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Outage Performance of Uplink (UL) NOMA Network

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Abstract

With the progress in the information technology and evolution of wireless technologies for next generation communications like Internet of Things (IoT) networks and smart sensor networks, non-orthogonal multiple access (NOMA) has emerged as a leading multiple access scheme for connecting these devices. IoT devices are low-powered, designed to stay connected for a more extended period without a frequent recharge, and need reliable connection. NOMA with cooperative relay is considered as a promising technique to connect these devices. In this paper, we analyse the outage performance of a two-hop decode-and-forward relay-assisted signal transmission between the users and a common destination with NOMA as a multiple access scheme. We have considered uplink NOMA, where users first send message signal to the relay with fixed power. Superposition coding is used to transmit the combined signal over a resource blocks at the transmitter side, while a multi-user detection such as successive interference cancellation technique is used to detect the signal at the relay and next at the destination. The effect of relay selection demonstrated in terms of outage probability of the system. A closed-form expression of outage probability for the considered network is theoretically analysed. The analytical result is validated by simulations and demonstrate that outage performance of the system depends on the transmit SNR of both the user. Serving multiple users in NOMA also degrades the outage performance of the system in higher SNR regime.

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Funding

(This research is supported by the Department of Ministry of Education, Government of India under the Institute PhD Fellowship Scheme administered by National Institute of Technology, Durgapur.)

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Authors and Affiliations

Authors

Contributions

(All authors contributed to the study conception and design. Analysis were performed by [Alok kumar Baranwal], [Shashibhushan Sharma], [Sanjay Dhar Roy] and [Sumit Kundu]. The first draft of the manuscript was written by [Alok kumar Baranwal] and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.)

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Correspondence to Alok Kumar Baranwal.

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(All the authors are working in the field of Wireless Communication, and we declare that any of the authors have no conflict of interest.)

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(Yes, This research is carried out in MaTLab Software Platform and coding is done in MaTLab only.)

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Appendices

Appendix A:-

Based on (34), \(I_1\) is derived as follows:-

$$\begin{aligned}&I_{1}= Pr \left( g_{1}> \frac{R_{1}(\rho _{2g2}+1)}{\rho _{1}},g_{2} > \frac{R_{2}(\rho _{1g1(ipr)}+1)}{\rho _{2}}\right) \end{aligned}$$
(67)
$$\begin{aligned}I_1 &= \int _{g1(ipr)=0}^{+\infty }\frac{1}{\delta _{1 (ipr)}^{2} \exp \left( \frac{-g1(ipr)}{\delta _{1(ipr)}^{2}}\right) d{g_{1(ipr)}} \int _{g2}=\frac{R_{2}(\rho _{1g1 (ipr)}+1)}{\rho _{2}}}^{+\infty } \frac{1}{\delta _{2}^{2}} \exp \left( \frac{-g_{2}}{\delta _{2}^{2}} \right) d{g_{2}} \int _{g1}\nonumber \\&=\frac{R_{1}(\rho _{2g2}+1)}{\rho _{1}}^{+\infty } \frac{1}{\delta _{1}^{2}} \exp \left( \frac{-g_{1}}{\delta _{1}^{2}} \right) d{g_{1}} \end{aligned}$$
(68)
$$\begin{aligned}&I_{1}= \exp \left( -A \right) \cdot \left[ \int _{g1(ipr)}=0^{+\infty } \frac{1}{\delta _{1(ipr)}^{2}} \exp \left( \frac{-g_{1(ipr)}}{\delta _{1(ipr)}^{2}} \right) d{g_{1(ipr)}} \int _{g2} =\frac{R_{2}(\rho _{1g1(ipr)}+1)}{\rho _{2}}^{+\infty } \frac{1}{\delta _{2}^{2}} \exp \left( {-g_{2b}} \right) d{g_{2}} \right] \end{aligned}$$
(69)
$$\begin{aligned}&I_{1}= \exp \left( -A \right) \cdot \exp \left( -B \right) \cdot \left[ \int _{g1(ipr)}=0^{+\infty } \frac{1}{\delta _{1(ipr)}^{2}} \exp \left( -g_{1(ipr)} \left( \frac{R_{2b}\rho _{1}}{\rho _{2}}+\frac{1}{\delta _{1(ipr)}^{2}} \right) \right) d{g_{1(ipr)}} \right] \end{aligned}$$
(70)
$$\begin{aligned}&I_{1}= \frac{\exp \left( -A \right) }{.}\exp \left( -B\right) \left( 1+A{\rho _{2}\delta _{2}^{2}}\right) .\left( 1+B\rho _{1} \delta _{1 (ipr)}^{2}\right) \end{aligned}$$
(71)

