Optimal Beam Design for UAV Emergency Communication Network

Jingmin Tang; Simiao Liu; Jie Wang

doi:10.3788/LOP202158.2106006

Journals >Laser & Optoelectronics Progress >Volume 58 >Issue 21 >Page 2106006 > Article

Laser & Optoelectronics Progress
Vol. 58, Issue 21, 2106006 (2021)

Optimal Beam Design for UAV Emergency Communication Network

Jingmin Tang, Simiao Liu^*, and Jie Wang

Author Affiliations

School of Information Engineering and Automation, Kunming University of Science and Technology, Kunming , Yunnan 650500China

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DOI: 10.3788/LOP202158.2106006 Cite this Article Set citation alerts

Jingmin Tang, Simiao Liu, Jie Wang. Optimal Beam Design for UAV Emergency Communication Network[J]. Laser & Optoelectronics Progress, 2021, 58(21): 2106006 Copy Citation Text

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Abstract

Aiming at the problem of limited power consumption and battery capacity in unmanned aerial vehicle(UAV)-assisted multi-user multiple input multiple output (MU-MIMO) emergency communication networks, a method is proposed for power-constrained conditions. The design of beamforming to maximize the total transmission rate of the system is optimized. First, a method for easy determination of UAV position without iteration is proposed. Second, considering that the problem is non-convex, the first-order Taylor approximation is used to approximate it convexly. The second-order cone programming (SOCP) reduces the computational complexity and solves the best beamforming vector. The simulation results show that the proposed method is suitable for multi-user communication systems. Although the interference cannot be reset to zero during the simulation process, the system's total transmission rate can be maximized by suppressing the interference.

Keywords

beamforming multiple input multiple output optical communications second-order cone programming unmanned aerial vehicle

h_{k} = \sqrt[]{N β_{0} d_{k}^{- α}} a (θ_{k})

，（1）

a (θ_{k}) = \frac{{[1, e x p (j 2 π \frac{d}{λ} {\hat{θ}}_{k}), e x p (j 2 π \frac{2 d}{λ} {\hat{θ}}_{k}), \dots, e x p [j 2 π \frac{d (N - 1)}{λ} {\hat{θ}}_{k}]]}^{T}}{\sqrt[]{N}}

，（2）

\begin{array}{l}  \end{array}

(1)

y = H^{H} W s + n

，（3）

y_{k} = h_{k}^{H} w_{k} s_{k} + \sum_{i \in Γ a n d i \neq k} h_{k}^{H} w_{i} s_{i} + n_{k}

。（4）

R_{k} = \frac{{|h_{k}^{H} w_{k}|}^{2}}{\sum_{i \in Γ a n d i \neq k} {|h_{k}^{H} w_{i}|}^{2} + σ_{n}^{2}}

，（5）

\begin{matrix} \underset{w_{1}, w_{2}, \dots, w_{K}}{m a x} & f (R_{1}, R_{2}, \dots, R_{K}) \end{matrix}

，

(1)

s . t . \begin{matrix} R_{k} \end{matrix} \geq r_{k} \begin{matrix} , & \forall k = 1,2, \dots, K \end{matrix}, \sum_{k = 1}^{K} {‖w_{k}‖}^{2} \leq P_{t o t a l}

，（6）

\begin{matrix} \underset{x_{u}, y_{u}}{m i n} & \sum_{k = 1}^{K} {(x_{u} - x_{k})}^{2} \end{matrix} + {(y_{u} - y_{k})}^{2}

，

(1)

\begin{matrix} s . t . & x_{m i n} \leq x_{u} \end{matrix} \leq x_{m a x}, y_{m i n} \leq y_{u} \leq y_{m a x}

，（7）

\frac{\partial \sum_{k = 1}^{K} {(x_{u} - x_{k})}^{2} + {(y_{u} - y_{k})}^{2}}{\partial x_{u}} = 2 K x_{u} - 2 \sum_{k = 1}^{K} x_{k}

，（8）

\frac{\partial \sum_{k = 1}^{K} {(x_{u} - x_{k})}^{2} + {(y_{u} - y_{k})}^{2}}{\partial y_{u}} = 2 K y_{u} - 2 \sum_{k = 1}^{K} y_{k}

。（9）

(x_{u}, y_{u}) = (\frac{\sum_{k = 1}^{K} x_{k}}{K}, \frac{\sum_{k = 1}^{K} y_{k}}{K})

。（10）

\begin{matrix} \underset{w_{1}, w_{2}, \dots, w_{K}}{m a x} & \sum_{k = 1}^{K} l b q_{k} \end{matrix}

，

(1)

s . t . \frac{{|h_{k}^{H} w_{k}|}^{2}}{\sum_{i \in Γ a n d i \neq k} {|h_{k}^{H} w_{i}|}^{2} + σ_{n}^{2}} \geq q_{k} - 1, \forall k = 1,2, \dots, K, \sum_{k = 1}^{K} {‖w_{k}‖}^{2} \leq P_{t o t a l}

，（11）

\begin{matrix} \underset{w_{1}, w_{2}, \dots, w_{K}}{m a x} & \prod_{k = 1}^{K} q_{k} \end{matrix}

