# A Novel Joint Channel Estimation and Symbol Detection Receiver for Orthogonal Time Frequency Space in Vehicular Networks

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## Abstract

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## 1. Introduction

- We propose an integrated OTFS-ISAC system that leverages a novel deep residual denoising network and OAMP algorithm for joint channel estimation and symbol detection. Specifically, we design a DNN-based denoising module, incorporating an element-by-element subtraction operation that concurrently exploits the spatial attributes of noise-infected channel matrices as well as the additive character of the perturbation. In addition, a subnetwork that can generate thresholds is utilized to eliminate irrelevant features, thereby enhancing the estimation accuracy.
- We employ the OAMP detector to carry out the OTFS symbol detection, as it has the potential for MMSE optimality and exhibits excellent detection performance.
- We demonstrate the effectiveness of the proposed system through simulations and compare its performance with traditional communication systems. The proposed system shows superior performance in challenging environments such as a high Doppler frequency and delay spread, making it a promising solution for future wireless communication systems.

## 2. System Model

#### 2.1. The Modulation of OTFS Signal

#### 2.2. Communication Signal

#### 2.3. Sensing Signal

#### 2.4. JCESD for OTFS-Based Vehicular Networks

## 3. The Joint Channel Estimation and Symbol Detection

#### 3.1. Pilot Placement

#### 3.2. The Architecture of the DL Network

#### 3.3. Estimation of Neural Network

#### 3.4. Communication Symbol Detection

## 4. Simulation Result

#### 4.1. Simulation Setups

#### 4.2. Sensing Channel Estimation

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 8.**NMSE comparisons with the proposed schemes and benchmarks with correlated noise (

**a**) and with t-distribution noise (

**b**).

**Figure 9.**Joint channel estimation and symbol detection (

**a**,

**b**). (

**a**) NMSE comparisons with the proposed schemes and benchmarks with Gaussian noise. (

**b**) BER comparisons with the proposed schemes and benchmarks.

Input layer: real-valued matrix with dimension $2{k}_{\mathrm{max}}\times {\mathrm{l}}_{\mathrm{max}}$ | ||

Denoising Module: D denoising blocks share the same construction | ||

Layers | Operation | Filter size |

1 | Conv + BN + ReLU | $128\times (3\times 2\times 2)$ |

2~$L-1$ | Conv + BN + ReLU | $128\times (3\times 2\times 128)$ |

3 | Conv | $2\times (3\times 2\times 128)$ |

Subnetwork: generate the threshold array | ||

Module Name | Operation | Parameters |

${f}_{1}(\xb7)$ | Conv + BN + ReLU | $32\times (3\times 2\times 2)$ |

${f}_{2}(\xb7)$ | FC + BN + ReLU | $2\times 1\times 1$ |

Output layer: recovery channel matrix of size $M\times N\times 2$ |

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## Share and Cite

**MDPI and ACS Style**

Zhang, X.; Wen, H.; Yan, Z.; Yuan, W.; Wu, J.; Li, Z.
A Novel Joint Channel Estimation and Symbol Detection Receiver for Orthogonal Time Frequency Space in Vehicular Networks. *Entropy* **2023**, *25*, 1358.
https://doi.org/10.3390/e25091358

**AMA Style**

Zhang X, Wen H, Yan Z, Yuan W, Wu J, Li Z.
A Novel Joint Channel Estimation and Symbol Detection Receiver for Orthogonal Time Frequency Space in Vehicular Networks. *Entropy*. 2023; 25(9):1358.
https://doi.org/10.3390/e25091358

**Chicago/Turabian Style**

Zhang, Xiaoqi, Haifeng Wen, Ziyu Yan, Weijie Yuan, Jun Wu, and Zhongjie Li.
2023. "A Novel Joint Channel Estimation and Symbol Detection Receiver for Orthogonal Time Frequency Space in Vehicular Networks" *Entropy* 25, no. 9: 1358.
https://doi.org/10.3390/e25091358