  The emerging orbital angular momentum (OAM) based wireless communication is
expected to be a high spectrum-efficiency communication paradigm to solve the
growing transmission data rate and limited bandwidth problem. Academic
researchers mainly concentrate on the OAM-based line-of-sight (LoS)
communications. However, there exist some surroundings around the transceiver
in most practical wireless communication scenarios, thus forming multipath
transmission. In this paper, a hybrid orthogonal division multiplexing (HODM)
scheme by using OAM multiplexing and orthogonal frequency division multiplexing
(OFDM) in conjunction is proposed to achieve high-capacity wireless
communications in sparse multipath environments, where the scatterers are
sparse. We first build the OAM-based wireless channel in a LoS path and several
reflection paths combined sparse multipath environments. We concentrate on less
than or equal to three-time reflection paths because of the severe energy
attenuation. The phase difference among the channel amplitude gains of the LoS
and reflection paths, which is caused by the reflection paths, makes it
difficult to decompose the OAM signals. We propose the phase difference
compensation to handle this problem and then calculate the corresponding
capacity in radio vortex wireless communications. Numerical results illustrate
that the capacity of wireless communications by using our proposed HODM scheme
can be drastically increased in sparse multipath environments.
