Stable QR Decomposition-Based EX-RLS Algorithms

• Numerically stable QR-based EX-RLS algorithms for real-time adaptive signal processing. • Kalman-equivalent tracking performance preserved under finite-precision constraints. • Robust operation in time-varying DSP applications, including channel tracking and digital predistortion. Extended Recursive Least Squares (EX-RLS) algorithms are widely used in adaptive digital signal processing for tracking rapidly time-varying systems with Kalman-equivalent performance. However, practical digital signal processing implementations—particularly under finite-precision arithmetic and complex-valued data—often suffer from numerical instability and covariance divergence. We introduce two QR-based EX-RLS variants: G-EX-RLS, which uses Givens rotations, and H-EX-RLS, which uses Householder reflectors. These algorithms preserve EX-RLS-like tracking accuracy, prevent covariance collapse and divergence, and maintain O ( m 2 ) complexity when square-root or Taylor-based covariance updates are applied. Simulations with real- and complex-valued signals confirm their robustness: in Rayleigh-fading tracking and in adaptive digital predistortion of a GaN power amplifier driven by a 5G-like OFDM waveform, the proposed variants remain stable in regimes where conventional RLS and EX-RLS fail. These properties make the proposed QR-based EX-RLS algorithms well-suited to real-time adaptive digital signal processing applications that require robust, numerically stable operation in dynamic environments.