A Proportionate Recursive Least Squares Algorithm and Its Performance Analysis

The proportionate updating (PU) mechanism has been widely adopted in least mean squares (LMS) adaptive filtering algorithms to exploit the system sparsity. In this brief, we propose a proportionate recursive least squares (PRLS) algorithm for the sparse system estimation, in which, an independent weight update is assigned to each tap according to the magnitude of that estimated filter coefficient. Its mean square performance is analyzed via the energy conservation principle in both the transient and steady-state stages. In this way, an explicit condition on the control parameter of the proportionate matrix of PRLS can be obtained to ensure a better steady-state performance than that of RLS. Simulation results in a system identification setting support the analysis.

Automated summary

The proportionate recursive least squares (PRLS) algorithm proposed in this study is designed for sparse system estimation, assigning independent weight updates to each tap based on the estimated filter coefficient magnitude. Its mean square performance is analyzed using the energy conservation principle to improve steady-state performance. An explicit condition on the control parameter of the proportionate matrix of PRLS is derived to ensure better performance than traditional RLS, supported by simulation results in a system identification setting.