Digital interpolation beamforming for low-pass and bandpass signals

Digital time-domain beamforming requires that samples of the sensor signals be available at a sufficient rate to realize accurate time delays for beam steering. For many applications, this input rate, which may be significantly higher than the Nyquist rate required for waveform reconstruction, places stringent requirements on A/D converter hardware and transmission cable bandwidth. Recently, a technique referred to as digital interpolation beamfonning was introduced which greatly relaxes the sampling requirement and provides substantial hardware savings through more flexible design options. In this approach, the sensor channels need only be sampled at a rate which satisfies aliasing requirements. The vernier beam-delay increments are then synthesized using digital interpolation which can be implemented at the beamformer input or output to minimize digital processing complexity. Previously, this concept was presented for the case of "low-pass" signals. This paper extends this work by examining the relationship between interpolation and beamforming for the important class of "bandpass" signals. Specifically, sampling methods are discussed whereby the original waveform can be reconstructed from samples taken at a rate consistent with the bandwidth of the bandpass signal. Beamformer implementations are presented which utilize these bandwidth-sampling techniques in conjunction with interpolation and which compute beam output points at the generally low rate dictated by the signal bandwidth. The interpolation beamformer achieves time-delay quantization (beam-steering accuracy) independent of both the input and output sampling rates. This approach generally requires less hardware than conventional procedures. Interpolation falter characteristics dictated by the bandwidth-sampling procedure are described and efficient methods of implementation employing nonrecursive digital bandpass and low-pass filters are presented.