Spatial Sigma-Delta Modulation for Few-Bit MIMO Precoding: Quantization Error Suppression According to Channel State Information

In this paper we consider a spatial Sigma-Delta (Sigma Delta) modulator design for massive MIMO downlink precoding with few-bit digital-to-analog converters (DACs). Spatial Sigma Delta modulation has recently been found to provide an effective way to contain the heavy quantization error effects caused by coarse quantization of the few-bit DACs. The idea is to shape the quantization errors as high-pass (or band-stop) noise, thereby serving users in a low-pass (or band-pass) angle sector with reduced quantization error effects. This paper studies a different idea where we shape the quantization errors according to users' channel state information. This allows more efficient quantization noise suppression in a user-targeted fashion. Our Sigma Delta modulator design is formulated and solved as a convex optimizaton problem. Numerical results show that the proposed user-targeted design significantly enhances the precoding performance compared to the existing first-order Sigma Delta modulator.