Instituto de Pesquisas Eldorado, Campinas 13083-898, Brazil.
Instituto Nacional de Telecomunicações, Santa Rita do Sapucaí 37540-000, Brazil.
Sensors (Basel). 2021 Mar 1;21(5):1674. doi: 10.3390/s21051674.
This work considers a base station equipped with an -antenna uniform linear array and users under line-of-sight conditions. As a result, one can derive an exact series expansion necessary to calculate the mean sum-rate channel capacity. This scenario leads to a mathematical problem where the joint probability density function (JPDF) of the eigenvalues of a Vandermonde matrix WWH are necessary, where W is the channel matrix. However, differently from the channel Rayleigh distributed, this joint PDF is not known in the literature. To circumvent this problem, we employ Taylor's series expansion and present a result where the moments of mn are computed. To calculate this quantity, we resort to the integer partition theory and present an exact expression for mn. Furthermore, we also find an upper bound for the mean sum-rate capacity through Jensen's inequality. All the results were validated by Monte Carlo numerical simulation.
这项工作考虑了一个配备 -天线均匀线性阵列和 个用户的基站，这些用户处于视距条件下。因此，可以推导出计算平均和速率信道容量所需的精确级数展开式。这种情况导致了一个数学问题，其中需要联合概率密度函数（JPDF）的 Vandermonde 矩阵 WWH 的特征值，其中 W 是信道矩阵。然而，与信道瑞利分布不同，该联合 PDF 在文献中是未知的。为了解决这个问题，我们采用泰勒级数展开，并提出了一种计算 mn 矩的结果。为了计算这个量，我们求助于整数划分理论，并给出了 mn 的精确表达式。此外，我们还通过 Jensen 不等式找到了平均和速率容量的上界。所有结果都通过蒙特卡罗数值模拟进行了验证。
