Inverse LDM' and LU Factorizations of a Partitioned Matrix with the Square-root and Division Free Version for V-BLAST

TL;DR

This paper introduces a novel inverse LDM' and LU factorization method for partitioned matrices that is square-root and division free, optimizing the V-BLAST algorithm's computational efficiency and avoiding complex operations.

Contribution

It presents a new square-root and division free inverse LDM' factorization applicable to V-BLAST, reducing divisions and computational complexity in MIMO detection algorithms.

Findings

Reduces divisions in initial error covariance computation.

Maintains similar computational complexity to existing methods.

Eliminates the need for square-root and division operations in V-BLAST.

Abstract

This letter proposes the inverse LDM' and LU factorizations of a matrix partitioned into 2x2 blocks, which include the square-root and division free version. The proposed squareroot and division free inverse LDM' factorization is applied to compute the initial estimation error covariance matrix Q for the recursive V-BLAST algorithm, which can save K-1 divisions (where K is the number of transmit antennas), and requires about the same computational complexity as the corresponding algorithm to compute Q in the existing recursive V-BLAST algorithm [8], [9]. The proposed square-root and division free inverse LDM' factorization can also be applied to propose the square-root and division free implementation for the squareroot V-BLAST algorithm in [5], where the wide-sense Givens rotation in [14] is utilized. With respect to the existing squareroot V-BLAST algorithms [5], [6], the proposed square-root and division free V-BLAST algorithm requires about the same computational complexity, and can avoid the square-root and division operations.