On Outage Probability and Ergodic Rate of Downlink Multi-User Relay Systems with Combination of NOMA, SWIPT, and Beamforming
Abstract
:1. Introduction
- We propose a downlink MIMO-NOMA with SWIPT relay system which aims to improve the energy and spectrum efficiencies of the system. To reduce the complexity and mitigate inter-user interference, users in the system are divided into several clusters and a suitable user clustering mode is found out. The relays are employed to mitigate the effect of fading and reduce the number of training sequences for estimating the CSI at the base station.
- We derive the closed-form expressions of the outage probability (OP) and ergodic rate (ER) for each user in any cluster. For the practical purpose, we investigate the proposed MIMO-NOMA with SWIPT relay system over Rayleigh channel. The time duration of EH is optimized in the sense of minimum OP. The analysis result provides insights to understand the performance of the MIMO-NOMA system with SWIPT through the mathematical expressions.
- We consider the system in the case of imperfect channel state information (CSI) caused by the downlink channel estimation error and both cases of perfect and imperfect successive interference cancellation (SIC). The result shows that the system performance is reduced significantly due to the imperfect CSI and imperfect SIC. All analysis results are compared with simulation results to confirm the correctness of the derived mathematical expressions.
2. System Model
2.1. CSI Condition and Channel Model
2.2. Energy Harvesting
3. Performance Analysis
3.1. Outage Probability
3.2. Ergodic Rate
4. Numerical Results
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
AF | amplify-and-forward |
AWGN | Additive white Gaussian noise |
BS | Base station |
CDF | Cumulative distribution function. |
CSI | Channel state information |
DF | Decode-and-forward |
EH | Energy harvesting |
ER | Ergodic rate |
IoT | Internet of Things |
i.i.d | Independent and identically distributed |
MIMO | Multiple input multiple output |
MMSE | Minimum mean squared error |
NOMA | Non-orthogonal multiple access |
MU | Multi-user |
OP | Outage probability |
Probability density function | |
RF | Radio Frequency |
SCI | Successive interference cancellation |
SINR | Signal to interference plus noise ratio |
SNR | Signal to noise ratio |
SWIPT | Simultaneous wireless information and power transfer |
TS | Time switching |
ZFBF | Zero-force beamforming |
Appendix A
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Notation | Description |
---|---|
Probability | |
Cumulative distribution function (CDF) | |
Probability density function (PDF) | |
A circularly symmetric complex Gaussian RV x with mean and variance | |
The statistical expectation operator | |
Gamma function [32] | |
The second kind of Bessel function, order n [32] | |
Exponential integral function n [32] | |
Meijer’s G-Function [9.3] [32] | |
M | Number of relay nodes |
N | Number of users in each cluster |
Transmission antennas of BS and reception antennas of relay | |
Correlation coefficient | |
Time switching ratio | |
Conversion efficiency | |
r | Data rate threshold |
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Chi Hieu, T.; Le Cuong, N.; Manh Hoang, T.; Thanh Quan, D.; Thanh Hiep, P. On Outage Probability and Ergodic Rate of Downlink Multi-User Relay Systems with Combination of NOMA, SWIPT, and Beamforming. Sensors 2020, 20, 4737. https://doi.org/10.3390/s20174737
Chi Hieu T, Le Cuong N, Manh Hoang T, Thanh Quan D, Thanh Hiep P. On Outage Probability and Ergodic Rate of Downlink Multi-User Relay Systems with Combination of NOMA, SWIPT, and Beamforming. Sensors. 2020; 20(17):4737. https://doi.org/10.3390/s20174737
Chicago/Turabian StyleChi Hieu, Ta, Nguyen Le Cuong, Tran Manh Hoang, Do Thanh Quan, and Pham Thanh Hiep. 2020. "On Outage Probability and Ergodic Rate of Downlink Multi-User Relay Systems with Combination of NOMA, SWIPT, and Beamforming" Sensors 20, no. 17: 4737. https://doi.org/10.3390/s20174737
APA StyleChi Hieu, T., Le Cuong, N., Manh Hoang, T., Thanh Quan, D., & Thanh Hiep, P. (2020). On Outage Probability and Ergodic Rate of Downlink Multi-User Relay Systems with Combination of NOMA, SWIPT, and Beamforming. Sensors, 20(17), 4737. https://doi.org/10.3390/s20174737