Enhancing the performance of downlink NOMA relaying networks by RF energy harvesting and data buffering at relay

Recently, non-orthogonal multiple access (NOMA) and energy harvesting (EH) from radio frequency (RF) have been considered as promising candidates for next-generation mobile communications. In this paper, we investigate a novel solution to enhance the reliability and the supply stability of a downlink NOMA relaying networks, in which we integrate two techniques: (i) simultaneous wireless information and power transfer, i.e. the relay node can harvest the energy from source signals and use this energy to help forward information from source node to two user nodes; and (ii) data buffer aid at relay node, i.e. the data packets received from the source can be stored in a buffer and then be re-transmitted to the destination nodes only when the channel condition is good. The performance of the proposed system is analyzed rigorously to derive the system outage probability (OP), throughput and the average packet delay. Furthermore, a power allocation optimization problem to minimize the OP is formulated and solution to this problem is also provided. In addition, the optimal transmission rates to maximize the throughput of each user are presented in numerical results. Monte Carlo simulations are conducted to verify the analytical results, which confirms that with data buffer at relay, the overall outage probability (OOP) can be reduced significantly.

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Not applicable.

1. This model can employ two antennas for the relay node and operate in a full-duplex mode.

2. The analytical approach in this paper can be applied to the power-splitting EH model [30] as well.

3. However, source or relay only sends signal if the data buffer is in some proper states, as described later.

4. At this moment, EH-RF should be developed only for sensor networks, health care and medical systems such as wireless body networks with short communication distance.

5. The storing of harvested energy in TS scheme is refered as charging-then-communicate. In contrast, PS scheme is refered as charging-and-communicate.

6. One packet consist of the decoded messages for \(x_1\) and \(x_2\).

7. The order of SIC decoding merely depends on the order of SNR or equivalently, the magnitude of the channel gains, at \({\mathrm{D}}_1\) and \({\mathrm{D}}_2\).

8. Moreover, if the relay knows the channel gains \(g_1\) and \(g_2\) and the total power factor \(a_1 + a_2\) is equal to one, we can allocate power for \({\mathrm{D}}_1\) and \({\mathrm{D}}_2\) by adapting to channel gains, i.e. \(a_1 = |g_2|^2/( |g_1|^2+|g_2|^2 )\), to ensure the fairness in outage performance.

There is no funding available for this work.

Authors and Affiliations

1. Nha Trang Telecommunications University, Nha Trang, Vietnam

   Tran Manh Hoang, Nguyen Nhu Thang & Ba Cao Nguyen

2. Wireless Communications Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

   Phuong T. Tran

Contributions

Conceptualization: TMH, NNT, methodology: TMH, BCN; formal analysis and investigation: TMH, NNT; writing—original draft preparation: BCN; simulation: BCN, writing—review and editing: PTT; resources: PTT; supervision: PTT.

Corresponding author

Correspondence to Phuong T. Tran.

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix A

The goal of this appendix is to derive the OOP of the SWIPT-NOMA system over Rayleigh fading channels. The overall OP of the system can be expressed as

From (4), we obtain the closed-form expression of the first term of (47) as

To obtain the closed-form expression of the second term of (47), we rewrite the second term of (47) as

From (49) and the condition \(\gamma _{{{\mathrm{D}}_1}}^{x_2\rightarrow x_1} > \gamma _{{{\mathrm{D}}_2}}^{x_2}\), we have:

By substituting (4), (7), and (8) into (50) and denoting \(|h_1|^2 = X\), \(|g_1|^2 = Y\), and \(|g_2|^2 = Z\), we obtain:

As seen from (51), the outage always occurs if \(a_1 \ge \frac{1}{1 + \gamma _{\mathrm{th}}}\). Thus, allocating more power to the \({\mathrm{D}}_2\) is required so that \(1-a_1(1+\gamma _{\mathrm{th}})>0\) always holds. The condition \(a_1 < \frac{1}{1 + \gamma _{\mathrm{th}}}\) is used throughout this paper. For simplicity, we can rewrite (51) as

where \(\varPsi _{\min } = \min \left\{ \frac{\gamma _{\mathrm{th}}}{a_1\phi P_{\mathrm{S}}},\,\frac{\gamma _{\mathrm{th}}}{\phi P_{\mathrm{S}}[ 1 - a_1( 1 + \gamma _{\mathrm{th}})]} \right\}\).

Based on the properties of conditional probability [40] and the assumption that the channel gains have exponential distributions, we have:

where \(F_Y(y) = 1 - e^{ \frac{-y}{\varOmega _2}}\) and \(f_X(x)= \frac{1}{\varOmega _1}e^{ \frac{-x}{\varOmega _1} }\) are the CDF of X and the PDF of Y, respectively.

