DSP Builder for Intel® FPGAs (Advanced Blockset): Handbook

ID 683337
Date 5/27/2022

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7.13.23. STAP Radar Forward and Backward Substitution

The QR decomposition reference design produces an upper triangular matrix and a lower triangular matrix.

The design applies this linear system of equations to the steering vector in the following two steps:

  • Forward substitution with the lower triangular matrix
  • Backward substitution with the lower triangular matrix

A command pipeline controls the routing of floating-point vectors. Nested ForLoop blocks generate these commands. Another FIFO unit queues the commands. This decoupled system of FIFO buffers maximizes the usage of the shared vector floating-point block while automatically throttling the rate of the ForLoop system.

This design uses advanced settings from the DSP Builder > Verify Design menu to access enhanced features of the automatically generated testbench. An application specific m-function verifies the simulation output, to correctly compare complex results and properly handle floating-point errors that arise from the ill-conditioning of the QRD output.

The model file is STAP_ForwardAndBackwardSubstitution.mdl.