# Review on Channel Estimation for Reconfigurable Intelligent Surface Assisted Wireless Communication System

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## Abstract

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## 1. Introduction

## 2. Objectives and Contributions

## 3. Channel Estimation in Different Frequency Bands

#### 3.1. Channel Estimation for RIS Systems in High Frequency Bands

#### 3.1.1. Channel Estimation for Fully-Passive RIS

**Single-user:**With passive characteristics of fully-passive RIS, it cannot complete the reception and transmission of the signal. Therefore, the existing channel estimation method is to complete the estimation of the cascaded channel, as shown in Figure 2a. To achieve good reflection characteristics, the channels of BS-RIS and RIS-UE are considered as the overall channel, and the CSI obtained through the cascaded channel is sufficient to complete the phase shift setting of the RIS. The sparsity of mmWave can be exploited to convert the channel estimation problem into a sparse channel recovery problem, which can be solved using a compressive sensing (CS) algorithm.

**Multi-user:**More pilot overhead and interference among UEs need to be considered in multi-user scenarios; therefore, a more suitable method for channel estimation needs to be found. Since the number of paths in the BS-RIS-UE will be few unlike conventional MIMO mmWave channels where only row sparsity is available, in RIS-assisted mmWave communication systems with row block sparsity, this feature can be exploited to further reduce the training overhead [25].

**Practical application:**The impact of its hardware cost and accidents on RIS need to be considered. The increase in the number of antennas in large-scale MIMO systems leads to high power consumption and high cost. Wang et al. [39] proposed to equip the BS with a small number of analog-to-digital converters (ADCs). The channel estimation was then completed using the bilinear generalized approximate message passing (BiG AMP) algorithm. The method in this paper requires only 8 bit quantization to achieve the same results as infinite bit.

**Wideband systems:**The proposed method for narrowband systems is not generally applicable in wideband systems. Wan et al. [43] proposed to use OFDM to overcome frequency selective fading in wideband, and then used BS-RIS as prior knowledge to design the pilot to estimate BS-UE and RIS-UE by the distributed OMP (DOMP) method jointly. Liu et al. [44] transformed the wideband channel estimation into a parameter recovery problem. Several pilot symbols were used to detect the channel parameters by a newtonian OMP (NOMP) algorithm. This method considered the phase and delay differences between the received signals at different BS antennas and RIS elements.

#### 3.1.2. Channel Estimation for Semi-Passive RIS

#### 3.2. Channel Estimation for RIS Systems in Low Frequency Bands

#### 3.2.1. Channel Estimation for Fully-Passive RIS

**MISO systems:**Mishra et al. [53] first proposed the ON/OFF channel estimation method. This method accomplishes channel estimation by sequentially turning on the RIS element. Since the cascaded channels are only estimated one by one, the estimated variance of each element is equal to 2. To reduce the variance, a minimum variance unbiased (MVU) estimator was proposed in [54]. This method can be T (training periods) times more accurate than the ON/OFF method of estimation. However, it required large pilot overhead.

**MIMO systems:**The increased number of users and antennas can make channel estimation more challenging. In [58], a three-stage channel estimation method was proposed considering the redundancy among channels without any assumption of sparsity and low rank. The channel matrix of a typical user directly to the BS and the channel matrix reflected by the RIS were estimated in the first two stages, respectively. Finally, the channel estimation for other users was completed using the strong correlation between other users and that user. This can reduce the pilot overhead and save estimation time in MIMO systems.

**Massive MIMO systems:**The larger number of antennas can make channel estimation more difficult to achieve. To complete the channel estimation, He et al. [68] proposed a two-stage cascaded channel estimation method. In the first stage, a BiG AMP algorithm with sparse matrix decomposition was used. In the second stage, a matrix-completed Riemannian streamlined gradient algorithm was used to accomplish accurate channel estimation. The size of sparsity affects matrix decomposition and completion.

