Shannon Capacity of LOS MIMO Channels with Uniform Circular Arrays

The Shannon capacity for the line-of-sight (LOS) multiple-input multiple-output (MIMO) channel between two perfectly aligned uniform circular arrays (UCAs) is derived from first principles in a tutorial fashion. It is well known that harmonically related complex exponentials (also known in the literature as orbital angular momentum (OAM) modes) are eigenmodes for the spatially continuous channel. We show that the corresponding eigenvalues can be expressed as Bessel functions of the first kind. We also show that the spatially discrete channel between two UCAs with the same finite number of Hertzian dipole antennas on both sides has eigenmodes that are spatially sampled continuous OAM modes, and discrete eigenvalues that are aliased versions of the continuous eigenvalues. Through numerical solution of Maxwell's equations, we verify that the discrete eigenvalues for UCAs with realistic dipole antennas are the same as with the Hertzian dipoles for the studied geometries (1 km hop distance, UCA radius 1 and 2 m, carrier frequency 70 GHz) as long as antenna spacing is not very dense.