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Efficient Spectrum Occupancy Prediction Exploiting Multidimensional Correlations through Composite 2D-LSTM Models^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. System Model and Preliminaries

#### 2.1. Prediction with Autoregressive Model

#### 2.2. Prediction with Bayesian-Inference

#### 2.3. Prediction with Long Short-Term Memory

#### 2.4. Prediction with Convolutional Long Short-Term Memory

## 3. The Proposed Method for Spectrum Occupancy Prediction Exploiting Time, Frequency, and Space Correlations

#### 3.1. Motivations for Time, Frequency, and Space Correlation Exploitation and Problem Sub-Division

#### 3.2. The Proposed Method

#### 3.3. A Note on Computational Complexity

## 4. Dataset Generation

#### 4.1. Measurement Setup

#### 4.2. Measurement Procedure and Geographical Locations

#### 4.2.1. City Center (Taksim)

#### 4.2.2. Rural Area (Silivri)

## 5. Parameter Settings and Experimental Results

#### 5.1. Hyperparameters of Deep Learning Models

- 1D-LSTM: This model uses two LSTM hidden layers and an output layer. Particularly, 256 and 128 hidden units were used in the first and second hidden layers, respectively. The rectified linear unit (ReLU) was used as activation functions. Afterward, the probability of the occupancies was calculated in the output layer, which uses a sigmoid activation function with 1 unit. We note that one unit is enough to represent the occupancies since there are only two classes (spectrum is occupied “1” or not “0”). In total, 461,441 parameters were used. Finally, the model was trained with a batch size of 256 and 18 epochs. Efficient adaptive moment estimation (ADAM) was used with an optimum learning rate of 0.0001 during the training. Also, the logarithmic loss function was used for binary classification.
- ConvLSTM: The ConvLSTM model was used with 3D data as the state-of-the-art method. The model includes two ConvLSTM layers, a flatten layer, and an output layer. In the first and second ConvLSTM layers, 256 and 128 units were used, respectively. Afterward, a flatten layer was used to prepare a vector for the output layer. Finally, an output layer WAS used with one unit. In the output layer, the sigmoid function was used. In total, 4,142,721 parameters were used. A batch size of 256 and 15 epochs were used to train the model. ADAM was used for the adaptive learning rate optimization with an optimum learning rate of 0.00005. Furthermore, the logarithmic loss function was used for binary classification.
- 2D-LSTM: This model uses two LSTM hidden layers and an output layer. More specifically, with ReLU activation functions 256 and 128 hidden units were used in the first and second LSTM hidden layers, respectively. Afterward, an output layer was used to calculate the probability of the occupancy. The sigmoid function was used in the output layer. In total, 467,585 parameters were used. Finally, the DL model was trained with a batch size of 256 and 15 epochs. ADAM was used for adaptive learning rate optimization and the optimum learning rate in this model was found at 0.00005. Again, for binary classification, the logarithmic loss function was employed.
- An end-classifier: A standard two-layer feed-forward network [47] was used as an end-classifier. This classifier consists of a hidden layer and an output layer. The sigmoid functions were used as activation functions. The MATLAB Neural-Network-Toolbox “nprtool” [47] was used for implementation. Scaled conjugate gradient (trainsscg), and cross-entropy (crossentropy) were used for training and performance metrics, respectively. The number of hidden neurons was set to 512 while the number of output neurons was set to one. Therefore, 25,600 parameters were used in total.

#### 5.2. Performance Evaluation and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

1D | one-dimensional |

2D | two-dimensional |

3D | three-dimensional |

5G | fifth-generation |

ADAM | adaptive moment estimation |

ARM | autoregressive model |

BIF | Bayesian inference |

BS | base station |

CNN | convolutional neural networks |

ConvLSTM | convolutional long short-term memory |

CPU | central processing unit |

CR | cognitive radio |

DL | deep learning |

LSTM | long-short term memory |

ML | machine learning |

PRB | physical resource block basis |

PUs | primary users |

ReLU | rectified linear unit |

RSSI | received signal strength indicator |

SB | subband |

SUs | secondary users |

UL | uplink |

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**Figure 11.**Composite two-dimensional (2D)-long short-term memory (2D-LSTMs) in spectrum occupancy prediction.

