  We examine the uplink spectral efficiency of a massive MIMO base station
employing a one-bit Sigma-Delta sampling scheme implemented in the spatial
rather than the temporal domain. Using spatial rather than temporal
oversampling, and feedback of the quantization error between adjacent antennas,
the method shapes the spatial spectrum of the quantization noise away from an
angular sector where the signals of interest are assumed to lie. It is shown
that, while a direct Bussgang analysis of the Sigma-Delta approach is not
suitable, an alternative equivalent linear model can be formulated to
facilitate an analysis of the system performance. The theoretical properties of
the spatial quantization noise power spectrum are derived for the Sigma-Delta
array, as well as an expression for the spectral efficiency of maximum ratio
combining (MRC). Simulations verify the theoretical results and illustrate the
significant performance gains offered by the Sigma-Delta approach for both MRC
and zero-forcing receivers.
