OAM-MIMO Multiplexing Transmission System for High-Capacity Wireless Communications on Millimeter-Wave Band

This paper presents the performance analysis and experimental demonstrations of our orbital angular momentum-multiple-input multiple-output (OAM-MIMO) multiplexing system. OAM is a fixed orthogonal basis set, so OAM multiplexing has a high affinity to analog processing. We extend OAM multiplexing to OAM-MIMO multiplexing technology, which effectively combines the advantage of OAM multiplexing with that of MIMO-based digital signal processing with multiple uniform circular arrays (multi-UCAs) for line-of-sight wireless transmission. Basically, OAM-MIMO is classified as a practical form of analog-digital hybrid MIMO technology. Our multi-UCA-based OAM-MIMO multiplexing transmission system has two hybrid analog-digital architectures. We evaluated its performance through a comparison with different antenna arrangements and configurations. We implemented antennas of quadruple UCAs, with each UCA having a broadband Butler matrix circuit that generates and separates OAM modes as an analog part of hybrid MIMO on a 28-GHz frequency band. We experimentally demonstrated 130-Gbit/s wireless data transmission with 11 streams using five OAM modes (0, ±1, ±2) at a distance of 10 m. We also demonstrated simultaneous use of OAM-MIMO and polarization multiplexing and achieved wireless transmission over 200 Gbit/s with 21 streams. These results indicate the practicality and effectiveness of our system for high-capacity wireless communication.


I. INTRODUCTION
T HE explosive growth in wireless data traffic constantly demands higher-capacity wireless transmission technology for various scenarios, including unprecedented ones.Wireless networks have grown over several generations, and fifth-generation (5G) technology is now in practical use.Certain institutes have begun discussing next-generation networks [1], [2].The aggregated capacity in these networks increases up to 1,000 times each generation, and 1-Tbit/s class is expected in the next generation of wireless networks.Accordingly, the front-and backhaul connection capacity of the networks must be increased, which will increase the demand on wireless transmission considering the deployment and maintenance costs incurred by optical fiber networks, as shown in Fig. 1.In fact, application scenarios of high-capacity wireless communication systems for future networks, such as integrated access back-haul [3], [4], [5], [6] and relay transmission for high-resolution video, have been.
Therefore, we are focusing on such high-capacity wireless transmission as an alternative to optical fiber transmission.
Multiple-antenna technology is a breakthrough technology that enhances wireless communications capacity by using a spatial resource with time and frequency resources in a real wireless communication system.The number of antenna elements contributes to the gain or multiplexing order, which can dramatically increase the capacity as the number of antenna elements increases [7], [8].Millimeter wave (mm-wave) technology has gathered much attention to enhance wireless communication capacity as high-frequency devices have increased.The licensed bandwidth on a higher frequency is usually wider because higher-frequency bands are relatively unoccupied, and the relative bandwidth tends to be low, which facilitates the design and fabrication of radio frequency (RF) devices.Thus, the mm-wave bands suit our target scenarios of high-capacity wireless transmission.However, the path loss is not ignorable even at a short distance on a higher-frequency band, necessitating multiple antennas to obtain large antenna gains and a high signal-to-noise ratio (SNR).Therefore, multiple-antenna technology has become more important than ever.However, the requirement on digital signal processing and number of RF chains increases dramatically as the number of antenna elements increases, which causes high computational complexity.This makes realtime processing difficult and increases operational costs such as power consumption.For example, the digital computational complexity of the multipleinput multiple-output (MIMO)-based channel equalization on the receiver side typically increases during the second order of the number of antenna elements.We have to consider digital computational complexity, especially when using wide bandwidth on mm-wave bands due to the high baud rate.Therefore, analog processing substituted for all or part of digital processing is one promising approach to reducing computational complexity and number of expensive RF chains.Thus, adequate function allocation to both digital and analog signal processing is necessary to reduce complexity and costs, and practical architectures have been derived, such as hybrid MIMO and beam-space MIMO [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25].Our high-capacity communication scenarios do not necessarily require extremely high mobility support, so using fixed orthogonal beams is suitable.The spatial resources are mostly insufficient due to the constraints of antenna deployment, fewer propagation paths, etc.Therefore, we have to design channels between transmitter (Tx) and receiver (Rx) antennas such as line-of-sight (LoS)-MIMO.
Orbital angular momentum (OAM) is a physical property of electromagnetic waves that forms orthogonal and spatially overlapped beams.Therefore, OAM can be used for multiplexing signals in the same direction.Research on OAM multiplexing has been reported in both optical and radio communication fields [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37].OAM multiplexing can also be used simultaneously with a multiplexing technique that uses the orthogonality of spin angular momentum, known as polarization, and frequency-and time-domain multiplexing techniques.OAM modes are defined by spatial phase distribution, so they have a certain spatial expanse.In the optical field, a laser source's size is much larger than the wavelength, so the distribution can easily be formed using optical devices such as holographic plates [38], [39].However, on microwave bands, antennas for OAM multiplexing require a very large space that cannot be deployed practically.However, the wavelength on the mm-wave band is relatively short, so the practical antenna size is convenient.OAM multiplexing generally differs from the MIMO technology using discretely arranged antenna arrays.However, studies have shown that OAM beams could be generated and separated using a uniform circular array (UCA), so OAM multiplexing using UCAs can be considered as MIMO technology [40], [41], [42].Only fixed signal processing, such as discrete Fourier transform (DFT), is required to generate and separate OAM modes, and such characteristics are suitable for analog devices.A disadvantage of using analog circuits is that the bandwidth is limited by their pass-band characteristics.The performance of analog circuits often depends on relative bandwidth; therefore, using the higher frequency band as mm-wave bands can provide a wider bandwidth.
To enhance the capacity of OAM multiplexing, one approach to parallel transmission is to arrange a few sets of Tx and Rx UCAs side-by-side to increase the amount of multiplexing [43], [44], [45].However, the streams in different sets of Tx and Rx UCAs are not independent even if the states of OAM have different values.Thus, countermeasures are necessary to isolate the streams, for example, keeping a certain distance between parallel transmission sets and sharpening the directivity of antennas or applying digital channel equalization processing over all streams.For further capacity enhancement, we focus on OAM-MIMO multiplexing transmission using multiple UCAs (multi-UCAs), in which UCAs are arranged concentrically.Research reports involving multi-UCAs generated one different OAM mode from each UCA [46], [47] and analyzed the capacity by approximating the beams generated from each UCA to Bessel beams as far field radiation patterns [48], etc.We propose an OAM-MIMO multiplexing transmission system with two practical system architectures that achieves high-capacity wireless transmission using multi-UCAs while taking advantage of the strengths of OAM multiplexing, which enables multiplexing of signals through fixed processing.The contributions of this paper are summarized as follows: 1) We mathematically organize multi-UCA-based OAM-MIMO multiplexing without any approximation and show that independent MIMO channels are provided by DFT processing in each OAM mode.On the basis of the mathematical expressions, we propose a multi-UCAbased OAM-MIMO multiplexing transmission system with two hybrid analog-digital architectures that adequately allocates spatial multiplexing functions to both analog and digital signal processing by using Butler matrix circuits as DFT processors.2) We describe the analysis of achievable transmission capacity, computational complexity, and tolerance to antenna misalignment and distance variation of our system and other multi-antenna technologies for system design.3) We experimentally demonstrated 75-to 130-Gbit/s wireless transmission with our system architectures and 200-Gbit/s wireless transmission combined with dual-polarization multiplexing at a distance of 10 m on a 28-GHz band in a shielded room.The remainder of this paper is as follows.In Section II, we give a brief introduction of OAM multiplexing technology.In Section III, we present our OAM-MIMO multiplexing transmission system and its performance analysis in terms of achievable transmission capacity, computational complexity, and tolerance to antenna misalignment and distance variation through a comparison with the other multi-antenna systems.In Section IV, we present our experimental demonstrations of OAM-MIMO multiplexing including introduction of our experimental setup, implemented signal processing driven at both analog and digital parts, and overall architecture of our system including waveform structure and adaptive modulation and coding (AMC).Finally, we provide a discussion and conclude the paper in Section V.

