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Exploiting HDU/FDU-NOMA Schemes for Reliable Communication in Post-disaster Scenario

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Abstract

This work presents a reliable communication system tailored for post-disaster scenarios, where the existing terrestrial communication infrastructure is entirely disrupted by natural calamities. To encounter the situation, a Temporary Base Station (TBS) is deployed in the heart of the disaster-stricken area. However, due to the limited coverage area of the TBS, reaching far users becomes unattainable. To address this, Unmanned Aerial Vehicles (UAVs) are proposed as flying relays with indirect connectivity, utilizing Half-Duplex/Full-Duplex (HD/FD) Non-Orthogonal Multiple Access (NOMA) schemes, abbreviated as HDU/FDU-NOMA. The UAVs, strategically positioned around the TBS on a circular path, can move radially outward or inward based on far user throughput demands and also serve as near-users. Moreover, a Weibull fading distribution (WD) is taken into account for both links, encompassing transmissions from far-users to UAVs and from UAVs to TBS. To assess communication reliability, exact and closed-form expressions for outage probability and throughput performance are derived. These expressions aid in identifying optimal UAV locations to achieve throughput fairness for both far-users and near-users, as well as maximizing throughput for far-users. Additionally, the proposed scheme’s outage and throughput performance is demonstrated to surpass that of corresponding Orthogonal Multiple Access (OMA) schemes in the uplink. Simulation results conform to the analytical results.

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No datasets were generated or analysed during the current study.

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Acknowledgements

I thank the valuable input of Dr. Arvind Kumar, Dr. Shyampratap Singh, and Dr. Nitish Kumar Guru. I express my gratefulness to the UGC for funding the research works.

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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Authors and Affiliations

  1. Department of Electronics and Communication Engineering, Birla Institute of Technology, Mesra, Ranchi, India

    Rampravesh Kumar & Sanjay Kumar

  2. Department of Electronics and Telecommunication Engineering, K K Wagh Institute of Engineering Education and Research, Nashik, Maharashtra, India

    Saurabh Srivastava

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Appendix

Appendix

1.1 Proof of Theorem 1

Substituting the value of \(\varpi = 1\) into (14) for FDU-NOMA, Outage probability at TBS for \({U_1}\) can be written as

$$\begin{aligned} \begin{array}{r} P_{OutBS,U1}^{FD} = 1 - pr\left\{ {|{h_1}{|^2} > \max \frac{1}{\rho _1}\left( {\frac{\gamma _{2th}^{x_{2U}}}{({a_2} - {a_1}\gamma _{2th}^{x_{2U}})},\frac{\gamma _{1th}^{x_{2U}}}{a_1}} \right) } \right\} \\ \end{array} \end{aligned}$$
(28)

Let

$$\begin{aligned} \begin{array}{l} {J_1} = {pr\left\{ {|{h_1}{|^2} > \max \frac{1}{{{\rho _1}}}\left( {\frac{{\gamma _{2th}^{{x_{2U}}}}}{{({a_2} - {a_1}\gamma _{2th}^{{x_{2U}}})}},\frac{{\gamma _{1th}^{{x_{1U}}}}}{{{a_1}}}} \right) } \right\} }\\ \end{array} \end{aligned}$$
(29)
$$\begin{aligned} \begin{array}{l} {J_1} = pr\left\{ {|{h_1}{|^2} > \frac{\xi }{\rho _1}} \right\} \\ = \int \limits _{\frac{\xi }{\rho _1}}^\infty {{f_{{{\left| {{h_1}} \right| }^2}}}\left( v \right) } dv = {e^{-\frac{{{{\left( {{\xi /{\rho _1}}} \right) }^{B/2}}}}{{{A_1}}}}} \end{array} \end{aligned}$$
(30)

where, \(\xi = \max \left\{ {\frac{{\gamma _{2th}^{{x_{2U}}}}}{{\left( {{a_2} - {a_1}\gamma _{2th}^{{x_{2U}}}} \right) }},\frac{{\gamma _{1th}^{{x_{1U}}}}}{{{a_1}}}} \right\} \).

By substituting the value of \({J_1}\) from Eq. (30) into Eq. (28), outage probability at TBS for U1 in FDU-NOMA is obtained. This concludes the proof of Theorem 1.

1.2 Proof of Theorem 2

Substituting the value of \(\varpi = 1\) into (18) for FDU-NOMA, outage probability at TBS for \({U_2}\) can be written as

$$\begin{aligned} \begin{array}{r} P_{OutBS,U2}^{FD} = 1 - pr\left\{ {|{h_2}{|^2}> \frac{{(\varpi |{h_{LI}}{|^2}{\rho _1} + 1)\gamma _{2th}^{{x_{2U}}}}}{{{\rho _2}}}},{|{h_1}{|^2} > \frac{1}{{{\rho _1}}}\left( {\frac{{\gamma _{2th}^{{x_{2U}}}}}{{({a_2} - {a_1}\gamma _{2th}^{{x_{2U}}})}}} \right) } \right\} \\ \end{array} \end{aligned}$$
(31)

