Channel Estimation in 5G-and-Beyond Wireless Communication: A Comprehensive Survey

Abstract

The next generation of mobile networks is predicted to deliver high data speeds, lower latency, and increase the spectral and energy efficiency of wireless communication systems. Several technologies are being investigated for usage in 5G networks. Massive multiple-input multiple-output (mMIMO) systems are one of the most promising technologies for enabling 5G. Even after the recent advancements and research, numerous challenges still exist for channel estimation for mMIMO systems. In the context of pilot contamination and feedback overhead, this study tracks the most recent developments in research on mMIMO system difficulties. The primary goals of this study are to identify the problems with channel estimation, provide a summary of the cutting-edge solutions suggested in the literature, and then discuss newly emerging open research issues that must be taken into account for the implementation of beyond-5G networks.

1. Introduction

Wireless communication is a rapidly developing component of the larger field of communications systems and one of the most active areas of technological advancement. This rapid expansion has been strongly associated with technological innovation, such as 5G and beyond-5G wireless communication technologies. The envisioned beyond-5G network architecture represents a paradigm shift in wireless communications, through the integration of heterogeneous network domains encompassing space, aerial, terrestrial, and underwater environments. This revolutionary architecture facilitates ubiquitous connectivity by leveraging multiple spectral bands, including millimeter-wave, terahertz, visible-light-spectrum, and unlicensed bands. To optimize spectral utilization and achieve unprecedented network capacity, several key enabling technologies require significant advancement and adaptation, notably massive multiple-input multiple-output (MIMO) systems, full-duplex communication, and sophisticated beamforming techniques [1].

The rising demands of next-generation internet of things (IoT) applications in areas such as extended reality, autonomous driving, and smart urban environments call for performance standards that surpass current 5G capabilities in data transmission, latency reduction, and security protocols [2]. Consequently, hundreds of devices and mobile users will be connected to a base station at any time. These phenomena will lead to the wireless environment varying rapidly. In addition to conventional 5G capabilities and applications, the delivery of mission-critical services (MCSs) over 5G networks has also become prevalent [3]. MCS applications are extensively incorporated in domains such as public safety, remote healthcare services, and industrial operations, where trustworthy and nearly zero-lag communication is crucial for effective emergency coordination. This constitutes a specific type of communication system that requires maintaining the key promises of a 5G communication system, which are enhanced mobile broadband (eMBB), ultra-reliable low-latency communication (URLLC), and massive machine-type communications (mMTC). As a result, it is crucial to understand the channel state in order to enhance the performance at the receiver end, so as to provide further processing, such as noise reduction or interference mitigation, of the received signal.

Access to accurate wireless channel states, such as channel state information (CSI) and received signal intensity, would allow for more immediate adaption of transmission parameters, resulting in higher throughput and transmission efficiency in 5G and beyond-5G communication systems. For instance, in a massive MIMO system, it is imperative to determine the precise direction in which the beam should be transmitted. Proper CSI and signal parameters can significantly enhance transmission and reception quality. As the mmWave has high attenuation loss, as is the case with mmWave communication systems, the signals are even more corrupted at the receiver end. As a result, there are much more significant difficulties in estimating the channel.

To avoid significant loss during transmission (attenuation loss or propagation loss), researchers have focused on developing channel estimate algorithms that enable CSI at the receiver, enabling the coherent detection of transmitted data in wireless communication systems. There exist various methodologies for channel estimation. Approaches such as pilot-assisted channel estimation, blind or semi-blind channel estimation, and decision-directed channel estimation techniques have attracted significant interest recently, and they need to be adequately investigated to understand next-generation communication systems better. Thus, this survey aims to fill the void that this field still faces.

Contribution and Uniqueness of Our Survey

This survey distinguishes itself from existing works in several key aspects, offering a unique contribution to the field of channel estimation in 5G-and-beyond wireless communication systems. While numerous surveys have broadly explored massive MIMO and channel estimation techniques, this paper provides a systematic and structured classification of the latest advancements, with a particular focus on two critical challenges: pilot contamination and feedback overhead. Below, we outline the key contributions and unique aspects of this work:

• Comprehensive classification framework: Unlike previous surveys that often have presented a broad overview of massive MIMO challenges, this paper introduces a distinct classification framework that organizes channel estimation techniques based on their approach to addressing pilot contamination and feedback overhead. This framework provides researchers with a clear roadmap for understanding state-of-the-art solutions and their applicability in different scenarios.
• Focus on emerging technologies: While many existing surveys focus on traditional channel estimation methods, this work extensively covers emerging technologies such as reconfigurable intelligent surfaces (RISs) and machine learning (ML)-assisted channel estimation. These technologies are critical for beyond-5G networks, and their inclusion in this survey provides a forward-looking perspective that is often missing in related works.
• Comparative analysis and future directions: This survey not only reviews existing techniques, but also provides a detailed comparative analysis of their advantages, limitations, and application scenarios (see

  Table 1. Comparative analysis of channel estimation techniques.