II. OVERVIEW OF OAM MULTIPLEXING
In LoS wireless communication on a mm-wave band, the channel between antennas is fixed and the environment is not multipath-rich, so the spatial resources are limited compared with multi-user MIMO, home Wi-Fi, etc. Spatially overlapped orthogonal beams can increase spatial-utilization efficiency.Beams with different OAM modes propagate coaxially and are orthogonal, making multiplex signals possible on the beams.The OAM modes are characterized by a spatial phase distribution.Fig. 2(a) shows the wavefronts of the OAM modes.OAM mode 0 is the same as a plane wave and has a flat phase front.However, the other OAM modes have different helical wavefronts.The descriptions look similar to circular polarization, so they are often confused.However, they are different physical properties and can be used for multiplexing simultaneously.Polarization is a direction of the electrical field defined at a point; conversely, OAM is the spatial intensity and phase distribution of the electric field and has a spatial extent that cannot be defined at a point.Therefore, OAM and polarization can independently multiplex as degrees of freedom, and combining OAM and polarization creates complex spatial modes [49], [50].Certain methods for combining OAM and polarization for multiplexing share each antenna element using a dual-polarized antenna or use double the number of UCAs and assign half to one polarization.When observing the phase distribution on a plane vertical to the propagation direction, as in Fig. 2(b), the phase rotates linearly and the number of rotations is an integer and the same as the state of the OAM mode, guaranteeing a periodicity for circumferential direction that maintains the OAM states during propagation.Therefore, a strength of OAM multiplexing is that the orthogonality between OAM modes does not depend on the propagation distance, making deployment flexible.
Studies on radio communications addressed methods of generating OAM beams using analog components such as helicoidally deformed parabolic antennas [51] and spiral phase plates [35].However, these analog components cannot simultaneously transmit multiple OAM beams coaxially, so beam splitters and exact mechanical alignment are necessary.Using a holographic plate also demonstrates only single-mode generation and transmission and cannot multiplex signals with different OAM modes.An interesting approach to generating multiple modes with reconfigurable antennas was investigated, but the proposed antenna was specialized to generate OAM modes 1 and −1 and was still not flexible enough [52].In light of the above, UCAs can be considered a practical means to generate and separate OAM modes.Previous studies used UCAs as antennas of the Tx and Rx and showed that coaxial OAM multiplexing is possible with a simple configuration.The integer number of linear phase rotation is generated and separated by the Fourier transform in the circumferential direction in a polar coordinate system.In fact, every analog component for OAM-mode generation and separation drives the Fourier transform.When using UCAs, the antenna elements are placed discretely, requiring DFT processing.One of the most widely used analog DFT processors is the Butler matrix circuit, which can execute butterfly computation [53].A constraint of using OAM and analog devices is the antenna arrangement.The antennas must be arranged coaxially opposite each other; however, they ideally do not require digital MIMO equalizations and can reduce the number of RF chains because we have to prepare them only for the OAM modes used for multiplexing.The number can be much smaller compared with the number of antenna elements in a UCA.It has been reported that the beam divergence of OAM modes [54] indicates that the energy of higher OAM modes spreads rapidly and the gains tend to be low, so it is better not to use them for long distance in some cases [48].Such characteristics can be a good reference to determine available OAM modes for multiplexing and reducible RF chains.

