标题： 两跳MIMO信道的基本极限：一种渐近方法 显示英文标题

标题： Fundamental Limits of Two-Hop MIMO Channels: An Asymptotic Approach

摘要： 多天线中继器和智能反射表面（IRSs）已被用于构建有利信道，以提高无线系统的性能。 中继系统和IRS辅助系统之间的共同特点是两跳多输入多输出（MIMO）信道。 因此，两跳MIMO信道的互信息（MI）已被广泛研究，并取得了非常有趣的结果。 然而，由于两跳（乘积）信道以及中继引入的噪声带来的困难，文献中尚未出现对两跳MIMO信道基本极限的严格研究，即第一阶和第二阶分析。 在本文中，我们采用大规模随机矩阵理论（RMT），特别是高斯工具，推导出互信息均值和方差的闭式确定性近似。 此外，我们确定了互信息均值、方差和特征函数的收敛速率，并证明了渐近正态性。 此外，我们还研究了描述闭式近似的基本方程的分析性质，并证明了解的存在性和唯一性。 然后提出了一种迭代算法来获得基本方程的解。 数值结果验证了理论分析的准确性。 显示英文摘要

摘要： Multi-antenna relays and intelligent reflecting surfaces (IRSs) have been utilized to construct favorable channels to improve the performance of wireless systems. A common feature between relay systems and IRS-aided systems is the two-hop multiple-input multiple-output (MIMO) channel. As a result, the mutual information (MI) of two-hop MIMO channels has been widely investigated with very engaging results. However, a rigorous investigation on the fundamental limits of two-hop MIMO channels, i.e., the first and second-order analysis, is not yet available in the literature, due to the difficulties caused by the two-hop (product) channel and the noise introduced by the relay (active IRS). In this paper, we employ large-scale random matrix theory (RMT), specifically Gaussian tools, to derive the closed-form deterministic approximation for the mean and variance of the MI. Additionally, we determine the convergence rate for the mean, variance and the characteristic function of the MI, and prove the asymptotic Gaussianity. Furthermore, we also investigate the analytical properties of the fundamental equations that describe the closed-form approximation and prove the existence and uniqueness of the solution. An iterative algorithm is then proposed to obtain the solution for the fundamental equations. Numerical results validate the accuracy of the theoretical analysis.