Method and controller for multi-mode orbital angular momentum (OAM) wave generation and beamforming, and method and system for OAM transmitter-receiver directional alignment

Abstract

A method of, as well as a corresponding controller for, multi-mode OAM wave generation and beamforming using a planar phased array antenna is provided. The method includes, for each mode of a multi-mode OAM wave to be generated: selecting a subset of antenna elements of the planar array of antenna elements for generating the mode of the multi-mode OAM wave; applying, for each antenna element of the selected subset, a first phase shift to the antenna element, the first phase shift determined based on an index of the antenna element and the mode of the multi-mode OAM wave for generating the mode of the multi-mode OAM wave; and applying, for each antenna element of the selected subset, a second phase shift to the antenna element, the second phase shift determined based on the index of the antenna element and a beamforming direction defined for the mode of the multi-mode OAM wave for beamforming the mode of OAM wave to the beamforming direction defined therefor. A method of, as well as a corresponding system for, OAM transmitter-receiver directional alignment is also provided. The method includes: obtaining, from each antenna element a plurality of antenna elements of a layer of antenna elements of the OAM receiver, a first phase value of a received signal of a first OAM wave of a first OAM mode incident at the plurality of antenna elements of the antenna element, whereby the first OAM wave is transmitted from the OAM transmitter; predicting a distance error between an intersection point of a transmitter beam axis of the OAM transmitter at the planar array of antenna elements of the OAM receiver and a center of the planar array of antenna elements of the OAM receiver based on the set of first phase values using a distance error machine learning model; predicting an azimuth angle error associated with the distance error based on the set of first phase values using an azimuth angle error machine learning model; and sending transmitter beam axis error information based on the predicted distance error and the predicted azimuth angle error to the OAM transmitter for adjusting the transmitter beam axis.

Description

METHOD AND CONTROLLER FOR MULTI-MODE ORBITAL ANGULAR MOMENTUM (OAM) WAVE GENERATION AND BEAMFORMING, AND METHOD AND SYSTEM FOR OAM TRANSMITTER-RECEIVER DIRECTIONAL ALIGNMENTCROSS-REFERENCE TO RELATED APPLICATION |00011 This application claims the benefit of priority of Singapore Patent Application No.10202500603P filed on 11 March 2025, the content of which being hereby incorporated by reference in its entirety for all purposes.TECHNICAL FIELD

[0002] The present invention generally relates to a method and a controller for multi-mode orbital angular momentum (OAM) wave generation and beamforming, and a method and a system for OAM transmitter-receiver directional alignment.BACKGROUND

[0003] Radio frequency orbital angular momentum (RF OAM), which may simply be referred to herein as OAM, is a promising type of electromagnetic (EM) wave which can not only multiplex wireless communication signals but also enhance radar sensing resolution. It has attracted increasing interest. OAM was first discovered and applied in optical fiber communication for capacity increasing. Due to the waveguide effect, the wavefront is stable at the receiver side even after long-distance propagation in optical fiber, and thus, the OAM wave can be detected and recovered well. However, in radio frequency (RF) applications without waveguide, the signal of OAM wave may significantly change at different locations. The performance of OAM wave detection at the OAM receiver is thus location sensitive. Therefore, it is important to be able to effectively control OAM beams to desired directions.

[0004] On the other hand, simultaneously generating multiple modes is important to enhance communication capacity and sensing resolution Most of existing research focuses on the way to generate fixed or various OAM modes one by one. Therefore, an effective method to simultaneously generate multiple modes of OAM wave (multi-mode OAM wave) with respective beamforming is needed.

[0005] For example, there has been disclosed a method of generating multi-mode 0AM wave using programmable metamaterial. It has a larger aperture than the typical metalens based method. Various modes of 0AM wave can be generated through the reconfigurable structure comprising an array of PIN diodes, which controls two-phase states of electric field. However, the method can only generate one mode in one configuration. Furthermore, the method does not perform 0AM wave beamforming.|0006| For example, there has also been disclosed a four-feed circular patch antenna for generating a dual-mode 0AM wave. Theoretical calculation and numerical simulation results were presented. It was demonstrated that the four-feed circular patch antenna operating in the TMnl mode can generate ±n 0AM waves A prototype of a four-feed circular TM21-mode patch antenna was fabricated and measured to verify the effectiveness of the theoretical analysis The 0AM beams generated are in a wide band. However, the four-feed circular patch antenna still needed new hardware design to generate multiple modes of 0AM wave besides the pair of ±n modes. Moreover, there is no way to control the 0AM wave radiation / transmission direction and gain.