where \(A =\frac{R_1}{\rho _1\delta _1^2}\), \(B =\frac{R_2b}{\rho _2}\), \(b =\frac{1+c}{\delta _2^2}\), and c=\(\frac{R_1\rho _2\delta _2^2}{\rho _1\delta _1^2}\)

Appendix B:-

Based on (32), \(I_4\) is derived as follows

$$\begin{aligned} I_4= Pr \left( g_{{RD}} > M \right) \end{aligned}$$
(72)

where \(M=\max (a,y)\)

such that \(a=\frac{R_{1}}{(\alpha _{1}\rho _{R}-\alpha _{2}\rho _{RR1})}\), and \(y=\frac{R_{2}(\alpha _{2}\rho _{Rg1(ipd)}+1)}{\alpha _{2}\rho _{R}}\)

CDF of M can be find as

\(F_m(M)=Pr(M \le m)=Pr(a \le m).Pr(y \le m)=F_a(m).F_y(m)\)

Since a is a constant, through which we get lower bound on m.

\(m \ge \frac{R_1}{(\alpha _1\rho _R-\alpha _2\rho _RR_1)}\)

Now, \(F_y(M)\) is solved as

$$\begin{aligned}&F_{y(M)}=1-Pr \left( g_{1 (ipd)} > \frac{(\alpha _{2}\rho _{Rm-R2})}{(\alpha _{2}\rho _{RR2})} \right) \end{aligned}$$
(73)
$$\begin{aligned}&F_{y(M)}=1- \left( \exp \left( \frac{-(\alpha _{2}\rho _{Rm-R2}}{\alpha _{2}\rho _{RR2}\delta _{1(ipd)}^{2}}\right) \right) \end{aligned}$$
(74)

\(F_m(M)\) is written as

$$\begin{aligned} F_{m(M)}=1- \left( \exp \left( \frac{-(\alpha _{2}\rho _{Rm}-R_{2})}{\alpha _{2}\rho _{RR2}\delta _{1 (ipd)}^{2}}\right) \right) ;m \ge \frac{R_{1}}{(\alpha _{1}\rho _{R}-\alpha _{2}\rho _{RR1})} \end{aligned}$$
(75)

Thus, \(I_4\) is solved as

$$\begin{aligned}&I_{4}= Pr(g_{RD} > m)= \int _{g{RD}=a}^{+\infty }F_{m(g{RD})}\frac{1}{\delta _{RD}^{2}} \exp \left( \frac{-g_{RD}}{\delta _{RD}^{2}}\right) d{g_{RD}} \end{aligned}$$
(76)
$$\begin{aligned}&I_{4}= \int _{gRD}=a^{+\infty }\frac{1}{\delta _{RD}^{2}} \exp \left( \frac{-g_{RD}}{\delta _{RD}^{2}}\right) d{g_{RD}}-\int _{gRD}=a^{+\infty }\frac{1}{\delta _{RD}^{2}} \exp (E) \exp \left( -g_{RD}F \right) d{g_{RD}} \end{aligned}$$
(77)
$$\begin{aligned}&I_{4}=\exp \left( \frac{-a}{\delta _{RD}^{2}}\right) -\frac{\exp \left( E-aF \right) }{\left( 1+G \right) } \end{aligned}$$
(78)

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Baranwal, A.K., Sharma, S., Roy, S.D. et al. Outage Performance of Uplink (UL) NOMA Network. Wireless Pers Commun 125, 1281–1305 (2022). https://doi.org/10.1007/s11277-022-09603-3

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