Adaptive Subband Forward Blind Source Separation Algorithms Based on Kalman Mechanism

In forward blind source separation (FBSS) scenarios, subband adaptive filtering (SAF) algorithms provide fast convergence due to the SAF decorrelation ability. However, existing SAF algorithms suffer from a signal delay stemmed from the utilization of the synthesis filters. To solve this problem, we propose a delayless multisampled multiband-structured subband FBSS (DMSFBSS) algorithm by inserting a delayless multisampled multiband SAF structure. For a fixed SAF step-size, there is also a tradeoff between the convergence speed and steady-state error. We break this relationship by further developing an optimal DMSFBSS (ODMSFBSS) algorithm that minimizes the mean squared deviation (MSD) of DMSFBSS with respect to the subband gain vectors, to provide simultaneously fast convergence and low steady-state behavior. Intrinsically, the ODMSFBSS algorithm is an extension of the Kalman filtering theory over the subband-based FBSS structure. We also present an analysis of the algorithm stability. A vectorized implementation of the ODMSFBSS algorithm is proposed to reduce the computational complexity from $\mathcal {O}(L^{2})$ to $\mathcal {O}(L)$ , where $L$ is the length of the adaptive filter. Since adaptive FBSS scenarios require a voice activity detection (VAD) technique to control the alternating update of two adaptive filters, we develop two VAD approaches not relying on the priori knowledge of the speech source signal, thereby guaranteeing the practicability of the proposed ODMSFBSS algorithm. Simulation results in high and low SNR environments confirm that the proposed ODMSFBSS algorithm outperforms existing state-of-the-art algorithms.