数据采集与处理  2018, Vol. 33 Issue (4): 732-739 PDF

1. 南京航空航天大学江苏省物联网与控制技术重点实验室, 南京, 211106;
2. 英国赫瑞瓦特大学工程与物理科学学院, 爱丁堡, EH14 4AS

Propagation Loss and Performance Evaluation of UAV Relay Link
Hu Xujun1, Chen Xiaomin1, Zhu Qiuming1,2, Zhu Mengqing1, Chen Bing1
1. Jiangsu Key Laboratory of Internet of Things and Control Technologies, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China;
2. School of Engineering & Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK
Abstract: For the dual-hop relay system of unmanned aerial vehicle (UAV), a propagation loss model of dual-hop relay link is established. The influence of fuselage feature, antenna characteristics, climate condition and channel fading are considered. Based on the model, the calculating methods of propagation loss are analyzed. Then the statistical characteristics of propagation loss with random fluctuation caused by composite fading including shadowing and multipath fading are derived. Furthermore, the theoretical expression of the outage probability and bit error rate (BER) of dual-hop UAV relay system is developed. Finally, through the numerical simulations in urban, mountainous and sea, the theoretical results accuracy obtained is verified and the impact of flight altitude, ground node position and communication scenarios on the performance of the dual-hop relay system is discussed.
Key words: unmanned aerial vehicle (UAV)    relay link    channel fading    propagation loss    outage probability

1 系统模型 1.1 无人机中继网络模型

 图 1 无人机中继系统典型场景 Fig. 1 Dual-hop UAV relay system

 $\varphi ' = \left\{ {\begin{array}{*{20}{c}} \begin{array}{l} {\varphi ''}\\ {\rm{ \mathsf{ π} }} - \varphi ''\\ - {\rm{ \mathsf{ π} }} - \varphi '' \end{array}&\begin{array}{l} 其他\\ \varphi '' > 0,{Y_2} < 0, - {\rm{ \mathsf{ π} }} \le \varphi ' \le {\rm{ \mathsf{ π} }}\\ \varphi '' < 0,{Y_2} < 0 \end{array} \end{array}} \right.$ (1)

 $\begin{array}{*{20}{c}} {\varphi '' = \arcsin \left( {\frac{{{Z_2}}}{{\sqrt {Y_2^2 + Z_2^2} }}} \right)}&{ - {\rm{ \mathsf{ π} /2}} \le \varphi '' \le {\rm{ \mathsf{ π} /2}}} \end{array}$ (2)

dR1R2在载体坐标系中的俯仰角θ′可表示为

 $\begin{array}{*{20}{c}} {\theta ' = \arccos \left( {\frac{{{X_2}}}{{\left| {{\mathit{\boldsymbol{d}}_{{R_1}{R_2}}}} \right|}}} \right) = \arccos \left( {\frac{{{X_2}}}{{\sqrt {X_2^2 + Y_2^2 + Z_2^2} }}} \right)}&{0 \le \theta ' \le {\rm{ \mathsf{ π} }}} \end{array}$ (3)
1.2 中继链路传播损耗

 $P_r^{{N_2}} = P_t^{{N_1}}G_t^{{N_1}}G_r^{{N_2}}G_r^{{R_1}}G_t^{{R_1}}G_r^{{R_2}}G_t^{{R_2}}A_F^{{R_1}}A_F^{{R_2}}{L_f}{L_R}\alpha _{{N_1}}^{{R_1}}\alpha _{{N_2}}^{{R_2}}$ (4)

 $P_r^{{N_2}} = P_t^{{N_1}}{G_D}\alpha$ (5)

2 中继链路传播损耗分析 2.1 传播损耗均值

 ${G_D} = G_t^{{N_1}}G_r^{{N_2}}G_r^{{R_1}}G_t^{{R_1}}G_r^{{R_2}}G_t^{{R_2}}A_F^{{R_1}}A_F^{{R_2}}{L_f}{L_R}$ (6)

 $L = {\left( {\frac{{4{\rm{ \mathsf{ π} }}f}}{c} \cdot D} \right)^2}$ (7)

 $A = {\gamma _R}{L_E}$ (8)

 $G = \eta * D = \eta * \frac{{4{\rm{ \mathsf{ π} }}}}{{\int_0^{2{\rm{ \mathsf{ π} }}} {\int_0^{\rm{ \mathsf{ π} }} {{F^2}\left( {\theta ,\varphi } \right)\sin \theta {\rm{d}}\theta {\rm{d}}\varphi } } }}$ (9)

