In applications involving system identification problems, some characteristics of the impulse response of the system to be identified are usually exploited to design adaptive algorithms with improved performance. In this context, this paper focuses on the identification of systems that own intrinsic symmetric or antisymmetric properties, which can be further formulated by using a combination of bilinear forms. Based on such an approach, the least-mean-square (LMS) and normalized LMS (NLMS) algorithms with symmetric/antisymmetric properties (termed here LMS-SAS and NLMS-SAS) are proposed. Simulation results are shown confirming the improved convergence speed achieved by the proposed algorithms as compared to the conventional LMS and NLMS counterparts for different operating scenarios.

This letter presents a time-varying autoregressive (TVAR) model aiming to characterize nonstationary behaviors often observed in real-world processes, which cannot be properly described by autoregressive processes such as first-order Markov and random-walk models. Specifically, general model expressions for the mean vector and covariance matrix of the TVAR model are firstly derived. Then, such expressions are used to guide the design of two special setups for the TVAR model. The capability of the developed model to reproduce important nonstationary behaviors is verified mathematically and through simulations.

This letter presents model expressions describing the steady-state behavior of proportionate normalized least-mean-square (PNLMS)-type algorithms, taking into account both complex- and real-valued correlated Gaussian input data. Specifically, based on energy-conservation arguments, general expressions for the excess mean-square error (EMSE) in steady state and misadjustment are obtained. Such general expressions are then applied to two well-known PNLMS-type algorithms, namely the improved PNLMS (IPNLMS) and the individual-activation-factor PNLMS (IAF-PNLMS). Simulation results are shown confirming the accuracy of the proposed model expressions under different operating conditions.