Abstract
Recently, academia and industry have shown keen interest in achieving ultra-reliable and low latency communication (URLLC) through short-packet communication to meet the strict demands concerning high reliability and latency for 5G and beyond applications. Un-manned aerial vehicle (UAV) has caught attention recently because of its cost, air time, and mobility, whereas, the non-orthogonal multiple access (NOMA) technique has proven effective in dense user network. Hence, a UAV based system with NOMA has been studied in this paper for remote coverage. In this system, devices communicate to the base station (BS) through a UAV relay where direct link from devices to BS is absent. As UAV has direct line of sight (LOS) to the remote devices, hence, all the analysis is done over a Rician fading channel. In this work, a closed-form expression of average block error rate (BLER) has been formulated for the given system model, which is used as performance metric to analyse the system performance. Moreover, exact BLER expression facilitates in optimization with partial channel state information (CSI) only, which reduces the latency and complexity. Furthermore, we derive an asymptotic expression for BLER in high signal to noise (SNR) regime. Also, a blocklength minimization problem is formulated and optimized with reliability constraints. Simulation results are presented to verify analytical work, as well as comparison of the results with orthogonal multiple access scheme are also shown.
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Appendices
Appendix 1: Derivation of instantaneous BLER
Let \(\theta _i^O\) denote the event that block destined to device i, where \(i\epsilon \{1,2\}\) is decoded in error at location O, where \(O\epsilon \{uav,D1,D2\}\). In addition, \({\overline{\theta }}_i^O\) denote the complement of \(\theta _i^O\), i.e. \({\overline{\theta }}_i^O=1-\theta _i^O\). The error probability is given by Eq. (3) as
where \(N_i\) denotes the number of message bits destined to device Di, and \(m_p\) denotes the pth phase blocklength, where \(p\epsilon \{1,2\}\). Instantaneous probability of error in decoding of message \(x_1\) at the uav is given by
where SINR \(\gamma _1^{uav}\) is given by Eq. (7a). Further, UAV performs SIC and decodes second message \(x_2\). Since, decoding of message \(x_2\) correctly depends on wether the message \(x_1\) was decoded correctly or not, hence, the total instantaneous probability of decoding message \(x_2\) at UAV in error, is given by
Due to SIC, it is impossible to decode \(x_2\) correctly when \(x_1\) was decoded in error. Therefore, \(P\left( \theta _2^{uav}\mid \theta _1^{uav}\right) \) is assumed to be 1. So from Eq. (34), the Eq. (36) can be expressed as
since under URLLC scenario errors are very small to the order of \(10^{-5}\), hence term \({\epsilon r}_1^{uav}{\epsilon r}_2^{uav}\) can be neglected without compromising the Eq. (37) and total instantaneous probability of \(x_2\) at UAV (\(\epsilon _2^{uav}\)) can be expressed as:
By using Eq. (3), \(\epsilon _1^{uav}\) and \( \epsilon _2^{uav} \)can be expressed as
and,
i.e.
Appendix 2: Proof of Eq. (24)
The proof of Eq. (24) is as follow:
By Eq. (23)
and by Eq. (14)
By Eqs. (41) and (18), (42) can be expressed as:
Both terms in Eq. (43) can be separately simplified. First term of the above expression indicating decoding error of \(x_1\) at UAV. Hence, \({E}\left( \ \epsilon r_1^{uav}\right) \) can be evaluated as follows:
Let \(I_1\) denote the integral in Eq. (45). Then
performing the following substitution \(\ t=\frac{\left( B^{uav}\right) z}{c_1-c_2z}\), integral’s new limits are evaluated as:
where \(B^{uav}=\frac{K_{b}+1}{\beta _ub}\).Therefore, the Eq. (46) is written as:
Using integral by parts Eq. (47) can be written as
Performing the following substitution and applying binomial expansion, \(B_{uav}+c_2t=x\),
by using equation (3.381) of [61] Eq. (49) can be evaluated as:
Here \(\Gamma \left( c,d\right) \) denotes the upper incomplete Gamma function, substituting \(l_1\) and \(l_2\) in (49), and writing equation in terms of lower gamma function yields
Substituting \(I_1\) in (45) and following the same procedure for the derivation of second term in Eq. (43) completes the proof.
Appendix 3: Proof of high SNR approximation given by Eq. (26)
The derivation of the expression is as follows: by Eq. (23), the CDF is given as
using equation (8.354.1) of [61], series expansion of incomplete lower gamma function can be written as
If \(t\ll 1\), only the first term dominates
Hence, for D1 \(z<\Delta _1^{D1}\),
From Eq. (53), \({E}\left( \epsilon ^{D1}\right) \) is expressed as:
employing equation (3.194.1) from [61], the proof is complete.
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Thapliyal, S., Pandey, R. & Charan, C. Analysis of NOMA based UAV assisted short-packet communication system and blocklength minimization for IoT applications. Wireless Netw 28, 2695–2712 (2022). https://doi.org/10.1007/s11276-022-02996-w
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DOI: https://doi.org/10.1007/s11276-022-02996-w