 图 2 中继链路相对传播损耗均值 Fig. 2 Relative mean of propagation loss of relay link

2.2 传播损耗衰落特性

 ${f_\beta }\left( x \right) = \frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} {\sigma _x}x}}\exp \left[ { - \frac{{{{\left( {\ln x - \ln \bar P} \right)}^2}}}{{2\sigma _x^2}}} \right]$ (10)

 ${f_\gamma }\left( x \right) = \frac{2}{{\mathit{\Gamma }\left( m \right)}}{\left( {\frac{m}{\mathit{\Omega }}} \right)^m}{x^{2m - 1}}{{\rm{e}}^{ - \frac{m}{\mathit{\Omega }}{x^2}}}$ (11)

 $\alpha = \alpha _{{N_1}}^{{R_1}}\alpha _{{N_2}}^{{R_2}} = {\beta _1}\gamma _1^2{\beta _2}\gamma _2^2$ (12)

 $\begin{array}{*{20}{c}} {f\left( x \right) = \int_0^\infty {{f_{{\gamma _i}}}\left( {x\left| \mathit{\Omega } \right.} \right){f_{{\beta _i}}}\left( y \right){\rm{d}}y} }&{i = 1,2} \end{array}$ (13)

 ${f_{\hat \beta }}\left( x \right) = \frac{{{x^{{m_{\rm{s}}} - 1}}}}{{\mathit{\Gamma }\left( {{m_{\rm{s}}}} \right){{\left( {{\mathit{\Omega }_{\rm{s}}}/{m_{\rm{s}}}} \right)}^{{m_{\rm{s}}}}}}}{{\rm{e}}^{ - x/\left( {{\mathit{\Omega }_{\rm{s}}}/{m_{\rm{s}}}} \right)}}$ (14)

 $\begin{array}{l} {m_{\rm{s}}} = 1/\left( {{{\rm{e}}^{\sigma _x^2}} - {\rm{1}}} \right)\\ {\mathit{\Omega }_{\rm{s}}} = \bar P{{\rm{e}}^{\sigma _x^2/2}} \end{array}$ (15)

 $\begin{array}{*{20}{c}} {{f_{\alpha _{{N_i}}^{{R_i}}}}\left( x \right) = \frac{4}{{\mathit{\Gamma }\left( {{m_i}} \right)\mathit{\Gamma }\left( {{m_{si}}} \right)}}{{\left( {\frac{{{m_i}{m_{si}}}}{{{\mathit{\Omega }_{si}}}}} \right)}^{\frac{{{m_i} + {m_{si}}}}{2}}} \cdot {x^{{m_i} + {m_{si}} - 1}}{K_{{m_{si}} - {m_i}}}\left( {2x\sqrt {\frac{{{m_i}{m_{si}}}}{{{\mathit{\Omega }_{si}}}}} } \right)}&{i = 1,2} \end{array}$ (16)

 $\begin{array}{*{20}{c}} {{M_{\alpha _{{N_i}}^{{R_i}}}}\left( s \right) = \int_0^\infty {\exp \left( { - s{y_i}} \right){f_{\alpha _{{N_i}}^{{R_i}}}}\left( {{y_i}} \right){\rm{d}}{y_i}} }&{i = 1,2} \end{array}$ (17)

 $\begin{array}{*{20}{c}} {{M_\alpha }\left( s \right) = \int_0^\infty {\int_0^\infty {\exp \left( { - s{y_1}{y_2}} \right){f_{\alpha _{{N_1}}^{{R_1}}}}\left( {{y_1}} \right){f_{\alpha _{{N_2}}^{{R_2}}}}\left( {{y_2}} \right){\rm{d}}{y_1}{\rm{d}}{y_2}} } = \frac{{1/\sqrt {\rm{ \mathsf{ π} }} }}{{\mathit{\Gamma }\left( {{m_1}} \right)\mathit{\Gamma }\left( {{m_{{s_1}}}} \right)\mathit{\Gamma }\left( {{m_2}} \right)\mathit{\Gamma }\left( {{m_{{s_2}}}} \right)}} \cdot }\\ {G_{2,4}^{4,2}\left( {\frac{{4{m_1}{m_{s1}}{m_2}{m_{s2}}}}{{{\mathit{\Omega }_{{s_1}}}{\mathit{\Omega }_{{s_2}}}{s^2}}}\left| \begin{array}{l} 1,1/2\\ {m_{{s_1}}},{m_1},{m_{{s_2}}},{m_2} \end{array} \right.} \right)} \end{array}$ (18)

