Vortex electromagnetic waves are conveniently produced by a uniform circular array (UCA). The mutual coupling matrix (MCM) of UCAs presents rotational symmetry, which can be employed to cut down the parameters in the circuit model. The impedance matrix also does not rely on a specific port. This work uses the rotational symmetry to expand the MCM into orbital angular momentum (OAM) mode domain. The OAM domain phase sequence is derived by the Discrete Fourier Transform (DFT) of the first row of the MCM. The connection between the number of OAM modes and excitation of elements is described. Furthermore, an improved propagator method (PM) for OAM based decoupled two-dimensional (2-D) angle estimation is proposed. This method employs original steering vector of OAM waves to process the receiving signal, which avoids error caused by the Bessel function approximation. The estimation error is also reduced by redefining the propagator matrix. In terms of computational complexity, the proposed method avoids spectral search and element level eigenvalue decomposition (EVD). The results demonstrate that the coupling is compensated effectively by the OAM mode domain MCM. The error of proposed method is less than 1 degree under the condition of snr = 20dB and 1000 snapshots. The computational complexity is reduced by 1 to 2 orders of magnitude compared to the origin propagator method. The method is also suitable for one-dimensional estimation scenarios.

Direction of arrival (DOA) estimation for conformal arrays is challenging due to non-omnidirectional element patterns and shadow effects. Conical conformal array (CCA) can avoid the shadow effect at small elevation angles. So CCA is suitable for DOA estimation on both azimuth and elevation angles at small elevation angles. However, the element pattern in CCA cannot be obtained by conventional directional element coordinate transformation. Its local element pattern also has connection with the cone angle. The paper establishes the CCA radiation pattern in local coordinate system using 2-D coordinate transformation. In addition, in the case of large elevation angle, only half elements of the CCA can receive signal due to the shadow effect. The array degrees of freedom (DOF) are reduced by halves. We introduce the difference coarray method, which increases the DOF. Moreover, we propose a more accurate propagator method for 2-D cases. This method constructs a new propagation matrix and reduces the estimation error. In addition, this method reduces computational complexity by using linear computations instead of eigenvalue decomposition (EVD) and avoids spectral search. Simulation and experiment verify the estimation performance of the CCA. Both demonstrate the CCA model established in this paper is corresponding to the designed CCA antenna, and the proposed algorithms meet the needs of CCA angle detection. When the number of array elements is 12, the estimation accuracy is about 5 degrees.