  Technique	Advantages	Limitations	Application Scenarios
  Pilot-assisted estimation	High accuracy in low-noise environments; well-suited for TDD systems.	High pilot overhead; susceptible to pilot contamination.	Single-cell environments with limited user mobility.
  Compressive sensing	Reduces pilot overhead; leverages channel sparsity.	Requires prior knowledge of sparsity; performance degrades in low SNR.	Sparse channel environments; FDD systems with limited feedback resources.
  Deep learning	Adapts to complex channel conditions; reduces feedback overhead.	High computational cost; requires extensive training data.	Dynamic environments with varying channel conditions; RIS-assisted systems.
  RIS-assisted estimation	Enhances signal propagation; reduces interference.	High pilot overhead; complex cascaded channel estimation.	Urban environments with high user density; mmWave communication systems.
  Hybrid pilot schemes	Balances pilot overhead and estimation accuracy.	Increased complexity in pilot design and scheduling.	Multi-user scenarios with varying channel coherence times.

  ). Additionally, it identifies specific open research challenges and future directions, such as scalability in ultra-dense networks, energy-efficient estimation, and integration with artificial intelligence (AI)/ML for real-time adaptation. These insights are particularly valuable for guiding future research efforts.
• Integration of practical considerations: Many existing surveys focus on theoretical aspects of channel estimation. In contrast, this paper emphasizes practical considerations, such as computational complexity, implementation challenges, and standardization issues. This practical focus makes the survey more relevant for engineers and practitioners working on real-world deployments of massive MIMO systems.

2. Challenges and Approaches of Channel Estimation on MIMO

In massive MIMO systems, as the number of base station (BS) antennas grows, efficient low pilot overhead channel estimation becomes increasingly important, as it can otherwise reduce the performance of wireless communications. The number of orthogonal pilots required for downlink channel estimation is proportional to both the number of BS antennas and the scheduled users [4,5]. Moreover, in multi-cell scenarios, pilot contamination remains a key challenge for massive MIMO deployment. Figure 1 illustrates an example of pilot contamination. For example, uplink channel state information (CSI) can deteriorate when multiple pieces of user equipment (UE) send non-orthogonal training signals using the same resources [6].

2.1. Approaches for Channel Estimation

In full-duplex MIMO systems, downlink channel estimation is more challenging than uplink, due to differences in antenna configurations between the base station (BS) and the mobile devices. As noted in [8], time-division duplexing (TDD) systems allow for the use of channel reciprocity, enabling the uplink channel state information (CSI) to be estimated from the downlink. However, this increases the demand for downlink channel estimation, and frequency division duplexing (FDD) is often viewed as superior to TDD, in terms of transmission delay, communication range, and mobility support [9,10]. Several conventional methods for channel estimation exist [11,12,13], but they are practical in MIMO systems only when the number of required orthogonal pilots scales with the BS antenna count. This results in significant pilot overhead, a limitation that traditional approaches are not well suited to solve.

2.2. Overhead Issues in Channel Estimation

The use of FDD portrays better performance than the TDD approach in MIMO. The statement is also valid for massive MIMO. The uplink and downlink in FDD massive MIMO systems share the same time block, with just the frequency domain separating them. Because there is a variation in frequency carrier between the uplink and downlink, the reciprocity of the channel, as in TDD systems, cannot be used in this circumstance [14]. As a result, each user estimates the CSI for the downlink and feeds it back to the BS. Because the BS has many antennas, users must estimate the numerous channels associated with each antenna. Consequently, there is a significant feedback pilot overhead. Therefore, to obtain the predicted high data rate for 5G, solutions for decreasing the high pilot overhead in FDD massive MIMO systems are required.

Several compressive sensing (CS)-based channel estimation techniques have been proposed, to mitigate the pilot overhead issue in large MIMO systems by leveraging the inherent sparsity of the channel [15,16,17,18,19]. CS can recover high-dimensional sparse signals from lower-dimensional measurements [11,20], allowing for efficient CSI estimation with reduced pilot overhead. Typically, conventional CS-based methods for channel estimation rely on prior knowledge of the channel’s sparsity level, such as the number of non-zero components in the channel impulse response (CIR). However, in real-world scenarios, channel sparsity varies over time and is difficult to measure accurately. Additionally, the physical propagation characteristics of multiple antennas and their close spacing at the BS result in correlated CIRs across different antennas [21,22], a factor that current estimation methods have yet to fully explore, to further reduce pilot overhead.

