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This paper focuses on channel estimation in single-user and multi-user MIMOsystems with multi-antenna base stations equipped with 1-bit spatialsigma-delta analog-to-digital converters (ADCs). A careful selection of thequantization voltage level and phase shift used in the feedback loop of 1-bitsigma-delta ADCs is critical to improve its effective resolution. We firstdevelop a quantization noise model for 1-bit spatial sigma-delta ADCs. Usingthe developed noise model, we then present a two-step channel estimationalgorithm to estimate a multipath channel parameterized by the gains, angles ofarrival (AoAs), and angles of departure (AoDs). Specifically, in the firststep, the AoAs and path gains are estimated using uplink pilots, which exciteall the angles uniformly. Next, in the second step, the AoDs are estimated byprogressively refining uplink beams through a recursive bisection procedure.For this algorithm, we propose a technique to select the quantization voltagelevel and phase shift. Through numerical simulations, we demonstrate that withthe proposed parametric channel estimation algorithm, MIMO systems with 1-bitspatial sigma-delta ADCs perform significantly better than those with regular1-bit ADCs and are on par with MIMO systems with high-resolution ADCs.

Channel Estimation in MIMO Systems with One-bit Spatial Sigma-delta ADCs