@article{Maruo_stochastic_2026,
	title = {Stochastic Analysis of the Deficient Length and Insufficient Order Affine Projection Algorithm for Unity Step-Size},
	journal = {Signal Processing},
	pages = {110802},
	year = {2026},
	issn = {0165-1684},
	doi = {https://doi.org/10.1016/j.sigpro.2026.110802},
	url = {https://www.sciencedirect.com/science/article/pii/S0165168426003154},
	author = {Marcos H. Maruo and Sérgio J.M. Almeida and José C.M. Bermudez},
	keywords = {Adaptive filtering, deficient length adaptive filter, Affine projections algorithm (APA), statistical analysis},
	abstract = {The Affine Projection Algorithm (APA) has encountered large applicability due to its faster convergence rate when compared to the least-mean-square (LMS) family of algorithms. For fastest convergence a unity step size is usually employed. Practical applications of APA may be subject to two conditions which may degrade the expected algorithm performance. The adaptive filter may have a deficient length (less taps than the actual response being identified), and the projection order of the APA may be insufficient to complete decorrelate the input signal samples. Despite its applicability, a study of the APA simultaneously subject to these two conditions is not yet available in the literature. This paper derives an analytical model for the APA behavior which assumes both inaccuracies. The derived results show behaviors that could not be predicted by the existing models. Simulation results verify the accuracy of the theoretical analysis and illustrate its applicability.}
}