 ${f_\alpha }\left( x \right) = {L^{ - 1}}\left[ {{M_\alpha }\left( s \right);x} \right] = \frac{2}{{x\mathit{\Gamma }\left( {{m_1}} \right)\mathit{\Gamma }\left( {{m_{{s_1}}}} \right)\mathit{\Gamma }\left( {{m_2}} \right)\mathit{\Gamma }\left( {{m_{{s_2}}}} \right)}} \cdot G_{0,4}^{4,0}\left( {\frac{{{m_1}{m_{s1}}{m_2}{m_{s2}}}}{{{\mathit{\Omega }_{{s_1}}}{\mathit{\Omega }_{{s_2}}}}}{x^2}\left| {\begin{array}{*{20}{c}} - \\ {{m_{{s_1}}},{m_1},{m_{{s_2}}},{m_2}} \end{array}} \right.} \right)$ (19)

 $R = \frac{{P_t^{{N_1}}{G_D}}}{{{N_0}}}{X^2}$ (20)

 ${f_R}\left( r \right) = \frac{1}{{r\mathit{\Gamma }\left( {{m_1}} \right)\mathit{\Gamma }\left( {{m_{{s_1}}}} \right)\mathit{\Gamma }\left( {{m_2}} \right)\mathit{\Gamma }\left( {{m_{{s_2}}}} \right)}} \cdot G_{0,4}^{4,0}\left( {\frac{{{m_1}{m_{{s_1}}}{m_2}{m_{{s_2}}}}}{{\bar R}}r\left| {\begin{array}{*{20}{c}} - \\ {{m_{{s_1}}},{m_1},{m_{{s_2}}},{m_2}} \end{array}} \right.} \right)$ (21)

 $\bar R = \frac{{P_t^{{N_1}}{G_D}}}{{{N_0}}}{\mathit{\Omega }_{{s_1}}}{\mathit{\Omega }_{{s_2}}}$ (22)

 图 3 不同场景瞬时信噪比分布 Fig. 3 Instantaneous SNR under different scenarios

2.3 衰落特性对系统性能的影响

 ${P_{{\rm{out}}}} = \int_0^{{r_0}} {{f_R}\left( r \right){\rm{d}}r}$ (23)

 ${P_{{\rm{out}}}} = \frac{1}{{\mathit{\Gamma }\left( {{m_1}} \right)\mathit{\Gamma }\left( {{m_{{s_1}}}} \right)\mathit{\Gamma }\left( {{m_2}} \right)\mathit{\Gamma }\left( {{m_{{s_2}}}} \right)}} \cdot G_{1,5}^{4,1}\left( {\frac{{{m_1}{m_{{s_1}}}{m_2}{m_{{s_2}}}}}{{\bar R}}{r_0}\left| {\begin{array}{*{20}{c}} 1\\ {{m_{{s_1}}},{m_1},{m_{{s_2}}},{m_2},0} \end{array}} \right.} \right)$ (24)

 $\overline {{P_{\rm{e}}}} = \int_0^\infty {{P_{\rm{e}}}\left( r \right){f_R}\left( r \right){\rm{d}}r}$ (25)

 ${P_{\rm{e}}}\left( r \right) = \frac{1}{{2\sqrt {\rm{ \mathsf{ π} }} }}G_{1,2}^{2,0}\left( {r\left| {\begin{array}{*{20}{c}} 1\\ {0,1/2} \end{array}} \right.} \right)$ (26)

 $\overline {{P_{\rm{e}}}} = \frac{1}{{\mathit{2}\sqrt {\rm{ \mathsf{ π} }} \mathit{\Gamma }\left( {{m_1}} \right)\mathit{\Gamma }\left( {{m_{{s_1}}}} \right)\mathit{\Gamma }\left( {{m_2}} \right)\mathit{\Gamma }\left( {{m_{{s_2}}}} \right)}} \cdot G_{2,5}^{4,2}\left( {\frac{{{m_1}{m_{{s_1}}}{m_2}{m_{{s_2}}}}}{{\bar R}}\left| {\begin{array}{*{20}{c}} {1,1/2}\\ {{m_{{s_1}}},{m_1},{m_{{s_2}}},{m_2},0} \end{array}} \right.} \right)$ (27)
3 数值仿真与验证

 图 4 不同信噪比门限接收机中断概率与飞行高度关系 Fig. 4 Outage probability of receivers with diffe rent SNR thresholds at different altitudes

 图 5 不同场景中断概率与飞行高度关系 Fig. 5 Ou tage probability under different scenarios at different altitudes

 图 6 不同场景平均误比特率与飞行高度关系 Fig. 6 ABER under different scenarios at different altitudes

4 结束语