Low-complexity separable beamformers for massive antenna array systems

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. We 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 beamforming with Tikhonov regularization. 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.

[1]  Yonina C. Eldar,et al.  Convex Optimization in Signal Processing and Communications , 2009 .

[2]  Markus Rupp,et al.  Energy Efficiency of mmWave Massive MIMO Precoding With Low-Resolution DACs , 2017, IEEE Journal of Selected Topics in Signal Processing.

[3]  Jacob Benesty,et al.  Linear System Identification Based on a Kronecker Product Decomposition , 2018, IEEE/ACM Transactions on Audio, Speech, and Language Processing.

[4]  Markus Rupp,et al.  A tensor LMS algorithm , 2015, 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[5]  Roy D. Yates,et al.  Interference management for CDMA systems through power control, multiuser detection, and beamforming , 2001, IEEE Trans. Commun..

[6]  Shuangzhe Liu,et al.  Hadamard, Khatri-Rao, Kronecker and Other Matrix Products , 2008 .

[7]  Harry L. Van Trees,et al.  Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory , 2002 .

[8]  Markus Rupp,et al.  Gradient-based approaches to learn tensor products , 2015, 2015 23rd European Signal Processing Conference (EUSIPCO).

[9]  Tamara G. Kolda,et al.  Tensor Decompositions and Applications , 2009, SIAM Rev..

[10]  Gene H. Golub,et al.  Matrix computations , 1983 .

[11]  Markus Rupp,et al.  Society in motion: challenges for LTE and beyond mobile communications , 2016, IEEE Communications Magazine.

[12]  André Lima Férrer de Almeida,et al.  Tensor beamforming for multilinear translation invariant arrays , 2016, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[13]  André Lima Férrer de Almeida,et al.  Identification of separable systems using trilinear filtering , 2015, 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP).

[14]  Markus Rupp,et al.  A low-complexity equalizer for massive MIMO systems based on array separability , 2017, 2017 25th European Signal Processing Conference (EUSIPCO).

[15]  S. Treitel,et al.  The Design of Multistage Separable Planar Filters , 1971 .

[16]  Lieven De Lathauwer,et al.  A Tensor-Based Method for Large-Scale Blind Source Separation Using Segmentation , 2017, IEEE Transactions on Signal Processing.

[17]  Long Liu,et al.  Robust tensor beamforming for polarization sensitive arrays , 2019, Multidimens. Syst. Signal Process..

[18]  Kaibin Huang,et al.  Hybrid Beamforming via the Kronecker Decomposition for the Millimeter-Wave Massive MIMO Systems , 2017, IEEE Journal on Selected Areas in Communications.

[19]  Erik G. Larsson,et al.  Massive MIMO for next generation wireless systems , 2013, IEEE Communications Magazine.

[20]  P. Comon,et al.  Tensor decompositions, alternating least squares and other tales , 2009 .

[21]  Byonghyo Shim,et al.  Overview of Full-Dimension MIMO in LTE-Advanced Pro , 2015, IEEE Communications Magazine.

[22]  Jacob Benesty,et al.  Efficient recursive least-squares algorithms for the identification of bilinear forms , 2018, Digit. Signal Process..

[23]  Lajos Hanzo,et al.  Two-Dimensional Precoding for 3-D Massive MIMO , 2017, IEEE Transactions on Vehicular Technology.

[24]  Kaare Brandt Petersen,et al.  The Matrix Cookbook , 2006 .

[25]  Florian Roemer,et al.  Generalized sidelobe cancellers for multidimensional separable arrays , 2015, 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP).

[26]  Cássio Guimarães Lopes,et al.  Nonlinear Adaptive Algorithms on Rank-One Tensor Models , 2016, ArXiv.