TY - GEN
T1 - Study of Sparsity Emanating from NKPD and its Utilization to Enhance NKPD based Adaptive Algorithms
AU - Bhattacharjee, Sankha Subhra
AU - Christensen, Mads Græsbøll
AU - Benesty, Jacob
PY - 2023
Y1 - 2023
N2 - Recently, the nearest Kronecker product (NKP) decomposition has become popular in several adaptive filtering (AF) applications owing to its fast convergence and tracking ability. In this paper, we study the nature of the smaller weight vectors resulting from NKP decomposition (NKPD) of a wide range of acoustic impulse responses (IRs). The study shows that the smaller weight vectors resulting from NKPD exhibit moderate to high degree of sparsity. To exploit this knowledge in AF problems, we propose a class of proportionate update based NKP normalized least-mean-square (NKP-NLMS) type algorithms: namely, the improved proportionate NKP-NLMS (NKP-IPNLMS) algorithm which uses the ℓ1-norm of the smaller weight vectors and the NKP-IPNLMS-ℓ0 which uses an approximation of the ℓ0-norm. Further, we propose a new approximation of the ℓ0-norm with reduced computational complexity, using which we also propose the NKP-IPNLMS-ℓ0-2 algorithm. Next, we present a comparison of computational complexity of the proposed algorithms. Simulation results show the improved performance achieved by the proposed algorithms, showing the advantage of exploiting sparsity in the smaller weight vectors in NKPD based adaptive algorithms.
AB - Recently, the nearest Kronecker product (NKP) decomposition has become popular in several adaptive filtering (AF) applications owing to its fast convergence and tracking ability. In this paper, we study the nature of the smaller weight vectors resulting from NKP decomposition (NKPD) of a wide range of acoustic impulse responses (IRs). The study shows that the smaller weight vectors resulting from NKPD exhibit moderate to high degree of sparsity. To exploit this knowledge in AF problems, we propose a class of proportionate update based NKP normalized least-mean-square (NKP-NLMS) type algorithms: namely, the improved proportionate NKP-NLMS (NKP-IPNLMS) algorithm which uses the ℓ1-norm of the smaller weight vectors and the NKP-IPNLMS-ℓ0 which uses an approximation of the ℓ0-norm. Further, we propose a new approximation of the ℓ0-norm with reduced computational complexity, using which we also propose the NKP-IPNLMS-ℓ0-2 algorithm. Next, we present a comparison of computational complexity of the proposed algorithms. Simulation results show the improved performance achieved by the proposed algorithms, showing the advantage of exploiting sparsity in the smaller weight vectors in NKPD based adaptive algorithms.
KW - Adaptive filter
KW - Proportionate algorithms
KW - Sparsity
KW - System identification
KW - nearest Kronecker product
UR - http://www.scopus.com/inward/record.url?scp=85178338970&partnerID=8YFLogxK
U2 - 10.23919/EUSIPCO58844.2023.10289967
DO - 10.23919/EUSIPCO58844.2023.10289967
M3 - Article in proceeding
SN - 979-8-3503-2811-0
T3 - Proceedings of the European Signal Processing Conference
SP - 361
EP - 365
BT - 31st European Signal Processing Conference, EUSIPCO 2023 - Proceedings
PB - IEEE
T2 - 31st European Signal Processing Conference, EUSIPCO 2023
Y2 - 4 September 2023 through 8 September 2023
ER -