Efficient implementation of matrix recursions in the multichannel affine projection algorithm for multichannel sound

Multichannel adaptive affine projection algorithms (multichannel AP) are currently under development for multichannel audio applications, mainly for transaural audio reproduction. These algorithms present several advantages for real time systems such as moderate computational cost, good stability, and adjustable convergence speed. However the basic version of the AP algorithm needs to be optimized to be used on digital signal processors working on real time. Thus several variants of AP and its fast version (FAP) have been developed. Regarding its computational cost and real time implementation, an N × N inverse matrix have to be calculated in each algorithm iteration, being N the affine projection order. This paper presents a comparison between several versions of the AP algorithm for real time multichannel audio and proposes a series of recommendations, such as the initialization parameters, to use the variants of the AP algorithm in multichannel sound.