Let

$$\begin{aligned} \begin{array}{l} {J_2} = pr\left\{ {|{h_2}{|^2} > \frac{{(\varpi |{h_{LI}}{|^2}{\rho _1} + 1)\gamma _{2th}^{{x_{2U}}}}}{{{\rho _2}}}} \right\} \\ = pr\left( {{{\left| {{h_2}} \right| }^2} \ge \left( {\varpi {{\left| {{h_{LI}}} \right| }^2}{\rho _1} + 1} \right) T} \right) \\ = \int \limits _0^\infty {\int \limits _{\left( {x\rho + 1} \right) T}^\infty {{f_{{{\left| {{h_{LI}}} \right| }^2}}}\left( x \right) } } {f_{{{\left| {{h_2}} \right| }^2}}}\left( y \right) dxdy \end{array} \end{aligned}$$
(32)

plugging the value of \({f_{{{\left| {{h_2}} \right| }^2}}}\left( y \right) \) from (2) into (32), we get

$$\begin{aligned} \begin{array}{l} {J_2} = \\ \int \limits _0^\infty {{f_{{{\left| {{h_{LI}}} \right| }^2}}}\left( x \right) } \left[ {\int \limits _{\left( {x\rho + 1} \right) T}^\infty {\frac{{B/2}}{{{A_2}}}{y^{(B/2 - 1)}}{e^{\frac{{ - {y^{B/2}}}}{{{A_2}}}}}dy} } \right] dx \end{array} \end{aligned}$$
(33)

After algebraic manupulation, further plugging the value of \({f_{{{\left| {{h_{LI}}} \right| }^2}}}\left( x \right) \) from (2) into (33), we get

$$\begin{aligned} {J_2} = \frac{B}{{2{A_{LI}}}}\int \limits _0^\infty {{x^{\left( {\frac{B}{2} - 1} \right) }}{e^{ - \left\{ {\frac{{{x^{B/2}}}}{{{A_{LI}}}} + \frac{{{{\left( {\left( {x\rho + 1} \right) T} \right) }^{B/2}}}}{{{A_2}}}} \right\} }}dx} \end{aligned}$$
(34)

where, \(T = \frac{{\gamma _{2th}^{{x_{2U}}}}}{{{\rho _2}}}\).

$$\begin{aligned} \begin{array}{r} {J_3} = pr\left\{ {|{h_1}{|^2} > \frac{1}{{{\rho _1}}}\left( {\frac{{\gamma _{2th}^{{x_{2U}}}}}{{({a_2} - {a_1}\gamma _{2th}^{{x_{2U}}})}}} \right) } \right\} \\ \end{array} \end{aligned}$$
(35)
$$\begin{aligned} \begin{array}{l} {J_3} = pr\left\{ {|{h_1}{|^2} > \frac{{Q} }{{{\rho _1}}}} \right\} \\ = \int \limits _{\frac{{Q} }{{{\rho _1}}}}^\infty {{f_{{{\left| {{h_1}} \right| }^2}}}\left( v \right) } dv = {e^{-\frac{{{{\left( {{{Q} /{\rho _1}}} \right) }^{B/2}}}}{{{A_1}}}}} \end{array} \end{aligned}$$
(36)

Multiplying Eq. (34) and Eq. (36), the obtained expression for J is given by

$$\begin{aligned} \begin{array}{l} J = {J_2} \times {J_3}\\ = \left\{ {\frac{B}{{2{A_{LI}}}}{e^{-\frac{{ {{\left( {{{Q} /{\rho _1}}} \right) }^{B/2}}}}{{{A_1}}}}}} \right\} \times \int \limits _0^\infty {{x^{\left( {\frac{B}{2} - 1} \right) }}{e^{ - \left\{ {\frac{{{x^{B/2}}}}{{{A_{LI}}}} + \frac{{{{\left( {\left( {x\rho + 1} \right) T} \right) }^{B/2}}}}{{{A_2}}}} \right\} }}dx} \end{array} \end{aligned}$$
(37)

Finally, substituting the value of J from Eq. (37) in Eq. (31), we get

$$\begin{aligned} \begin{array}{l} P_{Out,BS}^{FDR} = 1 - \left[ {\frac{{B/2}}{{{A_{LI}}}}{e^{\left( {\frac{{ - {{\left( {\xi /{\rho _1}} \right) }^{B/2}}}}{{{A_1}}}} \right) }}} \right] \int \limits _0^\infty {{x^{(B/2 - 1)}}{e^{\left[ {\frac{{ - {x^{B/2}}}}{{{A_{LI}}}} + \frac{{ - {{\left\{ {(x{\rho _1} + 1)T} \right\} }^{B/2}}}}{{{A_2}}}} \right] }}} dx \end{array}\ \end{aligned}$$
(38)

The proof of Theorem 2 is concluded by obtaining the outage probability at TBS for U2 in FDU-NOMA.

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Kumar, R., Srivastava, S. & Kumar, S. Exploiting HDU/FDU-NOMA Schemes for Reliable Communication in Post-disaster Scenario. Wireless Pers Commun 135, 1701–1724 (2024). https://doi.org/10.1007/s11277-024-11144-w

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