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Spatial ΣΔ sampling has recently been proposed to improve the performance of massive MIMO systems with low-resolution quantization for cases where the users are confined to a certain angular sector, or the array is spatially oversampled. We derive a linear minimum mean squared error (LMMSE) channel estimator for the ΣΔ array based on an element-wise Bussgang decomposition that reformulates the nonlinear quantizer operation using an equivalent linear model plus quantization noise. Both the case of one- and two-bit quantization is considered. We then evaluate the achievable rate of the ΣΔ system assuming that a linear receiver based on the LMMSE channel estimate is used to decode the data. Our numerical results demonstrate that ΣΔ architecture is able to achieve superior channel estimates and sum spectral efficiency compared to conventional low-resolution quantized massive MIMO systems.
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