Abstract
Acoustic sensor networks (ASNs) are an effective solution to implement active noise control (ANC) systems by using distributed adaptive algorithms. On one hand, ASNs provide scalable systems where the signal processing load is distributed among the network nodes. On the other hand, their noise reduction performance is comparable to that of their respective centralized processing systems. In this sense, the distributed multiple error filtered-x least mean squares (DMEFxLMS) adaptive algorithm has shown to obtain the same performance than its centralized counterpart as long as there are no communications constraints in the underlying ASN. Regarding affine projection (AP) adaptive algorithms, some distributed approaches that are approximated versions of the multichannel filtered-x affine projection (MFxAP) algorithm have been previously proposed. These AP algorithms can efficiently share the processing load among the nodes, but at the expense of worsening their convergence properties. In this paper we develop the exact distributed multichannel filtered-x AP (EFxAP) algorithm, which obtains the same solution as that of the MFxAP algorithm as long as there are no communications constraints in the underlying ASN. In the EFxAP algorithm each node can compute a part or the entire inverse matrix needed by the centralized MFxAP algorithm. Thus, we propose three different strategies that obtain significant computational saving: 1) Gauss Elimination, 2) block LU factorization, and 3) matrix inversion lemma. As a result, each node computes only between 25%—60% of the number of multiplications required by the direct inversion of the matrix. Regarding the performance in transient and steady states, the EFxAP exhibits the fastest convergence and the highest noise level reduction for any size of the acoustic network and any projection order of the AP algorithm compared to the DMEFxLMS and two previously reported distributed AP algorithms.
Highlights
T HE use of acoustic sensor networks (ASNs) [1] as an alternative to fixed multi-channel sound systems is an Manuscript received March 27, 2020; revised July 31, 2020 and November 17, 2020; accepted November 19, 2020
We introduce an exact multichannel FxAP (EFxAP) algorithm that gives the same solution as the MFxAP, but it can be computed in a distributed way over ASNs
We present the numerical simulations carried out to evaluate the performance of the proposed EFxAP algorithm compared to two previous approximated versions of the distributed affine projection (AP) algorithm, the DFxAP [16] and the DFxAPL [15], and to the distributed multiple error filtered-x LMS (FxLMS) (DMEFxLMS) [14]
Summary
T HE use of acoustic sensor networks (ASNs) [1] as an alternative to fixed multi-channel sound systems is an Manuscript received March 27, 2020; revised July 31, 2020 and November 17, 2020; accepted November 19, 2020. Motivated by the good trade-off between convergence speed and computational cost of the AP algorithms, two approaches that address the distribution of the AP processing over ASNs have been presented [15], [16] They are approximated distributed versions of the centralized multichannel FxAP (MFxAP) algorithm [31]–[34] and, from their analysis, it is not assured that they can obtain the same performance as the MFxAP. In this work we propose three robust strategies that reduce the computational requirements of the EFxAP at each node These approaches are the Gauss elimination (GE), the block LU factorization, and the matrix inversion lemma methods [41], which efficiently decrease the computational cost at each node but obtain the same good performance as the centralized MFxAP algorithm.
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