Sum-Rate Channel Capacity for Line-of-Sight Models

This work considers a base station equipped with an M-antenna uniform linear array and L 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.