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

A square-root-free matrix QR decomposition (QRD) scheme, dubbed QDR decomposition (QDRD), was rederived by Ren
et al.
based on a scheme by Björck in order to simplify computations when solving least-squares (LS) problems on embedded systems. The QDRD scheme aims at eliminating both the square-root and division operations in the QRD normalization and backward substitution steps in LS computations. It is claimed by Ren
et al.
(F. Ren
et al.
,
IEEE Embedded Syst. Lett.
, vol. 6, no. 4, pp. 73–76) 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. Multiple-input multiple-output (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.