**Wideband systems:**Zheng et al. [70] designed a novel phase-shifted channel estimation model for RIS-OFDM systems that satisfies the unit-mode constraint. With the same pilot overhead, this method improves gain by 14 dB over the ON/OFF method. Yang et al. [71] proposed a method using RIS grouping in SISO systems. Both methods provide accurate channel estimation results and a reduction in training overhead.

#### 3.2.2. Channel Estimation for Semi-Passive RIS

## 4. Signal Processing Algorithms for RIS Channel Estimation

#### 4.1. The Conventional Algorithms for RIS Channel Estimation

**LS/LMMSE:**LS estimation [77] and LMMSE are classical channel estimation methods for finding model solutions for channel estimation, which was widely used in RIS-aided systems for pilot-based channel estimation. The RIS channel estimation of conventional LS/LMMSE has a large channel estimation pilot overhead; to minimize the LS/LMMSE channel estimation error, the training reflection pattern and the transmit pilot sequence can be designed jointly [78,79].

**Grouping RIS:**To reduce the training overhead and make full use of the spatial correlation of the channel, a scheme of grouping RIS elements was proposed in [71]. The large RIS was divided into several small RIS groups and each group shared the same common reflection coefficients, which was widely used in the subsequent RIS channel estimation process.

**Kalman filtering (KF):**The channel coefficient matrix was kept constant during the coherent time and the channel was estimated for the elements of the multiple time blocks [84]. Mao et al. [85] used KF for mobile scenes and derived the best reflection coefficients for RIS elements according to the MMSE.

**Multi-stages:**To further improve the estimation accuracy, the distributed multi-stage algorithm was used for RIS channel estimation widely. To obtain higher accuracy channel estimation with lower pilot overhead, in [87], an anchor-assisted multi-stage multiuser wideband cascaded channel estimation scheme was proposed to estimate the cascaded channels. In the first stage, Qian et al. [87] obtained BS-RIS CSI based on cyclic prefix single carrier transmission and phase configuration at RIS. In the second stage, the cascade channel information was estimated in the frequency domain using partial BS-RIS channel states.

#### 4.2. Optimization-Based Algorithms for RIS Channel Estimation

#### 4.3. Compressed Sensing-Based Algorithms for RIS Channel Estimation

**OMP algorithm:**The conventional OMP algorithm directly used for RIS channel estimation leads to large complexity, and how to reduce the training overhead becomes a topic worth discussing. The number of RIS components is large and the calculated pressure of the composite channel is high. For the composite channel models, the channel estimation problem was formulated as a sparse recovery problem for a set of independent dictionaries in the angular and temporal domains.

**AMP algorithm:**The sparsity of the OMP algorithm is a fixed value, which is not compatible with the actual situation. The further proposed AMP algorithm has adaptive sparsity. A two-stage algorithm including matrix decomposition stage and matrix completion stage was proposed in [68].

#### 4.4. Deep Learning-Based Algorithms for RIS Channel Estimation

**End to end network:**Existing RIS systems have separate functions for coding and modulation, channel estimation, channel equalisation, decoding and demodulation. Actually, these modules can be also considered as a whole and modelled as an end to end network. The end to end network can further optimise the performance of the system by avoiding the system falling into local optima. Simultaneously, it optimizes the connection weight coefficients of the sender, RIS and receiver to minimize the cross-entropy loss function of the system [100].

**CNN:**Ahmet et al. [104] designed CNN networks for direct channel and cascade channel estimation, where the users accessed the network directly to estimate their own channels. A large amount of reflective surface channel information was coupled with each other, which were computationally difficult. Compensated learning-based neural network was proposed in [105] to dynamically track the CSI. Due to the powerful adaptive capability of deep learning networks, the estimation process learned the fading channel knowledge directly without the priori knowledge. Chen et al. [105] reduced the number of hidden nodes and introduced an offset learning module to improve the performance in the network. Kundu et al. [57] modelled the channel estimation as an image problem, using CNN networks to denoise and approximate the optimal MMSE channel results.

**GANet:**Tekbiyik et al. [107] used GANet for full duplex wireless communication link channel estimation. The training results are robust under different propagation channels with better performance compared with conventional LS estimation.

