SCIENTIA SINICA Informationis, Volume 51 , Issue 8 : 1360(2021) https://doi.org/10.1360/SSI-2020-0287

## Threat region development of covert wireless communication based on 3D beamforming

• AcceptedDec 14, 2020
• PublishedAug 2, 2021
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### References

[1] Wang J Q. Research on the key technologies for low probability of intercept wireless communication. Dissertation for Ph.D. Degree. Chengdu: University of Electronic Science and Technology, 2019. Google Scholar

[2] Yan S H, Zhou X Y, Hu J S, et al. Low probability of detection communication: opportunities and challenges. IEEE Wirel Commun, 2019, 26: 19-25. Google Scholar

[3] Bash B A, Goeckel D, Towsley D. Limits of reliable communication with low probability of detection on awgn channels. IEEE J. Sel. Areas Commun, 2013, 31: 1921-1930. Google Scholar

[4] He B, Yan S, Zhou X. On Covert Communication With Noise Uncertainty. IEEE Commun Lett, 2017, 21: 941-944 CrossRef Google Scholar

[5] Hien Q, Sang W. Covert communication under channel uncertainty and noise uncertainty. In: IEEE International Conference on Communications (ICC), Shanghai, China, 2019. 211-216. Google Scholar

[6] Lin Y D, Jin L, Zhou Y, et al. Performance analysis of beamforming based covert wireless communication with uncertain noise. Journal on Communications, 2020, 41: 49-58. Google Scholar

[7] Sobers T V, Bash B A, Guha S. Covert Communication in the Presence of an Uninformed Jammer. IEEE Trans Wireless Commun, 2017, 16: 6193-6206 CrossRef Google Scholar

[8] Soltani R, Goeckel D, Towsley D. Covert Wireless Communication With Artificial Noise Generation. IEEE Trans Wireless Commun, 2018, 17: 7252-7267 CrossRef Google Scholar

[9] He B, Yan S, Zhou X. Covert Wireless Communication With a Poisson Field of Interferers. IEEE Trans Wireless Commun, 2018, 17: 6005-6017 CrossRef Google Scholar

[10] Shahzad K, Zhou X Y, Yan S H. Covert communication in fading channels under channel uncertainty. In: Vehicular Technology Conference (VTC Spring), Sydney, 2017. 321-325. Google Scholar

[11] Tao L W, Yang W W, Yan S H, et al. Covert communication in downlink noma systems with random transmit power. IEEE Commun Lett, 2020, 12: 642-645. Google Scholar

[12] Zheng T X, Wang H M, Ng D, et al. Multi-antenna covert communications in random wireless networks. IEEE Trans Wirel Commun, 2019, 18: 1974-1987. Google Scholar

[13] Forouzesh M, Azmi P, Mokari N. Covert Communication Using Null Space and 3D Beamforming: Uncertainty of Willie's Location Information. IEEE Trans Veh Technol, 2020, 69: 8568-8576 CrossRef Google Scholar

[14] Shahzad K, Zhou X Y, Yan S H, et al. Achieving covert wireless communications using a full-duplex receiver, IEEE Trans Wirel Commun, 2018, 17: 8517-8530. Google Scholar

[15] Shahzad K, Zhou X, Yan S. Covert Wireless Communication in Presence of a Multi-Antenna Adversary and Delay Constraints. IEEE Trans Veh Technol, 2019, 68: 12432-12436 CrossRef Google Scholar

[16] Sun L L, Xu T Z, Yan S H, et al. On resource allocation in covert wireless communication with channel estimation. IEEE Trans Commun, 2020, 11: 4651-4663. Google Scholar

[17] Liu Z H, Liu J J, Zeng Y, et al. Covert wireless communications in IoT systems: hiding information in interference, IEEE Wirel Commun, 2017, 25: 46-52. Google Scholar

[18] Li X, Jin S, Suraweera H, et al. Line-of-sight based statistical 3D beamforming for downlink massive MIMO systems. In: IEEE International Conference on Communications (ICC), Kuala Lumpur, 2016. 421-426. Google Scholar

[19] Tandra R, Sahai A. SNR walls for signal detection. IEEE J. Sel. Topics in Signal Process, 2008, 2: 4-17. Google Scholar

[20] Song H T. Research on intrinsic security transmission technology for massive MIMO. Dissertation for Master's Degree. Zhengzhou: PLA Strategic Support Force Information Engineering University, 2018. Google Scholar

[21] Yan S, Malaney R. Location-Based Beamforming for Enhancing Secrecy in Rician Wiretap Channels. IEEE Trans Wireless Commun, 2016, 15: 2780-2791 CrossRef Google Scholar

• Figure 1

(Color online) System model of downlink covert wireless communication based on 3D beamforming