**Table 1.**Training and testing execution time (seconds) comparison of the tensor and 2D-based method.

Method | Execution Time (s) | |
---|---|---|

Training | Testing | |

The tensor-based method | 608 | 2.8 |

2D-LSTM-based method | 57.8 | 0.7 |

**Table 2.**The number of handover attempts between the main base station (BS) and neighboring BSs in one week.

BS | Area | |
---|---|---|

Taksim | Silivri | |

$B{S}_{2}$ | 6429 | 3178 |

$B{S}_{3}$ | 4442 | 3138 |

3GPP Band | Bandwidth | Frequency | Duplex | Technology |
---|---|---|---|---|

B20 | 10 MHz | 852–862 Mhz (UL) | Frequency division duplexing | Long term evolution-Advanced Pro (4.5 G) |

**Table 4.**The precision ($\pi $), recall ($\psi $), and ${F}_{1}$-score spectrum occupancy performances of the autoregressive model (ARM), Bayesian inference (BIF), 1D-LSTM, 2D-LSTM, ConvLSTM, and composite 2D-LSTMs (the proposed method) for the Taksim scenario.

Method | Measure | ||
---|---|---|---|

$\mathit{\pi}$ | $\mathit{\psi}$ | ${\mathit{F}}_{1}$-Score | |

ARM | 0.9210 | 0.9681 | 0.9440 |

BIF | 0.9264 | 0.9738 | 0.9495 |

1D-LSTM | 0.9602 | 0.9780 | 0.9690 |

2D-LSTM | 0.9720 | 0.9732 | 0.9726 |

ConvLSTM | 0.9760 | 0.9763 | 0.9762 |

Composite 2D-LSTMs | 0.9727 | 0.9742 | 0.9735 |

**Table 5.**The precision ($\pi $), recall ($\psi $), and ${F}_{1}$-score spectrum occupancy performances of ARM, BIF, 1D-LSTM, 2D-LSTM, ConvLSTM, and composite 2D-LSTMs (the proposed method) for the Silivri scenario.

Method | Measure | ||
---|---|---|---|

$\mathit{\pi}$ | $\mathit{\psi}$ | ${\mathit{F}}_{1}$-Score | |

ARM | 0.8863 | 0.8704 | 0.8783 |

BIF | 0.9336 | 0.9130 | 0.9232 |

1D-LSTM | 0.9465 | 0.9165 | 0.9312 |

2D-LSTM | 0.9462 | 0.9216 | 0.9338 |

ConvLSTM | 0.9479 | 0.9298 | 0.9388 |

Composite 2D-LSTMs | 0.9476 | 0.9233 | 0.9353 |

Method | Execution Time (s) | |
---|---|---|

Training | Testing | |

ConvLSTM | 608.7 | 2.7 |

Composite 2D-LSTMs | 58.1 | 0.7 |

Method | Execution Time (s) | |
---|---|---|

Training | Testing | |

ConvLSTM | 610.3 | 2.9 |

Composite 2D-LSTMs | 58.9 | 0.8 |

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## Share and Cite

**MDPI and ACS Style**

Aygül, M.A.; Nazzal, M.; Sağlam, M.İ.; da Costa, D.B.; Ateş, H.F.; Arslan, H.
Efficient Spectrum Occupancy Prediction Exploiting Multidimensional Correlations through Composite 2D-LSTM Models. *Sensors* **2021**, *21*, 135.
https://doi.org/10.3390/s21010135

**AMA Style**

Aygül MA, Nazzal M, Sağlam Mİ, da Costa DB, Ateş HF, Arslan H.
Efficient Spectrum Occupancy Prediction Exploiting Multidimensional Correlations through Composite 2D-LSTM Models. *Sensors*. 2021; 21(1):135.
https://doi.org/10.3390/s21010135

**Chicago/Turabian Style**

Aygül, Mehmet Ali, Mahmoud Nazzal, Mehmet İzzet Sağlam, Daniel Benevides da Costa, Hasan Fehmi Ateş, and Hüseyin Arslan.
2021. "Efficient Spectrum Occupancy Prediction Exploiting Multidimensional Correlations through Composite 2D-LSTM Models" *Sensors* 21, no. 1: 135.
https://doi.org/10.3390/s21010135