**DNN:**During the estimation of partially activated RIS element channel coefficients, a three-stage estimation scheme was proposed in [63] for direct channel. Active RIS element cascade channel and inactive RIS element cascade channel was continuously trained to achieve good accuracy. Jin et al. [36] used residual neural networks for cascaded channel estimation. The online cascade channel estimation was proposed to use the network as a multi-residual dense network.

**RNN:**Considering the large number of RIS components and the relatively short coherence time, Xu et al. [28] considered a deep learning scheme to infer the full channel from partial channels in the antenna domain. Xu et al. used a RNN network in the time domain to explore the connection among different time blocks.

**LSTM:**The work in [111] exploited the dual time-scale channel property, where the BS and RIS channels were static and the channel between the RIS and the user was dynamic. In the subsequent channel estimation process, Xu et al. designed a LSTM based neural network framework for the channel decomposition process and the channel prediction process. Xu et al. changed the connection layer according to the nonlinear mapping relationship between the input and the output, thus reducing the complexity.

#### 4.5. Composition-Based Algorithms for RIS Channel Estimation

**SemiDefinite relaxation (SDR)-deep learning:**Elements on the RIS were usually arranged in two dimensions, treating the channel information as a single image. Yin et al. [112] first used a SDR scheme and then built an end to end deep learning channel prediction model that predicted the entire CSI based on the pilot information. It outperforms existing approaches based on grouping of RIS elements in terms of achievable rate.

**LS-deep learning:**Wang et al. [45] modelled the channel information estimated by LS as a low-resolution image and then interpolate it into a high-resolution image linearly.

**OMP-deep learning:**Using the conventional CS OMP algorithm, it is assumed that the arrival and departure angle bases fall on the discrete grid during the computation exactly, which does not match the reality causing errors. Mao et al. [69] fused deep learning in the OMP algorithm to get results after the residual network to improve the performance.

**AMP-deep learning:**Conventional CS algorithms AMP algorithm can reduce the pilot overhead substantially, but the estimation accuracy is insufficient. Tsai et al. [113] proposed a hypernetwork-assisted based learned AMP network with dynamic shrinkage parameters, where the adaptive shrinkage parameters of the network output are used among layers instead of a fixed value, thus improving the estimation accuracy.

## 5. Conclusions

#### 5.1. Overall Discussion

#### 5.2. Future Work

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**A RIS-aided multi-user MIMO system consisting of a BS with M antennas, a RIS with N reflective elements, and K single-antenna users, green elements in RIS are passive, yellow elements in RIS are active: (

**a**) Cascade channel estimation and (

**b**) separate channel estimation.

Notation | Meaning |
---|---|

bold font lower case | Column vector |

bold font upper case | Matrix |

${(\xb7)}^{\mathrm{H}}$ | Conjugate transposition operation |

${(\xb7)}^{\mathrm{T}}$ | Transposition operation |

${\mathit{I}}_{M}$ | M × M identity matrix |

Diag $(\xb7)$ | Diagonal matrix |

⊗ | Kronecker product |

${\u2225\xb7\u2225}_{\mathrm{F}}^{}$ | Frobenius norm |

$\mathcal{C}\mathcal{N}(\mu ,{\sigma}^{2})$ | Complex Gaussian distribution with mean $\mu $ and variance ${\sigma}^{2}$ |

Ref. | Year | Main Direction | Major Contribution |
---|---|---|---|

Wu et al. [4] | 2021 | Reflection optimization and channel estimation | Reflection channel models, practical constraint, and hardware architecture |

Noh et al. [6] | 2022 | Channel estimation for RIS-assisted mmWave/sub-terahertz (THz) communication | Technical challenges, channel estimation frameworks, and training signal design |

Zheng et al. [14] | 2022 | Channel estimation and passive beamforming design | Discussed emerging RIS architectures, applications, and practical design problems |

Pan et al. [15] | 2022 | Channel estimation, transmission design, and radio localization | Channel estimation, transmission design, radio localization, etc. |

