A high-precision multi-arithmetic neural circuit for the efficient computation of the new filtered-X Kronecker product APL-NLMS algorithm applied to active noise control

Abstract

In recent years, active noise control (ANC) systems have attracted a lot of attention since they are considered as potential alternative for solving acoustic noise problems. Until now, some practical ANC applications have employed filtered-x least-mean-square (FXLMS) adaptive algorithm since exhibits low computational cost, however, it provides a slow convergence speed. The filtered-x affine projection-like (FXAPL) algorithm can be seen as a potential strategy to improve this factor. However, the achievement of a significant improvement of this property and computational cost are still remaining challenges. In this work, we present a new variant of the FXAPL algorithm based on nearest Kronecker product decomposition to create an efficient algorithm in terms of convergence speed and tracking capabilities because in ANC systems is essential to cancel the noise signal as quickly as possible. In addition, we use the normalized least mean square (NLMS) to update the right-singular vectors of the adaptive filter coefficients. As consequence, the computational cost of the proposed FXAPL algorithm is decreased. From the engineering point of view, the implementation of the Kronecker product decomposition demands a large number of matrix additions, subtractions and multiplications, which represents a large area consumption. Hence, we introduce, for the first time, a new high-precision multi-arithmetic neural circuit based on spiking neural P systems along with their cutting-edge variants, such as synaptic weights, astrocyte-like controls, rules on the synapses and dendritic behavior, to perform either the addition, subtraction or multiplication of two numbers efficiently. Specifically, we use the dendritic pruning feature to enable dynamic dendritic connectivity. As a consequence, the circuit can support multiple arithmetic operations using the same neurons with simple and homogeneous spiking rules. Besides, we develop an compact FPGA-based neuromorphic architecture, which supports dynamic dendritic connectivity, to efficiently implement the proposed parallel adder/subtractor/multiplier neural circuit. Our results demonstrate that the resulting filtered-x Kronecker product affine projection-like and normalized least mean square (FXKAPL-NLMS) algorithm along with the neuromorphic architecture have allowed us to develop practical real-time ANC applications.