# Deep Learning-Aided Modulation Recognition for Non-Orthogonal Signals

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## Abstract

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## 1. Introduction

- For the downlink non-orthogonal scenario, the superposition of signals can cause irregular signal shapes. The conventional hand-crafted features become inefficient. This poses a challenge to both the feature design and signal classification stages since the learning ability of the conventional classifier is limited.
- For uplink non-orthogonal scenarios, the challenge is more significant. With the increase in the transmit signal layers, the combinatorial number of classification types explodes exponentially. Traditional classification methods thus suffer from high computational complexity and low recognition rate.

- In the downlink scenario, we propose a modulation recognition method based on BiLSTM to extract the sequential information of the superimposed signals. For the scenario where the number of training samples is insufficient, transfer learning is used to improve the network modulation recognition ability in small sample scenarios.
- In the uplink scenario, we consider Spatio-Temporal Fusion Network based on Attention Mechanism (STFAN), which can deal with the explosive increase of the combinatorial number of classification types. The spatial feature extraction module uses an Inception block to efficiently reduce the computational complexity, and the temporal feature extraction module uses BiLSTM to mine the effective signal features in the time domain.
- Experiments show that the proposed AMR methods for non-orthogonal signals outperform the conventional methods as well as vanilla DL methods, such as CNN and LSTM, under various channel conditions. Significant advantages of the proposed methods with respect to both recognition accuracy and wireless channel robustness are observed, especially in a high SNR region.

## 2. Signals Model for Non-Orthogonal Transmission Systems

#### 2.1. Downlink Non-Orthogonal System Model

#### 2.2. Uplink Non-Orthogonal System Model

## 3. Proposed Deep Transfer Learning Incorporated BiLSTM for Downlink AMR

#### 3.1. Neural Network Architecture with BiLSTM

- Forget Gate$${f}_{t}=\sigma ({W}_{F}{x}_{t}+{W}_{f}{h}_{t-1}+{b}_{f})$$
- Input Gate$$\left\{\begin{array}{c}{i}_{t}=\sigma ({W}_{i}{x}_{t}+{W}_{i}{h}_{t-1}+{b}_{i}),\hfill \\ {a}_{t}=tanh({W}_{a}{x}_{t}+{W}_{a}{h}_{t-1}+{b}_{a})\hfill \end{array}\right.$$
- Output Gate$$\left\{\begin{array}{c}{o}_{t}=\sigma ({W}_{o}{x}_{t}+{W}_{o}{h}_{t-1}+{b}_{o}),\hfill \\ {h}_{t}={o}_{t}\xb7tanh\left({S}_{t}\right)\hfill \end{array}\right.$$
- Cell status update$${S}_{t}={f}_{t}{S}_{t-1}+{i}_{t}{a}_{t}$$

#### 3.2. Deep Transfer Learning Enhanced BiLSTM

## 4. Proposed Attention-Based Spatio-Temporal Fusion Network for Uplink AMR

#### 4.1. Proposed Neural Network Architecture

#### 4.1.1. Spatial Feature Extraction

#### 4.1.2. Temporal Feature Extraction

#### 4.1.3. Feature Fusion

#### 4.2. DNN Parameter Optimization

## 5. Simulation Results and Analysis

#### 5.1. Downlink Non-Orthogonal System

#### 5.1.1. Dataset and Parameters

^{−3}. The subsequent training set and test set settings are consistent with the Gaussian channel case. Additionally, the remaining parameters of the downlink non-orthogonal signal system are listed in Table 2.