Jian et al. [16] | 2022 | Channel estimation | Wireless communication standards, the current and future standardization activities |

Liang et al. [17] | 2021 | Channel estimation and system design | Reflection principle, channel estimation, system designs, etc. |

Chen et al. [18] | 2021 | Hardware design, channel estimation, etc. | Channel modeling, new material exploration, etc. |

Swindlehurst et al. [19] | 2022 | Channel estimation | Summarize the structured and unstructured system models in RIS systems |

Basharat et al. [20] | 2022 | CSI acquisition, passive beamforming optimization, etc. | Phase-shift optimization and resource allocation |

Babiker et al. [21] | 2022 | Channel estimation | Main recent techniques and various strategies |

Ref. | Year | System Setup | Problem | Method | Results Analysis |
---|---|---|---|---|---|

Wang et al. [26] | 2020 | MISO | High training overhead | Conversion to sparse channel recovery problem | Approximate NMSE of 0.04 obtained using the GAMP algorithm |

Wan et al. [43] | 2020 | MIMO | Wideband system estimation issues | DOMP algorithm and redundant dictionary | Pilot design and redundant dictionaries can improve performance significantly |

Liu et al. [50] | 2020 | MIMO | High training overhead | The deep denoising neural network assisted compressive channel estimation | 4 dB performance gain over initial estimation |

Shtaiwi et al. [34] | 2021 | MIMO | High training overhead | Estimate active users and use CNN’s STS framework to estimate inactive users | The larger the number of active users, the smaller the NMSE |

Li [40] | 2021 | MIMO | High cost/array block | An EM-NNL-GAMP method/Joint array diagnosis and channel estimation algorithm | Outperformed other algorithms at 2 bit/Different methods for different situations were effective for array diagnosis and channel estimation |

Liu et al. [44] | 2021 | MIMO | High pilot overhead | Convert a parameter recovery problem and use NOMP algorithm | Low SNR and small number of pilots had better performance than OMP |

Wang et al. [45] | 2021 | SISO | High training overhead | SR method in images | 10% rate improvement compared with LS (${r}_{\mathrm{SNR}}$ = 35 dB) |

Taha et al. [48] | 2021 | MIMO | High training overhead | Reconstruction of the full channel from subsampled channels using CS and deep learning | Achieved 90% of the best rates |

Hu et al. [49] | 2021 | MIMO | High hardware cost and energy consumption | The semi-passive RIS equipped with a partial 1-bit quantization, ADMM and GAMP algorithms | Better than baseline at high SNR |

Jin et al. [51] | 2021 | MIMO | Low estimation accuracy | Reshape the channel matrix into a two-dimensional image | As the proportion of active cells increases, EDSR had better NMSE performance and MDSR reduced complexity |

Lin et al. [52] | 2021 | MIMO | The problem of time-varying channels | Modeling as a CPD problem and solving tensor problems with algebraic algorithm | Reduced complexity and great results at high SNR |

Chung et al. [27] | 2022 | MISO | High training overhead | Two-stage beam training and FALS | FALS required 45% fewer training symbols compared with the OMP and ANM algorithms (${e}_{\mathrm{NMSE}}$= 0.1) |

Xu et al. [28] | 2022 | MISO | High training overhead | Deep DNN assisted compressed channel estimation algorithm | NMSE decreased with increasing spatial and temporal sampling |

He et al. [29] | 2022 | SIMO | High training overhead | The model-driven deep unfolding neural network | Achieved the same NMSE with 25% less training overhead than LS |

Zhou et al. [30] | 2022 | MISO | High training overhead | Multi-user correlation, channel sparsity, invariance of channel coherence blocks | 60% reduction in pilot overhead compared with baseline scheme (${e}_{\mathrm{NMSE}}$ = ${10}^{-3}$) |

Peng et al. [23] | 2022 | MIMO | High training overhead | A three-stage estimation protocol using the correlation between typical users and normal users | 50% reduction in pilot overhead compared with OMP (${e}_{\mathrm{NMSE}}$ = ${10}^{-2}$) |

