Target Capacity Based Power Allocation Scheme in Radar Network
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摘要: 针对现有网络化雷达功率资源利用率低的问题，该文提出一种基于目标容量的功率分配(TC-PA)方案以提升保精度跟踪目标个数。TC-PA方案首先将网络化雷达功率分配模型制定为非光滑非凸优化问题；而后引入Sigmoid函数将原问题松弛为光滑非凸优化问题；最后运用近端非精确增广拉格朗日乘子法(PI-ALMM)对松弛后的非凸问题进行求解。仿真结果表明，PI-ALMM对于求解线性约束非凸优化问题可以较快地收敛到一个稳态点。另外，相比传统功率均分方法和遗传算法，所提TC-PA方案可以最大限度地提升目标容量。Abstract: In view of the fact that low power resource utilization rate exists in radar network, a Target Capacity based Power Allocation (TC-PA) scheme is proposed to increase the number of the targets that satisfy tracking accuracy requirements. Firstly, this scheme formulates the power allocation model of radar network as a non-smooth and non-convex optimization problem. Then the original problem is relaxed into a smooth and non-convex problem through introducing Sigmoid function. Finally, the relaxed non-convex problem is solved by utilizing the Proximal Inexact Augmented Lagrangian Multiplier Method (PI-ALMM). Simulation results show that the PI-ALMM can quickly converge to a stationary point for solving the non-convex optimization problem with linear constraints. Moreover, the proposed TC-PA scheme outperforms the traditional uniform power allocation method and genetic algorithm, in terms of target capacity.
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Key words:
- Radar network /
- Multiple target tracking /
- Resource allocation /
- Non-convex optimization
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表 1 PI-ALMM求解流程
(1) 初始化参数$\rho > 0$,$\alpha > 0$, $0 < c \le {1 / {\bar L}}$, $\ell > - \tau $, $0 < \beta \le 1$，及迭代下标$j = 0$； (2) 初始化变量${\boldsymbol{p}}_{q,k}^j{\rm{ = }}{\left( {{{{{p}}_{{\rm{total}}}^1} / {Q{{,{{p}}_{{\rm{total}}}^2} / Q}{{, ··· ,{{p}}_{{\rm{total}}}^N} / Q}}}} \right)^{\rm{T}}}$, 令${\boldsymbol{p}}_k^j = \left( {{\boldsymbol{p}}_{1,k}^j;{\boldsymbol{p}}_{2,k}^j; ··· ;{\boldsymbol{p}}_{Q,k}^j} \right)$, ${\boldsymbol{b}}_k^j{\rm{ = }}{\boldsymbol{p}}_k^j$及${\boldsymbol{a} }_k^j{\rm{ = } }{ {{{\textit{0}}} }_{N \times 1} }$； (3) 计算$L\left( {{{\boldsymbol{p}}_k},{{\boldsymbol{b}}_k};{{\boldsymbol{a}}_k}} \right)$关于${{\boldsymbol{p}}_k}$的梯度 $\begin{array}{l} { {\text{∇} }_{ { {\boldsymbol{p} }_k} } }L\left( { { {\boldsymbol{p} }_k},{ {\boldsymbol{b} }_k};{ {\boldsymbol{a} }_k} } \right) = { {\nabla }_{ { {\boldsymbol{p} }_k} } }f\left( { { {\boldsymbol{p} }_k} } \right) + { {\boldsymbol{A} }^{\rm{T} } }{ {\boldsymbol{a} }_k} + \rho { {\boldsymbol{A} }^{\rm{T} } } \\ \begin{array}{*{20}{c} } {}&{}&{} \end{array}\left( { {\boldsymbol{A} }{ {\boldsymbol{p} }_k} - { {\boldsymbol{p} }_{ {\rm{total} } } } } \right) + \ell \left( { { {\boldsymbol{p} }_k} - { {\boldsymbol{b} }_k} } \right) \end{array}d{array}$； (4) 循环 (a) ${\boldsymbol{a}}_k^{j + 1} = {\boldsymbol{a}}_k^j + \alpha \left( {A{\boldsymbol{p}}_k^j - {{\boldsymbol{p}}_{{\rm{total}}}}} \right)$； (b) ${\boldsymbol{p} }_k^{j + 1} = {\left[ { {\boldsymbol{p} }_k^j - c \cdot { \nabla_{ {\boldsymbol{p} }_k^j} }L\left( { {\boldsymbol{p} }_k^j,{\boldsymbol{b} }_k^j;{\boldsymbol{a} }_k^{j + 1} } \right)} \right]_ + }$； (c) ${\boldsymbol{b}}_k^{j + 1} = {\boldsymbol{b}}_k^j + \beta \left( {{\boldsymbol{p}}_k^{j + 1} - {\boldsymbol{b}}_k^j} \right)$； (d) $j = j + 1$； (5) 直到$\left| {f\left( {{\boldsymbol{p}}_k^j} \right) - f\left( {{\boldsymbol{p}}_k^{j - 1}} \right)} \right| \le \varepsilon $($\varepsilon $为给定算法终止门限)，退
出循环，令功率分配结果${\boldsymbol{p}}_k^{{\rm{opt}}} = {\boldsymbol{p}}_k^j$。
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