A novel stochastic model for the steady-state performance of norm-penalized adaptive algorithms

This paper proposes a new model to estimate the asymptotic performance of adaptive algorithms with norm penalization of the adaptive coefficient vector. The attraction-to-zero term is modeled as a piecewise linear function, allowing the proposed approach to approximate, with arbitrary precision, the behavior of multiple algorithms from the literature. Assuming a white input signal, it is possible to derive a general model capable of predicting the algorithm's asymptotic performance in terms of mean square deviation. The closed-form expression obtained for the mean square deviation is then approximated using heuristics, allowing the optimal value of the parameter regulating the norm penalization to also be determined through a closed-form formula. The derived formulas were extensively tested and validated through simulations, demonstrating good accuracy, with a maximum error of 0.17 dB between the theoretical and simulated values.