Analytical expression of transmission for the orbital angular momentum (OAM) communication using loop antenna arrays and paraboloids is derived to achieve a communication distance of 100 m. With the field distribution of the single “transformed OAM mode” radiated by a loop antenna, the collimated field by the transmitting paraboloid and its diffracted field are analytically derived. Effects of frequencies, sizes of paraboloids, and shifts of transmitting and receiving arrays from the focal planes are included. With the diffracted field distribution on the focal plane of the receiving paraboloid, transmission between the transmitting and receiving loop antennas is analytically estimated. It is shown that the transmission between the antennas with different OAM modes is null, but the transmission between the antennas with the same mode can be reduced. To clarify the mechanism of the reduction, factors of the reduction are quantitatively defined, and the explicit formulae are derived. Based on the analytical results, numerical estimation for a communication distance of 100 m is demonstrated, where the frequency, the focal length, and the size of the paraboloid are 150 GHz, 50 cm and 100 cm, respectively. Where both arrays are located on each focal plane, the transmission for the signal is more than -7.78 dB for eight kinds of OAM modes. The transmission is the least for the highest-order mode. The transmission loss is shown to be mitigated by optimizing the shifts of transmitting and receiving arrays from their focal planes. The loss is made almost even by exploiting the tradeoff of the improvement for the mode orders. The transmission is improved by 5.98 dB, to be more than -1.80 dB, by optimizing the shifts of the arrays.