3. Channel Estimation Methodologies

3.1. Pilot Contamination-Related Estimation Methodologies

Addressing pilot contamination is a widely explored approach for improving channel estimation. In [23], the authors analyzed the impact of channel estimation on the performance of multi-cell massive MIMO TDD systems under time-varying frequency selective fading channels and frequency pilot-sequence re-use assumptions. They utilized two linear estimators, namely, the minimum mean square error (MMSE) and least square (LS), to evaluate channel estimators and perform a comparative analysis of the proposed methods. In [24], another method to address pilot contamination was proposed for Rician fading channels. This approach estimates the probable angle of arrivals (AoAs) of users served by a BS using channel statistical data, assuming a typical pilot structure where pilots are orthogonal within the same cell but re-used across different cells. Despite pilot contamination from other cell users, the line of sight (LOS) component of the intended user remains free of contamination when the BS has a large number of antennas. Using the AoAs and the contaminated CSI, the LOS component for each user is calculated, and data detection is performed using these LOS components. The key contribution of [25] involved developing a robust MMSE channel estimator under the worst-case scenario of pilot contamination in a single-cell multi-user setup. This study also introduced a modified greedy pilot re-use (PR) strategy, utilizing the joint angle-delay subspace to minimize mean square error in channel estimation (MSE-CE). By ensuring that the subspaces for multiple users re-using the same pilots remain non-overlapping, effective pilot scheduling can significantly reduce the estimation error.

When addressing pilot contamination, complexity is a key consideration. In [26], Wu et al. proposed a low-complexity semi-blind channel estimation algorithm. Their technique projects received signals into the least-interference subspace and iteratively calculates subspace bases using a modified power method. The channel estimation is initially performed using a small number of pilot symbols, and data symbols are used to refine the channel estimates. This approach, which leverages subspace projection and innovation, is simpler than conventional methods, and the mean square error of the estimates is inversely related to the length of the data symbols. Another approach, discussed in [27], tackles pilot contamination using a time-shifted pilot method. However, with a limited number of BS antennas, pilot interference from downlink transmission symbols cannot be minimized. The proposed two-stage channel estimation technique mitigates pilot interference by determining beamforming vectors in the first stage, while the second stage handles channel estimation, with orthogonal pilots re-used across cells. This method improves spectrum efficiency, even with a limited number of BS antennas. In [28], a new channel estimation scheme was introduced for massive MIMO systems with pilot contamination. This approach decomposes the space supported by the covariance matrix into three subspaces, generating an interference-free subspace for systems with many BS antennas, which enables accurate channel estimation. Additionally, this method reduces computational complexity by exploiting spatial correlation.

Inter-cell interference (ICI) caused by pilot contamination can severely degrade massive MIMO performance. Pilot assignment in large MIMO systems is often viewed as a vertex graph coloring problem, where pilot sequences are assigned like colors in a graph. In [29], the authors proposed a vertex graph coloring-based pilot assignment (VGC-PA) algorithm combined with post-processing discrete Fourier transform (DFT) filtering to reduce ICI. This approach significantly improves system capacity by mitigating interference between users sharing the same pilot sequence. Pilot contamination and data interference also affect the accuracy of superimposed pilot (SP)-based channel estimation. To address this, ref. [30] introduced a block-diagonal Grassmannian line packing (GLP) technique. In this method, GL-based sequences are used to create SP matrices for users across different cells. An iterative channel estimation (ICE) method based on Tikhonov regularization is then employed to reduce data interference during channel estimation. This technique enhances the signal-to-interference-plus-noise ratio (SINR) and determines the optimal power allocation factor for maximizing spectral efficiency. A semi-blind uplink interference suppression scheme for multicell massive MIMO was presented in [7], in which the constant modulus algorithm (CMA) is used to suppress ICI and inter-user interference (IUI). The CMA, initialized with CSI-assisted MMSE weights, captures signals effectively, despite pilot contamination. By iterating between MMSE and CMA, the approach successfully reduces ICI and IUI, thereby improving interference suppression and CSI estimation.

Few studies have focused solely on the computational load caused by pilot contamination. In [31], Ioushua et al. tackled this issue, using a Bayesian channel estimator. They designed prototype sequences and an analog combiner to reduce the number of RF chains while minimizing estimation error. By selecting users with the strongest relationships, this method optimizes the pilot sequence and achieves performance gains even when the receiver array is highly correlated. Superimposed pilots were proposed in [32] as an alternative to time-multiplexed pilots, to reduce pilot contamination in massive MIMO systems. The authors provided an equation for the uplink SINR, using a non-iterative superimposed pilot-based channel estimation method, and they proposed a data-aided iterative approach to further enhance channel estimation quality by reducing interference from broadcast data. For uplink massive MIMO links, Li et al. in [33] proposed a hybrid channel estimation method to reduce pilot contamination. This method combines time-multiplexed (TM) and time-superimposed (TS) pilots, balancing the advantages of both schemes. By deriving a closed-form approximation for the uplink rate, they showed that the hybrid pilot scheme outperformed either TM or TS pilots in various transmission scenarios.

