logo

SCIENCE CHINA Information Sciences, Volume 63 , Issue 8 : 180302(2020) https://doi.org/10.1007/s11432-019-2921-x

Machine-learning-based high-resolution DOA measurement and robust directional modulation for hybrid analog-digital massive MIMO transceiver

More info
  • ReceivedDec 29, 2019
  • AcceptedMay 19, 2020
  • PublishedJul 15, 2020

Abstract

At hybrid analog-digital (HAD) transceiver, an improved HAD estimation of signal parameters via rotational invariance techniques (ESPRIT), called I-HAD-ESPRIT, is proposed to measure the direction of arrival (DOA) of a desired user, where the phase ambiguity due to HAD structure is dealt with successfully. Subsequently, a machine-learning (ML) framework is proposed to improve the precision of measuring DOA. Meanwhile, we find that the probability density function (PDF) of DOA measurement error (DOAME) can be approximated as a Gaussian distribution by the histogram method in ML. Then, a slightly large training data set (TDS) and a relatively small real-time set (RTS) of DOA are formed to predict the mean and variance of DOA/DOAME in the training stage and real-time stage, respectively. To improve the precisions of DOA/DOAME, three weight combiners are proposed to combine the-maximum-likelihood-learning outputs of TDS and RTS. Using the mean and variance of DOA/DOAME, their PDFs can be given directly, and we propose a robust beamformer for directional modulation (DM) transmitter with HAD by fully exploiting the PDF of DOA/DOAME, especially a robust analog beamformer on RF chain. Simulation results show that: (1) the proposed I-HAD-ESPRIT can achieve the HAD Cramer-Rao lower bound (CRLB); (2) the proposed ML framework performs much better than the corresponding real-time one without training stage; (3) the proposed robust DM transmitter can perform better than the corresponding non-robust ones in terms of secrecy rate.


Acknowledgment

This work was supported in part by National Natural Science Foundation of China (Nos. 61771244, 61871229).


