Frequency-Domain Adaptive Filtering Algorithms for Nonstationary Environments

In nonstationary environments, existing frequency-domain adaptive filtering algorithms would exhibit poor tracking performance. To solve this issue, this paper focuses on developing new frequency-domain adaptive filtering algorithms based on single data. Using the circular matrix of the regression vector, we first establish a model and cost function suitable for a nonstationary system. Next, with resort to the stochastic gradient descent and power normalized methods, the frequency-domain least mean-square algorithm based on single data (SFDLMS) and its normalized version (named SFDNLMS) are derived. Even in the presence of correlated input signals, the proposed SFDNLMS algorithm can provide fast tracking/convergence performance. The transient and steady-state behavior is also studied. Finally, experiment results illustrate the advantages of the proposed algorithms and the reliability of the theoretical analysis.