Theoretical analysis and verification of convergence for the overall modeling algorithm in narrowband active noise control

Online secondary path modeling is essential for the robust performance of adaptive active noise control (ANC) systems. The Overall Modeling Algorithm (OMA) simultaneously models both the primary and secondary paths during control filter adaptation, featuring a simple algorithm structure and no need for auxiliary noise. While previous studies have analyzed its convergence only in broadband ANC systems, the convergence behavior in narrowband ANC (NANC) systems remains unclear. Therefore, this paper analyzes the convergence of OMA in NANC systems in both the time and frequency domains. The results show that OMA-based NANC systems converge when the lengths of the modeled primary path, the modeled secondary path, and the control filter are each at least twice the number of noise frequencies. If the modeled path length equals the true path length, full-band convergence can be achieved when the number of noise frequencies is at least half of the path length. This indicates that complete secondary path information can be obtained using only a limited number of tonal signals. The theoretical analysis is validated through simulations and experiments under various NANC scenarios.