Comments on "A Square-Root-Free Matrix Decomposition Method for Energy-Efficient Least Square Computation on Embedded Systems"

TL;DR

This paper critically examines a square-root-free QR decomposition method for least squares problems, revealing that it is unsuitable for constrained problems like MIMO detection which require norm computations for accurate results.

Contribution

It clarifies that the proposed method is only valid for unconstrained LS problems and not for constrained cases such as MIMO detection, highlighting a key limitation.

Findings

The method eliminates the need for square-root operations in unconstrained LS problems.

For constrained LS problems like MIMO detection, norm computations are still necessary.

The proposed scheme does not produce correct results for constrained least squares problems.

Abstract

A square-root-free matrix QR decomposition (QRD) scheme was rederived in [1] based on [2] to simplify computations when solving least-squares (LS) problems on embedded systems. The scheme of [1] aims at eliminating both the square-root and division operations in the QRD normalization and backward substitution steps in the LS computations. It is claimed in [1] that the LS solution only requires finding the directions of the orthogonal basis of the matrix in question, regardless of the normalization of their Euclidean norms. MIMO detection problems have been named as potential applications that benefit from this. While this is true for unconstrained LS problems, we conversely show here that constrained LS problems such as MIMO detection still require computing the norms of the orthogonal basis to produce the correct result.