，

(1)

s . t . \frac{{|h_{k}^{H} w_{k}|}^{2}}{q_{k} - 1} \geq \sum_{i \in Γ a n d i \neq k} {|h_{k}^{H} w_{i}|}^{2} + σ_{n}^{2}, \forall k = 1,2, \dots, K, \sum_{k = 1}^{K} {‖w_{k}‖}^{2} \leq P_{t o t a l}

。（12）

n (w, x, \bar{w}, \bar{x}) = n (\bar{w}, \bar{x}) + \frac{\partial n (\bar{w}, \bar{x})}{\partial x} (x - \bar{x}) + \frac{\partial n (\bar{w}, \bar{x})}{\partial w} (w - \bar{w})

，（13）

n (w, x, \bar{w}, \bar{x}) = \frac{a \bar{w} {\bar{w}}^{H} a^{H}}{\bar{x} - y} - \frac{a \bar{w} {\bar{w}}^{H} a^{H} (x - \bar{x})}{{(\bar{x} - y)}^{2}} + \frac{2 {\bar{w}}^{H} a a^{H} w}{\bar{x} - y} - \frac{2 {\bar{w}}^{H} a a^{H} \bar{w}}{\bar{x} - y}

，（14）

\begin{array}{l} n (w, x, \bar{w}, \bar{x}) = \frac{a \bar{w} {\bar{w}}^{H} a^{H}}{\bar{x} - y} - \frac{a \bar{w} {\bar{w}}^{H} a^{H}}{{(\bar{x} - y)}^{2}} (x - \bar{x}) + \frac{2 {\bar{w}}^{H} a a^{H} w}{\bar{x} - y} - \frac{2 {\bar{w}}^{H} a a^{H} \bar{w}}{\bar{x} - y} = \\ \frac{2 {\bar{w}}^{H} a a^{H} w}{\bar{x} - y} + \frac{{\bar{w}}^{H} a a^{H} \bar{w}}{\bar{x} - y} - \frac{{\bar{w}}^{H} a a^{H} \bar{w}}{{(\bar{x} - y)}^{2}} (x - \bar{x}) - \frac{2 {\bar{w}}^{H} a a^{H} \bar{w}}{\bar{x} - y} = \\ \frac{2 {\bar{w}}^{H} a a^{H} w}{\bar{x} - y} - \frac{{\bar{w}}^{H} a a^{H} \bar{w}}{{(\bar{x} - y)}^{2}} (x - \bar{x}) - \frac{{\bar{w}}^{H} a a^{H} \bar{w}}{{(\bar{x} - y)}^{2}} (\bar{x} - y) = \frac{2 {\bar{w}}^{H} a a^{H} w}{\bar{x} - y} - \frac{{\bar{w}}^{H} a a^{H} \bar{w}}{{(\bar{x} - y)}^{2}} (x - y) \end{array}

。（15）

n (w, q_{k}, \bar{w}, {\bar{q}}_{k}) = \frac{2 {\bar{w}}_{k}^{H} h_{k}^{H} h_{k} w_{k}}{{\bar{q}}_{k} - 1} - \frac{{\bar{w}}_{k}^{H} h_{k}^{H} h_{k} {\bar{w}}_{k}}{({\bar{q}}_{k} {- 1)}^{2}} (q_{k} - 1)

。（16）

w^{2} \leq x y, x \geq 0, y \geq 0 \Leftrightarrow ‖{[\begin{matrix} 2 w \\ x - y \end{matrix}]}^{*}‖ \leq x + y

。（17）

\begin{matrix} \underset{w_{k}, q_{k}}{m a x} & δ^{(0)} \end{matrix}

，

(1)

\begin{matrix} s . t . & ‖{[2 δ_{j}^{(p - 1)}, (q_{2 j - 1} - q_{2 j})]}^{H}‖ \end{matrix} \leq q_{2 j - 1} + q_{2 j} \begin{matrix} , & j = 2^{0}, 2^{1}, \dots \end{matrix}, 2^{p - 1}

，

(1)

\begin{matrix} ‖{[2 δ_{j}^{(p - 2)}, (δ_{2 j - 1}^{(p - 1)} - δ_{2 j}^{(p - 1)})]}^{H}‖ \leq δ_{2 j - 1}^{(p - 1)} + δ_{2 j}^{(p - 1)}, & j = 2^{0}, 2^{1}, \dots \end{matrix}, 2^{p - 2}

，

(1)

⋮

(1)

‖{[2 δ_{}^{(0)}, (δ_{1}^{(1)} - δ_{2}^{(1)})]}^{H}‖ \leq δ_{1}^{(1)} + δ_{2}^{(1)}, j = 1 。

（18）

\begin{matrix} s . t . {‖{[2 w_{1}^{H} h_{k}, 2 w_{2}^{H} h_{k}, \dots, 2 w_{i}^{H} h_{k}, n (w, q_{k}, \bar{w}, {\bar{q}}_{k}) - 1]}^{H}‖}^{2} \leq n (w, q_{k}, \bar{w}, {\bar{q}}_{k}) + 1, k \in Γ, \\ i \in Γ a n d i \neq k, {‖{[w_{1}^{H}, w_{2}^{H}, \dots, w_{K}^{H}]}^{H}‖}^{2} \leq \sqrt[]{P_{t o t a l}} 。 \end{matrix}

（19）

Jingmin Tang, Simiao Liu, Jie Wang. Optimal Beam Design for UAV Emergency Communication Network[J]. Laser & Optoelectronics Progress, 2021, 58(21): 2106006

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