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Performance analysis and optimization of ergodic secrecy rates for downlink data transmission in massive MIMO-NOMA networks

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Abstract

In this paper, we investigate the secrecy performance of a massive MIMO NOMA network. Specifically, we demonstrate a detailed training process in the network and derive downlink ergodic secrecy rates of legitimate users. In order to gain system’s insights, discussions on secrecy performance of the network in two special cases, i.e., large number of antennas and high transmit power at the BS, are provided. Furthermore, from the analysis, an optimization to maximize the users’ minimum secrecy rate in each NOMA cluster is proposed to aid the weak users’ secrecy performance. The correctness of our analysis and the efficiency of the proposed are confirmed through computer simulations.

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Notes

  1. The reason for choosing EPA as a benchmark is that an optimization algorithm for users’ minimum secrecy rate of the exact system model has not been developed in the literature yet. Therefore, in this situation, in the literature, equal power allocation is often preferred as in [7], [11] and the references therein. Besides, although the idea of this scheme is straightforward, it still provides secrecy transmissions for weakest users of the proposed system, i.e., non-zero ergodic secrecy rate, as seen in Figs. 5, 6, and 7. As a result, EPA is a decent benchmark of the proposed optimization algorithm.

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Acknowledgements

This research is funded by the Hanoi University of Science and Technology (HUST) under project number T2020-SAHEP-017.

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Authors and Affiliations

  1. School of Electronics and Telecommunications, Hanoi University of Science and Technology, Hanoi, Vietnam

    Nam-Phong Nguyen, Hong T. Nguyen, Tien-Hoa Nguyen & Chuyen T. Nguyen

  2. Department of Engineering, Dong Nai University, Bien Hoa, Vietnam

    Long D. Nguyen

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  1. Nam-Phong Nguyen
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  2. Long D. Nguyen
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  3. Hong T. Nguyen
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Correspondence to Chuyen T. Nguyen.

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This paper was presented in part at the 2019 International Conference on Advanced Technologies for Communications (ATC) in Hanoi, Vietnam [10]

Appendices

Appendices

$$\begin{aligned} \mathbb {E}\left\{ {\varvec{\hat{f}}_{n}^H}{\varvec{z}_n}\right\}&= \mathbb {E}\left\{ {\varvec{\hat{f}}_{n}^H}{\frac{\varvec{v}_n}{\Vert \varvec{v}_n\Vert }}\right\} = \mathbb {E}\left\{ {\varvec{\hat{f}}_{n}^H}{\frac{\varvec{\hat{f}}_n(\varvec{\hat{f}}_n^H\varvec{\hat{f}}_n)^{-1}}{\Vert \varvec{v}_n\Vert }}\right\} \nonumber \\&= \mathbb {E}\left\{ \frac{1}{\Vert \varvec{v}_n\Vert }\right\} = \mathbb {E}\left\{ \frac{1}{\sqrt{\varvec{v}_n^H\varvec{v}_n}}\right\} \nonumber \\&= \mathbb {E}\left\{ \sqrt{\frac{1}{(\varvec{\hat{f}}_n(\varvec{\hat{f}}_n^H\varvec{\hat{f}}_n)^{-1})^H(\varvec{\hat{f}}_n(\varvec{\hat{f}}_n^H\varvec{\hat{f}}_n)^{-1})}}\right\} \nonumber \\&=\mathbb {E}\left\{ \sqrt{\frac{1}{(\varvec{\hat{f}}_n^H\varvec{\hat{f}}_n)^{-1}}}\right\} = \frac{1}{\sqrt{2}}\mathbb {E}\left\{ X^{\frac{1}{2}}\right\} \nonumber \\&= \frac{1}{\sqrt{2}}\sqrt{2}\frac{P(\frac{1}{2} + \frac{2(M- C + 1)}{2})}{P(\frac{2(M- C + 1)}{2})} \nonumber \\&= \frac{P(M- C + 1 + \frac{1}{2})}{P(M- C + 1)} \overset{(a)}{\approx } M- C + 1, \end{aligned}$$
(39)

where X follows Chi-squared distribution with \(2(M- C + 1)\) degrees of freedom as described in [2]. Step (a) of (39) can be achieved when \(M\) is large [10].

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Nguyen, NP., Nguyen, L.D., Nguyen, H.T. et al. Performance analysis and optimization of ergodic secrecy rates for downlink data transmission in massive MIMO-NOMA networks. Wireless Netw 28, 355–365 (2022). https://doi.org/10.1007/s11276-021-02867-w

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