[0007] For example, there has been disclosed a single port finding RF 0AM generator. It can generate modes +1 or -1 0AM beams arbitrary by controlling the PIN diodes. Validation of the 0AM mode -1 and +1 generations and data encoding and decoding are conducted through simulation and experiment. The mode control is based on 4 phase shifters in principle The limitation of this proposal is that it can only generate Modes +1 and -1 without beamforming capability.

[0008] For example, there has been studied the generation and detection of 0AM wave in mmWave frequency. The phased arrays with ring, rectangular and circular shapes were studied and compared. 0AM beam steering was also studied. However, the study was limited to single 0AM mode even though the array was reconfigurable to generate different 0AM mode. Furthermore, the study does not present a method of generating multiple 0AM modes and respective beamforming.

[0009] For example, there has been disclosed a space-time-coding digital metasurface in microwave frequency to generate time-varying 0AM beams. Due to the time-varying mode, a higher-order twist can be further designed as an additional degree of freedom. The time-varying 0AM field patterns are dynamically mapped by developing a two-probe measurement technique. The approach of combining the programmability of space-time-coding digital metasurfaces and the two-probe measurement technique provides a platform for generating andobserving time-varying 0AM. However, the approach or platform cannot simultaneously generate multiple modes of 0AM wave and cannot control the directions of 0AM beams.

[0010] Accordingly, 0AM EM waves are promising in providing high-capacity wireless communications. It has attracted huge interest. In relation to 0AM wave generation, various multi-mode RF-OAM generators have been reported as discussed above, for example, with metamaterial, four-feed circular patch antenna, single port PIN diodes control and uniform circular array (UCA), respectively. In relation to the 0AM system, comparisons of 0AM systems and conventional multiple input and multiple input (MIMO) systems in wireless communications have shown that 0AM multiplexing achieves higher channel capacity than that of the typical MIMO system. There has also been proposed multi-mode RF-OAM in MIMO system which shares burden between analogue circuit and digital signal processor. There has also been disclosed a long-distance RF-OAM transmission system with distributed antennas. To synchronize the signals received by different antennas far from each other, a compensation network with feedback links was needed and designed. There has further been disclosed a communication system with multi-mode 0AM generation, reception. Therefore, 0AM (i.e., RF-OAM) is a good candidate for next generation wireless communication systems, since the additional 0AM multiplexing besides traditional time, frequency and space divisions leads to higher spectrum utilization rate. However, this potential rests on the basis of good alignment between the 0AM transmitter (Tx) and the 0AM receiver (Rx) In particular, directional misalignment will significantly affect RF-OAM performance. For example, there has been mentioned inter-mode interference due to misalignment, but did not quantitatively analyze it. Single mode degradation was not analyzed either. A misalignment solution consisted of distance and angle estimations based on 2D ESPRIT algorithm requiring Rx signal covariance matrix for eigen value decomposition (EVD), which can only be obtained with multiple snapshots of signal and hence last long time.

[0011] A need therefore exists, according to a first aspect of the present invention, to provide a method of 0AM wave generation and beamforming, as well as a controller thereof, that seeks to overcome, or at least ameliorate, one or more deficiencies in conventional methods of 0AM wave generation and / or beamforming, and more particularly, that is able to effectively generate a multi-mode 0AM wave and beamform multiple modes of the multi-mode 0AM wave to respective desired directions A need also exists, according to a second aspect of the present invention, to provide a method of 0AM transmitter-receiver (Tx-Rx) directional alignment, as well as a system thereof, that seeks to overcome, or at least ameliorate, one ormore deficiencies in conventional methods of OAM-based wireless communications, and more particularly, for correcting or improving 0AM transmitter-receiver directional alignment. It is against this background that the present invention has been developed.SUMMARY

