A Low-Complexity Parallel Two-Sided Jacobi Complex SVD Algorithm and Architecture for MIMO Beamforming Systems

Abstract

Singular Value Decomposition (SVD) is a very important matrix factorization technique in engineering applications. In multiple-input multiple-output (MIMO) systems, SVD is applied in transmit beamforming which provides high diversity advantages. This paper proposes a low-complexity parallel two-sided Jacobi complex SVD algorithm and architecture which are suitable for any m ×n (m ≤ 4, n ≤ 4) matrix. It performs two 2×2 complex SVD procedures in parallel, and employs master-slave CORDIC (coordinate rotation digital computer) to reduce the decomposition time. The proposed parallel algorithm for 4×4 complex SVD saves 52% decomposition time compared with the Golub-Kahan-Reinsch algorithm. Meanwhile, the Bit Error Rate (BER) performance of the proposed algorithm is almost the same with the ideal SVD.