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Cognitive IoT relaying NOMA networks with user clustering and imperfect SIC

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Abstract

To implement machine type communications (MTCs) in next generation mobile networks, Narrowband-Internet of Things (NB-IoT) need be studied. Such NB-IoT has been released by the third generation partnership project (3GPP) as a promising method to exhibit extended coverage and low energy consumption, especially for cheap MTC devices. However, the existing NB-IoT using orthogonal multiple access (OMA) scheme which cannot provide connectivity for a massive MTC devices. In this paper, we consider NB-IoT using non-orthogonal multiple access (NOMA). We find that power allocation factors for devices in clustering users as main enabler to exhibit differences in term of performance of devices. The worse situation of imperfect successive interference cancellation (SIC) is further studied due to main reason regarding degraded system performance. We derive closed-form expressions of outage probability for devices in a cluster to highlight main parameters affecting quality of devices. We verify our mathematical analysis via Monte-Carlo simulations.

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Author information

Authors and Affiliations

  1. Faculty of Electronics Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City, 700000, Vietnam

    Anh-Tu Le

  2. Department of Computer Science and Information EngineeringCollege of Information and Electrical Engineering, Asia University, Taichung, 41354, Taiwan

    Dinh-Thuan Do & Wen-Thong Chang

  3. Thai Nguyen University of Information and Communication Technology, Thai Nguyen city, Vietnam

    Chien-Thang Vu

Authors
  1. Anh-Tu Le
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  2. Dinh-Thuan Do
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  3. Wen-Thong Chang
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  4. Chien-Thang Vu
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Correspondence to Dinh-Thuan Do.

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This article is part of the Topical Collection: Special Issue on Cognitive Models for Peer-to-Peer Networking in 5G and Beyond Networks and Systems

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Appendices

Appendix A: Proof of proposition 1

With the help Eqs. 1, 4 and 5 we can write \(P_{U_{2} }\) as below

$$ \begin{array}{@{}rcl@{}} P_{U_{2} }^{P} &=& 1 - {\text{OP}} \left( \frac{\left| {g_{B2}} \right|^{2} K_{1} \eta_{B}} {\left| {g_{B2} } \right|^{2} K_{2} \eta_{B} + \left| {g_{R2} } \right|^{2} \eta_{R} + 1}\right.\\ &&\left. > \gamma_{th1} ,\frac{\left| {g_{B2} } \right|^{2} K_{2} \eta_{BS}} {\left|g_{R2} \right|^{2} \eta_{R} + 1} > \gamma_{th2} \right) \\ &=& 1 - \underbrace{\text{OP} \left( \left|g_{BP} \right|^{2} < \frac{\eta_{D}}{\eta},\left| {g_{B2}} \right|^{2} > \frac{\phi \left( \left| g_{R2} \right|^{2} \eta_{R} + 1 \right)}{\eta} \right)_{A_{1}}} \\ &-& \underbrace{\text{OP} \left( \left|g_{BP} \right|^{2} > \frac{\eta_{D}} {\eta},\left| g_{B2} \right|^{2} > \frac{\phi \left( \left|g_{R2}\right|^{2} \eta_{R} + 1 \right) \left| g_{BP} \right|^{2}} {\eta_{D}} \right).}_{A_{2}} \end{array} $$
(34)

Moreover, A1 can be rewritten as

$$ \begin{array}{@{}rcl@{}} A_{1} = {\text{OP}} \left( {\left| {g_{BP} } \right|^{2} < \frac{{\eta_{D}}} {\eta },\left| {g_{B2} } \right|^{2} > \frac{{\phi \left( {\left| {g_{R2} } \right|^{2} \eta_{R} + 1} \right)}} {\eta }} \right) \\ = \int\limits_{0}^{\frac{{\eta_{D}}} {\eta }} {f_{\left| {g_{BP} } \right|^{2} } \left( x \right)} \int\limits_{0}^{\infty} {f_{\left| {g_{R2} } \right|^{2} } \left( y \right)} \int\limits_{\frac{{\phi \left( {y\eta_{R} + 1} \right)}} {\eta }}^{\infty} {f_{\left| {g_{B2} } \right|^{2} } \left( z \right)} dzdydx. \end{array} $$
(35)

