is 4.23/0.83 bit/s/Hz for 20/40 users; runtime is 0.02/0.03 s.
Ribeiro et al. [30]	Single-cell, 3-sector uplink massive MIMO	512 registered users, 64 active; 3 sectors × 64 antennas	Pilot lengths 32/64/128; corresponding reuse factors 16/8/4	Spatially correlated 200-path channel at 6 GHz	Random PA, AoA grouping, SGPS, CMD, position-based	NMSE (E), detection MSE (L), sum rate (N)	Approaches the position-based benchmark; at reuse factors 8 and 16, it outperforms the other practical baselines.
Shaikh et al. [31]	7-site, 3-sector UL MIMO	7 BSs × 3 sectors × 32 antennas; 4000 offline and 1000 online users	10–80 pilots	3GPP 3D-UMa NLoS, multiple layouts	Full-information methods based on covariance, AoA, or location; random PA	NMSE (E), imputation/chart quality	Channel-chart imputation approaches the performance of full-information covariance-based assignment with much lower computational overhead.
Rehman et al. [32]	User-centric CF-mMIMO downlink (DL)	169 APs × 4 antennas; 40, 80, or 120 users	5 or 10 pilot symbols in a 100-symbol coherence block	Correlated Rayleigh fading; separate 60 km/h mobility test	Random PA, WGF, K-means, BGC, approximation-ratio	NMSE (E), SE (N), runtime	At 120 users, SE gains are 6.25%, 30.18%, and 14.22% over three reported baselines.
Zhao et al. [33]	User-centric CF-mMIMO DL	100 APs × 4 antennas; 20–100 users	10 pilot symbols in a 200-symbol coherence block	Correlated Rayleigh fading; 1.4 m/s nominal and 10 m/s robustness test	Greedy-based PA, user grouping, spectral clustering, DQN	NMSE (E), SE (N), runtime	With 80 users under interference-aware AP selection, the average NMSE is 0.06 and SE is 0.59 bit/s/Hz.
Rahmani et al. [35]	CF-mMIMO UL	100 APs × 2 antennas; 20–100 users	10 pilot symbols in a 200-symbol coherence block	3GPP UMi path loss/shadowing, static	Random PA, greedy-based PA, clustering	SE metrics (N)	Average and 95%-likely SE gains are 2.2% and 3.3% over the best competing method.
Oh et al. [36]	O-RAN CF-mMIMO UL/DL	4 O-DUs, 96 O-RUs, $K=24/36$	4 or 8 pilots	3GPP UMi, Rayleigh/Rician, 1–10 km/h	Random PA, exhaustive/Tabu Search, Hungarian algorithm	Sum-MSE (E), UL/DL SE (N), runtime	With 24 users and 4 pilots, sum-MSE is reduced by up to 27%; UL/DL SE reaches 10.18/9.40 bit/s/Hz.

Notes: P: pilot-domain metric; E: estimation level; L: link/receiver level; N: network level; N/R: not reported; PA: pilot assignment; SE: spectral efficiency; BS: base station; AoA: angle of arrival; mMIMO: massive multiple-input multiple-output; SGPS: statistic greedy pilot scheduling; CMD: covariance-matrix distance; NMSE: normalized mean-square error; MSE: mean-square error; 3GPP: 3rd Generation Partnership Project; 3D-UMa: three-dimensional Urban Macro; UMi: Urban Micro; NLoS: non-line-of-sight; WGF: weighted graph framework; BGC: beam-domain based graph coloring; DQN: deep Q-network; O-RAN: open radio access network; O-DU: O-RAN distributed unit; and O-RU: O-RAN radio unit. Only values stated or directly derivable from the source studies are reported.

shows that the ten Class I studies report performance at different evaluation levels. Eight studies report at least one network-level metric, and six report a channel-estimation metric. However, only Ribeiro et al. [30] report an explicit symbol-detection metric, while Masood [27] evaluates only the correlation between users sharing the same pilot. Moreover, the studies differ in system architectures, pilot settings, channel models, and network sizes. Therefore, the reported numerical gains should be interpreted in the context of their respective simulation settings.

Table 3. Learning methods, information requirements, deployment, and robustness of the ten Class I studies.