Albataineh et al. [31] | 2022 | MIMO | High pilot overhead | Extends the Re‘nyi entropy function as the sparsity-promoting regularizer | An improvement over the OMP |

Lin et al. [24] | 2022 | MIMO | Inefficient method | A MO and AM based method and a three-stage algorithm | The MO method had good results when the overhead was higher than 130. The CS method proposed in this paper is better than GAMP |

Zhou et al. [32] | 2022 | MISO | Grid mismatch issues and estimation performance degradation | Dictionary is optimized to adapt to channel characteristics | Better than the predefined dictionary method when the training overhead was small |

Dai et al. [35] | 2022 | MIMO | High training overhead | The DML algorithm | Used in different scenarios |

Jin et al. [36] | 2022 | MIMO | Low estimation accuracy | GAN-CBD, CBDNet, and MRDNet | MRDNet achieved better NMSE performance than GAN-CBD and CBDNet, with improvements of 5.63 dB and 4.51 dB, respectively |

Du et al. [37] | 2022 | MIMO | Low estimation accuracy | Semi-blind joint channel estimation and symbol detection algorithm | Better NMSE and BER performance |

Noh et al. [38] | 2022 | MIMO | Fewer training symbols | Two CRB-based training signal design algorithms for enhanced sparse channel estimation | Significant performance gain when the number of training symbols was less than the number of RIS reflection elements |

Ye et al. [41] | 2022 | SISO | Interference problems | Maximize power at desired users and eliminate interference at undesired users | The reflector element changed from 8 to 16, achieved a power gain of approximately 10 dB |

Chen et al. [42] | 2022 | MIMO | High mobility leads to CSI changes and requires high overhead | A reasonable configuration of the CSI acquisition time scale | The communication performance was improved in mobile vehicle scenarios |

Zheng et al. [46] | 2022 | MIMO | High training overhead | The received signal is represented as a low-rank third-order tensor | Significantly reduced training overhead and better performance compared with SOMP algorithm |

Ruan et al. [47] | 2022 | MIMO | High training overhead | Used reference points to aid estimation | NMSE was reduced by 2 dB compared with the best benchmark solution (${r}_{\mathrm{SNR}}$ = 10 dB) |

Chen et al. [22] | 2023 | MIMO | High training overhead | Two-stage channel estimation method using common sparse structure | 80% and 60% pilot overhead reduction in LS and MMV respectively (${e}_{\mathrm{NMSE}}$ = ${10}^{-2}$) |

Chung et al. [33] | 2023 | MIMO | High training overhead | Location-aware channel estimation based on ANM | 2D ANM location awareness was only at 32 training symbols, 3D ANM maximum training symbols was 32, both better than 1D ANM |

Wang et al. [39] | 2023 | MIMO | High cost | Low-resolution ADCs and Bayesian optimal estimation framework | The BiG AMP algorithm had better performance in few bit quantization, and 8 bit quantization was almost as good as infinite bit quantization |

Ref. | Year | System Setup | Problem | Method | Results Analysis |
---|---|---|---|---|---|

Mishra et al. [53] | 2019 | MISO | Fully-passive RIS cannot handle signals | ON/OFF method | Binary channel estimation method |

Jensen et al. [54] | 2020 | MISO | RIS increases the number of estimated links | MVU | Estimation accuracy was T (training periods) times better than the ON/OFF method |

Wang et al. [58] | 2020 | MIMO | High training overhead | The relevance of typical user and other users | Improve estimation performance, more time slots should be allocated for the second stage to reduce error propagation |

He et al. [68] | 2020 | MIMO | RIS cannot send and receive signals | Sparse matrix decomposition stage and matrix completion | Better than comparable matrix decomposition and matrix completion schemes. |

Zheng et al. [70] | 2020 | SISO | High training overhead | Transmission protocol with sequential channel estimation and reflection optimization | 14 dB gain improvement over ON/OFF method at the same pilot overhead |

