Linear Multi-Hop Wireless Network Design with Directional Antenna

Directional antennas can synergize with suitable network structure to complement each other in multi-hop wireless networks. This work addresses the combination of directional transmission and network structure to improve the capacity. Firstly, Z-chain structure considering the antenna radiation pattern is proposed, which is consistent with the best chain structure obtained by exhaustive search. Secondly, theoretical analysis indicates that spectral efficiency <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\eta_{S}$</tex> behaves as a sigmoid function of node density <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\rho$</tex>, with its asymptotic value increasing as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Theta\left[\log \left(G_{r} \sin ^{2} \theta\right)\right]\left(\theta \leq \theta^{*}\right)$</tex> for large values of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$G_{r}$</tex>, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$G_{r}$</tex> denotes the relative antenna gain, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\theta^{*}$</tex> is a function of the antenna beam width and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2 \theta$</tex> is the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{Z}$</tex>-chain link angle. Thirdly, energy efficiency and consumption is assessed from a traffic load perspective. The findings reveal that the Z-chain network can accommodate higher data traffic compared to conventional frequency reuse method and straight structure. Experiments conducted using OMNeT++ validate above conclusions.