# A Comprehensive Experimental Emulation for OTFS Waveform RF-Impairments

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## Abstract

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## 1. Introduction

#### 1.1. Related Work

#### 1.2. Motivation and Contribution

- Experimental research of the nonlinearity effect on the performance of the OTFS system has been investigated, taking into account a variety of delay bins N and Doppler bins M and comparing it with an OFDM waveform.
- The CFO influence was studied and emulated using a reverberation chamber and stirrer. The impact of CFO from LO mismatching and CFO from Doppler shift on the OTFS waveform’s performance is shown experimentally over a variety of normalized frequency offset values.
- We visualize and present the effect of the DC-offset on both the in-phase(${\gamma}_{I}$) and quadrature (${\gamma}_{Q}$) components, and then we show the effect of the DC-offset on the OTFS system performance and compare it with OFDM.
- Furthermore, the phase noise of a practical 2.4 GHz CMOS voltage control oscillator (VCO) is modeled to examine its impact on the OTFS performance.
- Finally, we study the influence of the I/Q-imbalance on the performance of the OTFS while taking into account imperfections in the local oscillator. We did this by comparing the OTFS and OFDM waveforms with different values of gain imbalance ($\u03f5$) and phase offset ($\mathsf{\Delta}\varphi $).

#### 1.3. Organization

## 2. Waveform Modulation and Demodulation

#### 2.1. OFDM Waveform

#### 2.2. OTFS Waveform

#### 2.3. Channel Estimation and MP Detection

## 3. Channel Effects Furthermore, RF-Impairments

#### 3.1. Carrier Frequency Offset

#### 3.1.1. CFO Due to Doppler Shift

#### 3.1.2. CFO Due to Frequency Mismatching between the TX and RX Oscillators

#### 3.2. Non-Linearity Impairments

#### 3.3. I/Q Imbalance

#### 3.4. DC Offset

#### 3.5. Phase Noise

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

5G | Fifth Generation |

6G | Sixth Generation |

A/D | Analog-to-Digital |

BER | Bit Error Rate |

CCDF | Cumulative Distribution Function |

CFO | Carrier Frequency Offset |

CP | Cyclic Prefix |

D/A | Digital-To-Analog() |

DC | Direct Current |

eMBB | Enhanced-Mobile Broadband |

I/Q imbalance | In-Phase And Quadrature Imbalance |

ICF | Iterative Clipping And Filtering |

ICI | Inter-Carrier Interference |

ISFFT | inverse symplectic finite Fourier transform |

ISI | Inter-Symbol Interference |

JRC | Joint Radar Communication |

LNA | Low-Noise Amplifier |

LS | Least Squares |

MIMO | Multi-Input Multi Output |

mMTC | Massive Machine Type Communications |

mm-Wave | millimeter wave |

MP | Message Passing |

NOMA | Non-Orthogonal Multiple Access |

OFDM | Orthogonal Frequency Division Multiplexing |

OTFS | Orthogonal Time-Frequency Space |

PA | Power Amplifier |

PAPR | Peak-To-Average Power Ratio |

PSW | Prolate Spheroida Waveform |

QAM | Quadrature Amplitude Modulation |

RF | Radio-Frequency |

SDR | Software-Defined Radio |

SFFT | Symplectic Finite Fourier Transform |

SLM | improved SeLective Mapping |

URLLC | Ultra-Reliable And Low Latency Communications |

VSA | Vector Signal Analyzer |

VSG | Vector Signal Generator |

RCF | Raised-cosine filter |

LO | Local oscillator |

HPA | high power amplifier |

OOB | out-of-band |

AWGN | additive white Gaussian noise |

CMOS | complementary metal-oxide-semiconductor |

VCO | voltage control oscillator |

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**Figure 2.**The transmitted and received signal structure in the delay-Doppler plane. (

**a**) Transmitted symbols; (

**b**) received signal; (

**c**) received embedded pilot.

**Figure 3.**Laboratory equipment setup connection for multi-path emulation using reverberation chamber.

**Figure 5.**Emulation of the Doppler shift (${f}_{D}\approx 370$ Hz) effect on the 5 GHz tone using reverberation chamber. (

**a**) Instantaneous spectrum stirrer-off; (

**b**) instantaneous spectrum stirrer-on; (

**c**) cumulative PSD when the stirrer-off; (

**d**) cumulative PSD when the stirrer-on; (

**e**) spectrogram when stirrer-off; (

**f**) spectrogram when stirrer-on.

**Figure 6.**BER performance comparison between OTFS waveform with $M=32,N=32$ and OFDM waveform with $N=1024$ affected by the Doppler shift using on the central frequency is 5 GHz reverberation chamber.

