title: Linear precoding based on polynomial expansion: reducing complexity in massive MIMO.
abstract: Massive multiple-input multiple-output (MIMO) techniques have the potential to bring tremendous improvements in spectral efficiency to future communication systems. Counterintuitively, the practical issues of having uncertain channel knowledge, high propagation losses, and implementing optimal non-linear precoding are solved more or less automatically by enlarging system dimensions. However, the computational precoding complexity grows with the system dimensions. For example, the close-to-optimal and relatively "antenna-efficient" regularized zero-forcing (RZF) precoding is very complicated to implement in practice, since it requires fast inversions of large matrices in every coherence period. Motivated by the high performance of RZF, we propose to replace the matrix inversion and multiplication by a truncated polynomial expansion (TPE), thereby obtaining the new TPE precoding scheme which is more suitable for real-time hardware implementation and significantly reduces the delay to the first transmitted symbol. The degree of the matrix polynomial can be adapted to the available hardware resources and enables smooth transition between simple maximum ratio transmission and more advanced RZF. By deriving new random matrix results, we obtain a deterministic expression for the asymptotic signal-to-interference-and-noise ratio (SINR) achieved by TPE precoding in massive MIMO systems. Furthermore, we provide a closed-form expression for the polynomial coefficients that maximizes this SINR. To maintain a fixed per-user rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and the signal-to-noise ratio.
authors.affiliation: Mathematical and Algorithmic Sciences Lab, France Research Center, Huawei Technologies Co. Ltd., Arcs de Seine Bâtiment A, 20 Quai du Point du Jour, Boulogne-Billancourt, 92100 France ; Alcatel-Lucent on Flexible Radio, SUPELEC, Plateau de Moulon, 3 Rue Joliot Curie, Gif-sur-Yvette, 91190 France.
authors.forename: Axel
authors.initials: A
authors.lastname: Mueller
authors.affiliation: KAUST, King Abdullah University of Science & Technology, Makkah Province, Thuwal, 23955-6900 Kingdom of Saudi Arabia ; Alcatel-Lucent on Flexible Radio, SUPELEC, Plateau de Moulon, 3 Rue Joliot Curie, Gif-sur-Yvette, 91190 France.
authors.forename: Abla
authors.initials: A
authors.lastname: Kammoun
authors.affiliation: Linköping University, Department of Electrical Engineering, Linköping, SE-581 83 Sweden ; Alcatel-Lucent on Flexible Radio, SUPELEC, Plateau de Moulon, 3 Rue Joliot Curie, Gif-sur-Yvette, 91190 France.
authors.forename: Emil
authors.initials: E
authors.lastname: Björnson
authors.affiliation: Mathematical and Algorithmic Sciences Lab, France Research Center, Huawei Technologies Co. Ltd., Arcs de Seine Bâtiment A, 20 Quai du Point du Jour, Boulogne-Billancourt, 92100 France ; Alcatel-Lucent on Flexible Radio, SUPELEC, Plateau de Moulon, 3 Rue Joliot Curie, Gif-sur-Yvette, 91190 France.
authors.forename: Mérouane
authors.initials: M
authors.lastname: Debbah
keywords: Linear precoding; Massive MIMO; Multiuser systems; Polynomial expansion; Random matrix theory