FPGA-based Calculation of Eigenvalues for Autocorrelation Matrix in DLMS Filter Suppressing RFI in Radio Detection of Cosmic Rays

The LMS filter is parametrized by the learning factor. Its value is crucial for stability. Low values provide stable operations, but rather slow converge, high values improve a converge speed, but may be a cause of instability. The learning factor should be smaller than an inverse maximal eigenvalue of the autocorrelation matrix. The paper presents the system calculating the eigenvalues of the auto-correlation matrix in the radio detector of in the Auger Engineering Radio Array in Argentinean real pampas conditions. The virtual NIOS^® processor embedded in the FPGA allows optimizing the learning factors for a perfect stability. The calculation speed is at the level of tens of seconds; however, this factor is not critical for relatively slow changing environmental conditions. Most important is an accuracy of calculations exactly the same as provided by Visual C++ or Mathematica.