Effect of time-delay errors on the beam pattern of a linear array

In conventional time-domain beam forming with sampled receiver outputs, the delays required to steer a beam in a given direction can only be approximated to within the nearest half sampling interval. For a linear array of equispaced receivers, and for certain directions, these errors give rise to high isolated sidelobes in the beam pattern. A model describing this beam pattern is used to predict the number, position, and height of these sidelobes. Degradation of the height of the main lobe is also considered. For coarse quantization, and in the absence of interpolation, the model suggests a recursive beamformer structure which significantly reduces the number of additions required. A simple interpolation scheme which reduces the height of these sidelobes is discussed and an Efficient scheme for implementing such interpolation is given.