Can We Rely on Gaussian Distribution for Few-Bit CSI Acquisition in Decentralized Distributed Massive MIMO?

We consider a decentralized distributed massive MIMO (DD-mMIMO) system with limited fronthaul capacity. This is a novel architecture of scalable cell-free massive MIMO (CF-mMIMO). In previous studies, the input signal of the quantizer in CF-mMIMO has been assumed to follow the Gaussian distribution based on the central limit theorem. However, this assumption may not hold when the number of variables is not large. In this paper, we derive the probability distribution function (pdf) for the sum of many products of two Gaussian-distributed variables plus an additional Gaussian-distributed variable. Using the actual pdf, we derive closed-form Bussgang decomposition coefficients and determine the optimum step interval by solving a maximization problem. Additionally, we derive an expression for the spectral efficiency (SE) under quantization. Our results indicate that the Gaussian distribution can be appropriately applied in Bussgang decomposition when the number of quantization bits is limited. However, there exists a 7.8% gap between the Gaussian method and our proposed Non-Gaussian method in terms of mean square error of channel estimates when using 8-bit quantization. Furthermore, the SE is significantly influenced by the choice of the number of quantization bits.