MIMO Capacity in Binomial Field Networks

We consider a multiple-input multiple-output (MIMO) communication in a binomial field of nodes scattered in a compact circular region. We first provide closed-form formulas for the Euler transform and Eulerian integral of H-function, which enable us to evaluate the integral in terms of again the H-function. We then derive the exact closed-form expression for the MIMO ergodic capacity between the transmitter and its nth nearest receiver to characterize the spatial ordering achieved by the random locations of nodes in binomial field networks. In high signal-to-noise (SNR) regimes, we also derive a simple mathematical expression for the MIMO capacity in terms of the high-SNR offset. We further analyze the asymptotic capacity when the number of antennas tends to infinity.