Delta-sigma noise shaping in 2D spacetime for uniform linear aperture array receivers

A multi-dimensional noise-shaping method based on delta-sigma modulation has been proposed. This method extends delta-sigma modulation into the two-dimensional (2-D) case (space, time). The proposed noise-shaping method employs lossless discrete integrators for realization in microwave and mm-wave array processing systems. The paper shows that 2-D noise-shaping reduces the spectral overlap of a desired array signal with that of noise. By reducing the overlap of the ROSs, 2-D filtering can be used to improve the overall noise figure of the array receiver. A noise figure improvement of 2.6 dB could be simulated for a 4-times spatially over-sampled array with 65 simulated elements for an input signal to noise ratio of 10 dB and LNA noise figure of 5 dB. Simulation results based on wideband signals on 33, 65, 129 and 257 element antenna arrays with 2, 4 and 8 times oversampling show the potential capability of the proposed system in improving overall noise figure. Although mathematical modeling shows potential improvements in receiver noise figure, RF integrated circuit realizations are challenging and have not been attempted yet.