Low-Complexity separable beamformers for massive antenna array systems
- Author(s): Lucas N. Ribeiro 1 ; André L.F. de Almeida 1 ; Josef A. Nossek 1, 2 ; João César M. Mota 1
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View affiliations
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Affiliations:
1:
Wireless Telecommunications Research Group , Federal University of Ceará , Fortaleza , Brazil ;
2: Department of Electrical and Computer Engineering , Technical University Munich , Munich , Germany
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Affiliations:
1:
Wireless Telecommunications Research Group , Federal University of Ceará , Fortaleza , Brazil ;
- Source:
Volume 13, Issue 4,
June
2019,
p.
434 – 442
DOI: 10.1049/iet-spr.2018.5115 , Print ISSN 1751-9675, Online ISSN 1751-9683
Future cellular systems will likely employ massive bi-dimensional arrays to improve performance by large array gain and more accurate spatial filtering, motivating the design of low-complexity signal-processing methods. The authors propose optimising a Kronecker-separable beamforming filter that takes advantage of the bi-dimensional array geometry to reduce computational costs. The Kronecker factors are obtained using two strategies: alternating optimisation and sub-array minimum mean square error (MMSE) beamforming with Tikhonov regularisation. According to the simulation results, the proposed methods are computationally efficient but come with source recovery degradation, which becomes negligible when the sources are sufficiently separated in space.
Inspec keywords: cost reduction; optimisation; array signal processing; spatial filters; least mean squares methods; mobile antennas; antenna arrays; cellular radio
Other keywords: massive bi-dimensional arrays; future cellular systems; low-complexity signal-processing methods; computational cost reduction; low-complexity separable beamformers; massive antenna array systems; bi-dimensional array geometry; array gain; alternating optimisation; Kronecker factors; Kronecker-separable beamforming filter; source recovery degradation; Tikhonov regularisation; spatial filtering; sub-array minimum mean square error beamforming
Subjects: Mobile radio systems; Filtering methods in signal processing; Interpolation and function approximation (numerical analysis); Optimisation techniques; Antenna arrays
References
-
-
1)
-
21. Ribeiro, L.N., De Almeida, A.L.F., Mota, J.C.M.: ‘Tensor beamforming for multilinear translation invariant arrays’. Proc. 2016 IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, 2016, pp. 2966–2970.
-
-
2)
-
15. Zhu, G., Huang, K., Lau, V.K., et al: ‘Hybrid beamforming via the kronecker decomposition for the millimeter-wave massive MIMO systems’, IEEE J. Sel. Areas Commun., 2017, 35, (9), pp. 2097–2114.
-
-
3)
-
26. Yener, A., Yates, R.D., Ulukus, S.: ‘Interference management for CDMA systems through power control, multiuser detection, and beamforming’, IEEE Trans. Commun., 2001, 49, (7), pp. 1227–1239.
-
-
4)
-
23. Comon, P., Luciani, X., De Almeida, A.L.: ‘Tensor decompositions, alternating least squares and other tales’, J. Chemometrics: A J. the Chemometrics Soc., 2009, 23, (7–8), pp. 393–405.
-
-
5)
-
1. Larsson, E.G., Edfors, O., Tufvesson, F., et al: ‘Massive MIMO for next generation wireless systems’, IEEE Commun. Mag., 2014, 52, (2), pp. 186–195.
-
-
6)
-
6. Boussé, M., Debals, O., De Lathauwer, L.: ‘A tensor-based method for large-scale blind source separation using segmentation’, IEEE Trans. Signal Process., 2017, 65, (2), pp. 346–358.
-
-
7)
-
27. Minka, T.: ‘The lightspeed MATLAB toolbox, version 2.8’. 2017. Available at https://github.com/tminka/lightspeed.
-
-
8)
-
16. Miranda, R.K., da Costa, J.P.C., Roemer, F., et al: ‘Generalized sidelobe cancellers for multidimensional separable arrays’. 2015 IEEE 6th Int. Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), Cancun, 2015, pp. 193–196.
-
-
9)
-
7. Rupp, M., Schwarz, S.: ‘A tensor LMS algorithm’. Proc. 2015 IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP), Brisbane, 2015, pp. 3347–3351.