Study	Learning Paradigm/Model	Inputs/Side Information	Training Data/Labels	Training/ Adaptation	Processing/ Deployment	Complexity/ Latency	Robustness/ Availability
Masood [27]	Supervised CNN	Channel-vector pairs	500,000 synthetic channel pairs; labels from a correlation threshold	Offline	Parallel pairwise classification	FLOPs/runtime N/R	BS-antenna sweep only; no OOD test; code/data N/R.
Li et al. [28]	Supervised naive Bayes	Large-scale fading and AoA overlap features	Pilot-reuse labels from exhaustive search	Offline	Inter-BS feature sharing required	PA $O\left(K^2{L}^2\right)$; latency N/R	Training-set size and AoA spread varied; no mobility/OOD test; code/data N/R.
Omid et al. [23]	Deep Q-learning	Pilot-assignment state and contamination costs	No labels; experience-replay samples with rewards	Online learning with experience replay	Single centralized agent	FLOPs/runtime N/R	Tracks temporal AoA/fading changes; no held-out OOD test; code/data N/R.
Zhao et al. [29]	Unsupervised spectral clustering	User-distance graph	No labels/learned parameters	No offline training; recomputed from current user locations	Central eigendecomposition + K-means	Runtime 0.02/0.03 s for 20/40 users	20- and 40-user static cases only; no mobility/OOD test; code/data N/R.
Ribeiro et al. [30]	Isomap charting + greedy reuse	Long-term channel covariance/pairwise covariance distance	Unlabeled long-term covariance statistics	Covariance/ chart updates required under mobility	Centralized BS; channel-chart maintenance required	Chart $O((M^3{S}^3+\nu +C+1)N^2+2N^3)$, reuse $O\left((C+1)N^2\right)$	Pilot reuse, angular spread, and antenna number varied; mobility requires chart updates; code/data N/R.
Shaikh et al. [31]	KNN/DNN + channel charting	Serving-cell path loss, AoA interval, or covariance	4000 offline users; neural network uses train/validation/test split	Offline predictor construction; online out-of-sample imputation	Feature imputation at BS/cell; centralized graph construction and coloring	KNN imputation $O\left(K{K}_{\mathrm{nn}}\right)$, similarity $O\left(K^2\right)$; covariance scales with $M^2$	6/7/8-BS layouts and antenna/pilot settings tested; no mobility or OOD test; code/data N/R.
Rehman et al. [32]	Clustering + MLP + Tabu Search	Geometry distance, AP overlap, and large-scale gains	150 setups, exact swap-gain labels	Offline MLP, event-triggered reassignment	Central CPU using serving-set information	Dominated by $O\left(K^2\right)$	User density, hardware impairment, and 60 km/h mobility tested; code/data N/R.
Zhao et al. [33]	Supervised GNN autoencoder + unsupervised GNN clustering	AP selection, large-scale fading	Supervised graph reconstruction; unlabeled clustering	Training over channel realizations; per-slot inference	Central CPU, global graph	Runtime 0.007–0.047 s for 20–100 users in the reported setting	Two AP-selection rules, 20–100 users, and a 10 m/s mobility test; code/data N/R.
Rahmani et al. [35]	Unsupervised DNN + multi-agent DQN	User locations and SINR	No ground-truth labels; unsupervised loss and replay-based RL	Pretrained user-selection network; iterative multi-agent Q-learning	Centralized training and decentralized execution	$O\left(P{K}^2\right)$; hardware latency N/R	User/pilot scaling only; no mobility/OOD test; code/data N/R.
Oh et al. [36]	Multi-agent DQN with message passing and codebook search	Channel-estimate power observations; optional inter-DU messages	No fixed dataset; online experience replay with reward-based targets	Near-real-time pilot updates; periodic non-real-time DQN training	Inter-DU message passing	Approx. linear in K; network/hardware latency excluded	Mobility, Rician fading, and topology variations tested; code/data N/R.

Notes: OOD: out of distribution; GNN: graph neural network; CNN: convolutional neural network; FLOPs: floating-point operations; MLP: multilayer perceptron; KNN: k-nearest neighbors; DNN: deep neural network; RL: reinforcement learning; CPU: central processing unit; SINR: signal-to-interference-plus-noise ratio. Complexity expressions use source-specific notation and are not directly comparable across implementations.

shows that evaluation under changing conditions also varies across the studies. References [32,33,36] explicitly evaluate user mobility, whereas the method in [23] is evaluated with time-varying AoA information and large-scale fading but without an explicit mobility model. Most of the studies primarily vary system parameters, such as the number of users, antennas, or pilots. Implementation costs are likewise reported inconsistently. The reported runtime values reflect algorithm execution under source-specific implementations and should not be interpreted as end-to-end network latency. None of the studies reports all of the following: computational complexity, memory usage, end-to-end latency, energy consumption, hardware validation, and public code or data availability.

Class I methods can reduce pilot contamination before channel estimation, but pilot reuse may still result in channel-estimation errors. Section 5 therefore considers intelligent methods for recovering channel information from contaminated or otherwise limited pilot observations.

5. Intelligent Channel Estimation with Contaminated or Limited Pilots

The Class II studies employ learning-based methods to estimate or reconstruct the desired channel from contaminated, sparse, quantized, or otherwise limited pilot observations. We categorize these methods into three groups: channel estimation under pilot contamination and nonorthogonal pilots, multi-stage channel refinement, and channel reconstruction from sparse or quantized pilots. Figure 5 illustrates the problem and the three recovery approaches.

5.1. Channel Estimation Under Pilot Contamination and Nonorthogonal Pilots

Among the methods that address channel estimation from nonorthogonal pilots, a key distinction lies in the output of the learned model. Hirose et al. [24] learn a direct mapping from contaminated LS channel estimates to the desired channels using a fully connected neural network and a CNN. Kasibovic et al. [37] instead use a variational autoencoder (VAE) to infer the means and covariances of the desired and interfering channel distributions, whereas Cao et al. [38] replace the nonlinear denoising module of orthogonal approximate message passing (OAMP) with a U-Net-based denoiser. Accordingly, the learned component is used for direct channel decontamination in [24], statistical inference for a linear estimator in [37], and nonlinear denoising within OAMP in [38].

Their information requirements during training and inference also differ. Reference [24] uses contaminated LS estimates as inputs and desired channels as supervised targets; Reference [37] learns from separate desired and interfering observations but performs estimation from contaminated observations; and reference [38] uses nonorthogonal-pilot measurements together with the sensing matrix and interference covariance.

5.2. Multi-Stage Channel Refinement

A second group improves an initial channel estimate through additional data samples or subsequent refinement stages. Hirose et al. [39] employ two CNNs: the first refines the LS channel estimate from received pilot signals, while the second exploits detected data symbols as pseudo-pilots to further refine the channel estimate. Hejazi et al. [40] refine an LS-based channel estimate using a U-Net and augment the offline training set with generative adversarial network (GAN)-generated channel samples. Jiang et al. [41] combine model-driven channel denoising, data-driven pilot interpolation, and low-complexity online refinement to improve robustness against channel-model mismatch.

These methods compensate for limited pilot information in different ways: reference [39] uses detected symbols, reference [40] augments the training data, and reference [41] refines the channel estimate online.

