$Δ-Σ$ Noise-Shaping in 2-D Space-Time for Wideband Antenna Array Receivers

This paper proposes multi-dimensional signal processing methods to extend Δ-Σ modulation into the two-dimensional (2-D) space, time case. The proposed 2-D noise-shaping methods employ lossless discrete integrators (LDIs) to reduce the spectral overlap of the regions of support (ROSs) of array signals with that of both thermal and quantization noise in microwave and mm-wave array processing systems. Spatio-temporal low-pass filtering can then be used to improve the overall noise figure, linearity, and resolution of the resulting N-port receiver. A proof-of-concept 65-port receiver that uses first-order Δ-Σ within both the low-noise amplifier and analog-to-digital converter (ADC) has been designed in the UMC 65-nm CMOS process. Detailed circuit simulations with wideband RF inputs at a center frequency of 4 GHz confirm that the proposed 2-D noise-shaping approach provides significant improvements in noise, linearity, and resolution. Specifically, noise figure (NF) improves by 1.5 dB, IIP3 improves by 15 dB, and the effective number of bits (ENOB) improves by 3.1 bits. Experimental results from a low-frequency board-level implementation of a 64-port ADC with first-order noise shaping are also presented.