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The channel matrix of the commonly used uniform circular array-based orbital angular momentum (UCA-OAM) system reaches the full-rank state when the degree of freedom (DoF) is limited only by the number of UCA antenna elements. The rank of the channel matrix of the UCA-OAM system is equal to DoF under this condition. However, the practical DoF of the UCA-OAM system is always affected by other transmission factors, such as the transmission distance and the radius of the receiving antenna. Therefore, by exploiting the practical DoF of the UCA-OAM system affected by the transmission distance and the radii of the receiving antenna and transmission antenna, a novel channel capacity model of the UCA-OAM communication system with a deficient-rank channel (DRC) matrix is first proposed. Moreover, the formulas of the channel matrix and channel capacity for the DRC matrix are analytically derived. The results of numerical simulations indicate that when the practical transmission factors including transmission distance and radii of the receiving antenna and transmission antenna are considered, the UCA-OAM communication system with the DRC matrix has less channel capacity than that with the full-rank channel (FRC) matrix. These simulated results provide helpful guidance on the practical application of the UCA-OAM communication system.