The adaptive multiple-input/output inverse theorem (A-MINT) multichannel equalization algorithm was proposed to address the computational complexity of the MINT algorithm. However, similar to MINT, A-MINT also assumes an arbitrary modeling delay for the target response which, if inappropriately chosen, results in misconvergence or poor performance. We present a new adaptive algorithm that exploits the sparsity of a target response to estimate equalization filters. The proposed algorithm automatically selects a suitable modeling delay for the equalized response so as to achieve a minimum-norm solution.

Equalization of acoustic channels usually involves inversion of acoustic impulse responses (AIRs), and generally employs multichannel techniques. In this paper, we propose three equalization algorithms, one in the Karhunen-Loève transform (KLT) domain and the other two in the frequency domain. Our proposed algorithm in the KLT domain provides a platform to achieve equalization in conjunction with denoising. Existing multiple-input/output inverse theorem (MINT)-based non-adaptive algorithms require the inversion of a matrix with dimension that is proportional to the AIR length, and is computationally expensive. To overcome this limitation, we propose the frequency-domain algorithm which is computationally very efficient and thus can be employed for the equalization of high-order AIRs in practical applications. In addition, the frequency-domain method is more robust to AIR estimation errors. To achieve further reduction in the complexity without significant performance degradation, we then propose a modified version of the frequency-domain algorithm.

It is well-known that the performance of acoustic multichannel equalization (MCEQ) algorithms depend on the modeling delay that has to be pre-defined. In this work, we propose a MCEQ algorithm which achieves full equalization of acoustic room impulse responses in the presence of blind-system identification error. We achieve the above by modeling the inverse filters using multiple delays via columns of the identity matrix which serve as basis vectors for this time-domain sub-space approach. We further show that the proposed algorithm allows one to determine an optimal set of inverse filters corresponding to an appropriate modeling delay.

Non-adaptive multichannel equalization (MCEQ) algorithms based on multiple input/output inverse theorem (MINT) is computationally expensive as MINT involves the inversion of a convolution matrix with dimension that is proportional to the length of the acoustic impulse responses. To address this, we propose a MINT-based algorithm that estimates inverse filters by minimizing a cost function iteratively. To further enhance the convergence rate, we formulate an algorithm that employs an adaptive step-size that is derived as a function of the sparseness measure. The proposed algorithm is then applied to existing MINT-based equalization algorithms such as A-MINT and the currently proposed MCEQ-based algorithms.

The multiple-input/output inverse theorem (MINT) algorithm for multichannel equalization is computationally demanding. Although adaptive MINT reduces the computational complexity, it suffers from slow convergence. In this letter, we propose a low-complexity fast-converging adaptive algorithm for multichannel equalization. The novelty of the approach lies in the adaptive equalization for each frequency bin and its ability to achieve fast convergence in a single step. The proposed algorithm can achieve better equalization of high-order acoustic impulse responses with significant reduction in complexity.