5.3. Channel Reconstruction from Sparse or Quantized Pilots

As pilot observations become sparser, channel recovery becomes increasingly underdetermined and relies more heavily on priors that capture the underlying channel structure. Guo et al. [42] compare CNN-based, generative pretrained transformer (GPT)-style, and frozen foundation-model priors within a unified unfolded reconstruction framework, demonstrating that the foundation-model prior remains substantially more robust as the pilot ratio falls to 1%. Zhang and Chen [43] address limited pilots in high-mobility massive MIMO systems using the Dual-order Adaptive ISTA Network (DoA-ISTA-Net), where ISTA denotes the iterative shrinkage-thresholding algorithm. It enforces data consistency between the reconstructed channel and the pilot-domain LS observations, while learning long-range time–frequency dependencies and suppressing pilot-domain noise. Rahman et al. [44] use a bidirectional long short-term memory (BiLSTM) to learn the mapping from 1-bit-quantized pilot measurements to channels.

Although these approaches differ in architecture, they all rely on learned representations of channel structure; their effectiveness therefore depends on how well these representations generalize across system configurations and channel conditions.

Near-field wideband XL-MIMO introduces additional structural challenges for channel estimation. As a related example, the method of Wang et al. [45] exploits angle-distance coupling and frequency-dependent polar-domain support caused by spherical-wave propagation and beam splitting, highlighting the need for estimators that remain robust to such structural changes.

5.4. Cross-Study Comparison and Channel-Estimation Limitations

The comparison in

Table 4. System and evaluation settings for the nine Class II studies.

Study	Architecture/Link	System Scale	Pilot Setting	Channel/ Dynamics	Baselines	Metrics/Level	Representative Result
Hirose et al. [24]	7-cell uplink massive MIMO	8–64 BS antennas; 1 UE/cell in the main tests; 2 UEs/cell in the aging test	Cross-cell pilot reuse; 10 pilot symbols in the main tests and 2 in the aging test	Spatially correlated fading, timing mismatch, normalized Doppler 0.005/0.05	LS, MMSE with known covariance, covariance-estimation method	NMSE (E)	At 64 BS antennas, CNN NMSE is approximately 0.26 versus 2.08 for LS.
Kasibovic et al. [37]	Multi-cell uplink channel estimation	1 desired UE and 1 interfering UE; 128 BS antennas for 3GPP and 32 for QuaDRiGa	Same orthogonal pilot set reused across cells	3GPP UMa with controlled AoA overlap, QuaDRiGa UMa, 6 GHz	LS, sample/genie-covariance estimator, single-cell VAE variants	NMSE (E)	Achieves lower NMSE than the single-cell VAE estimators, with larger gains when the desired and interfering AoAs are more separated.
Cao et al. [38]	THz UM-MIMO UL, hybrid far/near-field propagation	4 subarrays; 1024 antenna elements; 2 UEs; 5 paths	Simultaneous nonorthogonal pilots	300 GHz; target LoS path at 45 m; target scatterers spanning near and far fields	LS, OMP, OAMP variants, ResBlock-MU-LMMSE	NMSE (E), runtime	At 10 dB SNR, U2Net-MU-LMMSE achieves NMSE below $-11$ dB, nearly 1 dB better than ResBlock-MU-LMMSE.
Hirose et al. [39]	2-cell uplink massive MIMO	32-antenna ULA, 2 UEs/cell, 200-symbol block	2-symbol pilots reused across cells; detected data used as pseudo-pilots	Frequency-flat fading, $2°$ angular spread, normalized Doppler 0–0.05	CNN estimator, frame interpolation, data-aided estimation	NMSE over time/Doppler (E)	Lowest NMSE over most tested Doppler values, with a clear advantage above normalized Doppler 0.01.
Hejazi et al. [40]	Single-cell centralized uplink MU-mMIMO	32 BS antennas, 20 single-antenna UEs	i.i.d. complex Gaussian pilots; 20–128 pilot symbols	DeepMIMO outdoor ray tracing, quasi-static mmWave	LS, MMSE, OMP, LS–U-Net, LS–ViT	NMSE (E), SE (N)	With 40 pilot symbols, the proposed method reaches $-17.8$ dB NMSE, matching the reported LS/MMSE performance at 128 pilot symbols.
Jiang et al. [41]	U-MIMO-OFDM channel reconstruction	1 UE; 16/64 BS antennas; 56 subcarriers × 56 time slots	$14\times 14$ and $28\times 28$ pilot patterns, LS recovery at pilot positions	GBSM training; WINNER II mismatch test; stationary and spatially non-stationary channels	DIGI-AMP/LAMP, DIGI-YOLO-Newton, ReEsNet, eCNN-RN	NMSE, visibility-region error, processing delay (E)	Under channel-model mismatch at 2 dB SNR, online refinement improves NMSE by 3.5 dB and 4.63 dB in the stationary and non-stationary cases, respectively.
Guo et al. [42]	Wideband CSI reconstruction	128-antenna BS, 1 UE, 207 frequency bins	26/13/6/2 pilot lines, 12.6/6.3/2.9/1.0%	Urban V2I ray tracing, 0.26 m spatial sampling	CNN and GPT2 priors in the same unfolded framework	Correlation, NMSE (E)	At 1% pilots, ChannelLM reaches 0.7147 correlation and $-3.02$ dB NMSE, versus 0.5351 and $-1.42$ dB for GPT2.
Rahman et al. [44]	Single-user uplink massive MIMO, one-bit ADCs	2–100 BS antennas, 1 UE	2, 4, 5, 8, 10, and 16 pilot symbols	DeepMIMO I1_2p4 indoor ray-tracing, SNR 0–30 dB	EM-GM-GAMP, MLP, LSTM, CNN	NMSE (E)	With 10 pilots at 0 dB SNR, the proposed method achieves $-36$ dB NMSE, versus $-9$ to $-16$ dB for the compared models.
Zhang and Chen [43]	DL high-mobility massive MIMO-OFDM	64-element 8 × 8 UPA, 1 UE, 512 subcarriers × 14 OFDM symbols	Comb pilots with 2/4/6/10% ratios	DeepMIMO O1_28 at 28 GHz; 120–350 km/h; Doppler and ICI stress tests	LS interpolation, LMMSE, ISTA-Net+, Restormer-CE	NMSE (E), 64/256-QAM BER (L)	At 4% pilots and 10 dB SNR, NMSE is $-22.73\pm 0.07$ dB; the gain over Restormer-CE is 0.31–1.21 dB across the tested SNR range.

