Identification of Room Acoustic Impulse Responses via Kronecker Product Decompositions

The identification of room acoustic impulse responses represents a challenging problem in the framework of many important applications related to the acoustic environment, like echo cancellation, noise reduction, and microphone arrays, among others. The main issues are related to the long length of such impulse responses and their time-variant nature. Recently, a decomposition-based approach was developed for the identification of low-rank systems, which can also be applied (to some extent) for the identification of acoustic impulse responses. This approach exploits the nearest Kronecker product decomposition of the impulse response and solves a high-dimension system identification problem using a combination of low-dimension solutions (provided by shorter filters). Nevertheless, it does not consider the intrinsic nature of the room acoustic impulse responses, which contain specific components (e.g., early reflections and late reverberation) that can be very different in nature. In this article, we propose an improved decomposition-based method (via the Kronecker product) that takes into account these specific components and processes them separately. Following this approach, an iterative Wiener filter is firstly developed, followed by a recursive least-squares (RLS) algorithm. Both solutions outperform the conventional benchmarks. Moreover, they achieve superior performances as compared to the recently developed versions based on the nearest Kronecker product decomposition, also owning lower computational complexities than their previous counterparts. Simulations are performed in the framework of acoustic echo cancellation and the obtained results support the performance features of the proposed algorithms.