Spatial Multiplexing over LOS Channels with Circular Arrays: Analysis and Design

This paper models the line-of-sight (LOS) channel between two continuous circular antennas (CCAs) as a bounded linear normal operator whose kernel is defined by a deployment parameter: the product of the antenna radii divided by the product of the wavelength and transmission distance. Eigendecomposition reveals that orbital angular momentum (OAM) serves as the eigenmodes, with eigenvalues given by Bessel functions of the first kind, evaluated at the deployment parameter. By linking discrete circular arrays to CCAs through spatial sampling, we derive analytical expressions for the singular values of the LOS multiple-input multiple-output (MIMO) channel. The analysis considers two configurations: one where receive antennas form a single uniform circular array (UCA) with a rotational angular offset, and one with multiple sub-UCAs having different angular offsets, in both cases with the number of receive antennas being an integer multiple of the transmit antennas. For each setup, discrete Fourier transform (DFT)-based transceiver structures are proposed to achieve channel capacity. Numerical evaluations reveal: (i) The number of effective spatial degrees of freedom generally increases with the deployment parameter, but not monotonically (for fixed angular offsets); (ii) Channel capacity does not necessarily increase with the deployment parameter when the number of antennas is fixed; (iii) Angular offset significantly impacts performance when the number of antennas is small relative to the parameter; (iv) With a large number of antennas, the singular values of both configurations approach the CCA singular values, and the impact of angular offsets diminishes; (v) The non-uniform configuration studied in this paper yield small or no gains compared to the uniform configuration when angular offsets are optimized.