Notes: UE: user equipment; LS: least squares; VAE: variational autoencoder; LoS: line-of-sight; OMP: orthogonal matching pursuit; OAMP: orthogonal approximate message passing; MU-LMMSE: multi-user linear minimum mean-square error; SNR: signal-to-noise ratio; UMa: Urban Macro; QuaDRiGa: Quasi Deterministic Radio Channel Generator; ULA: uniform linear array; MU-mMIMO: multi-user massive MIMO; mmWave: millimeter-wave; ViT: Vision Transformer; i.i.d.: independent and identically distributed; U-MIMO-OFDM: ultra-massive MIMO with orthogonal frequency-division multiplexing; RN: residual network; GBSM: geometry-based stochastic model; DIGI: discrete Fourier transform-Gaussian interpolation; YOLO: You-Only-Look-Once; ChannelLM: channel large model; LAMP: learned approximate message passing; V2I: vehicle-to-infrastructure; CSI: channel state information; GPT2: Generative Pre-trained Transformer 2; ADC: analog-to-digital converter; EM: expectation-maximization; GM: Gaussian mixture; GAMP: generalized approximate message passing; LSTM: long short-term memory; UPA: uniform planar array; ICI: inter-carrier interference; ISTA: iterative shrinkage-thresholding algorithm; QAM: quadrature amplitude modulation; and BER: bit error rate. The corresponding source studies do not provide explicit expansions for the source-specific labels U2Net, ResBlock, ReEsNet, WINNER II, or Restormer-CE. Values read from clearly labeled curves are indicated by ≈; other values are reported by the corresponding source studies.

and 

Table 5. Learning methods, information requirements, deployment, and robustness of the nine Class II studies.

Study	Learning Paradigm/Model	Inputs/Side Information	Training Data/Labels	Training/ Adaptation	Processing/ Deployment	Complexity/Latency	Robustness/ Availability
Hirose et al. [24]	Supervised FC network/CNN	Real/imaginary parts of the contaminated LS channel estimate	20k training/10k test samples, desired-channel labels	Offline supervised training	BS-side channel estimation	Training time with 64 BS antennas: 209 s (FC network) and 498 s (CNN); parameter count, FLOPs, and inference latency N/R	Imperfect timing and Doppler mismatch tested; no cross-channel model OOD test; code/data N/R.
Kasibovic et al. [37]	Generative VAE + LMMSE	Contaminated channel observation	100k/10k/10k train/validation/test samples, separate desired signal and interference observations	Offline	Local BS estimation; no ground-truth covariance required	Online complexity stated to match the single-cell VAE method; FLOPs and latency N/R	3GPP and QuaDRiGa evaluated separately; code/data N/R.
Cao et al. [38]	Model-driven OAMP with MU-LMMSE and FPN U-Net	Nonorthogonal pilot measurements, sensing matrix, interference covariance	40k samples, 80/10/10 split, SNR 0–20 dB	Offline	Iterative BS-side channel estimation	Analytical operation count reported; 33.4 M parameters, 176 M MACs; runtime comparison reported; inference latency N/R.	Statistical interference covariance tested; no test under a different channel scenario; code/data N/R.
Hirose et al. [39]	Two supervised CNNs + smoothing	LS channel estimate; received data; detected symbols	200k/10k train/test samples; CNN II trained over normalized Doppler 0–0.05	Offline	BS-side pilot- and data-aided channel estimation	Parameters, FLOPs, runtime, and latency N/R	Doppler varied within the training range; no OOD test under different channel scenarios; code/data N/R.
Hejazi et al. [40]	Regularized LS + U-Net, GAN augmentation	Coarse LS estimate, known pilot matrix	DeepMIMO ray-traced channels; GAN-generated samples; true channels used as supervised labels	Offline training with mixed precision	BS-side estimate followed by U-Net channel refinement	U-Net: 8.35 M, 0.12 ms/sample, ViT: 0.34 M, $\approx 0.45$ ms/sample, FLOPs/platform N/R	GAN/hybrid-training ablation reported; no cross-channel OOD test; code/data N/R
Jiang et al. [41]	Model–data hybrid denoising + eCNN-RN-based interpolation + online refinement	LS channel estimates at pilot positions	5k training/2.5k validation samples, GBSM-generated channels	eCNN-RN trained offline; online refinement	BS-side uplink estimation with online refinement	Operation counts and processing-delay comparison reported; lower delay than DIGI–YOLO–Newton	GBSM-to-WINNER II channel-model mismatch test; online refinement improves robustness; code public, data N/R.
Guo et al. [42]	Unfolded reconstruction + frozen foundation-model prior	Sparse CSI observations and pilot mask	3931/1123/562 train/validation/test samples	Frozen foundation LLM backbone; input/output projections trained offline	BS-side iterative unfolded reconstruction	Higher inference complexity; parameters, FLOPs, memory, and latency N/R	No cross-scenario test; broader generalization left open; code/data N/R.
Rahman et al. [44]	Supervised bidirectional LSTM	Real/imaginary one-bit pilot measurements	105,981 samples, 70/30 train/test split, SNR 0–30 dB	Offline	BS-side uplink channel estimation	Parameters, FLOPs, runtime, and latency N/R; RTX 3060 used for training	Evaluated under matched antenna/pilot/SNR settings; no channel/array OOD test; DeepMIMO source data public, code N/R.
Zhang and Chen [43]	Nine-stage unfolding + dual-order bidirectional Mamba	LS-interpolated CSI, pilot mask, and observed pilots	Per pilot ratio: 7000/1000/2000 train/validation/test samples, SNR $\mathcal{U}(0,30)$ dB	Offline, separate model for each pilot ratio	BS-side inference; batch processing tested	1.310 M parameters, 9.420 G FLOPs, 19.59 ms/sample, 32.6 MB peak GPU memory	120–350 km/h, path-wise Doppler, pilot ICI, grid scaling, and batching tested; data on request and code N/R.

