Impact of beam steering errors on shifted sideband and phase shift beamforming techniques

The Shifted Sideband Beamformer (SSB) is a digital, time-domain beamformer intended for bandpass applications. Computational efficiency results from the digital processing of the complex envelope of the sensor data at a rate proportional to the bandwidth of the data. In a previous paper, the spatial response of the SSB was examined and compared to that of a conventional bandpass digital beamformer by modeling the beam steering quantization error as a uniformly distributed random variable. This paper examines, in detail, the specific case of a line array of uniformly spaced sensors where beam steering quantization is shown to produce systematic time-delay errors for both the conventional beamformer and SSB implementations. Expressions are presented for predicting the directions of grating side lobes in the spatial response pattern as a result of these errors. Also, the spatial response of the Phase Shift Beamformer (PSB), which is a limiting case of the SSB and intended for narrow-band applications, is examined. The systematic phase errors of the PSB for a planar array are shown to produce errors in the beam pointing direction for frequencies other than band center. Examples demonstrate this effect for the special case of a line array. Finally, it is shown that the SSB can be interpreted as time-domain beamforming with partial beam outputs formed from subclusters of adjacent sensors with a PSB.