无线能量传输-能量接收机的非线性接收模型（一）
Date: 2022.04.22 17:07 Author: Joffrey LC
Practical Non-Linear Energy Harvesting Model and Resource Allocation for SWIPT Systems. Elena Boshkovska et.al. IEEE Communications Letters, Dec. 2015 (pdf) (Citations 551)
Quick Overview
- 提出Energy Harvesting Model 是 non-linear的，并给出模型（需要根据具体测量值，拟合得到具体参数）
- 给出一种双重循环的快速解决方案（这部分简单看了一下）
如果噪声是矩阵形式，应该表示为\(\textbf{n}\sim\mathcal{CN}(\textbf{0},\sigma^2\textbf{I})\)，其中\(\sigma^2\)表示噪声的功率
主要内容
Energy Harvesting Model
Proposed a Non- Linear EH model based on the logistic (sigmoid) function: \[ \begin{aligned} \Phi_{\mathrm{ER}_{j}}^{\text {Practical }} &=\frac{\left[\Psi_{\mathrm{ER}_{j}}^{\text {Practical }}-M_{j} \Omega_{j}\right]}{1-\Omega_{j}}, \Omega_{j}=\frac{1}{1+\exp \left(a_{j} b_{j}\right)} \\ \Psi_{\mathrm{ER}_{j}}^{\text {Practical }} &=\frac{M_{j}}{1+\exp \left(-a_{j}\left(P_{\mathrm{ER}_{j}}-b_{j}\right)\right)} \end{aligned} \] 其中，\(\Phi_{\mathrm{ER}_{j}}^{\text {Practical }}\)代表\(j\)-th ER 接受到的总能量；\(\Psi_{\mathrm{ER}_{j}}^{\text {Practical }}\)代表logistic function with respect to the receive RF power \(P_{\mathrm{ER}_{j}}\)。其他参数例如$a_j,b_j,M_j$都是通过对实际电路模型的测量值进行拟合得到
并且由于\(\Omega_j\)并不影响\(\textbf{w}\)的设计，所以一般采用\(\Psi_{\mathrm{ER}_{j}}^{\text {Practical }}\)表示接收到的能量。有典型值<span class=“hint–top hint–rounded” aria-label=“T. Le, K. Mayaram and T. Fiez,”Efficient Far-Field Radio Frequency Energy Harvesting for Passively Powered Sensor Networks," in IEEE Journal of Solid-State Circuits, vol. 43, no. 5, pp. 1287-1302, May 2008, doi: 10.1109/JSSC.2008.920318. ↩︎">[1]：
\(M_j=20\text{mW},a_j=6400,b_j=0.003\)
双循环解法
原始问题建模：
C1：功率约束
C2：SINR约束
Proposal 流程
另外有一个重要理论（没有证明）：
Result
- Harvested Energy 随着Minimum required SINR 增大而减小
- Harvested Energy 随着单个ER的天线数量\(N_T\)的增大而增大：因为更多的天线带来更高的自由度，会得到更高效的资源分配方案
- Harvested Energy 随着ERs数量增大而增大，而且性能增益（Performance Gap between Non-Linear Model with Linear Model）增大：因为ERs数量增大，Baseline（Performance with Linear Model）的失配（mismatch）更严重
- T. Le, K. Mayaram and T. Fiez, “Efficient Far-Field Radio Frequency Energy Harvesting for Passively Powered Sensor Networks,” in IEEE Journal of Solid-State Circuits, vol. 43, no. 5, pp. 1287-1302, May 2008, doi: 10.1109/JSSC.2008.920318. ↩︎ ↩︎