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 [Formula: see text] are necessary, where [Formula: see text] 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 [Formula: see text] are computed. To calculate this quantity, we resort to the integer partition theory and present an exact expression for [Formula: see text]. 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.