A semi-blind estimator based on the space-alternating generalized expectation (SAGE) maximization method was proposed by Mawatwal et al. in [34] for multi-user massive MIMO systems affected by pilot contamination. This estimator alternates between pilot-aided initialization and iterative SAGE refinement using both pilot and data symbols. The proposed method enhances both CSI accuracy and spectral efficiency with minimal complexity and quickly converges in just two iterations. Simulations demonstrated that this approach outperforms pilot-aided techniques in terms of MSE, BER, and energy efficiency.

3.2. CSI Feedback Overhead-Related Methodologies

Many CSI signaling reduction strategies for FDD mMIMO systems have recently been presented. For example, in FDD mMIMO systems, numerous channel quantization methods have been proposed, to reduce the CSI feedback overhead. In [35], the authors stated that a typical approach involves channel quantization, with methods such as limited feedback relying on predefined codebooks, which are effective only for systems with fewer transmit antennas with a negligible feedback overhead. One typical strategy for scaling informed transmitter schemes in developing mMIMO systems with a large number of transmit antennas at the base station is to use TDD, leveraging implicit feedback derived from channel reciprocity. However, because most existing cellular deployments use FDD, huge MIMO improvements that are backward-compatible are of tremendous interest. The authors also introduced NTCQ (non-coherent trellis-coded quantization), a method whose encoding complexity increases in a straightforward way as the number of antennas grows. This technique works by leveraging a balance between encoding in a Grassmannian manifold (which helps find a vector in the codebook that boosts beamforming) and non-coherent sequence detection (which decodes optimally even when there is uncertainty in the channel). Moreover, they were able to simplify NTCQ encoding, using an off-the-shelf Viterbi algorithm, making the process more efficient, since non-coherent detection can almost match optimal performance by using a set of coherent detectors. The authors also constructed advanced NTCQ methods that use channel features, such as temporal and spatial correlations.

Fang et al. studied the challenge of downlink training and channel estimation in FDD mMIMO systems by incorporating a traditional one-ring model [36]. The model assumes a BS with many antennas serving multiple single-antenna users simultaneously, as shown in Figure 2. They explored how the MMSE estimator performs when the channel covariance matrix has a low-rank or a near-low-rank structure. Their findings show that the low-rank property of the channel covariance matrix can significantly reduce the training overhead. Specifically, the MMSE estimator can recover the channel accurately in low-noise conditions if the number of pilot symbols used exceeds the rank of the channel covariance matrix. They also proposed optimal designs for both single-user and multi-user pilot schemes.

On the other hand, Zhao et al. suggested an angular-domain pilot design and channel estimation method that reduces overhead by leveraging channel sparsity in the angle domain [37]. First, they estimated the dominant angular set for the downlink, using directional reciprocity in FDD channels, followed by an index calibration technique to account for varying wavelengths in FDD systems. For channel estimation, they introduced two angular-domain pilot design strategies: complete orthogonal pilot design and partial orthogonal pilot design, each with its corresponding feedback framework. As illustrated in Figure 3, most of the multipath components in the channel come from a few specific angular regions at the BS:

In the context of simplifying mmWave systems, ref. [38] proposed a channel estimation technique that identifies the most effective AoAs at both the BS and the users. To assist with channel estimation, users send orthogonal pilot symbols back to the BS using the identified strongest AoAs. This system does not require users to explicitly provide CSI feedback, and the signaling overhead is only proportional to the number of users, which is significantly lower compared to other approaches. Additionally, this method works effectively in both sparse and non-sparse mmWave channel conditions. For multi-user downlink transmission, the technique employs zero-forcing (ZF) pre-coding based on the estimated CSI, and it also derives a tight upper bound on the system’s achievable rate.

Alevizos et al., in [39], introduced a new limited feedback scheme that tackles the issue of increasing overhead as the number of base station (BS) antennas grows. Their approach uses full dictionaries to leverage the natural sparsity in double-directional MIMO channel representations. In the sublinear feedback regime, the method is specifically focused on FDD mMIMO systems. Instead of relying on the Rayleigh fading model, the authors applied a double-directional (DD) MIMO channel model [40,41], which utilizes all channel paths by factoring in both the angle of departure (AoD) at the BS and the AoA at the UE. Additionally, ref. [42] used the angle reciprocity of multipath components for both uplink and downlink, enabling the overhead of CSI in FDD mMIMO systems to scale only with the number of users, not the number of antennas. Simulations showed that this estimation strategy outperforms traditional subspace-based and gradient descent methods.