Yang et al. [71] | 2020 | SISO | High training overhead | Elements grouping | Better achievable rates than methods without RIS component grouping |

Alexandropoulos et al. [74] | 2020 | SISO | High training overhead | RIS architecture with a single RF | Produced best estimation performance with smaller training symbols than OMP and LS algorithms |

Zhang et al. [55] | 2021 | MISO | High training overhead | Matrix factorization | Lower overhead and higher accuracy |

Kun et al. [57] | 2021 | MISO | Low estimation accuracy | FFDNET and DNCNN | FFDNET outperformed DNCNN at low SNR but required noise variance information |

Hu et al. [59] | 2021 | MIMO | High training overhead | BS-RIS quasi-static features | Reduced pilot overhead, but worse performance than MVU |

Dearaujo et al. [62] | 2021 | MIMO | High training overhead | PARAFAC tensor modeling of the received signal | Robustness for amplitude and phase perturbations |

Gao et al. [63] | 2021 | MIMO | High training overhead | Integrated DNN to estimate the direct channel, active RIS and inactive RIS sequentially | 50% reduction in pilot overhead compared with OMP (${e}_{\mathrm{NMSE}}$ = ${10}^{-2}$) |

Wei et al. [64] | 2021 | MIMO | High training overhead | Cascaded channel estimation scheme based on DS-OMP | Improved NMSE performance as the number of common paths increased |

Wei et al. [66] | 2021 | MIMO | Large complexity for both channel estimation and signal recovery | Joint channel estimation and signal recovery algorithm | Only about 2.5 dB performance difference compared with LS scheme assuming perfect channel knowledge |

Huang et al. [56] | 2022 | MISO | High cost/array block | Iterative EM algorithm for semi-blind channel estimation | 85% reduction in pilot overhead compared with baseline scheme (${e}_{\mathrm{NMSE}}$ = ${10}^{-2}$) |

Yang et al. [61] | 2022 | MIMO | High training overhead | Anchor-assisted channel estimation | Approximately 50 training symbols can be reduced for the same performance as the baseline scheme |

Shan et al. [65] | 2022 | MIMO | High training overhead | A rank one decomposition-based message recovery and channel estimation algorithm for RIS-assisted URAs | Better separation than baseline solution for active devices |

Wei et al. [67] | 2022 | MIMO | Large complexity for both channel estimation and signal recovery | Joint channel estimation and signal recovery method | Approximately 18 dB gap from baseline approach when pilot length was 100 |

Mao et al. [69] | 2022 | MIMO | Grid mismatch issues and performance degradation | Residual networks to reduce NMSE | SN worked well at small training overheads, RS-OMP achieved better results at large training overheads |

Xu et al. [72] | 2022 | MIMO | High training overhead | Subsampled information is extrapolated to the full channel | 12 dB performance gain compared with LS (The number of active RIS elements was 1/16 of the total RIS elements) |

Jeong et al. [73] | 2022 | SISO | Carrier frequency offset | A joint CFO and CIR estimation | Up to 30 times higher performance relative to benchmark solutions |

Schroeder et al. [75] | 2022 | MIMO | Low estimated efficiency | Two-stage channel estimation scheme based on ANM | Better performance than passive RIS |

Hu et al. [76] | 2022 | MIMO | High training overhead | ESPRIT, TLS, MUSIC | Better performance than OMP and LMMSE methods |

Ref. | Year | Antenna/RIS Architecture | Channel Model | Major Algorithm | Performance Analysis |
---|---|---|---|---|---|

Zhou et al. [77] | 2021 | MIMO/Passive RIS | Static channel | AoA estimation and LS method | Improved estimation performance compared with the existing channel estimation algorithms (With low pilot overhead) |

Demir et al. [80] | 2022 | MIMO/Passive RIS | Static channel | Reduced-subspace LS and array geometry | Reduced the ${e}_{\mathrm{NMSE}}$ to −40 dB (${r}_{\mathrm{SNR}}$ = 0 dB) |

