Recently, a promising technology known as the cell-free (CF) massive multiple-input multiple-output (M-MIMO) network has emerged as an alternative wireless communication network that offers numerous advantages to wireless communication systems. During this work, we address the uplink (UL) pilot-based channel estimation (CE) and spectral efficiency (SE) for a CF M-MIMO network considering spatially correlated channels. The CE and SE are computed respectively, using the Bayesian minimum mean square error (MMSE) estimator and MMSE combining vector. Moreover, we investigate the SE metric and CE procedure for correlated and uncorrelated channels, where in the correlated case, we employ the Gaussian local multi-scattering (GLMS) model to describe the spatial correlation (SC). Furthermore, since the array geometry influence the SC, we deal with a CF M-MIMO network wherein each access point (AP) is outfitted either with a uniform linear array (ULA), a uniform circular array (UCA), or a uniform cylindrical array (UCLA). Inspired by the GLMS for the ULA arrangement, we propose the GLMS model for a CF M-MIMO network where each AP is equipped with a UCA arrangement. In other words, we propose and compute the expression of the channel co-variance matrix (CM) that describes the SC in a CF M-MIMO network where each AP is equipped with the UCA arrangement. Additionally, using the Kronecker product of the CM generated through the UCA arrangement and the CM generated through the ULA arrangement, we propose the GLMS model for a CF M-MIMO network generated through the UCLA arrangement. Our theoretical expressions are validated and reinforced using numerical results, where we evaluate the system performance using the normalized mean square error metric and bits of information per second per hertz (i.e., ).

中文翻译：

---

三维阵列对考虑空间相关信道的无小区大规模 MIMO 信道估计的影响

最近，一种被称为无小区 (CF) 大规模多输入多输出 (M-MIMO) 网络的有前途的技术已经成为一种替代无线通信网络，它为无线通信系统提供了许多优势。在这项工作中，我们解决了考虑空间相关信道的 CF M-MIMO 网络的上行链路 (UL) 基于导频的信道估计 (CE) 和频谱效率 (SE)。使用贝叶斯最小均方误差 (MMSE) 估计器和 MMSE 组合向量分别计算 CE 和 SE。此外，我们研究了相关和不相关通道的 SE 度量和 CE 程序，在相关情况下，我们采用高斯局部多散射 (GLMS) 模型来描述空间相关 (SC)。此外，由于阵列几何形状影响 SC，我们处理一个 CF M-MIMO 网络，其中每个接入点 (AP) 配备均匀线性阵列 (ULA)、均匀圆形阵列 (UCA) 或均匀圆柱阵列 (UCLA)。受 ULA 布置的 GLMS 启发，我们提出了 CF M-MIMO 网络的 GLMS 模型，其中每个 AP 都配备了 UCA 布置。换句话说，我们提出并计算了信道协方差矩阵 (CM) 的表达式，它描述了 CF M-MIMO 网络中的 SC，其中每个 AP 都配备了 UCA 布置。此外，使用通过 UCA 排列生成的 CM 和通过 ULA 排列生成的 CM 的克罗内克积，我们为通过 UCLA 排列生成的 CF M-MIMO 网络提出了 GLMS 模型。我们的理论表达式通过数值结果得到验证和强化，).