III. CONCEPT AND PERFORMANCE ANALYSIS OF PROPOSED MULTI-UCA-BASED OAM-MIMO MULTIPLEXING TRANSMISSION SYSTEM A. Mathematical Background
We now give the mathematical background of our multi-UCA-based OAM-MIMO multiplexing transmission system using an equivalent channel matrix that expresses the channel matrix between Tx and Rx RF chains and includes the effects of DFT processing.Fig. 3(a) shows a schematic of an OAM multiplexing transmission system.Let n be the number of antenna elements in a UCA, then the channel-response matrix between oppositely arranged UCAs H OAM = {h p,q } ∈ C n×n is a circulant matrix in which the number of antenna elements are the same, where h p,q is an element of the matrix H OAM corresponding to the channel coefficient between the q-th transmitting UCA and p-th receiving UCA given by h p,q = ρλ 4πd p,q e −j 2π λ dp,q , Here, d p,q is the distance between the antennas, λ is the wavelength, and ρ is a coefficient that contains all relevant constants such as gain, attenuation, and phase rotation on antenna elements.Then, H OAM can be diagonalized by a DFT matrix as where Λ OAMx,y is an element of the x-th row and y-th column of the matrix Λ OAM , and [ * ] H denotes the Hermitian conjugate of the matrix [ * ].The scalar complex value λ l is the channel coefficient of OAM mode l, and L is the total number of used OAM modes (L ≤ n).The DFT matrix D n,L ∈ C n×L is given by where d l is an eigenvector of the DFT matrix corresponding to OAM mode l, the vector length is n, and I is the identity matrix.The n limits the range of l as Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Equation ( 2) is almost singular value decomposition, but the components in the equivalent channel matrix are complex numbers, not real numbers.Of course, their magnitude is the same, so their channel capacities are equivalent and optimal.
We define the Λ OAM as the equivalent channel matrix of OAM multiplexing, which is a channel matrix that includes the effect of DFT processing.When UCA-based OAM multiplexing is executed with a fixed processing such as DFT, aliasing modes due to spatial discretization of a UCA must be noted.When an OAM mode in the range shown in ( 7) is generated, its aliasing modes outside the range of ( 7) are simultaneously generated.Therefore, these aliasing modes must not be mixed with other OAM modes due to aliasing in spatial sampling by the receiving UCA.Basically, if the number of elements in the Tx and Rx UCAs is the same, the aliasing mode is not a problem because aliasing modes simply come back to the original mode.The effect of aliasing modes can be determined by whether the circularity of H OAM is maintained and the equivalent channel matrix is diagonal as defined.We extend the above mathematical explanation from the single-UCA case to the multi-UCA case.Fig. 3(b) shows a schematic of our OAM-MIMO multiplexing transmission system.The channel matrix between multi-UCAs is given by where the partial matrix H OAM a,b ∈ C n×n is the channel matrix between Rx UCA a and Tx UCA b, and N R or N T is the number of UCAs in the Rx or Tx antenna, respectively.Each partial matrix can be diagonalized by the DFT matrices in the same manner as in (3) and transformed into the equivalent channel matrix for OAM multiplexing Λ OAM a,b , so the equivalent channel matrix of OAM-MIMO multiplexing transmission is formed by lining several Λ OAM a,b s vertically and horizontally.Thus, the rearranged equivalent channel matrix of OAM-MIMO multiplexing transmission Λ OAM-MIMO is a block diagonal matrix given by where the scalar complex value λ a,b is the channel of OAM mode l between Rx UCA a and Tx UCA b, meaning we can obtain isolated MIMO channels in each OAM mode as Here, r l is the received signal vector and s l is the transmitted signal vector.Therefore, we can apply the traditional MIMObased signal processing on the Rx and Tx sides with feedback of channel states information for the MIMO channel in each OAM mode individually.Note that only OAM mode 0 has energy at the center point because the point is phase singularity for the other modes.Therefore, when we put an antenna element at the center point, we isolate the channel for OAM mode 0. An extra degree of freedom is then added for the channel of OAM mode 0.

