# I/Q Imbalance and Imperfect SIC on Two-Way Relay NOMA Systems

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## Abstract

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## 1. Introduction

^{th}Generation (5G) systems [1,2,3]. Many new technologies such as massive multiple-input multiple-output (MIMO), non-orthogonal multiple access (NOMA), millimetre wave and device-to-device communication have been proposed to meet these demands [4]. Among these techniques, NOMA can significantly improve the spectral efficiency and reduce the system latency. Different from the conventional orthogonal multiple access (OMA), NOMA provides services for multiple users on the same resource by using superposition coding at the transmitter and successive interference cancellation (SIC) at the receiver [5,6]. Take an example of downlink: signals from the base station (BS) are superimposed and sent to NOMA users. Users with stronger channel gains decode signals of other users with lower channel gains before decoding their own signals based on the SIC technique [7]. Hence, NOMA can support multiple users with limited resources and improve spectral efficiency, which has attracted considerable attention from academia and industry. For instance, in [8,9], the authors discussed power allocation under various criteria for a downlink NOMA system. In order to improve the system throughput, a network NOMA technique was proposed and analysed for the uplink coordinated multi-point transmission (CoMP) in [10].

#### 1.1. Contributions

- Based on the above works, we investigate the effects of IQI and ipSIC on the performance of a TWR C-NOMA network over the Rician fading channels. It is worth noting that this is a valuable problem for practical system design and analysis. As far as the authors know, although a system with IQI or ipSIC has been studied in some papers, the TWR C-NOMA system model with the condition of IQI and ipSIC under Rician fading channels has not been previously studied.
- We derive analytical expressions for outage probabilities of both the far and near users. The results show that IQI and ipSIC have deleterious effects on the outage performance and residual IS. In order to gain better insights into the system performance, we compare the outage performance of NOMA and OMA for both the far and near users, and the results show that the outage performance of NOMA is better than that of OMA. By comparing Rician and Rayleigh fading channel conditions, it is found that the throughput of our considered system with Rician or Rayleigh fading channels is almost the same in ideal conditions, and IQI and ipSIC have worse effects on the system throughput with Rayleigh fading channels than on Rician.
- We carry out the asymptotic analysis in the high SNR region. Furthermore, based on asymptotic outage probability, the diversity order is derived to analyse the diversity gain of the system. It is demonstrated that residual IS can result in error floors for the outage probability and zero diversity orders.

#### 1.2. Organization

#### 1.3. Notations

## 2. System Model

#### 2.1. I/Q Imbalance Signal Model

#### 2.2. Signal Model of Joint TX/RX Impaired by IQI

## 3. Performance Analysis

#### 3.1. Outage Probability Analysis

**Theorem**

**1.**

**Proof.**

**Theorem**

**2.**

**Proof.**

#### 3.2. Asymptotic Outage Probability Analysis

**Proposition**

**1.**

**Proposition**

**2.**

#### 3.3. Diversity Orders

**Remark**

**1.**

#### 3.4. System Throughput Analysis

## 4. Numerical Examples and Discussions

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Proof of Theorem 1

## Appendix B. Proof of Theorem 2

## References

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**Figure 2.**Outage probability versus the transmit SNR of the proposed TWR C-NOMA system for ${D}_{1}$ and ${D}_{2}$ with data rate thresholds ${\overline{R}}_{1}=0.2BPCU$ and ${\overline{R}}_{2}=0.3BPCU$.

**Figure 3.**Outage probability versus the parameter of ipSIC for the system with IQI and ideal conditions.

**Figure 4.**Outage probability versus the parameter of phase mismatch for the system with ipSIC and pSIC conditions.

**Figure 5.**Outage probability versus the amplitude mismatch for the system with ipSIC and pSIC conditions.

**Figure 6.**System throughput versus the transmit SNR of the proposed TWR C-NOMA system for ${D}_{1}$ and ${D}_{2}$ with data rate thresholds ${\overline{R}}_{1}=0.2BPCU$ and ${\overline{R}}_{2}=0.3BPCU$.

Acronyms | Definition |
---|---|

NOMA | Non-orthogonal multiple access |

UE | User devices |

OMA | Orthogonal multiple access |

ipSIC | Imperfect successive interference cancellation |

pSIC | Perfect successive interference cancellation |

Probability density function | |

CDF | Cumulative density function |

5G | 5th Generation |

TWR C-NOMA | Two-way relay cooperative NOMA |

DF | Decode-and-forward |

BS | Base station |

COMP | Coordinated multi-point transmission |

MRC | Maximal ratio combining |

IGS | Improper Gaussian signalling |

TX | Transmitter |

RX | Receiver |

IQI | In-phase and quadrature imbalance |

OFDM-IM | Orthogonal frequency division multiplexing with index modulation |

LoS | Line-of-sight |

AWGN | Additive white Gaussian noise |

SNR | Signal-to-noise ratio |

SINR | Signal-to-interference plus noise ratio |

IS | Interference signals |

MIMO | Multiple-input multiple-output |

Monte Carlo Simulations Repeated | ${10}^{5}$ Iterations |
---|---|

Power allocation coefficients of NOMA | ${a}_{1}=0.7$, ${a}_{2}=0.3$, ${b}_{1}=0.8$ and ${b}_{2}=0.2$ |

Targeted data rates | ${\overline{R}}_{1}=0.2BPCU$, ${\overline{R}}_{2}=0.3BPCU$ |

The distance between R and ${D}_{1}$ or ${D}_{2}$ | ${d}_{1}=0.5$, ${d}_{2}=1$ |

Noise power | ${N}_{0}=1$ |

The parameters of ipSIC | $\epsilon =0.03$ |

Ideal RF front end | ${g}_{t}={g}_{r}=1$, ${\phi}_{t}={\phi}_{r}={0}^{\circ}$ |

The parameters of IQI | ${g}_{t}={g}_{r}=0.8$, ${\phi}_{t}={\phi}_{r}={5}^{\circ}$ |

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**MDPI and ACS Style**

Tian, X.; Li, Q.; Li, X.; Peng, H.; Zhang, C.; Rabie, K.M.; Kharel, R. I/Q Imbalance and Imperfect SIC on Two-Way Relay NOMA Systems. *Electronics* **2020**, *9*, 249.
https://doi.org/10.3390/electronics9020249

**AMA Style**

Tian X, Li Q, Li X, Peng H, Zhang C, Rabie KM, Kharel R. I/Q Imbalance and Imperfect SIC on Two-Way Relay NOMA Systems. *Electronics*. 2020; 9(2):249.
https://doi.org/10.3390/electronics9020249

**Chicago/Turabian Style**

Tian, Xinji, Qianqian Li, Xingwang Li, Hongxing Peng, Changsen Zhang, Khaled M. Rabie, and Rupak Kharel. 2020. "I/Q Imbalance and Imperfect SIC on Two-Way Relay NOMA Systems" *Electronics* 9, no. 2: 249.
https://doi.org/10.3390/electronics9020249