Square-Root-Free QRD-LSL Adaptive Algorithm with Improved Numerical Robustness

The QR-decomposition-based least-squares lattice (QRD-LSL) algorithm is one of the most attractive choices for adaptive filters applications, mainly due to its fast convergence rate and good numerical properties. In practice, the square-root-free QRD-LSL (SRF-QRD-LSL) algorithms are frequently employed, especially when fixed-point digital signal processors (DSPs) are used for implementation. In this context, there are some major limitations regarding the large dynamic range of the algorithm’s cost functions. Consequently, hard scaling operations are required, which further reduce the precision of numerical representation and lead to performance degradation. In this paper we propose a SRF-QRD-LSL algorithm based on a modified update of the cost functions, which offers improved numerical robustness. Simulations performed in fixed-point and logarithmic number system (LNS) implementation support the theoretical findings.