B. Capacity of Our Multi-UCA-Based OAM-MIMO Multiplexing Transmission System
We discuss the achievable capacity with our multi-UCAbased OAM multiplexing transmission system and that with other multi-antenna technologies.The capacity of full-digital MIMO depends on the channel between the Tx and Rx antennas, and the theoretical capacity is derived by traditional MIMO theory.OAM multiplexing and traditional full-digital MIMO using UCAs have been compared [40], [41], [42].Full-digital MIMO has the potential to achieve the theoretical maximum capacity derived from the channel matrix between antennas, and the achievable capacity of the other multiple-antenna technologies that include hybrid MIMO is the same or less due to a certain constraint.However, when using a massive number of antennas, connecting RF chains to the numerous antenna elements and applying a heavy full-digital MIMO equalization for the channel between all antenna elements are impractical.Therefore, both comparisons should also focus on practical implementation and realistic capacity.
We show the capacity equivalence between traditional MIMO and our OAM-MIMO multiplexing transmission system.First, the MIMO capacity between antenna arrays is given by where H denotes the channel matrix between the Tx and Rx antennas, "det" is the determinant, P t is the average transmitting power of each antenna element, and σ 2 n is the average noise power.The determinant relates to the capacity and is invariant with respect to the unitary transformation processing for H.
Regarding the processing in our system, the matrix that corresponds to OAM-mode generation processing at the Tx side can be described as where D i denotes the DFT processing for UCA i and is equal to the n-by-n DFT matrix D n,n .The D OAM-MIMO is a block diagonal matrix, and each diagonal block is unitary, so the matrix is also unitary.The rearrangement manipulation does not affect the determinant of a matrix.The matrix that corresponds to the rearrangement manipulation has only one "1" in each row and column, so it is unitary.Hence, the Λ OAM-MIMO in ( 9) is a unitary transformed matrix of H OAM-MIMO in (8).Therefore, their capacity is the same.The determinant of a block diagonal matrix is equivalent to the product of determinants of each block component as Therefore, the channel capacity of Λ OAM-MIMO can be transformed as Equations ( 12) and (15) show that the achievable capacity of parallel processing in each OAM mode is equivalent to the theoretical capacity between multi-UCAs.Thus, we can conclude that our DFT based system architectures can achieve the theoretical maximum capacity between oppositely arranged multi-UCAs.We can then simply reduce the number of RF chains for the OAM modes in the order of ascending channel capacity provided by their channel matrix Λ l .Such extraction of OAM modes to use is also important for practicality in the sense that it becomes relatively difficult to suppress the inter-mode interference in analog circuits as the number of OAM modes increases.Due to beam divergence, higher OAM modes tend to have lower gains as well as traditional OAM multiplexing, so using lower OAM modes is a simple means of reducing the RF chains and improve practicality.Fig. 4 shows the relative capacity, i.e., the ratio of the capacity achievable with a limited number of OAM modes to the maximum channel capacity between multi-UCAs using all available OAM modes obtained from (15).The number of antenna elements in each UCA is 16; hence, it follows that the maximum number of OAM modes is 16.Note that lower-order OAM modes are then preferentially used.For example, "three OAM modes" indicates OAM modes 0 and ±1, and "five OAM modes" indicates OAM modes 0, ±1, and ±2.The OAM-mode gain properties with respect to distance are strongly affected by antenna size and can be generalized by the square of the antenna size from the definition of the Rayleigh distance, as shown in a previous study [40].When the distance between antennas is not long compared with the square of the antenna size, the capacity of each OAM mode is nearly the same.However, the capacity of lower OAM modes accounts for a large portion of the maximum channel capacity as the transmission distance becomes longer.Therefore, adequate mode selection becomes important, and we can fix the antenna size and OAM modes to use (lower OAM modes) depending on the target distance, as explained above, which reduces RF chains for the unutilized OAM modes.