• Figure 8

(Color online) Thermogram of the maximum covert throughput and the covert threat region. (a) Matched group; (b) ${K_b}=~{K_w}=~30$; (c) $\Delta~d/\lambda~=~1.5$; (d) ULA with 32 antennas; (e) $\sigma~_n^2~=~-~20~{\rm{~dB}}$; (f) $\rho~=~1.5$; (g) $\delta~=~0.001$;protect łinebreak (h) $\varepsilon~=~0.01$

• Figure 9

(Color online) Thermogram of the optimal transmission power and the maximum covert throughput. (a) Covert threat region based on Algorithm 1; (b) error of ${P^~*~}$; (c) error of ${\eta~^~*~}$; (d) error ratio of ${\eta~^~*~}$

• Table 1   Simulation parameters
 Channel model Antenna model at Alice Antenna model at Bob and Willie Rician fading with ${K_b}~=~{K_w}~=~3$ $L~\times~M~=~8~\times~4$, $T~=~30~{\rm{~m}}$, $\Delta~d/\lambda~~=~1$ Single antenna Beamforming mode Service radius of base station Path loss exponent MRT $r~=~100~{\rm{~m}}$ $\alpha~~=~3$ Position of Alice Position of Bob Position of Willie (0, 0) (30, 30) (20, 25) Noise level Noise uncertainty level Maximum transmission power requirement $\sigma~_b^2~=~\sigma~_n^2~=~~-~30~{\rm{~dB}}$ $\rho~~=~1.1$ ${P_{\max~}}~=~10~{\rm{~W}}$ Covertness requirement Reliability requirement Maximum covert throughput requirement $\varepsilon~~=~0.1$ $\delta~~=~0.01$ ${\eta~_l}~=~0.1~{\rm{~bit/s/Hz}}$
•

Algorithm 1 Search algorithm for maximum covert throughput

Require:Covertness requirement $\varepsilon~$, reliability requirement $\delta~$, and maximum transmit power requirement ${P_{\max~}}$.

Output:Maximum covert throughput ${\eta~^~*~}$, optimal transmit power ${P^~*~}$, and optimal target rate ${R^~*~}$.

Transform the covertness constraint into an equality, and solve the integral equation ${\bar~\xi~^~*~}(P)~=~1~-~\varepsilon~$ for ${P^\Delta~}$ through binary search. Then, obtain ${P^~*~}~=~\min~\{~{P^\Delta~},{P_{\max~}}\}~$ under the maximum transmit power constraint;

Transform the reliability constraint into an equality, and obtain ${R^\Delta~}$ by solving the integral equation ${p_{{\rm{out~}}}}({P^~*~},R)~=~\delta~$;

Set the searching range as $R~\in~(0,{R^\Delta~}]$, and obtain ${R^~*~}$ and ${\eta~^~*~}$ through one-side exhaustive search.

•

Algorithm 2 Lightweight search algorithm for covert threat region

Require:Covertness requirement $\varepsilon~$, reliability requirement $\delta~$, maximum transmit power requirement ${P_{\max~}}$, and covert throughput requirement ${\eta~_l}$.

Output:Covert threat region ${{\mathop{\rm~Area}\nolimits}~_D}\left(~{x,y}~\right)$.

Calculate the fitting factor $\mu~$ through image method. Transform the fitting covertness constraint (28) into an equality and compute ${P^\Delta~}~=~\frac{{LM\sigma~_n^2\gamma~_w^{\rm~th}\left(~{{K_b}~+~1}~\right)\left(~{{K_w}~+~1}~\right)}}{{\mu~d_{aw}^{~-~\alpha~}\left(~{{K_b}{K_w}{g_{bw}}~+~LM\left(~{{K_b}~+~{K_w}~+~1}~\right)}~\right)}}$. Then, obtain ${P^~*~}~=~\min~\{~{P^\Delta~},{P_{\max~}}\}~$ under the maximum transmit power constraint (24d);

Compute the numerical solution of the maximum point ${R_{\max~}}$ for $\eta$, and obtain the corresponding $p_{\rm~out}^{\max~}$. Next, obtian ${\eta~^~*~}~=~\left(~{1~-~p_{\rm~out}^{\max~}}~\right){R_{\max~}}$ directly when $\delta~~\ge~p_{\rm~out}^{\max~}$. Otherwise, when $\delta~~<~p_{\rm~out}^{\max~}$, transform the reliability constraint (24c) into an equality and obtain ${R^\Delta~}$ by solving the integral equation ${p_{{\rm{out~}}}}({P^~*~},R)~=~\delta~$, as well as ${\eta~^~*~}~=~\left(~{1~-~\delta~}~\right){R^\Delta~}$;

Traverse the whole system service area with the position of Willie, and calculate ${\eta~^~*~}(x,y)$. At last, obtain ${{\mathop{\rm~Area}\nolimits}~_D}\left(~{x,y}~\right)$ with the comparison of ${\eta~_l}$.

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