Notes: FPN: fixed-point network; MAC: multiply–accumulate operation; N/R: not reported; FC: fully connected; GAN: generative adversarial network; GPU: graphics processing unit; LLM: large language model. Complexity values follow the respective source studies and are not directly comparable across different hardware platforms and implementations.

shows that all studies in this class report estimation-level performance, whereas only reference [43] evaluates receiver-level bit error rate (BER) and only reference [40] reports network-level spectral efficiency. Thus, the performance evaluation of Class II studies remains largely at the estimation level.

The studies also differ substantially in training and implementation: some use supervised offline training, some exploit detected-data feedback, and some include online adaptation. Broader cross-class comparisons of overhead, complexity, and out-of-distribution (OOD) robustness are provided in Section 7.

Class II methods recover the desired channel before downstream detection. The next section turns to intelligent methods that directly perform interference suppression or symbol detection when the available channel estimates remain unreliable or unavailable because of limited or imperfect pilot observations.

6. Intelligent Receiver Processing with Contaminated or Limited Pilots

Class III focuses on learning-based receiver processing in scenarios where pilots are contaminated, scarce, or even unavailable. Across the five studies, the considered pilot conditions include nonorthogonal or reused pilots, sparse demodulation reference signal (DMRS) configurations, the minimum pilot length required by an LS formulation, and pilotless transmission. These approaches directly produce detected data symbols or log-likelihood ratios (LLRs) as their final receiver outputs.

These studies follow two main approaches. The first explicitly recovers or updates channel information and uses it for data detection, while the second performs equalization or detection without an explicit CSI-refinement stage. Figure 6 summarizes these two approaches.

6.1. Joint Channel Recovery and Data Detection

Victor et al. [25] employ a fully convolutional neural network (FCNN) to refine an LS channel estimate. The refined channel, together with the received data, is then passed to an unfolded projected-gradient-descent (PGD) detector for symbol recovery. The proposed receiver is evaluated at both the channel-estimation and detection levels using normalized mean-square error (NMSE) and BER, respectively. Zhang et al. [46] develop a generalized expectation–maximization (GEM) framework for joint channel estimation and signal detection, in which channel estimation and symbol detection are performed iteratively. The GEM’s M-step uses a modified trainable projected-gradient (TPG) detector to recover the transmitted symbols. In their experiments, the pilot length is set to the minimum value $L_p=2N_t$ required by the adopted LS formulation, and channel estimation and data detection are then performed jointly.

The two approaches reflect different receiver-design trade-offs. FCNN-PGD is designed for a specific 5G orthogonal frequency-division multiplexing (OFDM) setting and requires scenario-specific training, whereas GEM-TPG uses only a few trainable parameters and is evaluated across a wider range of system settings. However, its repeated matrix operations increase computational cost. Thus, comparisons between receivers should consider not only BER but also complexity and adaptability.

6.2. Equalization and Detection Without CSI Refinement

DeepRx MIMO [47] follows a second receiver strategy that reduces the reliance on channel estimation by combining pilot information with the received data. It uses DMRS symbols and a channel estimate obtained by simple interpolation as inputs to a residual network (ResNet)-based receiver, which is trained directly using transmitted bit labels. Zecchin et al. [48] perform in-context learning (ICL) for cell-free multi-user MIMO. The transmitted pilots, quantized received pilots, received data, large-scale fading coefficients, and modulation information are organized into a prompt for a decoder-only transformer, which detects the transmitted data symbols. Adaptation is achieved through the prompt, without fine-tuning the model parameters. Korpi et al. [49] entirely eliminate pilots by jointly learning stream-specific constellations and a DeepRx-type receiver, enabling blind spatial-stream separation and soft-bit detection.

Reducing pilot dependence entails different design trade-offs. DeepRx MIMO relies on interpolated channel estimates and offline training, whereas ICL enables adaptation to different configurations without model fine-tuning but requires both pilot and data observations. Pilotless spatial multiplexing removes pilots altogether, but achieves this by jointly learning the transmit constellations and receiver.

6.3. Cross-Study Evaluation and Receiver-Processing Limitations

Table 6. System and evaluation settings for the five Class III studies.

