Raking the Cocktail Party

We present the concept of an acoustic rake receiver (ARR)---a microphone beamformer that uses echoes to improve the noise and interference suppression. The rake idea is well-known in wireless communications. It involves constructively combining different multipath components that arrive at the receiver antennas. Unlike typical spread-spectrum signals used in wireless communications, speech signals are not orthogonal to their shifts, which makes acoustic raking a more challenging problem. That is why the correct way to think about it is spatial. Instead of explicitly estimating the channel, we create correspondences between early echoes in time and image sources in space. These multiple sources of the desired and interfering signals offer additional spatial diversity that we can exploit in the beamformer design. We present several "intuitive" and optimal formulations of ARRs, and show theoretically and numerically that the rake formulation of the maximum signal-to-interference-and-noise beamformer offers significant performance boosts in terms of noise suppression and interference cancellation. We accompany the paper by the complete simulation and processing chain written in Python. The code and the sound samples are available online at \url{http://lcav.epfl.ch/people/ivan.dokmanic}.