QR Decomposition-Based RLS Algorithm for Complex-Valued AR Process Prediction

This documentation describes the methodology for predicting complex-valued AR processes using the QR decomposition-based RLS algorithm. This approach enables improved understanding and analysis of complex signal patterns through numerically stable matrix operations. The implementation achieves more accurate future signal predictions through recursive weight updates and orthogonal transformations, making it particularly suitable for applications in signal processing, communications, and control systems where complex-valued data is prevalent. The algorithm implementation involves key components including: - QR factorization of the input data matrix using Givens rotations or Householder reflections - Recursive updating of the inverse correlation matrix through orthogonal decomposition - Complex-valued arithmetic operations for handling in-phase and quadrature components - Adaptive filter weight adjustment via backward substitution in the triangular system Through implementing this method, developers gain deeper insights into QR decomposition techniques and RLS algorithm mechanics, particularly regarding numerical stability advantages over conventional RLS implementations. This knowledge foundation significantly benefits future learning and research in adaptive filtering and statistical signal processing. The code structure typically includes modules for data preprocessing, QR update routines, prediction error calculation, and real-time coefficient adaptation.