On the stochastic modeling of the IAF-PNLMS algorithm for complex and real correlated Gaussian input data

• A new methodology for the modeling of the IAF-PNLMS algorithm is developed.
• Model expressions considering complex- and real-valued Gaussian data are obtained.
• Analytical solutions for the normalized autocorrelation-like matrices are proposed.
• The novel methodology can also be used to model other PNLMS-type algorithms.
• Simulation results for different scenarios ratify the accuracy of the model.

This paper presents a stochastic model for the individual-activation-factor proportionate normalized least-mean-square (IAF-PNLMS) adaptive algorithm operating under correlated Gaussian input data. The proposed approach uses the contragredient transformation to obtain an analytical solution for the normalized autocorrelation-like matrices arising from the model development. Model expressions describing the learning curve and the second-order moment of the weight-error vector for the IAF-PNLMS algorithm are derived taking into account the time-varying characteristic of the gain distribution matrix. As a consequence, the obtained model predicts very well the algorithm behavior for both transient and steady-state phases. Through simulation results, considering different operating scenarios, the accuracy of the proposed model is attested (via learning curve) for both complex- and real-valued input data.