Xu et al. [81] | 2022 | SISO/Passive RIS | Time-varying and double selective channel | MMSE and the end-to-end system model | Reduced the required transmitted power across the range of locations spanning from 140 m to 800 m. |

Shtaiwi et al. [83] | 2021 | MIMO/Passive RIS | Static channel | SPD and Maximum-margin matrix factorization | Performance achieved up to 6 dB enhancement as the sub-RIS size increases |

You et al. [84] | 2020 | MIMO/Passive RIS | Time-varying channel | RIS-elements grouping and partition | Achieved close rate performance to the case with phase shifts when the number of bits was 3 |

Mao et al. [85] | 2021 | MIMO/Passive RIS | Time-varying channel | MMSE, KF, and state-space model | Exhibited a better BER performance than the MMSE estimator |

Cai et al. [86] | 2021 | MIMO/Passive RIS | Time-varying channel | KF and codebook-based low complexity design | Reduced computational complexity and improved estimation accuracy |

Xu et al. [82] | 2023 | SISO/Passive RIS | High-dimensional and high-Doppler reflected fading channels | MMSE interpolation and multiplicative concatenation of the channel coefficient | Reduced the error floor while achieving higher rates in high mobility systems |

Qian et al. [87] | 2023 | MIMO/Passive RIS | Static channel | Two-phase and anchor- aided channel estimation | Reduced polit overhead and improved estimation accuracy |

Ref. | Year | Antenna/RIS Architecture | Channel Model | Major Algorithm | Performance Analysis |
---|---|---|---|---|---|

Xu et al. [88] | 2022 | MIMO/Passive RIS | Static channel | Space-alternating GEM and ML estimation | Showed better performance with RIS designed by the ideal phase shift |

Zhang et al. [89] | 2023 | SISO/Passive RIS | Static channel | ML and CRB | Phase estimates were close to the Cramer Rao Bounds (${r}_{\mathrm{SNR}}$ = 20 dB) |

Guo et al. [60] | 2022 | MISO/Passive RIS | Static channel | Alternating optimization | Approximately 15 dB performance gain over ON/OFF method |

Lin et al. [24] | 2022 | MIMO/Passive RIS | Static channel | Alternating minimization and manifold optimization | Performance improvements achieved compared with several state-of-the-art benchmark schemes |

Ref. | Year | Antenna/RIS Architecture | Channel Model | Major Algorithm | Performance Analysis |
---|---|---|---|---|---|

He et al. [68] | 2020 | MIMO/Passive RIS | Time-varying channels | Sparse matrix factorization and completion | Improved channel estimation accuracy over the baseline methods |

Mirza et al. [93] | 2021 | MIMO/Passive RIS | Static channel | Bilinear generalized AMP | 50% reduction in transmit power compared with random algorithm when achievable rate was 3 bps/Hz |

Bayraktar et al. [94] | 2022 | MIMO/Passive RIS | Static channel | Multidimensional OMP | The error smaller than 20 cm for 80% of the user positions |

Xiong et al. [95] | 2023 | MIMO/Passive RIS | Static channel | Bilinear generalized AMP | Improve the performance with faster convergence |

Zhou et al. [96] | 2022 | MIMO/Passive RIS | Static channel | Generalized-AMP | 1/6 reduction in training pilot symbols compared with baseline scheme (${e}_{\mathrm{NMSE}}$ = ${10}^{-2}$) |

Wu et al. [97] | 2022 | MIMO/Passive RIS | Static channel | Three-step OMP | 50% reduction in pilot overhead compared with based scheme (${e}_{\mathrm{NMSE}}$ = −16 dB) |

Ref. | Year | Antenna/RIS Architecture | Channel Model | Performance Analysis of Deep Learning Model |
---|---|---|---|---|

Xu et al. [28] | 2022 | MISO/Passive RIS | Time-varying Channel | Designed a two-part network of the proposed time interpolation and space extrapolation to improve estimation accuracy and robustness |

Jin et al. [36] | 2022 | MIMO/Passive RIS | Static channel | Designed the GAN-CBD, CBDNet, and MRDNet to get better generalization and fitting ability |