C. Hybrid Architectures of OAM-MIMO Multiplexing Transmission System
Our OAM-MIMO multiplexing transmission system has two hybrid analog-digital architectures, i.e., clustered and fully connected, as shown in Fig. 5.Both architectures have the same number of RF chains, a comparatively smaller number than full-digital MIMO, and equipped with Butler matrices on each UCA as DFT processors.The Butler matrix is an RF passive analog circuit, which can contribute to reducing implementation cost and power consumption in beamforming, as mentioned in a previous study [41], as well as the other analog and hybrid beamforming technologies including hybrid MIMO and beam-space MIMO described earlier [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25].The hybrid configurations of these references consist of RF network circuits including variable phase shifters to cope with environmental variations, mobility, etc.Many variable phase shifters and RF paths are then required to connect the RF chains and antenna elements, and the system capacity is sometimes limited compared with the maximum channel capacity between antenna elements.Our application scenario, however, is a fixed/semi-fixed environment, such as mobile back/front-haul, and as discussed previously, the OAM-MIMO multiplexing transmission system is a hybrid configuration made possible by Butler matrix circuits and multi-UCAs while maintaining the potential to achieve maximum channel capacity between antenna elements.The difference between the proposed two architectures is whether the digital signal processing for precoding and/or equalization is applied across the OAM mode.This affects the removal performance of inter-mode interference.When the channel matrix size is M × M , the most complex part of minimum mean square error (MMSE)-based channel estimation is to obtain the inverse of the M × M matrix that requires O(M 3 ), and linear equalization processing needs M ×M matrix multiplication that requires O(M 2 ).Therefore, we focus on the complexity of channel estimation and channel equalization.Therefore, in our application scenario of mobile back/front-haul, channel estimation is not frequently required since the channel between the antennas is almost static for a certain time, but equalization processing is required in real time.In an application scenario of mobile access networks, OAM modes are used as an analog beam-former, and the channel between the base station and mobile devices generally varies dynamically, so the computational complexity for channel estimation becomes dominant.
Table I shows a comparison of our OAM-MIMO multiplexing transmission system designs, computational complexity, and various tolerances.Other LoS-MIMO designs using a conventional two-dimensional uniform rectangular array (2D-URA) are also shown as reference.For simplicity, we set N R = N T = N UCA .The numbers of antenna elements in architectures I through V are denoted as N I through N V , respectively, and the number of RF chains in the two hybrid analog-digital architectures of our system are defined as N OAM .Each item in Table I is described in detail in the remainder of this section.
Architecture I: Ideally, multi-UCA based OAM-MIMO multiplexing requires only inner-mode equalization when there is no inter-mode interference between the OAM modes, as described in Section III.Therefore, the ports of the Butler matrix circuits corresponding to the same OAM mode are clustered, as shown in Fig. 5(a), and digital signal processing is conducted in each OAM mode.This is equivalent to applying equalization for each MIMO channel Λ l in (10) individually, and the matrix size of each Λ l is much smaller than the entire channel H OAM-MIMO in (8).Therefore, the computational complexity can be lowered compared with that for channel estimation and equalization over the entire channel H OAM-MIMO .
Architecture II: Sometimes the channels between UCAs are not perfect circulant matrices due to antenna misalignment, multipath effects, imperfections of the analog circuit, etc.Therefore, they cannot be diagonalized perfectly by DFT processing, which causes inter-mode interference between OAM modes [55], [56], [57], [58] and deteriorates performance.We can obtain better practical performances when the digital signal processing extends over the OAM modes as the fully connected architecture shown in Fig. 5(b).It is equivalent to applying channel equalization for the whole Λ OAM-MIMO shown in (9).In this case, leakage from the other OAM modes is also used for channel equalization to prevent performance deterioration caused by inter-mode interference.Of course, we can reduce the number of RF chains for unused OAM modes as well.Computational complexity is comparatively higher than in the clustered architecture, so there is a tradeoff between cost and performance.
Architecture III: This is a multi-UCA and full-digital architecture of OAM-MIMO multiplexing transmission in which all antenna elements are connected to RF chains directly without any RF analog circuits such as Butler matrices.We show this architecture as a reference because the performance of OAM multiplexing technology is discussed on the basis of this pattern in most cases and can achieve the best performance.However, we argue that this traditional full-digital architecture Architecture IV: Antenna elements are arranged in a grid at optimal intervals for a specific distance [59], [60].In this case, the intervals are precisely fixed depending on the distance between the Tx and Rx antennas, and the beamforming and equalization processing is achieved by the Fourier transform.Therefore, it does not require any digital signal processing for channel equalization if the Butler matrices are used as DFT processors.The optimal space d is given by where λ and D denote the wavelength and distance between the Tx and Rx antennas, respectively, N LoS is the number of antenna elements, and m is an integer more than or equal to 0. This architecture does not require any digital signal processing for equalization, however, it works as intended at a specific distance and a little sensitive to misalignment.Architecture V: Antenna elements are arranged in a grid.Full-digital MIMO-based channel precoding and equalization is applied, so the achievable performance is high, but device and computational complexity also become high.This is a conventional MIMO architecture.

D. Complexity and Performance Comparison
Table III shows a comparison of the number of RF chains and relative computational complexity with the specific parameters listed in Table II.The relative computational complexity of Architecture I is taken as one.For a comparison in terms of device and computational complexity, two types of architecture V are described, V-1 and V-2, with differences in the numbers of RF chains and antenna elements.The number of RF chains of Architectures I, II, IV, and V-1 is N OAM = 20, and that of Architectures III and V-2 is 64.Note that the occupation area of all architectures is set to be almost the same for a fair comparison.Accordingly, the antenna arrangement of Architectures IV and V-1 is set to a 4 × 5 grid pattern, and the optimal intervals of antenna elements for 10 m transmission are 16.36 and 14.63 cm for vertical and horizontal directions, respectively, derived from (16).
There is a well-known antenna arrangement in which the antenna elements are arranged in a grid at half lambda intervals; however, this architecture requires more than 10,000 RF chains, so we consider it impractical and inappropriate for this comparison.Such an architecture using massive antennas is generally an assembly of sub-arrays like Architectures IV and V.
Fig. 6 shows channel-capacity comparisons with the simulation parameters listed in Table II.The total transmitting power is set to 10 dBm and equally allocated to all multiplexed streams.In Architectures I and II, lower OAM modes (0, ±1, and ±2) are used and the others are terminated for RF-chain reduction.Fig. 6(a) shows the distance characteristics of each architecture.Architectures I and II without misalignment show the same characteristics explained in Sub-section B. Architecture IV work well for a specific distance, since this interval is optimized for a transmission distance of 10 m.In contrast, Architectures I and II show good performance against distance variability.The capacity of Architectures I and II is better than that of the full-digital architectures III and V-2 as the distance becomes longer because of the appropriate mode selection and power allocation, as described in Sub-section B. Fig. 6(b) shows antenna-misalignment tolerability on the capacity of each architecture with misalignment angles within 1 degree at a distance of 10 m.The performance deterioration of Architectures I and IV prominently occurs when the antenna misalignment is more than roughly 0.1 degrees.However, the misalignment of 0.1 degrees corresponds to 18-mm deviation from the propagation axis at a distance of 10 m.Therefore, it is not difficult to fix visually, for example, by using optical lasers or optical sights for fixed wireless communications.The capacity of Architecture II hardly changes in spite of the increase in antenna misalignment because of the inter-mode equalization.This is the same for Architecture V. Thus, they have a strong resistance to antenna misalignment.
We have discussed the effects of the propagation environment primarily in terms of antenna misalignment, but a similar problem, inter-mode interference, occurs in environments affected by multipath, and several papers have presented methods for its analysis [55], [56].Note that the multipath effects can be prevented up to a certain distance by simply increasing the gain of antenna elements or by deploying the Tx and/or Rx antenna at higher locations, such as on the roof of buildings.If multipath effects cannot be eliminated, it is recommended to use configurations that can compensate for inter-mode interference, such as Architecture II.

