QR Matrix Decomposition Reference Design

The use of this design is governed by, and subject to, the terms and conditions of the Intel Design Example License Agreement.


The QR matrix decomposition (QRD) reference design implements QR matrix decomposition, sometimes referred to as orthogonal matrix triangularization. The basic operation 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 that are increasingly important for applications such as multiple-input multiple-output (MIMO), digital pre-distortion (DPD), channel estimation, and joint detection.

The QRD reference design uses the well-known systolic array and CORDIC to perform the Givens rotation algorithm, which is well suited for FPGAs. Using a common method of back substitution, a full QRD-RLS algorithm can be easily realized in our devices, providing an optimized and cost-effective hardware implementation.


  • Run time configurable QRD and QRD-RLS implementation
  • Run time configurable support for different input matrix size decompositions
  • Run time configurable support for single matrix decomposition or parallel multiple matrix decompositions
  • Run time configurable support for one or more output columns of data
  • Fixed-point implementation for real or complex data
  • Bit-accurate configurable MATLAB model and MATLAB testbench
  • Register transfer level (RTL) design written in VHDL
  • ModelSim*-Intel® FPGA VHDL self-checking testbench
  • Sample data sets for different configurations of QRD design

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Figure 1. QRD Design Block

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