Supplement

Appendix

Derivation of RAB ${\tilde{V}_{~RF}}$

Considering the DOA measurement error, the nonzero element of ${\boldsymbol~V}_{\rm~RF,RAB}$ can be represented as \begin{align}\hat{v}_{k,m}&=\int_{-\Delta\theta_\mathrm{{max}}}^{\Delta\theta_\mathrm{{max}}}{\rm e}^{-{\rm j}\frac{2\pi d}{\lambda}[(k-1)M+m-\frac{N+1}{2}]\cos(\hat{\theta}-\Delta\theta)}\cdot p(\Delta\theta){\rm d}(\Delta\theta) \\ &=\int_{-\Delta\theta_\mathrm{{max}}}^{\Delta\theta_\mathrm{{max}}}{\rm e}^{-{\rm j}\alpha_{k,m}\cos(\hat{\theta}-\Delta\theta)}\cdotp p(\Delta\theta){\rm d}(\Delta\theta) \\ &=\int_{-\Delta\theta_\mathrm{{max}}}^{\Delta\theta_\mathrm{{max}}}{\rm e}^{-{\rm j}\alpha_{k,m}[\cos(\hat{\theta})\cos(\Delta\theta)+\sin(\hat{\theta})\sin(\Delta\theta)]}\cdotp p(\Delta\theta){\rm d}(\Delta\theta), \tag{69} \end{align} where \begin{align}\alpha_{k,m}=\frac{2\pi d}{\lambda}\left[(k-1)M+m-\frac{N+1}{2}\right]. \tag{70} \end{align} By utilizing the second-order Taylor expansion, we can expand $\cos(\Delta\theta)$ and $\sin(\Delta\theta)$ at point $\Delta\theta=0$ as \begin{align} \cos(\Delta\theta)\approx1-\frac{1}{2}(\Delta\theta)^2, \sin(\Delta\theta)\approx\Delta\theta. \tag{71} \end{align} Substituting Eq. (71) in (69) yields \begin{align} \hat{v}_{k,m} &=\int_{-\Delta\theta_\mathrm{{max}}}^{\Delta\theta_\mathrm{{max}}}{\rm e}^{-{\rm j}\alpha_{k,m}[\cos(\hat{\theta})\cos(\Delta\theta)+\sin(\hat{\theta})\sin(\Delta\theta)]}\cdot p(\Delta\theta){\rm d}(\Delta\theta) \\ &=\int_{-\Delta\theta_\mathrm{{max}}}^{\Delta\theta_\mathrm{{max}}}{\rm e}^{-{\rm j}\alpha_{k,m}[\cos(\hat{\theta})-\cos(\hat{\theta})\cdot\frac{1}{2}(\Delta\theta)^2+\sin(\hat{\theta})(\Delta\theta)]} p(\Delta\theta){\rm d}(\Delta\theta) \\ &=\xi_{k,m}\int_{-\Delta\theta_\mathrm{{max}}}^{\Delta\theta_\mathrm{{max}}}{\rm e}^{{\rm j}\alpha_{k,m}[\cos(\hat{\theta})\cdot\frac{1}{2}(\Delta\theta)^2-\sin(\hat{\theta})(\Delta\theta)]}p(\Delta\theta){\rm d}(\Delta\theta) \\ &=\xi_{k,m}\int_{-\Delta\theta_\mathrm{{max}}}^{\Delta\theta_\mathrm{{max}}}\{\cos(\alpha_{k,m}\psi)+{\rm j}\sin(\alpha_{k,m}\psi)\}p(\Delta\theta){\rm d}(\Delta\theta) \\ &=\zeta_{k,m}+{\rm j}\eta_{k,m}, \tag{72} \end{align} where \begin{align}\xi_{k,m}={\rm e}^{-{\rm j}\alpha_{k,m}\cos(\hat{\theta})}, \tag{73} \end{align} and \begin{align}\psi=\left[\cos(\hat{\theta})\cdot\frac{1}{2}(\Delta\theta)^2-\sin(\hat{\theta})(\Delta\theta)\right]. \tag{74} \end{align} Similarly, by utilizing the second-order Taylor expansion, $\cos(\alpha_{k,m}\psi)$ can be represented as \begin{align} \cos(\alpha_{k,m}\psi)=&\,\cos\left(\alpha_{k,m}\left[\cos(\hat{\theta})\cdot\frac{1}{2}(\Delta\theta)^2-\sin(\hat{\theta})(\Delta\theta)\right]\right) \\ \approx&\,1-\frac{1}{2}\alpha_{k,m}^2\left[\cos(\hat{\theta})\cdot\frac{1}{2}(\Delta\theta)^2-\sin(\hat{\theta})(\Delta\theta)\right]^2 \\ =&\,1-\frac{1}{8}\alpha_{k,m}^2\cos(\hat{\theta})^2(\Delta\theta)^4-\frac{1}{2}\alpha_{k,m}^2\sin(\hat{\theta})^2(\Delta\theta)^2 \\ &+\frac{1}{2}\alpha_{k,m}^2\cos(\hat{\theta})\sin(\hat{\theta})(\Delta\theta)^3. \tag{75} \end{align} Since the last term of Eq. (75) is an odd function of $\Delta\theta$, then \begin{align}\int_{-\Delta\theta_\mathrm{{max}}}^{\Delta\theta_\mathrm{{max}}}\frac{1}{2}\alpha_{k,m}^2\cos(\hat{\theta})\sin(\hat{\theta})(\Delta\theta)^3\cdot p(\Delta\theta){\rm d}(\Delta\theta)=0. \tag{76} \end{align} Now, let us define \begin{align}\chi_1=&\,\int_{-\Delta\theta_\mathrm{{max}}}^{\Delta\theta_\mathrm{{max}}}(\Delta\theta)^4\cdot p(\Delta\theta){\rm d}(\Delta\theta) \\ =&\,\frac{2}{K_d\sqrt{2\pi \sigma^2}}\left\{-\sigma^2\cdot\Delta\theta_\mathrm{{max}}^3 {\rm e}^{-\frac{\Delta\theta_\mathrm{{max}}^2}{2\sigma^2}}-3\sigma^4\Delta\theta_\mathrm{{max}}{\rm e}^{-\frac{\Delta\theta_\mathrm{{max}}^2}{2\sigma^2}} +\frac{3\sqrt{2\pi}}{2}\sigma^5 \mathrm{erf}\left(\frac{\Delta\theta_\mathrm{{max}}}{\sqrt{2}\sigma}\right)\right\}, \tag{77} \end{align} and \begin{align}\chi_2&=\int_{-\Delta\theta_\mathrm{{max}}}^{\Delta\theta_\mathrm{{max}}}(\Delta\theta)^2\cdot p(\Delta\theta){\rm d}(\Delta\theta) \\ &=\frac{2}{K_d\sqrt{2\pi\sigma^2}}\left\{-\sigma^2\Delta\theta_\mathrm{{max}}\cdot {\rm e}^{-\frac{\Delta\theta_\mathrm{{max}}^2}{2\sigma^2}}+\frac{\sqrt{2\pi}}{2}\sigma^3{\rm erf}\left(\frac{\Delta\theta_\mathrm{{max}}}{\sqrt{2}\sigma}\right)\right\}. \tag{78} \end{align} Then the real part $\zeta_{k,m}$ of Eq. (72) can be expressed as \begin{align}\zeta_{k,m}=\xi_{k,m}\left(K_d-\frac{1}{8}\alpha_{k,m}^2\cos(\hat{\theta})^2\chi_1-\frac{1}{2}\alpha_{k,m}^2\sin(\hat{\theta})^2\chi_2\right). \tag{79} \end{align} In the same manner, we can have the $\eta_{k,m}$ as follows: \begin{align}\eta_{k,m}=\frac{1}{2}\xi_{k,m}\cdot\alpha_{k,m}\cos(\hat{\theta})\chi_2. \tag{80} \end{align} Until now, we complete the derivation of $\hat{v}_{k,m}$. That is, $\hat{v}_{k,m}=\zeta_{k,m}+j\eta_{k,m}$. Owing to the special structure of analog precoder, we only need the phase of $\hat{v}_{k,m}$. Therefore we can reformulated the analog $v_{k,m}$ as \begin{align}v_{{\rm RAB}, k,m}=\frac{1}{\sqrt{M}}\exp(j*\angle(\hat{v}_{k,m})), \tag{81} \end{align} which is what we need.


