Abstract
In this study, non-orthogonal multiple access (NOMA) together with cognitive radio (CR) benefit to the vehicle-to-everything (V2X) as promising application with high spectrum efficiency. We have higher priority to evaluate system performance of the secondary network in such CR-NOMA system operating in the context of V2X. We first arrange vehicles belonging to serving group in this CR-NOMA assisted V2X, and it is beneficial to serve massive connections for vehicles. There are two scenarios studied in this paper, with and without the support of CR scheme. In our proposed system, two system metrics need be investigated to evaluate performance of vehicles that need higher quality of service (QoS). Our results indicate that the outage performance gap among two vehicles exists since different transmit power allocation factors were assigned to them. In particular, the outage probability is first derived in exact forms and then the bit error rate (BER) can be further achieved. In specific situations, the optimal outage probability can be obtained by numerical simulations. Simulation results are also provided to verify the correctness of the derived expressions and it exhibits advantages of the proposed CR-NOMA assisted V2X system in terms of two main metrics such as outage probability and BER.
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Appendices
Appendix A
In (8) we have \(P_1\) is calculated
where \({{\bar{\chi }} _{max}} = \max \left( {\frac{{{\varepsilon _2}}}{{{\rho _{RSU}}\left[ {\alpha - {\varepsilon _2}\left( {1 - \alpha } \right) } \right] }},\frac{{{\varepsilon _1}}}{{\left( {1 - \alpha } \right) {\rho _{RSU}}}}} \right)\) and \({{\tilde{\chi }} _{max}} = \max \left( {\frac{{{\varepsilon _2}}}{{{\rho _Q}\left[ {\alpha - {\varepsilon _2}\left( {1 - \alpha } \right) } \right] }},\frac{{{\varepsilon _1}}}{{{\rho _Q}\left( {1 - \alpha } \right) }}} \right)\)
The outage probability of fist term and second terms (33) can be obtained as \({A_1}\) and \({A_2}\), respectively in following proposition.
\({A_1}\) can be calculate as
Similarly, \({A_2}\) can be expressed as
where \(\zeta = \frac{{{\Omega _{{h_{S{D_1}}}}}}}{{{\Omega _{{h_{C{D_1}}}}}\kappa {{\tilde{\chi }} _{max}}{\rho _{CUE}}}}\).
We using [29, Eq.(3.352.2)], \({A_2}\) is given as
where \(Ei\left( . \right)\) is exponential integral function.
Substituting (36) and (34) into (33), \({P_1}\) is given by
The proposition 1 is completed.
Appendix B
In (20), we have \({F_X}\left( x \right)\) of \(P_{{D_1}}^{BER}\) calculated as
Substituting (38) into (20), the BER of \(D_1\) is written as
where \(\Phi = \frac{{{\Omega _{{h_{S{D_1}}}}}\left( {1 - \alpha } \right) {{{\bar{\rho }} }_{RSU}}}}{{{\mu _1}{\Omega _{{h_{SP}}}}}}\), \(\psi = \left( {\frac{{{\bar{b}}}}{2} + \frac{{{\mu _1}}}{{{\Omega _{{h_{S{D_1}}}}}\left( {1 - \alpha } \right) {{\bar{\rho }}_{RSU}}}}} \right)\) and \(\xi = \left( {\frac{{{\bar{b}}}}{2} + \frac{{{\mu _1}{\rho _Q}}}{{{\Omega _{{h_{S{D_1}}}}}\left( {1 - \alpha } \right) {\bar{\rho }} _{RSU}^2}}} \right)\)
Based on [29, Eq. (3.361.2)], [29, Eq. (3.383.10)] and after few steps, (39) can then be further derived as
where \(\Gamma \left( . \right)\) is the Gamma function and \(\Gamma \left( {.,.} \right)\) is the upper incomplete Gamma function
The proposition 2 is completed.
Appendix C
Similar to (22), we have
where \({{\mathcal {X}}} = \frac{{{\Omega _{{h_{S{D_2}}}}}{\rho _Q}}}{{{\Omega _{{h_{SP}}}}{\mu _2}}}\)
Substituting (41) into (22), \(P_{{D_2}}^{BER}\) is given by
The first integral in (42) can be easily obtained as in [29, Eq. (3.361.1)]. For the second integral, setting \(t = \frac{{2\left( {1 - \alpha } \right) x}}{\alpha }\) results in \(x = \frac{{\alpha \left( {t + 1} \right) }}{{2\left( {1 - \alpha } \right) }}\). Hence, (42) is given as
where \(\phi = \left( {1 - {e^{ - \frac{{{\rho _Q}}}{{{\Omega _{{h_{SP}}}}{{{\bar{\rho }} }_{RSU}}}}}}} \right)\), \({{\mathcal {S}}}\left( t \right) = \frac{{\alpha \left( {t + 1} \right) }}{{2\left( {1 - \alpha } \right) }}\) and \(\Phi \left( . \right)\) is the Error function [29, Eq. (3.321.1)]
Using the Gaussian-Chebyshev quadrature method in [32], we can obtain \(P_{{D_2}}^{BER}\) as
where \({\varphi _t} = \cos \left( {\frac{{2t - 1}}{{2T}}\pi } \right)\)
The proposition 3 is completed.
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Le, CB., Do, DT., Zaharis, Z.D. et al. System Performance Analysis in Cognitive Radio-Aided NOMA Network: An Application to Vehicle-to-Everything Communications. Wireless Pers Commun 120, 1975–2000 (2021). https://doi.org/10.1007/s11277-021-08273-x
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DOI: https://doi.org/10.1007/s11277-021-08273-x