# Semi-Supervised Extreme Learning Machine Channel Estimator and Equalizer for Vehicle to Vehicle Communications

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## Abstract

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## 1. Introduction

- We propose a regularized ELM subject to SS learning as channel estimator and equalizer to enhance the performance of a representative IEEE 802.11p OFDM-based system in terms of Bit Error Rate (BER). To this end, we add a novel parameter denoted by $\delta $ in the Semi-supervised Extreme Learning Machine (SS-ELM) to address the time-domain fluctuations of the channel. Furthermore, a frequency-domain localized mapping is used to properly recover the OFDM signal, namely to address the frequency-selective channel;
- Taking the simulation framework of the evaluated system into account, we compute the sub-optimal SS-ELM hyper-parameters to diminish BER via extensive simulations. We also show that a supervised ELM does not improve the BER performance of a vehicular IEEE 802.11p system;
- We compare the proposed technique with current state-of-the-art machine-learning-based channel estimation schemes as well as traditional techniques in an urban environment for several values of Energy per Bit to Noise Power Spectral Density Ratios (${E}_{b}/{N}_{0}$). The addressed techniques are also contrasted in terms of the required processing time.

## 2. Background

#### 2.1. The IEEE 802.11p Standard

#### 2.2. Single Ring Geometrical Scattering Channel Model

#### 2.3. Extreme Learning Machine

Algorithm 1: ELM algorithm. |

#### 2.4. Semi-Supervised Extreme Learning Machine

Algorithm 2: SS-ELM algorithm. |

## 3. Proposed SS-ELM Equalizer

Algorithm 3: SS-ELM training and equalization. |

## 4. Simulation Results and Discussions

#### 4.1. Numerical Optimization of the SS-ELM Hyper-Parameters

#### 4.2. Impact of the $\delta $ Parameter on the BER Metric

#### 4.3. Performance Comparison

#### 4.4. Execution Time Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

ANN | Artificial Neural Network |

AWGN | Additive White Gaussian Noise |

BER | Bit Error Rate |

BPSK | Binary Phase Shift Keying |

CDP | Constructed Data Pilots |

CFR | Channel Frequency Response |

CP | Cyclic Prefix |

CPU | Central Process Unit |

C-ELM | Complex Extreme Learning Machine |

C-V2X | Cellular Vehicular to Anything |

DC | Direct Current |

DL | Deep Learning |

ELM | Extreme Learning Machine |

ETSI | European Telecommunication Standards Institute |

FFT | Fast Fourier Transform |

FPGA | Field-Programmable Gate Array |

GPU | Graphics Processing Unit |

IFFT | Inverse Fast Fourier Transform |

LS | Least Squares |

ML | Machine Learning |

MMSE | Minimum Mean-Square Error |

OFDM | Orthogonal Frequency Division Multiplexing |

PHY | Physical Layer |

RAM | Random Access Memory |

SS | Semi-Supervised |

SS-ELM | Semi Supervised Extreme Learning Machine |

STA | Spectral Temporal Averaging |

SNR | Signal to Noise Ratio |

VCS | Vehicular Communication Systems |

V2V | Vehicle to Vehicle |

V2I | Vehicle to Infrastructure |

WiFi | Wireless Fidelity |

WSSUS | Wide-Sense Stationary Uncorrelated Scattering |

ZF | Zero Forcing |

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**Figure 5.**Single ring geometrical channel scattering model. The vehicle on the left side is the transmitter, while the vehicle on the right side represents the receiver.

**Figure 8.**BER countour plot in terms of the regularization parameter C, number of hidden neurons, and different ${E}_{b}/{N}_{0}$ values for system configuration 1.

**Figure 9.**BER countour plot in terms of the regularization parameter C, number of hidden neurons, and different ${E}_{b}/{N}_{0}$ values for system configuration 2.

**Figure 10.**BER contour plot of $\lambda $ and $\mu $ for different ${E}_{b}/{N}_{0}$ values and system configuration 1.

**Figure 11.**BER contour plot of $\lambda $ and $\mu $ for different ${E}_{b}/{N}_{0}$ values and system configuration 2.

**Figure 12.**BER of the proposed SS-ELM scheme with $\delta $ as parameter and the LS algorithm for system configuration 1.