Study	Architecture/Link	System Scale	Pilot Setting	Channel/Dynamics	Baselines	Metrics/Level	Representative Result
Victor et al. [25]	7-cell UL 5G massive-MIMO	128 BS antennas; 1 single-antenna user/cell; 64-QAM	Nonorthogonal SRS	3GPP UMi, TDL-A–E, 4 GHz, 30 km/h	LS, M-MMSE, DNN, DRCNN, MMSE-SD, MdNet	NMSE (E), BER (L)	FCNN outperforms DNN/DRCNN above 5 dB but remains below M-MMSE; 20-layer FCNN–PGD closely follows MMSE-SD in BER.
Zhang et al. [46]	Pilot-assisted point-to-point MIMO	$4\times 4$, $16\times 16$, $16\times 32$; QPSK, 16/64-QAM	Pilot length set to $L_p=2N_t$	Independent/ correlated Rayleigh; noise with outliers	LS/LMMSE + ZF/MMSE/TPG/SD; MdNet, JCESD	BER (L)	GEM-based joint methods outperform separate estimation/detection pipelines.
Korpi et al. [47]	5G single-user UL MIMO	4 spatial streams, 16 receive antennas, 312 subcarriers, 16-QAM	1 or 2 DMRS symbols per 14-symbol TTI	Train: TDL-B/C/D; held-out validation: TDL-A/E; 2.6 GHz; 0–325 Hz Doppler	Practical LMMSE with one/two DMRS symbols; genie-aided LMMSE	Uncoded/ coded BER (L)	On TDL-E, DeepRx with one DMRS symbol is about 2 dB better than the practical two-DMRS LMMSE baseline; DeepRx with two DMRS symbols nearly reaches genie-aided LMMSE.
Zecchin et al. [48]	Cell-free multi-user uplink, quantized fronthaul	4 APs with 2 antennas each, 1–4 users, central CPU	8-symbol Walsh–Hadamard pilots; pilot reuse tested	Correlated Rayleigh; 3GPP UMi and local scattering; 2 GHz	Centralized LMMSE; infinite-fronthaul LMMSE; MAML	Data-symbol MSE (L)	Under pilot reuse, ICL achieves lower MSE than LMMSE, especially at high SNR.
Korpi et al. [49]	Single-user MIMO-OFDM spatial multiplexing	2 spatial streams, 4 receive antennas, 72 subcarriers, learned constellations	No pilots, baseline uses 2 DMRS symbols/slot	CDL-A/B training; CDL-C validation; 3.5 GHz; 0–5 m/s	K-best with DMRS-based channel estimates or perfect CSI	BLER, spectral efficiency (L)	The pilotless scheme achieves about 15–20% higher spectral efficiency below 15 dB SNR; the gain largely disappears at higher SNR.

Notes: DMRS: demodulation reference signal; SRS: sounding reference signal; TDL: tapped delay line; FCNN: fully convolutional neural network; DRCNN: deep residual convolutional neural network; PGD: projected-gradient descent; GEM: generalized expectation-maximization; TPG: trainable projected gradient; ZF: zero forcing; MMMSE: multicell minimum mean-square error; SD: sphere decoder (in [46]); JCESD: joint channel estimation and signal detection; TTI: transmission time interval; MAML: model-agnostic meta-learning; ICL: in-context learning; CDL: clustered delay line; QPSK: quadrature phase-shift keying; BLER: block error rate. MMSE-SD and MdNet are source-specific labels. Reference [25] describes them, respectively, as a traditional MMSE linear receiver and a model-driven deep-learning network. Numerical values are included only when stated in the corresponding study or directly supported by its reported configuration.

shows that all five studies report receiver-level performance. Reference [25] additionally reports channel NMSE, whereas the other studies evaluate BER, block error rate (BLER), data-symbol mean-square error (MSE), or spectral efficiency. However, none of these studies reports network-level metrics, such as multi-cell sum spectral efficiency, fairness, or cell-edge throughput.

The pilot assumptions also differ across these studies. References [25,48] consider pilot contamination caused by nonorthogonal sounding reference signals (SRSs) and pilot reuse, respectively. Reference [46] uses the minimum pilot length required by the channel-estimation model, while [47] considers sparse pilot configurations. At the other extreme, reference [49] removes pilots entirely.

Table 7. Learning methods, information requirements, deployment, and robustness of the five Class III studies.

Study	Learning Paradigm/Model	Inputs/Side Information	Training Data/Labels	Training/ Adaptation	Processing/ Deployment	Complexity/Latency	Robustness/Availability
Victor et al. [25]	Supervised FCNN pilot decontamination + unfolded PGD detection	Contaminated LS channel estimate, received OFDM grid	24,960/8320/8320 train/validation/test samples; semi-blind channel targets and transmitted-grid labels	Staged offline Adam, 8 epochs	gNB-side processing; inter-cell exchange N/R	7.37 M parameters; reported elapsed time 6.98 s vs. 11.97 s for MdNet; per-sample latency N/R	TDL-A–E evaluated at fixed 30 km/h; no cross-channel OOD test; code/data N/R.
Zhang et al. [46]	Probabilistic GEM with Student’s t noise model + unfolded TPG	Pilot/data observations, constellation information	5000 samples per round over 8 training rounds; 1000 test samples	Incremental offline training with Adam	Iterative joint channel estimation and detection	17 shared parameters; analytical complexity order reported	Tested under changes in channel correlation, modulation, SNR, antenna size, and noise outliers; code/data N/R.
Korpi et al. [47]	Supervised DeepRx with learned multiplicative transformation	Received grid, interpolated pilot-based channel estimate	500,000 TTIs per dataset; 60% for training; transmitted bits as labels	160k iterations, batch size 96, 8 V100 GPUs	Receiver-side processing	Parameters, FLOPs, memory, and per-TTI latency N/R	Trained on TDL-B/C/D and validated on TDL-A/E; SNR, delay, Doppler, and pilot settings randomized; code/data N/R.
Zecchin et al. [48]	Decoder-only transformer with ICL	Pilot sequences, quantized received pilots/data, large-scale fading, modulation	8192 tasks × 1024 examples, transmitted symbols as targets	Offline pretraining, prompt adaptation without fine-tuning	AP-to-CPU quantized observations, centralized equalization	4-layer transformer, embedding dimension 64, 4 heads; FLOPs and latency N/R	User count, fronthaul capacity, pilot reuse, and SNR varied; no broader cross-scenario OOD test; simulation code available.
Korpi et al. [49]	Learned constellations + DeepRx receiver	Received grid; no channel estimate	Differentiable link with bit labels; CDL-A/B training, CDL-C validation	Offline end-to-end Adam; BCE + constellation penalty	Learned transmitter constellations + DeepRx receiver	DeepRx blocks use 512–2048 convolutional filters; total parameters, FLOPs, memory, and latency N/R	CDL-C used for validation; performance degrades with 64-point constellations at high SNR; code/data N/R.

