A novel multi-dimensional noise-shaping method is proposed to extend Δ-Σ modulation to the two-dimensional (2-D) (space, time) case. It uses spatial oversampling to provide another degree of freedom for ADC designers to shape quantization noise when temporal oversampling is limited. The method uses lossless discrete integrators (LDIs) to implement spatial integrators and is suitable for use in microwave and mm-wave array processing systems. The resulting 2-D noise shaping reduces the spectral overlap of a desired array signal with that of quantization noise. Shaped noise can then be removed from the region of support (ROS) of the array signal using 2-D filtering, thus improving the overall signal-to-quantization noise ratio (SQNR) and effective number of bits (ENOB). Simulation results from an integrated 64-channel converter in UMC 65nm CMOS prove the functionality of the approach. Experimental results from a board-level 64-channel converter are also presented.