## 1 Introduction  
Since 1992, much effort has been devoted to the exploitation of the property of waves called orbital angular momentum (OAM). Although it appears to be newly-appropriated from the physics community, OAM has been known previously, especially in the RF (Radio Frequency) community, as phase modes. Phase modes were useful for synthesizing excitations of circular arrays in radio direction-finding and null-steering applications since the 1960's [1; 2; 3; 4]. Since the advent of multi-input multi-output (MIMO) technology in radio communications, OAM came to be recognized as another spatial dimension to be exploited for enhancing capacity of radio communications, and also optical communications in free space as well as fiber. An excellent historical summary of the development of OAM applications is given in [5].  
No shortage of literature exists about how to generate and characterize OAM radio and optical waves [6]. Relatively few investigations focus on applications in radio communications, which is our interest in this paper, along the lines of [7; 8].  
Even fewer investigations focus on the receiving end of OAM communications links, with most of them relying on spatial techniques employing the same principles as those for generating the OAM modes at the transmitting end.  
Consequently, most attempts at exploiting the OAM modes to enhance capacity of radio links suffer from the limitations imposed upon the receiver and antennas due to the spatial minima of all nonzero-order OAM modes' beams on their axes, in the far field beyond the Rayleigh distance [7], where the receiver is situated. These limitations lead to low signal-to-noise ratios (SNRs), or very large receiving antennas, limitation to very short wavelengths, or limitations to short ranges comparable to the Rayleigh distance, or some combination of these. Additionally, real-world effects of antenna imperfections, multipath and dispersive propagation only add to the difficulties of reliably receiving and resolving the OAM modes and extracting the information streams from them.  
Of all the more than 300 references cited in [6], only two [9; 10] are about methods of reception and resolution of OAM modes that do not rely on variations of the spatial matched-filter concept whereby the helical phase fronts of the OAM beams are \"untwisted\" back to planar ones by the receiving antenna structure.  
In this paper, a variation of the method of [10] is pursued to show mathematically, and via simulation, how it can be applied to the transmission and reception of multiple OAM modes simultaneously without incurring most of the limitations of prior methods cited above. A patent-pending apparatus for realizing this method at a radio receiver in real-time is also described, coupled with a signal-processing algorithm to resolve the different data streams carried on the OAM beams.  
Section 2 presents the background and pseudo-Doppler principles behind the \"virtual rotational antenna\" of [10] and relates it to the context of radio beams possessing OAM. Transmission of OAM-bearing radio beams is also briefly reviewed. Section 3 presents the expression for the received OAM radio signals at the output of the pseudo-Doppler modulated antenna apparatus and relates its parameters to the physical geometry of the antennas and radio link. Section 4 describes the signal processing algorithm which processes the pseudo-Doppler aggregate signal to resolve the data streams carried on the individual OAM modes and examines some of its variants and limitations. It also contains preliminary simulation results to support the analyses. Conclusions and directions for future work are presented in Section 5. Select mathematical details are contained in the appendices.