References

[1] Godara L C. Application of antenna arrays to mobile communications. II. Beam-forming and direction-of-arrival considerations. Proc IEEE, 1997, 85: 1195-1245 CrossRef Google Scholar

[2] Chen J C, Kung Yao J C, Hudson R E. Source localization and beamforming. IEEE Signal Process Mag, 2002, 19: 30-39 CrossRef ADS Google Scholar

[3] Stoica P, Babu P, Li J. SPICE: A Sparse Covariance-Based Estimation Method for Array Processing. IEEE Trans Signal Process, 2011, 59: 629-638 CrossRef ADS Google Scholar

[4] Zhang X, Xu L, Xu L. Direction of Departure (DOD) and Direction of Arrival (DOA) Estimation in MIMO Radar with Reduced-Dimension MUSIC. IEEE Commun Lett, 2010, 14: 1161-1163 CrossRef Google Scholar

[5] Shafin R, Liu L, Zhang J. DoA Estimation and Capacity Analysis for 3-D Millimeter Wave Massive-MIMO/FD-MIMO OFDM Systems. IEEE Trans Wireless Commun, 2016, 15: 6963-6978 CrossRef Google Scholar

[6] Wan L, Han G, Jiang J. DOA Estimation for Coherently Distributed Sources Considering Circular and Noncircular Signals in Massive MIMO Systems. IEEE Syst J, 2017, 11: 41-49 CrossRef ADS Google Scholar

[7] Huang H, Yang J, Huang H. Deep Learning for Super-Resolution Channel Estimation and DOA Estimation Based Massive MIMO System. IEEE Trans Veh Technol, 2018, 67: 8549-8560 CrossRef Google Scholar

[8] Tuncer T E, Friedlander B. Classical and Modern Direction-of-Arrival Estimation. New York: Elsevier, 2009. Google Scholar

[9] Capon J. High-resolution frequency-wavenumber spectrum analysis. Proc IEEE, 1969, 57: 1408-1418 CrossRef Google Scholar

[10] Bartlett M S. An Introduction to Stochastic Processes with Special References to Methods and Applications. New York: Cambridge University Press, 1961. Google Scholar

[11] Schmidt R. Multiple emitter location and signal parameter estimation. IEEE Trans Antennas Propag, 1986, 34: 276-280 CrossRef ADS Google Scholar

[12] Roy R, Kailath T. ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Trans Acoust Speech Signal Processing, 1989, 37: 984-995 CrossRef Google Scholar

[13] Malioutov D, Cetin M, Willsky A S. A sparse signal reconstruction perspective for source localization with sensor arrays. IEEE Trans Signal Process, 2005, 53: 3010-3022 CrossRef ADS Google Scholar

[14] Hyder M M, Mahata K. Direction-of-Arrival Estimation Using a Mixed $\ell~_{2,0}$ Norm Approximation. IEEE Trans Signal Process, 2010, 58: 4646-4655 CrossRef ADS Google Scholar

[15] Li Q L, Zhang X L, Li H. Online direction of arrival estimation based on deep learning. In: Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2018. Google Scholar

[16] Chakrabarty S, Habets E A P. Broadband DOA estimation using convolutional neural networks trained with noise signals. In: Proceedings of IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA), 2017. Google Scholar

[17] Shu F, Qin Y, Liu T. Low-Complexity and High-Resolution DOA Estimation for Hybrid Analog and Digital Massive MIMO Receive Array. IEEE Trans Commun, 2018, 66: 2487-2501 CrossRef Google Scholar

[18] Sidiropoulos N D, Bro R, Giannakis G B. Parallel factor analysis in sensor array processing. IEEE Trans Signal Process, 2000, 48: 2377-2388 CrossRef ADS Google Scholar

[19] Wang H M, Zheng T X, Yuan J. Physical Layer Security in Heterogeneous Cellular Networks. IEEE Trans Commun, 2016, 64: 1204-1219 CrossRef Google Scholar

[20] Chen X, Ng D W K, Gerstacker W H. A Survey on Multiple-Antenna Techniques for Physical Layer Security. IEEE Commun Surv Tutorials, 2017, 19: 1027-1053 CrossRef Google Scholar

[21] Babakhani A, Rutledge D B, Hajimiri A. Transmitter Architectures Based on Near-Field Direct Antenna Modulation. IEEE J Solid-State Circuits, 2008, 43: 2674-2692 CrossRef ADS Google Scholar

[22] Daly M P, Bernhard J T. Directional Modulation Technique for Phased Arrays. IEEE Trans Antennas Propag, 2009, 57: 2633-2640 CrossRef ADS Google Scholar

[23] Tennant A, Shi H Z. Enhancing the security of communication via directly modulated antenna arrays. IET Microwaves Antennas Propag, 2013, 7: 606-611 CrossRef Google Scholar

[24] Ding Y, Fusco V F. A Vector Approach for the Analysis and Synthesis of Directional Modulation Transmitters. IEEE Trans Antennas Propag, 2014, 62: 361-370 CrossRef ADS Google Scholar