**Figure 7.**BER performance comparison between OTFS waveform with $M=32,N=32$ and OFDM waveform with $N=1024$ considering different normalized frequency offsets values in 2.4 GHz carrier without using reverberation chamber.

**Figure 9.**BER performance comparison between OTFS waveform with $M=32,N=32$ and OFDM waveform with $N=1024$ considering different gains imbalance ($\u03f5$) and phase mismatch ($\mathsf{\Delta}\varphi $) I/Q imbalances at 2.4 GHz carrier frequency.

**Figure 10.**Constellation diagram shows the effect of the different I/Q and DC offset on the $M=32,N=32$ OTFS received information symbols of $\widehat{y}[k,l]$ for 4-QAM at $2.4$ GHz carrier frequency. (

**a**) $\u03f5=0,\mathsf{\Delta}\varphi =0$; (

**b**) $\u03f5=0,\mathsf{\Delta}\varphi =10$; (

**c**) $\u03f5=0.5,\mathsf{\Delta}\varphi =0$; (

**d**) $\u03f5=0.5,\mathsf{\Delta}\varphi =10$; (

**e**) ${\gamma}_{I}=0.75,{\gamma}_{Q}=0$; (

**f**) ${\gamma}_{I}=0,{\gamma}_{Q}=0.75$.

**Figure 11.**Comparison of the BER performance between OTFS waveform with $M=32,N=32$ and OFDM waveform with $N=1024$ considering different DC-offest in both I-component (${\gamma}_{I}$) and Q-component (${\gamma}_{Q}$) at 2.4 GHz carrier frequency.

**Figure 12.**BER performance for OTFS waveform with $M=32,N=32$ under different values of DC-offset in both I-component (${\gamma}_{I}$) and Q-component (${\gamma}_{Q}$) at 2.4 GHz carrier frequency.

**Figure 13.**Phase noise of the local oscillator. (

**a**) Ideal oscillator, (

**b**) practical oscillator, and (

**c**) phase noise power level in dBc/Hz with $\mathsf{\Delta}f$ offset.

**Figure 16.**Comparison of the effect of the phase noise on the BER performance for both OTFS waveform with $M=32,N=32$ and OFDM waveform with $N=1024$ at 2.4 GHz carrier frequency.

Symbol | Parameters | Value (OTFS) | Value (OFDM) |
---|---|---|---|

${f}_{c}$ | Carrier frequency | $2.4$ GHz, 5 GHz | $2.4$ GHz, 5 GHz |

M | Number of subcarriers | 432, 256 | 256, 1024 |

N | Number of symbols | 432, 256 | 1 |

${T}_{s}$ | Symbol duration | $10\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$s | |

${M}_{mod}$ | Modulation order | 4-QAM | |

$\mathsf{\Delta}{f}_{s}$ | Sub-carrier spacing | 100 KHz | |

${f}_{o}$ | Normalized frequency offset | $0,\phantom{\rule{3.33333pt}{0ex}}0.05,\phantom{\rule{3.33333pt}{0ex}}0.1,\phantom{\rule{3.33333pt}{0ex}}0.3$ | |

$\u03f5$ | I/Q gain imbalance | $0\%,\phantom{\rule{3.33333pt}{0ex}}50\%$ | |

$\mathsf{\Delta}\varphi $ | I/Q phase imbalance | ${0}^{\circ},\phantom{\rule{3.33333pt}{0ex}}{10}^{\circ}$ degree | |

${\gamma}_{I},{\gamma}_{Q}$ | DC-offset | ($0\%,\phantom{\rule{3.33333pt}{0ex}}20\%,\phantom{\rule{3.33333pt}{0ex}}50\%,\phantom{\rule{3.33333pt}{0ex}}75\%)\sqrt{{E}_{s}}$ |

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## Share and Cite

**MDPI and ACS Style**

Abushattal, A.; Zegrar, S.E.; Yazgan, A.; Arslan, H.
A Comprehensive Experimental Emulation for OTFS Waveform RF-Impairments. *Sensors* **2023**, *23*, 38.
https://doi.org/10.3390/s23010038

**AMA Style**

Abushattal A, Zegrar SE, Yazgan A, Arslan H.
A Comprehensive Experimental Emulation for OTFS Waveform RF-Impairments. *Sensors*. 2023; 23(1):38.
https://doi.org/10.3390/s23010038

**Chicago/Turabian Style**

Abushattal, Abdelrahman, Salah Eddine Zegrar, Ayhan Yazgan, and Hüseyin Arslan.
2023. "A Comprehensive Experimental Emulation for OTFS Waveform RF-Impairments" *Sensors* 23, no. 1: 38.
https://doi.org/10.3390/s23010038