Time Domain Sonar Beamforming

This note outlines the techniques routinely used in sonar systems to implement time domain and frequency domain beamforming systems. It takes a very simplistic approach to the problem and should not be considered as definitive in any sense. Consider an array of hydrophones receiving signals from an acoustic source in the far-field (Figure 1a). If the outputs from the 'phones are simply added together then, when the source is broad-side to the array, the 'phone outputs are in phase and will add up coherently. As the source is moved around the array (or the array rotated), then 'phones across the array receive signals with differential time delays, so the 'phone outputs no longer add coherently and the summer output drops (Figure 1b). If we plot the signal level as the array is rotated, we get the array beam-pattern: in this case, where all 'phone outputs are weighted uniformly, a classical sinc function. In order to reduce the effects of the spatial side-lobes of the beam-pattern, an array shading function is applied across the array (often a Hamming or Hanning weighting).