Substituting PDF of X into (53) yields

By using the Taylor’s series expansions of the exponential function, doing some algebras on (54), and using [27, 3.351.4], we obtain the second term of (47) as

We obtain the OP expression of the system by combining (48) and (55). When the transmission power is high, we have \(\gamma _{\mathrm{th}} \ll P_{\mathrm{S}}\). Then, (54) can be approximated as

From (56), by using [27, 3.324.1], i.e. \(\int \nolimits _0^\infty { e^{ - \frac{\beta }{4x} - \gamma x}dx}~=~\sqrt{\frac{\beta }{\gamma }} {K_1}\left( {\sqrt{\beta \gamma }} \right)\), and after some mathematical manipulations, we have the approximation of (19) at high SNR regime. The proof of Theorem 1 is completed. \(\square\)

Appendix B

Due to the imperfect detection at the relay node, it may forward wrongly decoded signals to \({\mathrm{D}}_1\) and \({\mathrm{D}}_2\) and cannot apply SIC technique on symbol \(x_2\) at \({\mathrm{D}}_1\). Hence, similarly to [41], for any modulation scheme, the dual-hop of the links \({\mathrm{S}}\rightarrow {\mathrm{R}}\rightarrow {\mathrm{D}}_1\) or \({\mathrm{S}}\rightarrow {\mathrm{R}}\rightarrow {\mathrm{D}}_2\) can be modeled as an equivalent one-hop channel whose output SINR \(\mathcal{X}_i\), \(i\in \{1,2\}\), at high SNR regime can be tightly approximated.

Let \({\mathcal{X}_1}\) and \({\mathcal{X}_2}\) denote the SINRs obtained at \({\mathrm{D}}_{1}\) and \({\mathrm{D}}_{2}\), respectively [4].

To find the OP of \({\mathrm{D}}_1\), from (57), we have the OP expression of \({\mathrm{D}}_1\) as

where \(\mathcal{Q}_{\max } = \max \left\{ \frac{\xi _1}{a_1\phi P_{\mathrm{S}}},\frac{\xi _1}{\phi P_{\mathrm{S}}(1 - a_1(1 + \xi _1))} \right\}\).

By using the conditional probability [40], we can rewrite (59) as

Since the CDF and PDF of X and Y are exponential distribution functions, we have:

By using the Taylor series expansions of the exponential function, after some manipulations of (61) using [27, 3.351.4], we obtain the expression of the OP of \({\mathrm{D}}_1\) as presented in (20).

For the case of imperfect SIC, we replace \(\gamma _{\mathrm{D_1}}^{x_1}\) from (9) into (59), then OP are derived similar to (59) to (61). After some manipulations, we have \(\varDelta _{\mathrm{max}} = \max \left\{ \frac{\xi _1}{\phi P_{\mathrm{S}}(a_1-\xi _1\kappa (1-a_2) )},\frac{\xi _1}{\phi P_{\mathrm{S}}(1 - a_1(1 + \xi _1))}\right\},\) and this term is used instead of \(\mathcal{Q}_{\max }\) in (61).

Next, we calculate the OP expression at \({\mathrm{D}}_2\). With the given SINR at \({\mathrm{D}}_2\) and the notation \(\mathcal{X}_2 = \min (\gamma _{\mathrm{R}},\gamma _{D_2}^{x_2})\), we can write:

Substituting (4) and (6) into (62) yields

Then, by applying similar calculations as in Appendix A we can obtain the OP of \({\mathrm{D}}_2\) as

By using the Taylor’s series expansions of the exponential function \(e^{\frac{-b}{x\varOmega _2}}=\sum \nolimits _{t=0}^{\infty }{\frac{(-1)^t}{t!}\left( \frac{b}{x\varOmega _2}\right) ^t}\) and using [27, 3.351.4], from (64) we can obtain the closed-form expression of the OP of \({\mathrm{D}}_2\) as given in (21) after some mathematical manipulations. The proof of Theorem 2 is completed. \(\square\)

Appendix C

From (6) and (8), the expression of \(\mathcal{O}_{\mathrm{RD}}\) can be expressed as

Based on the definition of the conditional probability, we can write:

where \({\mathcal {A}}=\frac{\gamma _{\mathrm{th}}}{a_1\phi P_{\mathrm{S}}}\), \({\mathcal {B}}=\frac{\gamma _{\mathrm{th}}}{\phi P_{\mathrm{S}}(1-a_1(1+\gamma _{\mathrm{th}}))}\). After some manipulations, we get (33), which completes the proof of Theorem 4. \(\square\)

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