A novel delta-sigma (Δ - Σ) modulation method is proposed for extending noise-shaping to two dimensions: space and time. The goal is to improve the noise figure (NF) and linearity of low noise amplifiers (LNAs) for use in microwave and mm-wave antenna arrays. We show that a spatially-oversampled antenna array coupled to an N-port noise-shaped LNA can diminish in-band additive noise and distortion by shaping the multi-dimensional spectrum of these unwanted components towards higher spatial frequencies that are outside the space-time region of support (ROS) of all possible propagating electromagnetic waves. The shaped noise is then removed by spatial filtering with a linear beamformer. This paper analyzes the concept and presents simulation results for a 33, 65, and 129-port noise-shaped LNAs in 65nm CMOS operating at 4GHz.