We present the concept of an acoustic rake receiver---a microphone beamformerthat uses echoes to improve the noise and interference suppression. The rakeidea is well-known in wireless communications; it involves constructivelycombining different multipath components that arrive at the receiver antennas.Unlike spread-spectrum signals used in wireless communications, speech signalsare not orthogonal to their shifts. Therefore, we focus on the spatialstructure, rather than temporal. Instead of explicitly estimating the channel,we create correspondences between early echoes in time and image sources inspace. These multiple sources of the desired and the interfering signal offeradditional spatial diversity that we can exploit in the beamformer design. We present several "intuitive" and optimal formulations of acoustic rakereceivers, and show theoretically and numerically that the rake formulation ofthe maximum signal-to-interference-and-noise beamformer offers significantperformance boosts in terms of noise and interference suppression. Beyondsignal-to-noise ratio, we observe gains in terms of the \emph{perceptualevaluation of speech quality} (PESQ) metric for the speech quality. Weaccompany the paper by the complete simulation and processing chain written inPython. The code and the sound samples are available online at\url{http://lcav.github.io/AcousticRakeReceiver/}.
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