Putting Eq. 10 into Eq. 35, we get

$$ \begin{array}{@{}rcl@{}} A_{1} = \frac{{\left( {1 - e^{- \frac{{\eta_{D}}} {{G_{BP} \eta }}} } \right)e^{- \frac{\phi } {{G_{B2} \eta }}} }} {{G_{R2} }}\int\limits_{0}^{\infty} {e^{- \left( {\frac{{G_{B2} \eta + G_{R2} \phi \eta_{R} }} {{G_{R2} G_{B2} \eta }}} \right)x} } dx \\ = \frac{{\left( {1 - e^{- \frac{{\eta_{D}}} {{G_{BP} \eta }}} } \right)G_{B2} \eta e^{- \frac{\phi } {{G_{B2} \eta }}} }} {{\left( {G_{B2} \eta + G_{R2} \phi \eta_{R} } \right)}}. \end{array} $$
(36)

Then, the term A2 is calculated as

$$ \begin{array}{@{}rcl@{}} A_{2} = {\text{OP}} \left( {\left| {g_{BP} } \right|^{2} > \frac{{\eta_{D}}} {\eta },\left| {g_{B2} } \right|^{2} > \frac{{\phi \left( {\left| {g_{R2} } \right|^{2} \eta_{R} + 1} \right)\left| {g_{BP} } \right|^{2} }} {{\eta_{D}}}} \right) \\ = \int\limits_{\frac{{\eta_{D}}} {\eta }}^{\infty} {f_{\left| {g_{BP} } \right|^{2} } \left( x \right)} \int\limits_{0}^{\infty} {f_{\left| {g_{R2} } \right|^{2} } \left( y \right)} \int\limits_{\frac{{\phi \left( {y\eta_{R} + 1} \right)x}} {{\eta_{D}}}}^{\infty} {f_{\left| {g_{R2} } \right|^{2} } \left( z \right)} dzdxdy. \end{array} $$
(37)

Similarly, it is rewritten as

$$ \begin{array}{@{}rcl@{}} A_{2} = \frac{1} {{G_{BP} G_{R2} }}\int\limits_{\frac{{\eta_{D}}} {\eta }}^{\infty} {e^{- \frac{\phi } {{\eta_{D}G_{B2} }}x - \frac{x} {{G_{BP} }}} } \int\limits_{0}^{\infty} {e^{- \frac{{\phi \eta_{R} x}} {{\eta_{D}G_{B2} }}y - \frac{y} {{G_{R2} }}} } dxdy \\ = \frac{{G_{B2} \eta_{D}}} {{G_{BP} G_{R2} \phi \eta_{R} }}\int\limits_{\frac{{\eta_{D}}} {\eta }}^{\infty} {\frac{{e^{- \left( {\frac{{G_{B2} \eta_{D} + G_{BP} \phi }} {{G_{BP} G_{B2} \eta_{D}}}} \right)x} }} {{x + \frac{{G_{B2} \eta_{D}}} {{G_{R2} \phi \eta_{R} }}}}} dy. \end{array} $$
(38)

Based on [36, Eq. 3.352.2], A2 can be obtained as

$$ \begin{array}{@{}rcl@{}} &&A_{2} = - \frac{{G_{B2} \eta_{D}e^{\frac{{G_{B2} \eta_{D} + G_{BP} \phi }} {{G_{BP} G_{R2} \phi \eta_{R} }}} }} {{G_{BP} G_{R2} \phi \eta_{R} }}\\ &&Ei\left( { - \frac{{G_{B2} \eta_{D} + G_{BP} \phi }} {{G_{BP} G_{B2} \eta }} - \frac{{G_{B2} \eta_{D} + G_{BP} \phi }} {{G_{BP} G_{R2} \phi \eta_{R} }}} \right). \end{array} $$
(39)

Substituting Eqs. 36 and 38 into Eq. 34, the proof is completed.