[0012] According to a first aspect of the present invention, in various embodiments, there is provided a method of multi-mode 0AM wave generation and beamforming using a planar phased array antenna comprising a planar array of antenna elements, the method comprising, for each mode of a plurality of modes of a multi-mode 0AM wave to be generated:selecting a subset of antenna elements of the planar array of antenna elements for generating the mode of the multi-mode 0AM wave;applying, for each antenna element of the selected subset of antenna elements, a first phase shift to the antenna element, the first phase shift determined based on an index of the antenna element and the mode of the multi-mode 0AM wave for generating the mode of the multi-mode 0AM wave; andapplying, for each antenna element of the selected subset of antenna elements, a second phase shift to the antenna element, the second phase shift determined based on the index of the antenna element and a beamforming direction defined for the mode of the multi-mode 0AM wave for beamforming the mode of 0AM wave to the beamforming direction defined therefor.

[0013] According to the first aspect of the present invention, in various embodiments, there is provided a controller for controlling a planar phased array antenna comprising a planar array of antenna elements for multi-mode 0AM wave generation and beamforming, the controller comprising:at least one memory; andat least one processor communicatively coupled to the at least one memory and configured to, for each mode of a plurality of modes of a multi-mode 0AM wave to be generated:select a subset of antenna elements of the planar array of antenna elements for generating the mode of the multi-mode 0AM wave;apply, for each antenna element of the selected subset of antenna elements, a first phase shift to the antenna element, the first phase shift determined based on an index of the antenna element and the mode of the multi-mode 0AM wave for generating the mode of the multi-mode OAM wave; andapply, for each antenna element of the selected subset of antenna elements, a second phase shift to the antenna element, the second phase shift determined based on the index of the antenna element and a beamforming direction defined for the mode of the multi-mode 0AM wave for beamforming the mode of 0AM wave to the beamforming direction defined therefor.

[0014] According to the first aspect of the present invention, in various embodiments, there is provided an 0AM transmitter for multi-mode 0AM wave generation and beamforming, comprising:a planar phased array antenna comprising a planar array of antenna elements; and a controller according to the above-mentioned first aspect of the present invention communicatively coupled to the planar phased array antenna for controlling the planar phased array antenna for multi-mode 0AM wave generation and beamforming.

[0015] According to a second aspect of the present invention, in various embodiments, there is provided a method of 0AM transmitter-receiver directional alignment between an 0AM transmitter and an 0AM receiver, the 0AM receiver comprising a planar phased array antenna comprising a planar array of antenna elements, the method comprising:obtaining, from each antenna element of a plurality of antenna elements of a layer of antenna elements of the planar array of antenna elements of the 0AM receiver, a first phase value of a received signal of a first 0AM wave of a first 0AM mode incident at the antenna element to obtain a set of first phase values of the received signals of the first 0AM wave incident at a plurality of antenna elements of the layer of antenna elements, wherein the first 0AM wave is transmitted from the 0AM transmitter;predicting a distance error between an intersection point of a transmitter beam axis of the 0AM transmitter at the planar array of antenna elements of the 0AM receiver and a center of the planar array of antenna elements of the 0AM receiver based on the set of first phase values of the received signals of the first 0AM wave using a distance error machine learning model, the distance error machine learning model trained to predict the distance error based on the set of first phase values of the received signals of the first 0AM wave;predicting an azimuth angle error associated with the distance error based on the set of first phase values of the received signals of the first 0AM wave using an azimuth angle error machine learning model, the azimuth angle error machine learning model trained to predict the azimuth angle error based on the set of first phase values of the received signals of the first 0AM wave; andsending transmitter beam axis error information based on the predicted distance error and the predicted azimuth angle error to the 0AM transmitter for adjusting a transmitter beam axis of the 0AM transmitter for 0AM transmitter-receiver directional alignment.