Kundu et al. [57] | 2021 | MISO/Passive RIS | Static channel | Designed a denoising CNN to reduced computational complexity and improved estimation accuracy |

Gao et al. [63] | 2021 | MIMO/Semi-passive RIS | Static channel | Designed a three-stage training strategy RNN to reduced pilot overhead and improved estimation accuracy |

Ahmetm et al. [104] | 2020 | MIMO/Passive RIS | Static channel | Designed a CNN network to improved channel estimation accuracy |

Chen et al. [105] | 2022 | MIMO/Passive RIS | Static channel | Used a learning-based CNN to reduced computational complexity and improved channel estimation accuracy (when the the number of pilots was more than 120, ${e}_{\mathrm{NMSE}}$ < 0.2) |

Tekbiyik et al. [107] | 2021 | MIMO/Passive RIS | Static channel | Used a graph attention network to enhanced system robustness and reduced pilot overhead |

Liu et al. [106] | 2022 | MIMO/Passive RIS | Static channel | Designed the deep residual network and CNN network to improved estimation accuracy and reduced reflective elements by 70% compared with LMMSE (${e}_{\mathrm{NMSE}}$ = −8 dB) |

Zhang et al. [108] | 2021 | MISO/Passive RIS | Static channel | Designed a channel extrapolation network to improved estimation accuracy and enhanced network generalization |

Xu et al. [109] | 2020 | MIMO/Passive RIS | Time-varying channels | Used a deep reinforcement learning network to increased system capacity and suppressed interference |

Li et al. [110] | 2023 | MIMO/Passive RIS | Static channel | Designed a double deep learning network to reduced computational complexity |

Xu et al. [111] | 2022 | MISO/Passive RIS | Time-varying channel | Designed a sparse-connected LSTM network to improved estimation accuracy, reduced time delay and pilot overhead |

Ref. | Year | Antenna/RIS Architecture | Major Problem | Performance Analysis of Deep Learning Model |
---|---|---|---|---|

Wang et al. [45] | 2021 | SISO/Passive RIS | High complexity of conventional algorithms | Proposed a high resolution network with low-precision by linear interpolation to achieve 92% accuracy rate (${r}_{\mathrm{SNR}}$ = 35 dB) |

Mao et al. [69] | 2022 | MIMO/Passive RIS | Insufficient estimation performance of the CS algorithm | Proposed residual network to improve the performance to outperform the OMP (${r}_{\mathrm{SNR}}$ = 35 dB) |

Tsai et al. [113] | 2022 | MIMO/Passive RIS | Insufficient performance of AMP algorithm estimation | Proposed a hypernetwork-assisted LAMP network with dynamic shrinkage parameters to reduce memory overhead by 50% and execution time by 93% |

Yin et al. [112] | 2022 | SISO/Passive RIS | Insufficient performance of conventional algorithm estimation | Designed an end to end deep learning model to reduce channel estimation overhead |

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**MDPI and ACS Style**

Yu, Y.; Wang, J.; Zhou, X.; Wang, C.; Bai, Z.; Ye, Z.
Review on Channel Estimation for Reconfigurable Intelligent Surface Assisted Wireless Communication System. *Mathematics* **2023**, *11*, 3235.
https://doi.org/10.3390/math11143235

**AMA Style**

Yu Y, Wang J, Zhou X, Wang C, Bai Z, Ye Z.
Review on Channel Estimation for Reconfigurable Intelligent Surface Assisted Wireless Communication System. *Mathematics*. 2023; 11(14):3235.
https://doi.org/10.3390/math11143235

**Chicago/Turabian Style**

Yu, Yun, Jinhao Wang, Xiao Zhou, Chengyou Wang, Zhiquan Bai, and Zhun Ye.
2023. "Review on Channel Estimation for Reconfigurable Intelligent Surface Assisted Wireless Communication System" *Mathematics* 11, no. 14: 3235.
https://doi.org/10.3390/math11143235