#### 5.1.2. Gaussian Channel

#### 5.1.3. Channel with Random Phase Bias

#### 5.2. Uplink Non-Orthogonal System

#### 5.2.1. Dataset and Parameters

#### 5.2.2. Gaussian Channel

#### 5.2.3. Channel with Random Phase Bias

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Spatio-temporal fusion network architecture based on attention mechanism. (

**a**) Structure of Inception. (

**b**) Structure of SENet. (

**c**) Self-attention feature implementation of BiLSTM. (

**d**) Structure of STFAN.

Name | Parameters | Activation Function | Output Data Stream | ${\mathit{N}}_{\mathit{p}}$ ^{1} |
---|---|---|---|---|

Input Layer | / | / | (128,2) | / |

BiLSTM_1 | ${N}_{FL}=128,{N}_{BL}=128$ ^{2} | Tanh/Sigmoid | (12,256) | 140,288 |

BiLSTM_2 | ${N}_{FL}=64,{N}_{BL}=64$ | Tanh/Sigmoid | (1,128) | 164,352 |

FC layer | 64 | ReLU | (1,64) | 8256 |

Output Layer | 5 | Softmax | 5 | 325 |

^{2}${N}_{FL}$ is the number of forward LSTM neurons, and ${N}_{BL}$ is the number of backward LSTM neurons.

Parameters Name | Parameters Value |
---|---|

Multiplexing Type | SCMA, MUSA, PDMA, PD-NOMA, WSMA |

Carrier Frequency | $1.2$ GHz |

Symbol Rate | $15.36$ MHz |

Sampling Rate | $122.88$ MHz |

${N}_{I/Q}$ ${}^{1}$ | 128 |

${N}_{U}$ ${}^{2}$ | 6 |

${N}_{R}$ ${}^{2}$ | 4 |

Oversampling Rate | $1.5$ |

SNR Range | $-10$ dB∼20 dB |

^{1}${N}_{I/Q}$ denotes the complex baseband $I/Q$ data points per path.

^{2}${N}_{U}$ is number of users, and ${N}_{R}$ is number of resources.

Models | FC-DNN | LSTM | BiLSTM |
---|---|---|---|

Total parameters | 822,533 | 797,957 | 313,221 |

Epochs | 50 | 30 | 30 |

Training time (s)/epoch | 602 | 524 | 489 |

Prediction time ($\mathsf{\mu}$s)/sample | 192 | 175 | 173 |

FLOPS | 19,784,965 | 191,868,832 | 59,445,664 |

Parameters Name | Parameters Value |
---|---|

Modulation Type | 2ASK, QPSK, 16QAM |

Carrier Frequency | $1.2$ GHz |

Symbol Rate | $15.36$ MHz |

Sampling Rate | $122.88$ MHz |

${N}_{I/Q}$ | 128 |

${P}_{A}/{P}_{B}/{P}_{C}$ | $0.2/0.3/0.5$ |

${N}_{U}$ | 3 |

${N}_{R}$ | 1 |

Oversampling Rate | 3 |

SNR Range | $-10$ dB∼20 dB |

Models | CNN | ResNet | STFAN |
---|---|---|---|

Total parameters | 8,593,563 | 4,214,922 | 23,370,448 |

Epochs | 50 | 40 | 40 |

Training time (s)/epoch | 631 | 598 | 721 |

Prediction time ($\mathsf{\mu}$s)/sample | 193 | 188 | 189 |

FLOPS | 81,259,328 | 158,353,019 | 273,799,168 |

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**MDPI and ACS Style**

Fan, J.; Wu, L.; Zhang, J.; Dong, J.; Wen, Z.; Zhang, Z.
Deep Learning-Aided Modulation Recognition for Non-Orthogonal Signals. *Sensors* **2023**, *23*, 5234.
https://doi.org/10.3390/s23115234

**AMA Style**

Fan J, Wu L, Zhang J, Dong J, Wen Z, Zhang Z.
Deep Learning-Aided Modulation Recognition for Non-Orthogonal Signals. *Sensors*. 2023; 23(11):5234.
https://doi.org/10.3390/s23115234

**Chicago/Turabian Style**

Fan, Jiaqi, Linna Wu, Jinbo Zhang, Junwei Dong, Zhong Wen, and Zehui Zhang.
2023. "Deep Learning-Aided Modulation Recognition for Non-Orthogonal Signals" *Sensors* 23, no. 11: 5234.
https://doi.org/10.3390/s23115234