# Efficient Channel Estimation in OFDM Systems Using a Fast Super-Resolution CNN Model

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## Abstract

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## 1. Introduction

## 2. Related Work

**Development of a Novel Deep Learning-Based Channel Estimation Framework:**We propose a FSRCNN tailored for channel estimation in 5G and beyond networks. This framework effectively addresses the challenges posed by high-mobility and high-frequency environments, offering a robust solution for modern wireless communication systems.**Enhanced Accuracy and Robustness in High-Mobility Scenarios:**Our FSRCNN-based method significantly improves the accuracy of channel estimation, particularly in scenarios with high Doppler shifts and frequency selectivity, where traditional methods such as LS and MMSE estimation often struggle.**Comprehensive Comparative Analysis:**We conduct extensive simulations comparing the performance of our proposed method against conventional channel estimation techniques. The results demonstrate superior performance in terms of MSE, highlighting the practical benefits of our approach.**Scalability to Future Wireless Networks:**The proposed FSRCNN framework is designed with scalability in mind, making it adaptable to future wireless communication systems, including beyond 5G (B5G) and 6G networks. This adaptability ensures that the framework remains relevant as wireless technologies continue to evolve.

## 3. Conventional Methods

## 4. Motivation for Using CNNs in Applications for Channel Estimation

**Feature Extraction Capabilities:**CNN are highly effective at automatically extracting features from data, particularly images. In the context of channel estimation, the channel state information can be treated as an image where spatial correlations and patterns are present. CNNs can effectively capture these patterns.**Spatial Invariance:**CNNs are designed to recognize patterns regardless of their position in the input image. This property is known as spatial invariance. For channel estimation, this means that CNNs can detect important features such as signal strength variations and interference patterns consistently across different regions of the input data.**Robustness to Noise by Learning Local Patterns:**The use of convolutional layers enables CNNs to learn local patterns efficiently. In wireless communications, local variations in the channel characteristics can significantly affect performance. CNNs can learn these local variations through filters that capture local dependencies, leading to more accurate channel estimation. The ability of CNNs to filter out noise while preserving important features improves the reliability of channel estimation.

## 5. Proposed Fast Super-Resolution Convolutional Neural Network (FSRCNN)

#### Architecture of FSRCNN

**Input Layer:**A low-resolution image fed directly into the network without any pre-processing upscaling step. This input is represented by a tensor of shape (H, W, C), where H and W are the height and width of the image and C is the number of color channels.**Feature Extraction Layer:**The first layer of FSRCNN performs convolution to extract initial features from the input image. A Parametric Rectified Linear Unit (PReLU) activation function is applied to introduce non-linearity and help the network learn more complex features.

- III.
**Shrinking Layer:**A second convolution layer reduces the dimensionality of the feature maps to decrease computational complexity while retaining essential information.

- IV.
**Mapping Layers:**These layers perform the mapping from low-resolution to high-resolution feature space. Multiple convolution layers are used here to transform the shrunken feature maps. Each layer is followed by a PReLU activation.

- V.
**Expanding Layer:**A convolution layer increases the dimensionality of the feature maps back to a higher resolution, preparing the data for the final deconvolution step.

- VI.
**Deconvolution Layer:**This final layer performs the upscaling to convert the low-resolution feature maps into high-resolution images.

## 6. System Model

#### Complexity Discussion

## 7. Results and Discussions

## 8. Conclusions

## 9. Future Scope

## 10. Contribution to Sensor and Actuator Networks

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Our proposed channel estimation (

**a**) Detailed process of channel estimation (

**b**) A simplified example for channel estimation.

**Figure 4.**MSE of various channel estimation methods for VehA channel model (

**a**) MSE comparison of FSRCNN (zero padding) and SRCNN (zero padding) only (

**b**) MSE comparison of Proposed model with state of the art and other tradition techniques.

**Figure 5.**The real parts of the estimates of the channel response from various estimation methods are compared with the actual response shown in solid blue lines. The channel response and the estimates are plotted for all subcarriers and 4 time slots as indicated.

Year | Method/Technique | Key Features | Performance Metrics | Results/Outcomes | Novel Contributions |
---|---|---|---|---|---|

2019 [21] | Combines Image Super-Resolution and Image Restoration Techniques | Enhanced channel estimation by leveraging image processing techniques | MSE, Computational Complexity | Achieves comparable performance to MMSE, efficient in low-SNR scenarios | Integrates deep learning with traditional image processing techniques for better channel estimation |

2023 [17] | Learned Approximate Message Passing Network | Near-field channel estimation for XL-MIMO systems | Normalized MSE (NMSE), Computational Complexity | Efficient estimation with lower complexity | Uses AMP-based learning for near-field channels |

2024 [25] | ADMM-Based Channel Estimation for XL-MIMO | Alternating Direction Method of Multipliers (ADMM) | NMSE, Computational Time | Effective estimation with reduced pilot overhead | ADMM approach for reducing pilot overhead in XL-MIMO systems |

2024 [16] | SWOMP Algorithm for Hybrid-Field Channel Estimation | Joint near-field and far-field estimation; Low complexity | NMSE, SNR | High accuracy in hybrid-field channels; Reduced complexity | Introduces a joint hybrid-field channel estimation using SWOMP |