Appendix B: Proof of proposition 2

To compute the outage probability for user U1, B1 can be first written as

$$ \begin{array}{@{}rcl@{}} B_{1} = {\text{OP}} \left( {\left| {g_{BP} } \right|^{2} < \frac{{\eta_{D}}} {\eta },\left| {g_{BR} } \right|^{2} > \frac{{\varepsilon_{1} \left( {\eta_{R} \left| {g_{R} } \right|^{2} + 1} \right)}} {\eta }} \right) \\ + {\text{OP}} \left( {\left| {g_{BP} } \right|^{2} > \frac{{\eta_{D}}} {\eta },\left| {g_{BR} } \right|^{2} > \frac{{\varepsilon_{1} \left( {\eta_{R} \left| {g_{R} } \right|^{2} + 1} \right)\left| {g_{BP} } \right|^{2} }} {{\eta_{D}}}} \right) \\ = \int\limits_{0}^{\frac{{\eta_{D}}} {\eta }} {f_{\left| {g_{BP} } \right|^{2} } \left( x \right)} \int\limits_{0}^{\infty} {f_{\left| {g_{R} } \right|^{2} } \left( y \right)} \int\limits_{\frac{{\varepsilon_{1} \left( {\eta_{R} y + 1} \right)}} {\eta }}^{\infty} {f_{\left| {g_{BR} } \right|^{2} } \left( z \right)} dzdydx \\ + \int\limits_{\frac{{\eta_{D}}} {\eta }}^{\infty} {f_{\left| {g_{BP} } \right|^{2} } \left( x \right)} \int\limits_{0}^{\infty} {f_{\left| {g_{R} } \right|^{2} } \left( y \right)} \int\limits_{\frac{{\varepsilon_{1} \left( {\eta_{R} y + 1} \right)x}} {{\eta_{D}}}}^{\infty} {f_{\left| {g_{BR} } \right|^{2} } \left( z \right)} dzdydx. \end{array} $$
(40)

Similarly, we can obtain B1 as

$$ \begin{array}{@{}rcl@{}} B_{1} = \frac{{\left( {1 - e^{- \frac{{\eta_{D}}} {{G_{BP} \eta }}} } \right)G_{BR} \eta e^{- \frac{{\varepsilon_{1} }} {{G_{BR} \eta }}} }} {{\left( {G_{BR} \eta + G_{R} \varepsilon_{1} \eta_{R} } \right)}} - \frac{{G_{BR} \eta_{D}e^{\frac{{G_{BR} \eta_{D} + G_{BP} \varepsilon_{1} }} {{G_{BP} G_{R} \varepsilon_{1} \eta_{R} }}} }} {{G_{BP} G_{BR} \varepsilon_{1} \eta_{R} }}\\ \times Ei\left( { - \frac{{G_{BR} \eta_{D} + G_{BP} \varepsilon_{1} }} {{G_{BP} G_{BR} \eta }} - \frac{{G_{BR} \eta_{D} + G_{BP} \varepsilon_{1} }} {{G_{BP} G_{R} \varepsilon_{1} \eta_{R} }}} \right). \end{array} $$
(41)

Furthermore, B2 can be calculated by

$$ B_{2} = {\text{OP}} \left( {\left| {g_{R1} } \right|^{2} > \frac{{\gamma_{th1} }} {{\eta_{R} }}} \right) = e^{- \frac{{\gamma_{th1} }} {{\eta_{R} G_{R1} }}} . $$
(42)

Finally, combining Eqs. 16 and 17 the closed-form for outage probability of U1 is given as Eq. 27.

It completes the proof.

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Le, AT., Do, DT., Chang, WT. et al. Cognitive IoT relaying NOMA networks with user clustering and imperfect SIC. Peer-to-Peer Netw. Appl. 14, 3170–3180 (2021). https://doi.org/10.1007/s12083-020-01061-7

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