A. Experimental Setup
We constructed a prototype of our OAM-MIMO multiplexing transmission system and designed Tx and Rx antennas.Fig. 7 shows the antenna design and structure of our experimental system.The antennas had quadruple UCAs with a center antenna element.Thus, OAM mode 0 had five degrees of freedom, and the other modes had four degrees of freedom.Each UCA had 16 antenna elements, so the UCAs could use 16 OAM modes (from −7 to +8).We also designed and implemented 16 × 5 broadband Butler matrix circuits on the Tx side and 5×16 on the Rx side as analog DFT processors in our experimental system, enabling us to generate and separate five OAM modes (0, ±1, and ±2), as shown in Fig. 8. Fig. 8(a) shows a block diagram of our implemented Butler matrix.Traditional Butler matrix processing is similar to DFT, but the phase rotation in the output ports is an odd multiple of π.However, we needed an integer multiple of 2π to generate and separate OAM modes.Thus, we inserted phase shifters with different shift quantities in the output side for appropriate DFT processing, highlighted with the dotted line in Fig. 8(a).We also combined two 8 × 8 Butler matrices to support the 16 antenna elements in a UCA.The 16 output ports were connected to the antenna elements alternately, as shown in Fig. 8(b), and the input ports of one Butler matrix were given specific phase shifts that corresponded to the phase rotation associated with the antenna disposition.For example, the angle between adjacent antenna elements was π/8, so the phase rotation between the adjacent antenna elements was kπ/8 for OAM mode k.Notably, input ports that corresponded to the unused modes helping reduce RF chains were terminated.The same occurred at the Rx with a reverse operation, so we prepared only one type of analog circuit.On the Rx side, the received energy was concentrated by the Butler matrix at the ports corresponding to used OAM modes.
The Butler matrices were originally used for analog beamforming; however, our use case requires much higher accuracy to generate orthogonal basis.To evaluate the performance of the Butler matrices, we introduce the "mode isolation" index.A response matrix D ′ n,L of the actual Butler matrices can be  expressed as where the real number α represents the loss factor, and the matrix Ω represents the deviation factor from ideal operation that causes inter-mode interference.We then define mode isolation vector Υ as a ratio of the desired mode's signal power to inter-mode interference level as where The mode isolation is independent of the loss factor.As the definition of mode isolation indicates, the higher the mode isolation is, the lower the inter-mode interference and energy loss due to the leakage to unused OAM modes are.Thus, if the Butler matrices work ideally (Ω is zero matrix), there is no inter-mode interference and the mode isolation becomes infinite.The response matrix D ′ n,L can be obtained by measuring the S-parameter of the Butler matrices.Fig. 9 shows our implemented wideband 16 × 5 Butler matrix, and Fig. 10 shows measured mode isolation results of an implemented wideband Butler matrix for a 28-GHz band.We could obtain roughly more than 20-dB mode isolation over a wide band by designing the circuit layout to be symmetric and wiring length to be as uniform as possible.RF chains were also implemented for each data stream as up and down converters for the Tx and Rx antennas, respectively.The mixers in the RF chains of their respective antennas had a common local signal source, so all converters of the respective antennas were synchronized.As a result, there were 65 antenna elements, but there were 21 RF chains, which was equivalent to the total degrees of freedom in our prototype.
We also implemented an offline digital-signal-processing algorithm in our system.Digital intermediate frequency (IF) waveforms were created with an adaptive quadrature amplitude modulation (QAM) system of a single-carrier frequency domain equalization (SC-FDE) [61] to compensate for frequency distortion.The created waveforms were converted to analog IF signals by using synchronized arbitrary waveform generators (AWGs) as digital-to-analog converters, and the received IF waveforms were captured on a digital serial analyzer (DSA), a type of digital sampling oscilloscope used as an analog-to-digital converter.The equipment of our DSA sequentially sampled the received IF waveforms by using multiport electromechanical coaxial switches.This had minimal effect on the experimental results because the propagation channel's condition was static during the measurements in our shielded room.A digital matched filter (root raised cosine filter with a roll-off factor of 0.1) was applied to both transmitted and received signal waveforms.A frame timing and carrier frequency offset estimator and correlator were designed and implemented in the Rx digital signal processing to cancel errors in the actual system.Data streams were coded with a low-density parity-check (LDPC) code and Bose-Chaudhuri-Hocquenghem (BCH) code on the basis of a digital video broadcasting second generation (DVB-S.2) standard used as forward error collection.We estimated the equivalent channel matrix and applied the MMSE frequency domain-channel equalization to the data streams.Finally, we estimated the SNR of the data streams and fed the streams back to the Tx antenna then adaptively updated the modulation order and coding rate for each data stream in accordance with the SNRs.We prepared an error-free SNR for each combination of modulation orders and coding rates as a table in advance.We first conducted numerical simulations to look for SNRs with a bit error rate (BER) less than a threshold of 10 −7 .We allowed a 1-dB margin of the SNRs for each set of modulation orders and coding rates.Therefore, the BERs were approximately zero because they fell rapidly at a certain SNR.We then sorted the combinations of modulation orders and coding rates in accordance with their physical-layer data rates for each combination.Finally, we chose a lower and closer combination than the estimated SNR for each stream, which worked as AMC.We used manual rotary tools to align our antennas.The Tx and Rx antennas equipped with two optical lasers at their corners made it easy to align them visually.Table IV lists the specific parameters of our experimental setup, and Fig. 11 shows a photograph of the actual experimental environment in our shielded room.The Tx and Rx antennas were placed 10 m apart.