Notes: BCE: binary cross-entropy; ResNet: residual network; gNB: next-generation Node B. Runtime and operation counts are not directly comparable across different hardware platforms and implementations.

reveals differences in deployment and implementation requirements. Reference [48] requires the APs to quantize and forward the received pilot and data signals to the central processing unit (CPU). In contrast, reference [49] requires joint learning of the transmitter and receiver. Complexity reporting is also uneven across the studies. Reference [46] provides analytical time and space complexity, whereas [25] reports both the parameter count and hardware-dependent elapsed time. Reference [47], meanwhile, reports substantial offline training requirements, including the use of eight V100 graphics processing units (GPUs) for 160,000 iterations.

Another notable observation concerns covariance-based receiver processing. Although our literature search explicitly included terms related to covariance estimation and IRC, we identified no eligible studies that use learning-based methods to estimate the interference-plus-noise covariance matrix from a limited number of pilot observations for IRC receivers. This finding suggests that learning-based covariance estimation from limited samples remains underexplored for IRC receivers in large-scale MIMO systems.

7. Comparative Analysis and Research Gaps

7.1. Cross-Class Evidence and Complementary Roles

The three classes play complementary roles in the pilot-limited processing chain: Class I determines or updates pilot assignment, Class II estimates or reconstructs channel information, and Class III performs downstream equalization, interference suppression, or data detection. Given the differences in system architectures, pilot conditions, and available information across these classes, cross-class comparisons focus on evaluation evidence and practical deployment considerations.

The evaluation evidence varies markedly across the three classes. In Class I, eight studies report at least one network-level metric, six include estimation-level metrics, and one reports a receiver-level detection metric. All nine Class II studies report estimation-level performance, but only one also reports BER and one reports network-level spectral efficiency. In contrast, all five Class III studies report receiver-level performance, whereas none includes a network-level metric.

The studies also differ in deployment requirements and robustness evaluation. Table 3, Table 5 and Table 7 summarize their information requirements, processing architectures, information exchange, training and adaptation strategies, and evaluations under test conditions that differ from those used for training. No study reports all of the following: trainable parameter count, floating-point operations (FLOPs), memory, end-to-end latency, energy consumption, and hardware validation. The following subsections therefore compare the studies by learning paradigm and present a minimum set of benchmarking requirements.

7.2. Classification by Learning Method

The stage-based classification identifies where learning is applied in the processing chain, but studies at the same processing stage may differ substantially in how they are trained, adapted, and deployed. To capture these differences,

Table 8. Classification of the 24 surveyed studies according to their primary learning paradigm.

Primary Learning Paradigm	Studies	Class	Data/Supervision	Deployment/Adaptation	Main Strength	Main Limitation
Supervised data-driven learning (9)	[24,27,28,31,39,40,44,47,49]	I–III	Labels include pilot decisions, CSI or channel features, and transmitted symbols; training data are mainly simulated or ray-traced.	Mostly offline training followed by fixed inference; changing test conditions may require retraining.	Learns task-specific mappings directly from labeled examples.	Requires labeled training data and can be sensitive to training–test mismatch.
Unsupervised clustering and representation learning (3)	[29,30,33]	I	Mostly unlabeled graphs or channel statistics; Ref. [33] also uses supervised graph reconstruction before unsupervised clustering.	Clustering requires updating when user geometry or channel conditions change.	Label-free use of spatial structure.	Depends on the quality of the features, graphs, or channel charts.
Reinforcement learning (3)	[23,35,36]	I	States, actions, rewards, and interaction experience; no ground-truth pilot-assignment labels.	Interaction-based learning with online, iterative, or near-real-time updates, depending on the study.	Learns sequential or distributed assignment policies without optimal pilot labels.	Interaction cost and convergence depend on reward design and exploration.
Generative and pretrained-prior learning (2)	[37,42]	II	Ref. [37] learns channel distributions from separated observations; Ref. [42] trains CSI reconstruction based on a frozen pretrained backbone.	Offline training followed mainly by fixed inference.	Provides learned priors for contaminated or sparse observations.	Sensitive to prior/channel mismatch; pretrained models can increase inference cost.
Model-driven and deep-unfolded learning (4)	[25,38,43,46]	II–III	Model-based iterations are combined with trainable modules using CSI or symbol supervision.	Offline training followed by iterative or fixed-stage model-based inference.	Preserves model-based processing structures and can reduce the number of trainable parameters.	Repeated stages and matrix operations remain computationally costly.
Model–data hybrid and learning-assisted methods (2)	[32,41]	I–II	Ref. [32] uses pilot-swap gains as labels to train a pruning model for Tabu Search; Ref. [41] combines model-driven denoising with a supervised CNN interpolator.	Offline training; Ref. [41] uses online model-based refinement.	Combines learning methods with model-based processing.	Multiple modules increase implementation and adaptation complexity.
In-context learning (1)	[48]	III	Quantized pilot/data observations, channel statistics and modulation.	Prompt-based adaptation without parameter updates.	Adapts at inference without retraining or fine-tuning.	Requires prompt/context construction.

classifies the surveyed studies according to their primary learning paradigm and summarizes their training data, adaptation strategies, main strengths, and limitations.

Within the 24 surveyed studies, reinforcement learning (RL) appears only in Class I, where it is used for pilot assignment. As a related example, Kim et al. [50] use RL to select reliable detected symbols as additional pilots for data-aided channel estimation in point-to-point MIMO.

7.3. Minimum Benchmarking Requirements

The surveyed studies use different system models, pilot settings, training procedures, baselines, and evaluation metrics, which makes direct numerical comparison difficult.

