The widely linear block quaternion least mean square algorithm for fast computation in 3D audio systems

In this paper we propose an algorithm which operates weight adaptation by means of a periodic law and is based on the Widely Linear Quaternion Least Mean Square (WL-QLMS) algorithm. The WL-QLMS successfully handles real-world signals, either proper or improper. However, because of the introduction of full second order statistics into the algorithm, its computational cost is quadruplicated with respect to its precursor QLMS. The proposed Widely Linear Block Quaternion Least Mean Square (WL-BQLMS) algorithm speeds up the execution, thus revealing itself as a good solution in 3D audio signal processing applications, where huge amounts of data are usually treated and signals are typically improper. Simulations exploiting 3D Ambisonic B-Format audio signals provide a report of the WL-BQLMS behavior in comparison with BQLMS.