Effect of Random Misalignment in the Capacity of Millimeter-Wave OAM

Since the discovery of vortex beams by Allen et al., there has been a growing interest in exploring the applications of orbital angular momentum (OAM) in communication. Among all these researches, especially radio frequency (RF) wireless communication based on OAM should be one of the most promising research topics since the frequency resource is increasingly scarce and OAM can provide us with a new degree of freedom besides frequency, time, and space. In the context of wireless communication, millimeter wave and terahertz communication have gained extensive attention to harness spectrum resources. However, due to the short wavelength at these frequencies, line of sight (LOS) channels dominate. OAM, even in LOS channels, offers an additional degree of freedom compared to conventional multiple input multiple output systems. Yet, there are strict requirements for free-space OAM, one of which is the strict alignment between antenna arrays. To the best of our knowledge, there has not been any work about the capacity analysis of OAM communication under random misalignment. In this article, we obtain accurate closed-form intensity for a given misalignment value for both indoor and outdoor situations. Moreover, based on these intensity formulas, we analyze the average capacity under 2-D Gaussian random misalignment numerically and validate its accuracy by simulation. Besides, we illustrate that the Gauss-Laguerre quadrature can be used to reduce the computation complexity in the real environment. Moreover, we analyze the relationship between the average capacity and system parameters such as the array radii, signal-to-noise ratio, and misalignment distribution standard deviation for both indoor and outdoor situations. At last, we verify our work is also effective for the concentric circular array. This work could be a reference to the implementation of a practical RF OAM communication system.