Table 9. Minimum benchmarking requirements for learning-based methods under inadequate pilots.

Benchmark Criterion	Minimum Requirement
System and channel setting	Specify the system architecture and antenna scale. Report the bandwidth, channel and interference models, mobility, and major hardware assumptions.
Inadequate-pilot condition	Report the pilot length, pilot reuse or nonorthogonality, pilot locations, transmit power, and pilot correlation when applicable. Evaluate more than one pilot condition, including a less impaired reference case when meaningful.
Training, testing, and reproducibility	For trained models, report the train/validation/test split, sample counts, label source, and main hyperparameters. Use independent test data and, for stochastic training, report variation across multiple runs. State whether code, data, and configurations are available.
Baselines	Compare with conventional and competitive learning-based baselines using the same available information. Include a perfect-information benchmark or optimal solution when meaningful.
Performance metrics	Report the main metric for the target task, such as channel-estimation error, pilot-assignment performance, BER/BLER, or spectral efficiency. For example, if improved channel estimation is claimed to improve detection, report both channel-estimation error and receiver performance.
Additional information and overhead	Report any extra or reference samples, covariance/AoA/location information, pseudo-pilots, prompt information, and inter-node messages required by the method.
Complexity and implementation cost	Report trainable parameters, operation count or analytical complexity, memory use, inference latency, and the hardware/software platform. Report training and online-adaptation costs separately.
Robustness and adaptation	Test the method under at least one channel or system condition that differs from training, such as a different SNR, mobility, pilot pattern, user density, array size, channel model, or topology. State whether the model is used unchanged, fine-tuned, refined online, or adapted through in-context learning, and report the adaptation cost.

therefore summarizes a minimum set of benchmarking requirements for more consistent evaluation of learning-based methods under inadequate pilots.

Comparisons should clearly specify the system and pilot conditions and account for any extra information required by the method. If improved channel estimation is claimed to improve receiver processing, the evaluation should also report the corresponding receiver performance. Learning-based methods should also be tested under channel or system conditions different from those used for training, with the adaptation method and its cost reported. For emerging 6G systems, relevant tests may include near-field propagation in XL-MIMO systems, high mobility, hardware impairments, and changes in cell-free or integrated sensing and communication (ISAC) network topologies [51,52,53].

7.4. Evidence-Based Research Gaps

The cross-class comparison reveals four main research gaps in the surveyed studies. First, evaluation is often limited to the processing stage: Class I studies rarely report receiver-level performance, Class II studies mainly focus on channel-estimation accuracy, and Class III studies do not provide network-level evaluation. Second, robustness and adaptation under changing conditions are not evaluated consistently. Third, among the studies satisfying our selection criteria, none directly addresses learning-based estimation of the interference-plus-noise covariance matrix from a limited number of pilot observations for IRC receivers. Fourth, implementation costs such as latency, memory usage, and coordination overhead, as well as code and data availability, are reported inconsistently.

8. Future Directions for Intelligent Processing Under Inadequate-Pilot Conditions

The gaps identified in Section 7.4 motivate several directions for future research: lightweight online adaptation, joint processing across stages, and learning-based covariance estimation for IRC. Emerging 6G systems also introduce additional challenges related to near-field propagation, spatial non-stationarity, and inaccurate angular information.

Lightweight online adaptation with manageable computational cost represents a promising direction for future research. Model-driven learning and deep unfolding can incorporate existing signal-processing algorithms into trainable models [54]. Hypernetworks can further adjust model parameters according to changing channel conditions [55]. Few-shot learning can adapt pretrained models to new environments using only a small amount of newly collected training data [56], while online learning allows models to update in real time as wireless conditions change [57]. Future studies should therefore separately report the computational and latency costs of training, inference, and online adaptation.

Joint processing across stages can incorporate information from pilot assignment and channel estimation into downstream receiver processing. Kocharlakota et al. [58] show that pilot-allocation information can improve subsequent decision-making, while Zheng et al. [59] demonstrate that channel-estimation errors can be incorporated into beamforming design and throughput optimization. A related gap is learning-based estimation of the interference-plus-noise covariance matrix for IRC receivers when only a limited number of observations are available, which is not directly addressed by the surveyed Class III studies. Future work should jointly consider channel and covariance uncertainty when designing receiver processing.

Emerging 6G systems introduce additional challenges. Near-field propagation and spatial non-stationarity can cause the channel response to vary with frequency and across the array aperture [45,60], while gain and phase errors can reduce DOD/DOA estimation accuracy [34]. As a result, angular information such as AoA estimates may be less reliable for pilot assignment. Future methods should therefore remain robust to changing propagation conditions and inaccurate angular information.

9. Conclusions

This survey reviews learning-based approaches for large-scale MIMO systems with inadequate pilots and organizes the existing literature into three categories: pilot-domain mitigation, intelligent channel estimation, and intelligent receiver processing. We compare the surveyed studies across multiple dimensions, including system and pilot settings, evaluation metrics, learning and training strategies, information requirements, computational complexity, deployment requirements, and robustness. Our comparison shows clear differences in evaluation scope across the three categories: pilot-domain studies more often report network-level performance; channel-estimation studies primarily focus on estimation accuracy; and the surveyed receiver-processing studies do not report network-level metrics. Our literature search also suggests a need for further investigation of learning-based estimation of the interference-plus-noise covariance matrix for IRC receivers when only a limited number of pilot observations are available. In addition, robustness and practical implementation costs are reported inconsistently across the literature. To facilitate more consistent cross-study comparisons, we propose a minimum set of benchmarking requirements. Based on these findings, future research should further explore lightweight online adaptation, joint processing across stages, learning-based covariance estimation for IRC receivers, and robust processing for large-array architectures in emerging 6G systems.