This paper proposes an analog eigenmode transmission technique suitable for a short-range multiple-input multiple-output (SR-MIMO) system consisting of arbitrary power-of-two number of antennas utilizing the idea of orbital angular momentum. In the proposed technique, uniform circular arrays that are coaxially arranged are used at both the transmitting (Tx) and receiving (Rx) sides. With this array configuration, the channel matrix is always a circulant matrix regardless of antenna type, array radius, Tx-Rx distance, and rotation about the coaxis. Due to the characteristics of a circulant matrix, the channel matrix can be diagonalized independently of the above-mentioned factors by fixed-weight beamforming based on a discrete Fourier transform (DFT) matrix uniquely determined by just the number of antennas. In this paper, the operating principle of the proposed technique is discussed from the viewpoints of linear algebra, and some example network configurations are presented with the determination of the DFT-matrix weight. Numerical analyses confirm the two important features of the proposed technique: 1) support of more than 4x4 SR-MIMO and 2) independence with regard to rotation about the coaxis. Furthermore, an experiment on a fabricated DFT circuit confirmed the feasibility of the proposed technique in realizing practical short-range communication.