Joint beamforming and echo cancellation combining QRD based multichannel AEC and MVDR for reducing noise and non-linear echo

The problems of echo and noise contaminating a desired talker signal in a communication or an entertainment device are considered. In the following, we propose a combined method comprising a linear echo-canceller followed by a weighted minimum variance distortionless response (MVDR) beamformer designed to reduce noise and echo residues. For the echo-canceller stage we use a fast-converging multichannel QR decomposition (QRD)-recursive least squares (RLS) method. For the beamformer stage, we adopt and modify our recently proposed method of a fast-tracking QRD based MVDR beamformer [1]. We model that the residual echo is dominated by non-linearly distorted components which undergo the same echo paths as the non-distorted component. Thereby, the MVDR beamformer is designed to minimize a weighted sum of the powers of the noise and of the non-linear echo while maintaining the desired talker undistorted. The computational and memory complexities of the proposed algorithm are sufficiently low, making it appropriate for implementation in mobile devices. The performance of the proposed method is tested using real recordings from two commercial devices, a mobile-phone and a smart-speaker.