TY - GEN
T1 - Minimum mean square deviation in ZA-NLMS algorithm
AU - Al-Shabili, Abdullah
AU - Jimaa, Shihab
AU - Weruaga, Luis
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/6/16
Y1 - 2017/6/16
N2 - The ZA-NLMS (for zero-attractor) represents arguably the seminal sparsity-aware gradient adaptive algorithm. As it is constraint by the ℓ1-norm of the filter weights, the underlying problem turns convex, hence with unique solution (in expected sense). Despite these friendly properties, the algorithm convergence and, more important, the best-performing sparsity tradeoff are yet to be effectively studied. This paper presents a comprehensive analytical study on ZA-NLMS' convergence, which results in the optimal (constant) sparsity tradeoff. The value of this decisive hyperparameter from a practitioner point of view turns out related to the 3/2-power of the adaptive filter length. This outcome, difficult to argue intuitively, as well as the convergence model, have been exhaustively validated with numerical experiments.
AB - The ZA-NLMS (for zero-attractor) represents arguably the seminal sparsity-aware gradient adaptive algorithm. As it is constraint by the ℓ1-norm of the filter weights, the underlying problem turns convex, hence with unique solution (in expected sense). Despite these friendly properties, the algorithm convergence and, more important, the best-performing sparsity tradeoff are yet to be effectively studied. This paper presents a comprehensive analytical study on ZA-NLMS' convergence, which results in the optimal (constant) sparsity tradeoff. The value of this decisive hyperparameter from a practitioner point of view turns out related to the 3/2-power of the adaptive filter length. This outcome, difficult to argue intuitively, as well as the convergence model, have been exhaustively validated with numerical experiments.
KW - mean square deviation
KW - modal analysis
KW - NLMS
KW - optimal tradeoff
KW - Sparsity
KW - ℓ norm
UR - http://www.scopus.com/inward/record.url?scp=85023766644&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2017.7952881
DO - 10.1109/ICASSP.2017.7952881
M3 - Conference contribution
AN - SCOPUS:85023766644
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 3869
EP - 3873
BT - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
Y2 - 5 March 2017 through 9 March 2017
ER -