Performance Analysis for UAV-Assisted mmWave Cellular Networks

Abstract

It is feasible to increase coverage area and throughout with unmanned aerial vehicle (UAV), as an assist to ground base station (GBS). In this paper, a 3-dimension (3-D) channel model, where UAVs are modeled by 3-D Poisson point process (PPP) and GBSs are modeled by 2-dimension (2-D) PPP, is proposed. Different path loss model for line-of-sight (LOS), non-LOS (NLOS) links and directional beamforming are considered. Moreover, the general expressions for signal-to-interference-plus-noise ratio (SINR) coverage probabilities, user throughput and area spectral efficiency (ASE) are derived. Our numerical and simulation results show that with the proposed 3-D channel model, the coverage probability of mmWave networks is greatly improved compared with sub-6GHz networks. Furthermore, the effects of the beamwidth of the main lobe, the main lobe directivity gain and UAV density on the performance of mmWave networks are analyzed.

Supported by the Natural Science Foundation of Chongqing, China, under the grant number cstc2019jcyj-msxmX0602.

A Appendix

The total interference from the BSs in $k^{th}$ tier received by the typical UE can be expressed as

$$\begin{aligned} I_{j,k}^\varepsilon = I_{j,k}^{\varepsilon ,{M_b}{M_u}} + I_{j,k}^{\varepsilon ,{M_b}{m_u}} + I_{j,k}^{\varepsilon ,{m_b}{M_u}} + I_{j,k}^{\varepsilon ,{m_b}{m_u}} = \sum \limits _G {I_{j,k}^{\varepsilon ,G}} \end{aligned}$$

(27)

where $G \in \left\{ {{M_b}{M_u},{M_b}{m_u},{m_b}{M_u},{m_b}{m_u}} \right\}$. Therefore, the Laplace transform of the interference that the typical UE receives from the $k^{th}$ tier can be expressed as

$$\begin{aligned} {\mathcal{L}_{I_{j,k}^\varepsilon }}\left( {{\mu _{j,s}}} \right) = \mathbb {E} \left[ {{e^{ - {\mu _{j,s}}\sum \limits _G {I_{j,k}^{\varepsilon ,G}} }}} \right] = \prod \limits _G {{\mathcal{L}_{I_{j,k}^{\varepsilon ,G}}}\left( {{\mu _{j,s}}} \right) } \end{aligned}$$

(28)

The Laplace transform of the interference from LOS or NLOS UAV with antenna gain G received by the typical UE can be calculated as

$$\begin{aligned} \begin{aligned} {\mathcal{L}_{I_{j,U}^{\varepsilon ,G}}}\left( {{\mu _{j,s}}} \right)&= {\mathbb {E}_{\varPhi _U^\varepsilon ,{h_i}}}\left[ {\exp \left( { - {\mu _{j,s}}\sum \limits _{i \in \varPhi _U^\varepsilon } {{P_U}{h_i}{G_i}L_i^{ - 1}} } \right) } \right] \\&\mathop = \limits ^{\left( a \right) } \exp \left( { - {\lambda _U}{p_G}\int _{{R^3}} {\left( {1 - {\mathbb {E}_{{h_i}}}\left[ {\exp \left( { - {\mu _{j,s}}{P_U}{h_i}{G_i}L_i^{ - 1}} \right) } \right] } \right) dx} } \right) \\&\mathop = \limits ^{(b)} \exp \left( { - 2\pi {\lambda _U}{p_G}\int _{Q_{Uj}^{s\varepsilon }\left( r \right) }^\infty {\left( {1 - \frac{1}{{{{\left( {1 + {\mu _{j,s}}{P_U}{G_i}L_i^{ - 1}N_\varepsilon ^{ - 1}} \right) }^{{N_\varepsilon }}}}}} \right) } } \right. \\&\left. { \quad \quad \quad \quad \quad \times p_U^\varepsilon \left( {\arctan \left( x \right) } \right) \cos \left( {\arctan \left( x \right) } \right) \frac{{{x^2}}}{{1 + {x^2}}}dx} \right) \end{aligned} \end{aligned}$$

(29)

where (a) follows from the probability generating functional (PGFL) of the PPP, and (b) is obtained by MGF of the gamma random variable h.

Similarly, the Laplace transform of the interference from LOS or NLOS GBS with antenna gain G received by the typical UE can be calculated as

$$\begin{aligned} \begin{aligned} {\mathcal{L}_{I_{j,G}^{\varepsilon ,G}}}\left( {{\mu _{j,s}}} \right) = \exp&\left( { - 2\pi {\lambda _G}{p_G}\int _{Q_{Gj}^{s\varepsilon }\left( r \right) }^\infty } \right. \\&\ \ \ \times \left. {\left( {1 - \frac{1}{{{{\left( {1 + {\mu _{j,s}}{P_G}{G_i}L_i^{ - 1}N_\varepsilon ^{ - 1}} \right) }^{{N_\varepsilon }}}}}} \right) p_G^\varepsilon \left( {{y}} \right) {y}d{y}} \right) \end{aligned} \end{aligned}$$

(30)

By combining (29) and (30), (20) can be obtained.