**Figure 13.**BER of the proposed SS-ELM scheme with $\delta $ as parameter and the LS algorithm for system configuration 2.

**Figure 14.**BER as a function of ${E}_{b}/{N}_{0}$ for different evaluated techniques and system configuration 1.

**Figure 15.**BER as a function of ${E}_{b}/{N}_{0}$ for different evaluated techniques and system configuration 2.

Parameter | Value |
---|---|

Number of data subcarriers $\left({N}_{SD}\right)$ | 48 |

Number of pilot subcarriers (${N}_{SP}$) | 4 |

Number of subcarriers total (${N}_{ST}$) | 52 |

Subcarrier frequency spacing ($\Delta f$) | 0.15625 MHz |

IFFT/FFT periods (${T}_{FFT}$) | 6.4 µs (1/$\Delta f$) |

PHY preamble duration (${T}_{PREAMBLE}$) | 32 µs |

Duration of the Signal BPSK-OFDM symbol (${T}_{SIGNAL}$) | 8 µs |

Training symbol guard interval duration (${T}_{GI}$) | 3.2 µs |

Symbol interval (${T}_{sym}$) | 8 µs |

Short training sequence duration (${T}_{SHORT}$) | 16 µs |

Long training sequence duration (${T}_{LONG}$) | 16 µs |

Parameter | Configuration 1 | Configuration 2 |
---|---|---|

Carrier Frequency (${f}_{c}$) | 5.9 GHz | 5.9 GHz |

Bandwidth (B) | 10 MHz | 10 MHz |

Modulation | BPSK | BPSK |

Number of OFDM symbols per package (L) | 128 | 128 |

Transmitter velocity (${\mathit{V}}_{\mathit{T}}$) | 40 km/h | 20 km/h |

Receiver velocity (${\mathit{V}}_{\mathit{R}}$) | 40 km/h | 20 km/h |

Transmitter movement angle (${\mathit{\gamma}}_{\mathit{T}}$) | 105° | 10° |

Receiver movement angle (${\mathit{\gamma}}_{\mathit{R}}$) | 70° | 70° |

Transmitter acceleration angle (${\mathit{\beta}}_{\mathit{T}}$) | 105° | 15° |

Receiver acceleration angle (${\mathit{\beta}}_{\mathit{R}}$) | 250° | 70° |

Initial distance (D) | 300 m | 100 m |

Radius of the ring (d) | 30 m | 30 m |

Component | Model |
---|---|

Central Processing Unit (CPU) | Intel i5 10400F 2.9 GHz–4.1 GHz |

Random Access Memory (RAM) | 16 GB 2133 MHz |

Graphics Processing Unit (GPU) | GTX1060 6 GB |

Algorithm | Time [ms] |
---|---|

LS | 0.0269 ± 0.0095 |

STA | 13.5 ± 0.344 |

CDP | 18.4 ± 0.471 |

ELM | 40.5 ± 5.1 |

C-ELM [13] | 127 ± 9.74 |

SS-ELM | 658 ± 10.4 |

Parallel SS-ELM | 167 ± 2.6 |

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**MDPI and ACS Style**

Salazar, E.; Azurdia-Meza, C.A.; Zabala-Blanco, D.; Bolufé, S.; Soto, I.
Semi-Supervised Extreme Learning Machine Channel Estimator and Equalizer for Vehicle to Vehicle Communications. *Electronics* **2021**, *10*, 968.
https://doi.org/10.3390/electronics10080968

**AMA Style**

Salazar E, Azurdia-Meza CA, Zabala-Blanco D, Bolufé S, Soto I.
Semi-Supervised Extreme Learning Machine Channel Estimator and Equalizer for Vehicle to Vehicle Communications. *Electronics*. 2021; 10(8):968.
https://doi.org/10.3390/electronics10080968

**Chicago/Turabian Style**

Salazar, Eduardo, Cesar A. Azurdia-Meza, David Zabala-Blanco, Sandy Bolufé, and Ismael Soto.
2021. "Semi-Supervised Extreme Learning Machine Channel Estimator and Equalizer for Vehicle to Vehicle Communications" *Electronics* 10, no. 8: 968.
https://doi.org/10.3390/electronics10080968