【应用手册】QR Matrix Decomposition

【应用手册】QR Matrix Decomposition
QR matrix decomposition (QRD), sometimes referred to as orthogonal
matrix triangularization, is the decomposition of a matrix (A) into an
orthogonal matrix (Q) and an upper triangular matrix (R). QRD is useful
for solving least squares’ problems and simultaneous equations.
In wireless applications, there are prevalent cases where QRD is useful.
Multiple-input multiple-output (MIMO) orthogonal frequency-division
multiplexing (OFDM) systems often require small multiple matrix (for
example, 4 × 4) inversions. These systems typically use a non-recursive
technique, such as QRD. Digital predistortion (DPD) and joint detection
applications often require large single matrix (for example, 20 × 20)
inversions. DPD often also requires a recursive technique, such as the
QRD recursive least squares (QRD-RLS) algorithm, because the equations
are overspecified—matrix A has more rows than there are unknowns (N)
to calculate.
QR Matrix Decomposition


February 2008, ver. 2.0 Application Note 506



Introduction QR matrix decomposition (QRD), sometimes referred to as orthogonal
matrix triangularization, is the decomposition of a matrix (A) into an
orthogonal matrix (Q) and an upper triangular matrix (R). QRD is useful
for solving least squares’ problems and simultaneous equations.

In wireless applications, there are prevalent cases where QRD is useful.
Multiple-input multiple-output (MIMO) orthogonal frequency-division
multiplexing (O