The authors in [43] proposed a beam-blocked compressive channel estimation method along with an enhanced CSI quantization feedback mechanism. This approach aims to reduce the estimation complexity and feedback overhead challenges in FDD mMIMO systems. They introduced an optimal blocked orthogonal matching pursuit (OBOMP) algorithm, which helps recover the essential parameters of mMIMO. The OBOMP can estimate user channels effectively while requiring fewer pilot symbols. Additionally, the authors examined the asymptotic behavior of pilot coherence when the BS operates with a large number of antennas. They also developed a quantization algorithm for feedback of received signals, using separate amplitude and phase quantization for practical implementations. To handle this, they proposed a modified basis pursuit de-quantization (MBPDQ) algorithm with hard threshold iteration to individually quantize the amplitude and phase of feedback signals.

In [44], the authors proposed a compressive sensing-based method to recover CSI at the BS from restricted and quantized feedback. The approach quantizes the received compressed pilots by retaining partial amplitude data and one bit of directional information per dimension. The CS algorithms are then used to reconstruct the CSI from this feedback sent to the BS. The results indicate that the approach effectively reduces the training and feedback overhead in FDD mMIMO systems, although it incurs a significant computational cost.

In [45], the authors introduced a block Bayesian matching pursuit (BBMP) method for channel estimation. This technique models the channel estimation issue as a block sparse recovery problem, deriving prior probabilities for the block support set. The block index is selected based on a metric that maximizes probability and the equivalent sensing matrix. Each iteration updates the selection metric, using a matching pursuit approach as the dominant support set grows. Additionally, to further decrease feedback overhead in channel estimation, a combination of CS, structured compressive sampling matching pursuit (S-CoSaMP), AoD, and block iterative support detection (Block-ISD) algorithms was presented in [46]. The simulation results show that this method significantly reduces pilot feedback overhead, improving overall system performance and efficiency.

Saraereh et al., in [47], proposed an enhanced structured sparse adaptive compressive sampling matching pursuit (CoSaMP) method tailored for FDD mMIMO systems. Based on the simulation results, this approach performs effectively even in low SNR environments and helps reduce pilot overhead, leading to improved SE. In [48], the authors tackled the channel matrix estimation problem in mMIMO systems by introducing a novel approach based on CS. Their system model includes a BS with a large number of antennas communicating with multiple single-antenna unmanned terminals (UTs) over a realistic scattering environment. They proposed a low-rank matrix approximation using CS, which is solved through quadratic semi-definite programming (SDP), assuming that the channel matrix has fewer degrees of freedom than free parameters. Their analysis and experimental results show that this method surpasses existing techniques, in terms of estimation error performance and training power requirements, without the need for prior knowledge of the statistical or physical characteristics of the propagation channel.

Xiong et al. [49] introduced a threshold-based approach for channel estimation, proposing an enhanced estimator to leverage beam-domain channels. Their methodology employs the MSE technique to determine an optimal threshold based on sparsity, noise variance, and channel variation. The authors considered two distinct scenarios, contingent on whether the channel variance in the beam domain is known or unknown. For the former case, they proposed a threshold to identify common support by aggregating channel vector energy across all user terminals (UTs). Subsequently, they extended this concept to establish a threshold for local support. Zhang et al. [50] highlighted the significant drawback of reference signal (RS) overhead in CSI for FDD mMIMO systems. To mitigate this issue, they developed an improved CSI acquisition strategy utilizing beamformed CSI RS transmission, aimed at reducing the aforementioned overhead concerns.

As the number of base stations increases, the RS overhead for the downlink channel grows correspondingly. Furthermore, when multiple users’ channels are closely correlated, conventional CSI acquisition methods face substantial challenges, as the same beamforming vector may be selected to serve these users, resulting in significant multi-user interference and reduced system throughput. To address these issues, Zhang et al. proposed two limited feedback algorithms, each comprising multiple stages and incorporating various wideband beamforming vector selection techniques. These algorithms consider different cost-performance trade-offs between overall system performance and CSI feedback overhead.

Figure 4 provides an overview of the proposed CSI scheme incorporating reference signals (RSs). The process begins with the transmission of multiple sets of cell-specific beamformed CSI-RSs from the base station for downlink channel estimation. Subsequently, each antenna column is assigned to a single CSI-RS port for every CSI-RS set, employing a pre-coding operation with an identical beamforming vector across different antenna columns. This multi-stage CSI acquisition methodology is adopted to address the challenges posed by the substantial feedback requirements and computational complexity inherent in the system.

