Off-the-beaten-path Solutions for Decomposition-based Zero-forcing Precoding in xDSL Multi-user Downlinks

Abstract

However broad the Decomposition-based Zero-forcing (DBZF) precoder acceptance may be, reducing the computational complexity of its implementation is an absolute necessity for the VDSL networking professionals. The paper digs deeper into this problem from the perspective of matrix inversion which is inherent in the very nature of the DBZF. Five strategies considered here differ in mode of action: three of them include matrix inversion, and two others drop implementing the procedure. While the baseline strategy itemized under No. 1 acts with the Gaussian LU-decomposition, strategy No. 2 deals with the Jordanian LU-decomposition thereby enabling mild reduction of the operation count. Strategy No. 3 works for more significant reduction as it operates with the elimination form of the inverse matrix. The most cost-cutting are strategies excluding the question of matrix inversion and replacing it by far more straightforward linear system solution, as it is in Strategy No. 4. An alternative strategy No. 5 uses the least squares-based square-root-type sequential system solution and it is the most accurate computational procedure when compared with other strategies.