We present the concept of an acoustic rake receiver---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 spread-spectrum signals used in wireless communications, speech signals
are not orthogonal to their shifts. Therefore, we focus on the spatial
structure, rather than temporal. 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 the interfering signal offer
additional spatial diversity that we can exploit in the beamformer design.
We present several "intuitive" and optimal formulations of acoustic rake
receivers, 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 and interference suppression. Beyond
signal-to-noise ratio, we observe gains in terms of the \emph{perceptual
evaluation of speech quality} (PESQ) metric for the speech quality. 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.github.io/AcousticRakeReceiver/}.Comment: 12 pages, 11 figures, Accepted for publication in IEEE Journal on
Selected Topics in Signal Processing (Special Issue on Spatial Audio