-
-
10)
-
25. Palomar, D.P., Eldar, Y.C.: ‘Convex optimization in signal processing and communications’ (Cambridge University Press, Cambridge, 2010).
-
-
11)
-
24. Liu, S., Trenkler, G.: ‘Hadamard, Khatri-Rao, Kronecker and other matrix products’, Int. J. Inf. Syst. Sci., 2008, 4, (1), pp. 160–177.
-
-
12)
-
19. Haykin, S.: ‘Adaptive filtering theory’ (Prentice-Hall, Englewood Cliffs, NJ, 1996).
-
-
13)
-
10. Ribeiro, L.N., de Almeida, A.L., Mota, J.C.M.: ‘Identification of separable systems using trilinear filtering’. Proc. of the 2015 IEEE 6th Int. Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2015, pp. 189–192.
-
-
14)
-
8. Rupp, M., Schwarz, S.: ‘Gradient-based approaches to learn tensor products’. Proc. 2015 23rd European Signal Processing Conf. (EUSIPCO), Nice, 2015, pp. 2486–2490.
-
-
15)
-
20. Petersen, K.B., Pedersen, M.S.: ‘The matrix cookbook’ (Technical University of Denmark, Copenhagen, 2012).
-
-
16)
-
17. Liu, L., Xie, J., Wang, L., et al: ‘Robust tensor beamforming for polarization sensitive arrays’, Multidimens. Syst. Signal Process., 2018, doi: 10.1007/s11045-018-0580-6.
-
-
17)
-
12. Elisei-Iliescu, C., Stanciu, C., Paleologu, C., et al: ‘Efficient recursive least-squares algorithms for the identification of bilinear forms’, Digit. Signal Process., 2018, 83, pp. 280–296.
-
-
18)
-
5. Treitel, S., Shanks, J.L.: ‘The design of multistage separable planar filters’, IEEE Trans. Geosci. Electron., 1971, 9, (1), pp. 10–27.
-
-
19)
-
9. Pinheiro, F.C., Lopes, C.G.: ‘Nonlinear adaptive algorithms on rank-one tensor models’. arXiv preprint arXiv:1610.07520, 2016.
-
-
20)
-
2. Schwarz, S., Rupp, M.: ‘Society in motion: challenges for LTE and beyond mobile communications’, IEEE Commun. Mag., 2016, 54, (5), pp. 76–83.
-
-
21)
-
11. Paleologu, C., Benesty, J., Ciochina, S.: ‘Linear system identification based on a kronecker product decomposition’, IEEE/ACM Trans. Audio, Speech, Language Process., 2018, 26, (10), pp. 1793–1808.
-
-
22)
-
3. Ji, H., Kim, Y., Lee, J., et al: ‘Overview of full-dimension MIMO in LTE-advanced pro’, IEEE Commun. Mag., 2017, 55, (2), pp. 176–184.
-
-
23)
-
18. Ribeiro, L.N., Schwarz, S., Rupp, M., et al: ‘A low-complexity equalizer for massive MIMO systems based on array separability’. Proc. 2017 25th European Signal Processing Conf. (EUSIPCO), Kos, 2017, pp. 2522–2526.
-
-
24)
-
4. Ribeiro, L.N., Schwarz, S., Rupp, M., et al: ‘Energy efficiency of mmWave massive MIMO precoding with low-resolution DACs’, IEEE. J. Sel. Top. Signal. Process., 2018, 12, (2), pp. 298–312.
-
-
25)
-
28. Golub, G.H., Van Loan, C.F.: ‘Matrix computations’, vol. 3 (JHU Press, Baltimore, MD, 2012).
-
-
26)
-
13. Van Trees, H.L.: ‘Optimum array processing: part IV of detection, estimation and modulation theory’ (John Wiley & Sons, New Jersey, 2002), p. 1.
-
-
27)
-
14. Wang, Z., Liu, W., Qian, C., et al: ‘Two-dimensional precoding for 3-D massive MIMO’, IEEE Trans. Veh. Technol., 2017, 66, (6), pp. 5485–5490.
-
-
28)
-
22. Kolda, T., Bader, B.: ‘Tensor decompositions and applications’, SIAM Rev., 2009, 51, (3), pp. 455–500.
-
-
1)