# Doppler Shift Time Expansion Resolution and Spectral Performance in Wideband Real-Time RF Channel Emulators

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Multipath System-Level Models

- ${R}_{d}\left(t\right)$ equal to the distance (instantaneous) travelled by the direct path between transmitter and receiver;
- ${c}_{o}\sim 3\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{8}$ m/s equal to the speed of light;
- $\Delta {R}_{k}\left(t\right)$ equal to the difference between the k-th path and the direct path.

#### 2.2. Required Sampling Step Size for the Emulation of the Effects of the Electromagnetic Propagation

#### 2.3. Required Sampling Step Size for the Emulation of the Time Expansion

## 3. Results

## 4. Conclusions

## Funding

## Conflicts of Interest

## Abbreviations

UAV | Unmanned Aerial Vehicle |

DEM | Digital Elevation Model |

DSP | Digital Signal Processing |

GPU | Graphical Processing Unit |

## References

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**Figure 3.**Representation of the multipath signal in the complex envelope domain with delays and time-discrete amplitudes.

**Figure 4.**Representation of the multipath signal in the complex envelope domain with delays and time-discrete amplitudes without absolute Doppler information.

**Figure 5.**Normalized amplitude transfer function for a two-ray model and different differential delays.

**Figure 10.**Sidelobe level as a function of fractional quantum q = $\frac{1}{100}$, spur @ 837 KHz, SLL∼ 32 dB.

**Figure 11.**Sidelobe level as a function of fractional quantum q = $\frac{1}{1000}$, spur @ 8.62 MHz, SLL∼ 51 dB.

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**MDPI and ACS Style**

Rossi, M. Doppler Shift Time Expansion Resolution and Spectral Performance in Wideband Real-Time RF Channel Emulators. *Appl. Syst. Innov.* **2019**, *2*, 8.
https://doi.org/10.3390/asi2010008

**AMA Style**

Rossi M. Doppler Shift Time Expansion Resolution and Spectral Performance in Wideband Real-Time RF Channel Emulators. *Applied System Innovation*. 2019; 2(1):8.
https://doi.org/10.3390/asi2010008

**Chicago/Turabian Style**

Rossi, Massimiliano. 2019. "Doppler Shift Time Expansion Resolution and Spectral Performance in Wideband Real-Time RF Channel Emulators" *Applied System Innovation* 2, no. 1: 8.
https://doi.org/10.3390/asi2010008