LAUSR

One-bit quantization opens up opportunities for massive MIMO implementation using cheap and power-efficient radio-frequency front-ends, but unfortunately brings severe amplitude distortion. The spatial $\Sigma -\Delta$ structure is one important manner that can recover the amplitude information from one-bit quantized signals. In this paper, we demonstrate that the upper bound of the spatial degree of quantization noise reduction (DQNR) is 3 for the considered spatial $\Sigma -\Delta$ structure. However, the upper bound is hard to be achieved via the zero forcing (ZF) or the maximum ratio combination (MRC) schemes, and the achieved spatial DQNR is even not greater than 1 in the worst case. Thus the distortion suppression is inefficient. To address this issue, we propose a random beam shaping (RBS) scheme and prove it can achieve the spatial DQNR of 3. Through the random beam shaping, the beams are smeared into the whole beamspace. Meanwhile, the random beam shaping results in the power leakage of the beams and it may limit the distortion suppression when considering the additive noise. To reduce the power leakage, we further propose an accurate beam shaping (ABS) scheme, in which the vector for the beam shaping is optimized through the alternative minimization algorithm and the beams are concentrated around the region with low power of quantization noise. The simulation results illustrate that the proposed beam shaping schemes can more efficiently exploit the large-scale antenna array to recover the amplitude information.