Our Work | FSRCNN-Based Channel Estimation | Fast super-resolution CNN; High mobility and SNR scenarios | MSE, SNR, BER | Superior performance in high-mobility scenarios; Real-time applicability | Novel application of FSRCNN for channel estimation in 5G/B5G |

Acronyms | Definitions |
---|---|

MMSE | Minimum Mean Square Error |

LS | Least Square |

CNN | Convolutional Neural Network |

SISO | Single-Input Single-Output |

OFDM | Orthogonal Frequency Division Multiplexing |

CSI | Channel State Information |

SNR | Signal-to-Noise Ratio |

SRCNN | Super-Resolution Convolution Neural Network |

FSRCNN | Fast Super-Resolution Neural Network |

List of Parameters | Their Descriptions |
---|---|

${N}_{c}$ | Number of Subcarriers |

${N}_{t}$ | Number of time slots |

$j$ | $j$th time slot |

$i$ | $i$th subcarrier |

${S}_{ij}$ | Transmitted Symbols |

${H}_{ij}$ | Channel Coefficient at $i$th and $j$th locations |

$H$ | Channel matrix |

$h$ | Vectorized $H$ |

${h}_{p}$ | Vectorized $H$ at pilot location |

${N}_{ij}$ | White Gaussian Noise |

${\sigma}^{2}$ | Noise Variance |

${Y}_{ij}$ | Received Signal |

${N}_{p}$ | Number of Pilots |

${\widehat{h}}_{p}^{LS}$ | Estimated Channel Coefficient at pilot location using Least Squares estimator in vector form |

${y}_{p}$ | Vectorized Received Symbol at pilot locations |

${C}^{MMSE}$ | MMSE Estimator |

${\widehat{h}}^{MMSE}$ | Estimated Channel using MMSE |

$\epsilon $ | Mean Square Error |

${R}_{{h}_{p}}$ | $\mathrm{Autocorrelation}\mathrm{matrix}\mathrm{of}{h}_{p}$ |

${R}_{h,{h}_{p}}$ | $\mathrm{Cross}\text{-}\mathrm{Correlation}\mathrm{of}\mathrm{all}\mathrm{channel}\mathrm{coefficients}\mathrm{in}\mathrm{the}\mathrm{subframe}h\triangleq vectorize\left\{H\right\}$$\mathrm{and}\mathrm{the}\mathrm{channel}\mathrm{coefficients}\mathrm{at}\mathrm{only}\mathrm{pilot}\mathrm{positions}\mathrm{in}\mathrm{the}\mathrm{subframe}{h}_{p}$ |

$\epsilon $ | Mean Squared Error |

SRCNN: | Filter Size |

Layers | |

1 | $64\times \left(9\times 9\times 2\right)$ |

2 | $32\times \left(1\times 1\times 64\right)$ |

3 | $2\times \left(5\times 5\times 32\right)$ |

DnCNN: | Filter Size |

Layers | |

1 | $64\times \left(3\times 3\times 2\right)$ |

2~19 | $64\times \left(3\times 3\times 64\right)$ |

20 | $2\times \left(3\times 3\times 64\right)$ |

FSRCNN: | Filter Size |

Layers | |

1 | $56\times \left(5\times 5\times 2\right)$ |

2 | $12\times \left(1\times 1\times 56\right)$ |

3~6 | $12\times \left(3\times 3\times 12\right)$ |

7 | $56\times \left(1\times 1\times 12\right)$ |

8 | $2\times \left(9\times 9\times 56\right)$ |

Simulation Parameters | Values |
---|---|

Subcarriers | 72 |

Time slots | 14 |

Carrier frequency | 2.1 GHz |

UE speed | 50 km/h |

Learning rate | 0.001 |

Training SNR | 12 dB and 22 dB |

Testing SNR | 0 dB to 30 dB |

Pilot length | 48 |

Optimizer | Adam |

Optimizer parameter beta 1 | 0.99 |

Optimizer parameter beta 2 | 0.999 |

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## Share and Cite

**MDPI and ACS Style**

Khichar, S.; Santipach, W.; Wuttisittikulkij, L.; Parnianifard, A.; Chaudhary, S.
Efficient Channel Estimation in OFDM Systems Using a Fast Super-Resolution CNN Model. *J. Sens. Actuator Netw.* **2024**, *13*, 55.
https://doi.org/10.3390/jsan13050055

**AMA Style**

Khichar S, Santipach W, Wuttisittikulkij L, Parnianifard A, Chaudhary S.
Efficient Channel Estimation in OFDM Systems Using a Fast Super-Resolution CNN Model. *Journal of Sensor and Actuator Networks*. 2024; 13(5):55.
https://doi.org/10.3390/jsan13050055

**Chicago/Turabian Style**

Khichar, Sunita, Wiroonsak Santipach, Lunchakorn Wuttisittikulkij, Amir Parnianifard, and Sushank Chaudhary.
2024. "Efficient Channel Estimation in OFDM Systems Using a Fast Super-Resolution CNN Model" *Journal of Sensor and Actuator Networks* 13, no. 5: 55.
https://doi.org/10.3390/jsan13050055