  We consider channel estimation for an uplink massive multiple-input
multiple-output (MIMO) system where the base station (BS) uses an array with
low-resolution (1-2 bit) analog-to-digital converters and a spatial Sigma-Delta
($\Sigma\Delta$) architecture to shape the quantization noise away from users
in some angular sector. We develop a linear minimum mean squared error (LMMSE)
channel estimator based on the Bussgang decomposition that reformulates the
nonlinear quantizer model using an equivalent linear model plus quantization
noise. We also analyze the uplink achievable rate with maximal ratio combining
(MRC), zero-forcing (ZF), and LMMSE receivers and provide a lower bound for the
achievable rate with the MRC receiver. Numerical results show superior channel
estimation and sum spectral efficiency performance using the $\Sigma\Delta$
architecture compared to conventional 1- or 2-bit quantized massive MIMO
systems.
