Multichannel Filtered-X Error Coded Affine Projection-Like Algorithm with Evolving Order

Abstract

Affine projection (AP) algorithms are commonly used to implement active noise control (ANC) systems because they provide fast convergence. However, their high computational complexity can restrict their use in certain practical applications. The Error Coded Affine Projection-Like (ECAP-L) algorithm has been proposed to reduce the computational burden while maintaining the speed of AP, but no version of this algorithm has been derived for active noise control, for which the adaptive structures are very different from those of other configurations. In this paper, we introduce a version of the ECAP-L for single-channel and multichannel ANC systems. The proposed algorithm is implemented using the conventional filtered-x scheme, which incurs a lower computational cost than the modified filtered-x structure, especially for multichannel systems. Furthermore, we present an evolutionary method that dynamically decreases the projection order in order to reduce the dimensions of the matrix used in the algorithm's computations. Experimental results demonstrate that the proposed algorithm yields a convergence speed and a final residual error similar to those of AP algorithms. Moreover, it achieves meaningful computational savings, leading to simpler hardware implementation of real-time ANC applications.

A Time-Efficient Method for Determining an Optimal Scaling Factor and the Encoder Resolution in the Multichannel FXECAP-L Algorithm with Evolving Order for Active Noise Control

“…The FXECAP-L algorithm with evolving order was introduced by Avalos et al [6]. This algorithm aims at reducing the computational cost by employing two techniques.…”

“…The first technique is linked to the update of the filter coefficients based on the estimation error, i.e., there is an update process when the error is higher than a pre-determined threshold. The second technique is based on the calculation of projection order in each iteration [6]. The block diagram of a multichannel ANC system using the FXECAP-L algorithm is shown in Figure 1.…”

“…As mentioned in [6], when the error is encoded with a lower number of bits, the convergence speed is slower. However, using a large number of bits increases the convergence speed, but the update threshold is not reached, and thus the algorithm updates its coefficients in almost all the iterations.…”

“…Nevertheless, this variant has not been applied for active noise control, for which the adaptive configuration is very different. To adjust the number of bits for the encoder in each iteration, the instantaneous value of the steady-state mean square error (see [6]) was used. Thus, the number of bits is adjusted as follows:…”

“…However, many of them have some restrictions rendering their use unfeasible in practical applications. Recently, Avalos et al [6] introduced a new variant of the AP algorithms based on an affine projection-like-I (APL-I) algorithm. The authors proposed a strategy to update the filter coefficients only when the estimation error is higher than a pre-determined threshold and it uses a method to adjust the projection order dynamically.…”