  This paper investigates full-duplex (FD) multi-user multiple-input
multiple-output (MU-MIMO) system design with coarse quantization. We first
analyze the impact of self-interference (SI) on quantization in FD single-input
single-output systems. The analysis elucidates that the minimum required number
of analog-to-digital converter (ADC) bits is logarithmically proportional to
the ratio of total received power to the received power of desired signals.
Motivated by this, we design a FD MIMO beamforming method that effectively
manages the SI. Dividing a spectral efficiency maximization beamforming problem
into two sub-problems for alternating optimization, we address the first by
optimizing the precoder: obtaining a generalized eigenvalue problem from the
first-order optimality condition, where the principal eigenvector is the
optimal stationary solution, and adopting a power iteration method to identify
this eigenvector. Subsequently, a quantization-aware minimum mean square error
combiner is computed for the derived precoder. Through numerical studies, we
observe that the proposed beamformer reduces the minimum required number of ADC
bits for achieving higher spectral efficiency than that of half-duplex (HD)
systems, compared to FD benchmarks. The overall analysis shows that, unlike
with quantized HD systems, more than 6 bits are required for the ADC to fully
realize the potential of the quantized FD system.
