The receiver may utilize Givens rotations to perform the decomposition, which may be performed using coordinate rotation digital computer (CORDIC) modules....

The receiver may utilize Givens rotations to perform the decomposition, which may be performed using coordinate rotation digital computer (CORDIC) modules.performing a QR decomposition of the channel response matrix using Givens rotations, wherein performing the QR decomposition comprises performing a plurality of rotations using a plurality of angles on at least a portion of the channel response matrix, the plurality of rotations including two rotations, (1) for phase cancellation to remove imagery parts of vectors and (2) to zero matrix elements that are below a diagonal matrix by rotating angles to zero the elements in the diagonal matrix;a QR decomposition module that performs a QR decomposition on a received channel response matrix using Givens rotations, wherein the QR decomposition module performs a plurality of rotations using a plurality of angles on at least a portion of the channel response matrix, the plurality of rotations including two rotations, (1) for phase cancellation to remove imagery parts of vectors and (2) to zero matrix elements that are below a diagonal matrix by rotating angles to zero the elements in the diagonal matrix, and produces an upper triangular matrix R based on a result of the performed plurality of rotations, wherein the QR decomposition module further calculates an inverse of the R matrix from the matrix R;means for performing a QR decomposition on a received channel response matrix using Givens rotations, wherein the means for performing the QR decomposition comprises means for performing a plurality of rotations using a plurality of angles on at least a portion of the channel response matrix, the plurality of rotations including two rotations, (1) for phase cancellation to remove imagery parts of vectors and (2) to zero matrix elements that are below a diagonal matrix by rotating angles to zero the elements in the diagonal matrix;a QR decomposition module that performs a QR decomposition on the channel response matrix using Givens rotations, wherein the QR decomposition module performs a plurality of rotations using a plurality of angles on at least a portion of the channel response matrix, the plurality of rotations including two rotations, (1) for phase cancellation to remove imagery parts of vectors and (2) to zero matrix elements that are below a diagonal matrix by rotating angles to zero the elements in the diagonal matrix, and produces an upper triangular matrix R based on a result of the performed plurality of rotations, wherein the QR decomposition module calculates an inverse of the R matrix from the matrix R; means for performing a QR decomposition on the channel response matrix using Givens rotations, wherein the means for performing the QR decomposition comprises means for performing a plurality of rotations using a plurality of angles on at least a portion of the channel response matrix, the plurality of rotations including two rotations, (1) for phase cancellation to remove imagery parts of vectors and (2) to zero matrix elements that are below a diagonal matrix by rotating angles to zero the elements in the diagonal matrix;, wherein means for estimating a plurality of transmitted signals comprises means for applying the inverse of the R matrix to an output of the means for applying rotations to the plurality of received signals.

In this paper, an efficient and optimized implementation of QR decomposition on TMS320C6678 floating point DSP is introduced.This algorithm can be divided into two main stages: optimization problem and least square problem (LSP).The most complex and time consuming step of OMP is the LSP resolution.The third approach seeks to combine the best attributes of the first two. Contents 1 Introduction and problem statement 1 2 Motivating Examples 3 3 Approximation methods 4 3.1 SVD-based approximation methods .