Ma et al. [51] proposed an alternative cooperative CSI feedback overhead management scheme based on the interference alignment and soft-space-re-use (IA-SSR) method. This approach was utilized to establish a cooperative transmission structure within a two-stage pre-coding framework. To fully exploit the geographical degrees of freedom, the scheme treated cell-edge and cell-center users distinctly. Subsequently, an optimal power allocation policy was devised, to maximize network capacity. The IA-SSR methodology was employed to create a cooperative transmission structure within a two-stage pre-coding framework. To leverage the geographical degrees of freedom effectively, cell-edge and cell-center users were explicitly handled as separate entities. Following this, an optimal power allocation policy was designed with the aim of maximizing the network’s overall capacity. Afterwards, to validate the efficacy of the proposed algorithm, the authors presented a series of numerical results. These included metrics such as sum rate per cell-edge and cell-center clusters, as well as the MSE performance of the suggested channel training scheme. Figure 5 provides a schematic representation of the proposed IA-SSR scheme, illustrating its key components and operational flow.

When estimating the users’ downlink covariance matrix from uplink pilots, the authors of [52] provided an estimation that made use of the reciprocity of the angular scattering function. The suggested technique can be employed even if the available downlink pilot dimension is smaller than the inherent dimension of the channel vectors, which simulations demonstrate can lead to superior performance than CS-based estimate methods. In addition, ref. [53] provided an estimating framework built utilizing the improved Newtonized (eNOMP) method. The downlink training scheme may be developed using the frequency-independent parameters extracted from the uplink using the technique. According to numerical data, the suggested framework can rebuild the CSI with little feedback and training overhead. Figure 6 represents the proposed downlink channel reconstruction and data transmission scheme. First, users communicate with the BS via sounding RSs. The BS uses the sounding RSs to obtain the channel’s frequency-independent properties. The BS broadcasts downlink-training pilots after estimating the down tilts, azimuths, delays, and weights of the downlink-training beams for the users. Each user calculates its downlink gains of the propagation pathways based on known down tilts, azimuths, delays, and beam weights. Afterwards, users transmit to the BS their expected downlink gains. The BS reconstructs the multi-user channel, based on spatial reciprocity using downlink gains and frequency-independent parameters. The BS creates interference-canceling pre-coders and maximizes the spatial multiplexing benefit by serving every user concurrently in the downlink when there is full CSI at the transmitter.

In order to improve CSI estimation, the intrinsic tensor feature of the FD-MIMO channel was investigated by Zhou et al. in [19]. The expectation-maximization framework served as the foundation for the suggested estimate technique, which used tensor as the processing data structure. The Cramér–Rao lower bound was also used as a metric for evaluation. The use of a pilot-data superposition technique to realize trade-off points between uplink and downlink throughput was made flexible by the simulation results, which indicated an increase in CSI estimations. Since there is no short-term channel reciprocity in mMIMO, the FDD mMIMO system had to use uplink feedback to obtain channel state information with a reasonable overhead. Han et al. [14] suggested creating a combined pre-coding and scheduling technique in an FDD multi-cell network to address this problem. The channel correlation matrix data were used in the method to first group all users. At the first pre-coding step, inter-group interference that existed between intra-cell and intercell was then removed. At the second pre-coding step, users were then adaptively scheduled and beamformed based on the low-dimension effective channel. Finally, simulations were used to demonstrate the usefulness of the suggested algorithm.

4. Learning-Based Channel Estimation and Usage Scenarios in Beyond-5G Communications

4.1. Deep Learning-Aided Channel Estimation

A deep neural network (DNN) technique was suggested by Jiang et al. in [54] as an alternative to using linear CSI structures to achieve dimensionality reduction. The suggested technique may properly estimate the CSI, decrease pilot feedback overhead, and, hence, improve the performance of the wireless system, according to case studies based on ray-tracing simulation. Figure 7 illustrates the architecture of the proposed UDN scheme with a single MBS and several SBSs. Qing et al., in [55], proposed another deep learning (DL)-based scheme combined with superimposed coding (SC) as a promising solution for CSI feedback overhead. This method involves spreading the downlink CSI throughout the uplink user data sequences before superimposing it. The recovery of the downlink CSI and the uplink user data sequences is then offered at the BS, followed by the unfolding of two iterations of the MMSE criterion-based interference reduction. A subnet-by-subnet technique is also used to speed up the convergence rate for network training and make parameter adjustment easier. The simulations demonstrated that 5G mMIMO systems improve CSI estimation without significantly consuming UL bandwidth resources.

