Modified Gram-Schmidt core implemented in a single field programmable gate array architecture

A method of implementing a modified Gram-Schmidt (MGS) QR decomposition (QRD) in a single field programmable gate array (FPGA), wherein the MGS QRD decomposes an input matrix A into an output matrix Q and an output matrix R, the method comprising:

• normalizing a column of the input matrix to compute an element of an R matrix, R(i,i), wherein the elements of the input matrix column are added in a parallel pipelined fashion, thereby decimating a number of sub-total additions performed in each clock cycle;
• multiplying two columns of the input matrix to compute an element of the R matrix R(j,i), wherein products of the multiplying are added in a parallel pipelined fashion, thereby decimating the number of sub-total additions performed in each clock cycle;
• calculating an intermediate column vector for the Q matrix;
• calculating a final column vector for the Q matrix using a complex divider to divide the intermediate column vector by the computed matrix element R(i,i);
• and
• outputting a calculated element of one of output matrix Q and output matrix R.

A non-transitory machine-readable medium upon which are stored instructions, the instructions when executed by a processor cause the processor to perform the steps of:

• normalizing a column of the input matrix to compute an element of an R matrix, R(i,i), wherein the elements of the input matrix column are added in a parallel pipelined fashion and decimate a number of sub-total additions performed in each clock cycle;
• multiplying two columns of the input matrix to compute an element of the R matrix R(j,i), wherein products of the multiplying are added in a parallel pipelined fashion, decimating the number of sub-total additions performed in each clock cycle;
• calculating an intermediate column vector for the Q matrix;
• calculating a final column vector for the Q matrix using a complex divider to divide the intermediate column vector by the computed matrix element R(i,i);
• and
• outputting a calculated element of one of output matrix Q and output matrix R.