Analysis of the Distortion Mechanism in Delta–Sigma Beamforming

Dynamic receive beamforming on a Delta-Sigma modulator's low-resolution output bit-stream suffers from a severely increased noise floor, rendering the promising method infeasible. This paper addresses the mechanism behind the increased noise floor. By using multirate theory and bifrequency analysis, we show that the increased noise floor is caused by aliasing/imaging of the powerful quantization noise from specific frequency regions according to the focus depth. We analyze both the conventional delay-and-sum method and the previously proposed insert zero compensation method. For the latter technique, we show that the alias/image bands have the first-order suppression because of a zero at the origin. This finding leads to the proposal of an architecture combining a cascaded integrator-comb filter with the insert zero compensation method. Backed by simulations of beamformed Delta-Sigma modulated sequences and point spread functions, we compare this architecture to different compensation methods and the ideal Delta-Sigma beamformer. The proposed technique is shown to have low implementation cost and achieve levels of dynamic range comparable to those of the ideal Delta-Sigma beamformer.