B. Experimental Results
We evaluated the feasibility of our OAM-MIMO multiplexing transmission system with two hybrid analog-digital architectures.We started by describing the normalized power of an equivalent channel matrix between the Tx and Rx antennas in Fig. 12.The equivalent channel matrix was almost a block diagonal matrix, but we observed a few interferences between OAM modes due to the reasons mentioned in Section III.The inter-mode interferences were less than 20 dB lower compared with the received signal power in any OAM mode.We also observed that the inter-mode interference mostly came from adjacent OAM modes.
Next, we evaluated the performance of our system and a series of signal processing by testing our received signal processing.The quadruple UCAs received 16-QAM signals with five different OAM modes (0, ±1, and ±2) transmitted from UCA 1 and composed using the MMSE equalizer, which worked as a maximum ratio combining diversity receiver.Fig. 13 shows constellation diagrams of the received signals.
The correctly arranged signal points show that our received signal processing worked accurately.We also tested the multiplexing of 20 data streams with quadrature phase shift keying (QPSK) modulation and an error-correction coding rate of 1/4 by using all UCAs (four streams for each OAM mode).Normalized color chart of equivalent channel matrix between Tx and Rx antennas described in (9).The indexes that correspond to UCA 1 to 4 are arranged from left to the right in each Tx OAM mode and from top to bottom in each Rx OAM mode, and center antenna is placed leftmost and topmost in Tx and Rx OAM mode 0. The 20 streams were successfully demodulated without error.However, the total data rate was less than 20 Gbit/s, so the AMC could double the data rate due to the high correlation between streams in each OAM mode.
After these tests, we evaluated the performance of our OAM-MIMO multiplexing transmission system then applied AMC.We conducted three demonstrations: OAM-MIMO of a clustered architecture, OAM-MIMO of a fully connected architecture, and a combination of OAM-MIMO and polarization multiplexing.There are ways of using the OAM-MIMO channels as typical MIMO.In our experimental demonstration, we applied an antenna-selection algorithm that selects the best combination of Tx antennas while taking into account system complexity.Fig. 14(a) shows the power of the equivalent channel matrix of the first two demonstrations.We used all the UCAs on the Rx side, so there were 21 degrees of freedom on that side.We selected an optimal set of UCAs as the Tx datastream sources-which were UCA 2 and UCA 4 and the center antenna element-to maximize the summation of the data rate.Therefore, OAM mode 0 had three degrees of freedom, and the other modes had two degrees of freedom on the Tx side.
Accordingly, we multiplexed 11 data streams with the optimum modulation order and coding rate and achieved a  The received signals' BERs without coding were 0.96, 1.00, and 1.77 %, respectively, and were error-free (less than 10 −7 ) after decoding.We then gave a 1-dB margin for the AMC from the actual SNR.We confirmed that the results are reproducible with multiple experiments.Fig. 16(a) and (b) show the actual SNR calculated by error vector magnitude (EVM), the adaptive modulation order, and adaptive error correction coding rate for each stream.We also confirmed that the results in symmetry modes were almost the same in the full-digital case."Symmetry modes" means a pair of OAM modes with the same absolute value and unlike signs.The major cause of the slight variation in symmetry modes might be the misalignment of the antennas and a slight characteristic variation in the analog circuit.Such problems have a greater effect on individual digital support, so the symmetry was a little worse compared with the full-digital support.
Finally, we evaluated a combination of OAM-MIMO and polarization multiplexing using the same antennas.Our antenna elements and analog circuits only supported vertical polarization, so we turned half of the antenna elements 90 degrees-specifically the antenna elements in UCA 1 and 3 of the Tx and Rx antennas-to use horizontal polarization simultaneously.The isolation between the polarizations was more than 20 dB, so we regarded them as isolated OAM-MIMO channels.Fig. 14(b) shows the power of the equivalent channel matrix of this case.We achieved a total data rate of 200 Gbit/s in a simultaneous transmission, as shown in Fig. 16(c).