Zhang et al., in [56], exploited a generative adversarial network (GAN) and a deep convolutional neural network (CNN) for accurate channel estimation in the mmWave mMIMO system. Although the noise is generally assumed to follow fixed probability distribution in many cases, actual noise in unknown environments may significantly decrease channel estimation accuracy. The proposed GAN-CNN blind de-noiser (BCBD) first extracts a set of approximate noise blocks. The noise blocks are adopted to train the GAN to learn the complex noise distribution, and then noise samples are generated by the GAN. With the obtained noise samples, a CNN-based de-noiser is processed. Doshi et al., in [57], studied an unsupervised channel estimation method that utilizes noisy pilots to train a deep generative model to obtain beamspace MIMO channel realization. The conditional GAN is trained without assumptions on channel model or LOS conditions to represent real-world channel environments. With noisy pilot measurements, GAN is trained. The proposed estimation algorithm also adopts federated implementation to distribute the GAN training over multiple users, reducing computational complexity on the user side. On the other hand, Zhang et al., in [58], studied a potent channel estimation scheme that is based on a generative model, with a focus of reducing estimation overhead. GAN is utilized to create a mapping between low-dimensional and high-dimensional channel spaces, enabling the learning of probability distributions using a limited number of pilots. To enhance the robustness of the proposed channel estimation method across diverse scenarios, the number of multi-paths is incorporated as conditional information. This approach allows the model to adapt to varying channel conditions and propagation environments, potentially improving its performance and and its application in heterogeneous environments.

4.2. Channel Estimation for RIS

Reconfigurable intelligent surfaces (RISs) have attracted significant interest because of their ability to manipulate the propagation environment by controlling the passive RIS elements in wireless communication systems beyond 5G. RIS systems address and apply two fundamental challenges of adopting traditional communication technology [59]. To begin with, passive elements of RIS cannot propagate, receive, or process the transmitted pilots. Next, the RIS usually incorporates hundreds of components.

Learning-based approaches have gained significant traction in channel estimation for RIS systems in recent years. These systems introduce a high-dimensional cascaded channel, presenting unique challenges compared to conventional setups. Shen et al. [60] leveraged CNNs for channel estimation in RIS-aided wireless systems. They framed the channel estimation task as a super-resolution and image restoration problem, aiming to reconstruct the channel matrix. Their proposed method combines a super-resolution CNN (SRCNN) to generate a coarse channel matrix with a de-noising CNN (DnCNN) to further refine the estimation, thereby enhancing overall performance. In a related study, Ye et al. [61] developed a conditional GAN (cGAN) for channel estimation in RIS-assisted communication systems. Their approach utilizes received signals to estimate the cascaded channels, adapting the power of generative models to the specific challenges posed by RIS environments. These learning-based methods demonstrate promising avenues for addressing the complexities introduced by RIS in wireless channel estimation.

On the other hand, because of the significantly greater channel dimension compared to the conventional system, utilizing RIS also causes a substantial rise in the pilot overhead for channel estimation. Estimating the channel components in an RIS-assisted system presents significant challenges. Specifically, accurately characterizing the channel between the BS and the RIS, as well as the channel between the RIS and the user, proves to be a complex task. This difficulty arises from the unique propagation characteristics and cascaded nature of these channel segments in RIS-aided communications. To alleviate the challenges, [59] suggested dividing the total cascaded channel estimation approach into a few quick stages to help with the difficulties. During this process, every stage only estimates a single column vector corresponding to a single RIS element. If the vector array has N elements, for the nth stage, among all the RIS elements, only the nth element is turned on, whereas $N-1$ elements are turned off. The cascaded channel comprised of N columns may be entirely calculated after N steps. However, the channel estimation accuracy may suffer because this ON/OFF approach only allows one RIS element to reflect the pilot signal to the BS. In addition, the required pilot overhead is also considerably high. Nadeem et al. [62] suggested a channel estimation technique utilizing the discrete Fourier transform (DFT) mechanism, in which all the RIS components are always switched on. The entire cascaded channel estimation procedure is still separated into N steps in this approach. The reflecting vector at the RIS, however, is specifically created at each stage as a DFT matrix column vector. According to the LS algorithm, in N stages the cascaded channel may be immediately predicted, based on all the received pilot signals at the BS after N stages. It should be mentioned that the DFT matrix formed by the sum of the reflecting matrices for all N stages has been shown to be the best option for ensuring the correctness of the channel estimate. Moreover, the pilot overhead in this approach is also significantly high.

One of the approaches to alleviating the pilot overhead challenges in the RIS is utilizing the two-timescale channel property [63,64,65]. Hu et al., in [63], provided a framework for two-timescale channel estimation, in which the two separate pilot transmission algorithms are made specifically for estimating the large- and small-timescale channels, respectively, as shown in Figure 8. First, the dual-link pilot transmission [63] approach is used to estimate the high-dimensional channel once over a long period of time. Due to its huge dimension, the pilot overhead needed for calculating large timeframe channels is substantial, but from a long-term viewpoint it is insignificant. The low-dimensional channels may then be calculated before data transmission in a short amount of time based on the commonly utilized uplink pilot transmission approach. The needed pilot overhead is minimal for these channels, despite the fact that they must be estimated more often due to their modest diameters. As a result, by using the two-timescale channel characteristic, the typical pilot overhead may be greatly decreased.

