Modified Conjugate Gradient Algorithms for Gram Matrix Inversion of Massive MIMO Downlink Linear Precoding
D. Subitha1, J. M. Mathana2, J. S. Leena Jasmine3, R. Vani4
1D. Subitha, Assistant Professor, Department of ECE, Saveetha School for Engineering, Chennai (Tamil Nadu), India.
2J. M. Mathana, Principal, Chennai Institute of Technology, Chennai (Tamil Nadu), India.
3S. Leena Jasmine, Associate Professor, Department of ECE, Velammal Engineering College Chennai (Tamil Nadu), India.
4R. Vani, Associate Professor, Department of ECE, SRM University, Chennai (Tamil Nadu), India.
Manuscript received on 17 October 2019 | Revised Manuscript received on 25 October 2019 | Manuscript Published on 02 November 2019 | PP: 2834-2840 | Volume-8 Issue-2S11 September 2019 | Retrieval Number: B13510982S1119/2019©BEIESP | DOI: 10.35940/ijrte.B1351.0982S1119
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: This paper deals with various low complexity algorithms for higher order matrix inversion involved in massive MIMO system precoder design. The performance of massive MIMO systems is optimized by the process of precoding which is divided into linear and nonlinear. Nonlinear precoding techniques are most complex precoding techniques irrespective of its performance. Hence, linear precoding is generally preferred in which the complexity is mainly contributed by matrix inversion algorithm. To solve this issue, Krylov subspace algorithm such as Conjugate Gradient (CG) was considered to be the best choice of replacement for exact matrix inversions. But CG enforces a condition that the matrix needs to be Symmetric Positive Definite (SPD). If the matrix to be inverted is asymmetric then CG fails to converge. Hence in this paper, a novel approach for the low complexity inversion of asymmetric matrices is proposed by applying two different versions of CG algorithms- Conjugate Gradient Squared (CGS) and Bi-conjugate Gradient (Bi-CG). The convergence behavior and BER performance of these two algorithms are compared with the existing CG algorithm. The results show that these two algorithms outperform CG in terms of convergence speed and relative residue.
Keywords: Massive MIMO, Linear Precoding, Krylov Subspace Algorithms, Convergence Speed, Relative Residue.
Scope of the Article: VLSI Algorithms