## 3 Proposed Algorithm
In this simulation, we set \(\bar{R}^{c}=1\) bps/Hz, \(\bar{E}^{c}=50\) dBm, \(\bar{E}^{e}=0\) dBm, \(P=80\) dBm, \(P_{1}=40\) dBm and \(P_{2}=60\) dBm. We can see that our proposed algorithm has much lower complexity than the conventional 1-D method in [29]. Figure 7: Average CPU time with respect to the number of transmit antennas at the macrocell sink node. ## 5 Conclusions

Considering the security transmission with PS-enabled SWIPT approach, we have investigated the AN-based beamforming design problem in a two-tier MIMO HWSN where a femtocell is underlaying a macrocell. The jointly design problem of the transmit beamforming vectors, the AN and PS ratio has been modeled to maximize the MSC of the M-SNs subject to the secrecy capacity constraint, the harvested energy constraint and the transmit power constraint. To reduce the performance loss from the rank relaxation, an novel SCA-SPCA-based iterative algorithm has been proposed and its convergence property is proved. Numerical results have demonstrated that the proposed SCA-SPCA-based algorithm always outperforms the conventional non-AN, null-AN and \"fixed PS ratio\" schemes. As a future work, the proposed algorithm can be extended to a multi femtocell scenario in a macrocell. In that case, interference between femtocells needs to be considered. In addition, the dependency of non-linear power-splitting EH model and EH efficiency on the received user characteristic can be an extension of this work. Conceptualization, Z.Z. and W.H. ; Methodology, W.G., Z.Z. and Z.C. ; Software, W.G., Z.Z. and Y.W. ; Formal analysis, W.G., Z.Z. and Z.C. ; Supervision, Z.W. ; Writing-original draft preparation, Z.Z. and W.G. ; Writing-review and editing, Z.Z. and W.G. ; Visualization Q.W. and W.G. This work was supported in part by the National Nature Science Foundation of China under grants 61801434, 61571402, 61771431 and 61801435, in part by the Project funded by China Postdoctoral Science Foundation under Grant 2018M642784, in part by the Scientific and Technological Key Project of Henan Province under Grant 1921023178, 192102210246, in part by the National Science and Technology Major Project under grant 2017 ZX00801001. This work of [PERSON] was supported in part by the National Natural Science Foundation of China under Grant No. 61701197, the Project funded by China Postdoctoral Science Foundation under Grant No. 2018M641354, 2018M633733, the Open Research Fund of National Mobile Communications Research Laboratory, Southeast University, under Grant No. 2018D15. This work of [PERSON] was supported in part by the Open Fund of the Shaanxi Key Laboratory of Information Communication Network and Security under Grant ICNS201801. The authors declare no conflict of interest. ## Abbreviations

The following abbreviations are used in this manuscript: \begin{tabular}{l l} HWSN & heterogeneous wireless sensor networks \\ SWIPT & simultaneous wireless information and power transfer \\ AN & artificial noise \\ SCA & successive convex approximation \\ SPCA & sequential parametric convex approximation \\ SOCP & second order cone programming \\ IoT & Internet-of-Things \\ WSN & wireless sensor network \\ MBS & macrocell base station \\ FBS & femtocell base station \\ SN & sensor node \\ HP-SN & high-priority sensor node \\ LP-SN & low-priority sensor node \\ M-SN & macrocell sensor node \\ HetNet & heterogeneous networks \\ WPT & wireless power transmission \\ WIT & wireless information transmission \\ MISO & multiple-input single-output \\ MIMO & multiple-input multiple \\ CoMP & coordinated multi-point \\ CSI & channel state information \\ PLS & physical-layer security \\ PS & power splitting \\ MSC & minimal secrecy capacity \\ \end{tabular} 

MSCM MSC maximization AWGNadditive white Gaussian noiseIDimformation decodingEHenergy harvestingQoLoLquadratic-over-linear

## Appendix A

**Proof of Lemma 1. ** Let \(a=\text{rank}(\mathbf{A})\). The case of \(a\geq 0\) is trivial.