[25] Hu J, Shu F, Li J. Robust Synthesis Method for Secure Directional Modulation With Imperfect Direction Angle. IEEE Commun Lett, 2016, 20: 1084-1087 CrossRef Google Scholar

[26] Shu F, Wu X, Li J. Robust Synthesis Scheme for Secure Multi-Beam Directional Modulation in Broadcasting Systems. IEEE Access, 2016, 4: 6614-6623 CrossRef Google Scholar

[27] Shu F, Zhu W, Zhou X. Robust Secure Transmission of Using Main-Lobe-Integration-Based Leakage Beamforming in Directional Modulation MU-MIMO Systems. IEEE Syst J, 2018, 12: 3775-3785 CrossRef ADS arXiv Google Scholar

[28] Zhu W, Shu F, Liu T T, et al. Secure precise transmission with multi-relay-aided directional modulation. In: Proceedings of the 9th International Conference on Wireless Communications and Signal Processing (WCSP), 2017. Google Scholar

[29] Zhou X B, Li J, Shu F, et al. Secure swipt for directional modulation aided af relaying networks. 2018,. arXiv Google Scholar

[30] Hu J, Yan S, Shu F. Artificial-Noise-Aided Secure Transmission With Directional Modulation Based on Random Frequency Diverse Arrays. IEEE Access, 2017, 5: 1658-1667 CrossRef Google Scholar

[31] Shu F, Wu X, Hu J. Secure and Precise Wireless Transmission for Random-Subcarrier-Selection-Based Directional Modulation Transmit Antenna Array. IEEE J Sel Areas Commun, 2018, 36: 890-904 CrossRef Google Scholar

[32] Xinying Zhang , Molisch A F, Sun-Yuan Kung A F. Variable-phase-shift-based RF-baseband codesign for MIMO antenna selection. IEEE Trans Signal Process, 2005, 53: 4091-4103 CrossRef ADS Google Scholar

[33] Sohrabi F, Yu W. Hybrid Analog and Digital Beamforming for mmWave OFDM Large-Scale Antenna Arrays. IEEE J Sel Areas Commun, 2017, 35: 1432-1443 CrossRef Google Scholar

[34] Sohrabi F, Yu W. Hybrid Digital and Analog Beamforming Design for Large-Scale Antenna Arrays. IEEE J Sel Top Signal Process, 2016, 10: 501-513 CrossRef ADS arXiv Google Scholar

[35] Yu X, Shen J C, Zhang J. Alternating Minimization Algorithms for Hybrid Precoding in Millimeter Wave MIMO Systems. IEEE J Sel Top Signal Process, 2016, 10: 485-500 CrossRef ADS arXiv Google Scholar

[36] Gao X, Dai L, Han S. Energy-Efficient Hybrid Analog and Digital Precoding for MmWave MIMO Systems With Large Antenna Arrays. IEEE J Sel Areas Commun, 2016, 34: 998-1009 CrossRef Google Scholar

[37] Ramadan Y R, Minn H, Ibrahim A S. Hybrid Analog-Digital Precoding Design for Secrecy mmWave MISO-OFDM Systems. IEEE Trans Commun, 2017, 65: 5009-5026 CrossRef Google Scholar

[38] Heath R W, Gonzalez-Prelcic N, Rangan S. An Overview of Signal Processing Techniques for Millimeter Wave MIMO Systems. IEEE J Sel Top Signal Process, 2016, 10: 436-453 CrossRef ADS arXiv Google Scholar

[39] Horn R A, Johnson C R. Pattern Recognition and Machine Learning. Berlin: Springer 2013. Google Scholar

[40] Shu F, Wan S M, Yan S H, et al. Secure directional modulation to enhance physical layer security in IoT networks. 2018,. arXiv Google Scholar

Copyright 2020  CHINA SCIENCE PUBLISHING & MEDIA LTD.  中国科技出版传媒股份有限公司  版权所有

京ICP备14028887号-23       京公网安备11010102003388号