V. DISCUSSION AND CONCLISION
We proposed an OAM-MIMO multiplexing transmission system with two practical system architectures that uses multi-UCAs and Butler matrices for scenarios that require high-capacity wireless transmission.The OAM modes could be approximately generated and separated using a UCA, so OAM multiplexing with a UCA can be considered a form of MIMO technology.OAM multiplexing has a high affinity to analog processing such as a Butler matrix, and we extended this to OAM-MIMO technology, enabling us to multiplex multiple data streams in respective OAM modes and enhance the space-utilization efficiency compared with traditional OAM multiplexing technology.The most notable characteristics of our OAM-MIMO multiplexing transmission system is that functions of signal processing for spatial multiplexing are adequately allocated to both analog and digital signal processing, enabling us to efficiently reduce digital computational complexity and the number of expensive RF chains.Our system requires additional hardware; however, the Butler matrix is a passive analog circuit, so it is quite advantageous in terms of implementation and operational costs as well as the other hybrid beamforming technologies.We organized the mathematical expression of our OAM-MIMO multiplexing transmission system as a practical form of hybrid MIMO technology.We also derived the channel capacity between multi-UCAs and showed the capacity equivalence between traditional full-digital MIMO and our OAM-MIMO multiplexing transmission system.Moreover, we show that the capacity of lower OAM modes accounts for a large portion of the maximum channel capacity as the transmission distance becomes longer.Thus, we can efficiently reduce RF chains by fixing the antenna size and OAM modes to use (lower OAM modes) depending on the target distance.
Then, we introduced a prototype equipped with quadruple UCAs placed concentrically and an antenna element at the center.The system also had RF chains and broadband Butler matrix circuits for each UCA used as analog DFT processors to generate and separate OAM modes on the 28-GHz frequency band.We then implemented RF chains for five OAM modes (OAM modes 0, ±1, and ±2).The degrees of freedom were five for OAM mode 0 and four for the other OAM modes.We evaluated two OAM-MIMO architectures with different digital support levels and demonstrated 75-and 130-Gbit/s wireless transmission at a distance of 10 m by multiplexing 11 streams in a shielded room.Slight inter-mode interference was observed in the channel obtained in the actual OAM-MIMO experimental system, and the performance depended on whether the inter-mode interference was compensated.The major factors of the inter-mode interference in OAM-MIMO multiplexing are antenna misalignment, multipath effects, and imperfections of the analog circuit.The simulation results also indicate that while the impact of inter-mode interference on capacity is larger with less digital support, it can be very small when a certain amount of digital support is allowed.Thus, the architecture should be chosen in accordance with application scenarios and acceptable system complexity.Moreover, we evaluated a combination of OAM-MIMO and polarization multiplexing and achieved 200-Gbit/s wireless transmission by multiplexing 21 streams with the same antenna.
We were able to demonstrate high-capacity wireless transmission with a practical configuration.We plan to further improve the circuit performance and antenna-alignment correction as well as experimentally investigate the possibility of achieving high-capacity long-distance transmission.

Fig. 2 .
Fig. 2. (a) Wavefront shapes of OAM modes and (b) spatial phase distribution on plane vertical to propagation axis.

Fig. 4 .
Fig.4.Ratio of capacity with different numbers of used OAM modes to maximum channel capacity using all OAM modes.a represents maximum diameter of UCAs in multi-UCA.

Fig. 5 .
Fig. 5. Architectures of our OAM-MIMO multiplexing transmission system.(a) Clustered architecture with minimized digital support and (b) fully connected architecture with inter-mode digital signal processing.They have trade-off between system complexity and performance.

Fig. 6 .
Fig. 6.Capacity comparison of (a) distance characteristics without antenna misalignment and (b) antenna-misalignment tolerability at distance of 10 m.

Fig. 8 .
Fig. 8. (a) Block diagram of 8 × 8 Butler matrix.Phase shifters surrounded with dotted line are inserted for OAM multiplexing.(b) Configuration of 16 × 5 Matrix, which is combination of two 8 × 8 Butler matrices, and connections corresponding between output ports and antenna elements.

Fig. 11 .
Fig. 11.Photograph of experiments in a shielded room.

Fig. 12 .
Fig. 12.Normalized color chart of equivalent channel matrix between Tx and Rx antennas described in(9).The indexes that correspond to UCA 1 to 4 are arranged from left to the right in each Tx OAM mode and from top to bottom in each Rx OAM mode, and center antenna is placed leftmost and topmost in Tx and Rx OAM mode 0.

Fig. 14 .
Fig. 14.Normalized color charts of equivalent channel matrixes representing received intensity of (a) 130-Gbit/s transmission and (b) 200-Gbit/s transmission combined with polarization multiplexing, arranged as in Fig. 12.

Fig. 16 .
Fig. 16.Measured SNR calculated by EVM and adaptive parameters of each data stream for (a) 75-Gbit/s transmission of fully connected OAM-MIMO, (b) 130-Gbit/s transmission of clustered OAM-MIMO, and (c) 200-Gbit/s transmission that combined fully connected OAM-MIMO and polarization multiplexing.

TABLE I COMPARISON
OF SEVERAL ANTENNA DESIGNS AND SPATIAL-EQUALIZATION ALGORITHMS lacks one of the most important benefits of the cost and complexity reduction of OAM multiplexing technology.

TABLE IV SPECIFIC
PARAMETERS OF EXPERIMENTAL SETUP