Spatial Sigma-Delta Modulation for the Massive MIMO Downlink

In massive MIMO, replacing high-resolution ADCs/DACs with low-resolution ones has been deemed as a potential way to significantly reduce the power consumption and hardware costs of massive MIMO implementations. In this context, the challenge lies in how the quantization error effect can be suppressed under low-resolution ADCs/DACs. In this paper we study a spatial sigma-delta (ΣΔ) modulation approach for massive MIMO downlink precoding under one-bit DACs. ΣΔ modulation is a classical signal processing concept for coarse analog-to-digital/digital-to-analog conversion of temporal signals. Fundamentally its idea is to shape the quantization error as high-frequency noise and to avoid using the high-frequency region by oversampling. Assuming a uniform linear array at the base station (BS), we show how ΣΔ modulation can be adapted to the space, or MIMO, case. Essentially, by relating frequency in the temporal case and angle in the spatial case, we develop a spatial ΣΔ modulation solution. By considering sectored array operations we study how the quantization error effect can be reduced, and the effective SNR improved, for zero-forcing (ZF) precoding. Our simulation results show that ZF precoding under spatial ΣΔ modulation performs much better than ZF precoding under direct quantization.