Multi-user correlation-based channel estimation offers a promising method to reduce pilot overhead in wireless systems. In [66], the authors describe how this approach leverages the correlation between users to estimate the cascaded channels directly. As for RIS-assisted communication systems, users communicate with the BS via the same RIS, and the cascaded channels of different users are inherently correlated. This correlation allows for a reduction in the pilot overhead required for estimating the cascaded channels, improving system efficiency.

Alternatively, overhead reduction can be achieved by exploiting channel sparsity in the angular domain, as discussed in [67,68]. In conventional wireless communication, the angular domain channels exhibit sparsity due to the limited number of propagation paths. This characteristic enables the use of sparse signal recovery techniques, such as compressive sensing, to tackle the channel estimation problem with significantly fewer pilots. Similarly, in RIS-assisted systems, the cascaded channels display sparsity when transformed into the angular domain. The estimation of these cascaded channels can be framed as a sparse signal recovery problem, where traditional CS algorithms such as OMP can estimate the angular cascaded channels with reduced pilot overhead. However, the performance of these conventional CS algorithms is limited in low SNR scenarios, leading to suboptimal estimation accuracy.

To address this limitation, a sparse matrix recovery-based channel estimation approach was introduced in [68] to improve estimation accuracy. The key insight is that, since different users share the same RIS-to-BS channel matrix, the angular channels of all users can be projected onto the same subspace. This method improves estimation accuracy by exploiting this shared channel structure. Nonetheless, despite these advancements, the required pilot overhead remains considerable, as the sparsity of the angular cascaded channel in RIS-assisted systems is not as pronounced as in conventional communication systems.

5. Comparative Analysis and Future Directions

5.1. Comparative Analysis of Channel Estimation Techniques

In this study, we have provided a comprehensive comparative analysis of the various channel estimation methodologies discussed in the previous sections. Table 1 above summarizes the key techniques, their advantages, limitations, and potential application scenarios. This comparative analysis aims to highlight the trade-offs between different approaches, such as pilot contamination mitigation, feedback overhead reduction, and computational complexity, which are critical for the deployment of massive MIMO systems in 5G and beyond.

5.2. Future Directions and Open Research Challenges

Despite the significant progress in channel estimation techniques for 5G, beyond-5G, and massive MIMO systems, several open challenges remain that require further investigation. Below, we outline potential future research directions:

• Scalability in ultra-dense networks: As the number of connected devices continues to grow, especially in IoT and smart city applications, scalable channel estimation techniques that can handle ultra-dense networks with minimal overhead are needed. Future research could explore distributed and federated learning approaches, to address this challenge.
• Integration with RIS: RIS technology offers promising opportunities for enhancing channel estimation by dynamically controlling the propagation environment. However, the cascaded channel estimation in RIS-assisted systems remains a complex problem. Future work could focus on developing low-complexity algorithms that exploit the unique properties of RIS, such as two-timescale channel estimation.
• Robustness in dynamic environments: Current channel estimation techniques often assume quasi-static channel conditions, which may not hold in highly dynamic environments such as vehicular networks or drone-assisted communications. Future research should aim to develop adaptive algorithms that can quickly respond to rapid channel variations.
• Energy-efficient estimation: With the increasing emphasis on green communication, energy-efficient channel estimation techniques are crucial. Future studies could explore the use of low-power hardware and energy-aware algorithms to reduce the computational and feedback overhead associated with channel estimation.
• Integration with AI/ML for real-time adaptation: While DL has shown promise in channel estimation, its real-time implementation remains challenging, due to the high computational requirements. Future research could focus on lightweight AI/ML models that can be deployed in real-time systems, possibly leveraging edge computing and federated learning frameworks.
• Standardization and interoperability: As 5G-and-beyond networks evolve, standardization of channel estimation techniques across different network architectures and devices will be critical. Future work could explore the development of standardized frameworks that ensure interoperability between different massive MIMO deployments.

6. Conclusions

The next generation of wireless networks, particularly 5G, is expected to be driven by massive MIMO technology. This approach enables simultaneous communication with multiple users sharing the same resources, leveraging a large number of antennas at the BS. Consequently, both spectral and energy efficiency can be significantly enhanced. However, before its full integration into 5G networks, massive MIMO faces several critical challenges that require resolution. In this survey, we present a systematic mapping analysis of recent research initiatives addressing antenna design issues and channel estimation problems. While numerous secondary studies in the literature cover massive MIMO challenges broadly, our paper provides a distinct classification framework for proposed solution techniques in the existing literature, with a specific focus on pilot contamination and feedback overhead. This survey aims to serve as a comprehensive roadmap for researchers in the field, offering insights into the current state of massive MIMO technology, its potential applications, and the ongoing efforts to overcome its inherent limitations. By synthesizing and categorizing the latest advancements, we provide a structured overview of the progress made in addressing key challenges, thereby facilitating future research and development in this crucial area of wireless communication.