[0016] According to the second aspect of the present invention, in various embodiments, there is provided a system for 0AM transmitter-receiver directional alignment between an 0AM transmitter and an 0AM receiver, the 0AM receiver comprising a planar phased array antenna comprising a planar array of antenna elements, the system comprising:at least one memory; andat least one processor communicatively coupled to the at least one memory and configured to:obtain, from each antenna element of a plurality of antenna elements of a layer of antenna elements of the planar array of antenna elements of the 0AM receiver, a first phase value of a received signal of a first 0AM wave of a first 0AM mode incident at the antenna element to obtain a set of first phase values of the received signals of the first 0AM wave incident at the plurality of antenna elements of the layer of antenna elements, wherein the first 0AM wave is transmitted from the 0AM transmitter;predict a distance error between an intersection point of a transmitter emission axis of the 0AM transmitter at the planar array of antenna elements of the 0AM receiver and a center of the planar array of antenna elements of the OAM receiver based on the set of first phase values of the received signals of the first OAM wave using a distance error machine learning model, the distance error machine learning model trained to predict the distance error based on the set of first phase values of the received signals of the first OAM wave;predict an azimuth angle error associated with the distance error based on the set of first phase values of the received signals of the first OAM wave using an azimuth angle error machine learning model, the azimuth angle error machine learning model trained to predict the azimuth angle error based on the set of first phase values of the received signals of the first OAM wave; andsend transmitter beam axis error information based on the predicted distance error and the predicted azimuth angle error to the OAM transmitter for adjusting a transmitter beam axis of the OAM transmitter for OAM transmitter-receiver directional alignment.

[0017] According to the second aspect of the present invention, in various embodiments, there is provided an OAM-based wireless communication system comprising:an OAM transmitter configured to generate and beamform multi-mode 0AM waves, the OAM transmitter comprising a planar phased array antenna comprising a planar array of antenna elements; andan OAM receiver configured to receive and process the multi-mode OAM waves from the OAM transmitter, the OAM receiver comprising a planar phased array antenna comprising a planar array of antenna elements, whereinthe OAM receiver comprises the at least one memory and the at least one processor of the system according to the above-mentioned second aspect of the present invention communicatively coupled to the planar phased array antenna of the OAM receiver and configured to perform OAM transmitter-receiver directional alignment.BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Embodiments of the present invention will be better understood and readily apparent to one of ordinary skill in the art from the following written description, by way of example only, and in conjunction with the drawings, in which:FIG. 1 depicts a schematic diagram of a method of multi-mode OAM wave generation and beamforming, according to various embodiments of the first aspect of the present invention;FIG. 2 depicts a schematic block diagram of a controller for controlling a planar phased array antenna for multi-mode OAM wave generation and beamforming, according to various embodiments of the first aspect of the present invention;FIG. 3 depicts a schematic diagram of a method of OAM transmitter-receiver (Tx-Rx) directional alignment between an OAM transmitter and an OAM receiver, according to various embodiments of the second aspect of the present invention;FIG. 4 depicts a schematic block diagram of a system for OAM transmitter-receiver directional alignment, according to various embodiments of the second aspect of the present invention;FIG. 5 depicts a schematic drawing of an OAM transmitter for multi-mode OAM wave generation and beamforming, according to various embodiments of the first aspect of the present invention;FIG. 6 depicts a schematic drawing of an OAM-based wireless communication system, according to various embodiments of the second aspect of the present invention;FIG. 7 depicts a flow chart of an example method of multi-mode 0AM wave generation and beamforming, according to various example embodiments of the first aspect of the present invention;FIG. 8 depicts a schematic drawing of a planar array of antenna elements with example selected antenna elements shown shaded for generating and beamforming a mode x 0AM wave, according to various example embodiments of the first aspect of the present invention;FIG. 9 depicts a schematic drawing of a planar array of antenna elements with example selected antenna elements shown shaded for illustrating simultaneous 0AM wave generation and beamforming, according to various example embodiments of the first aspect of the present invention;FIG. 10 depicts a schematic drawing of a planar array of antenna elements with example selected antenna elements shown shaded for illustrating beamforming different 0AM mode waves to different directions, according to various example embodiments of the first aspect of the present invention;FIG. 11 depicts a schematic drawing of a planar array of antenna elements with example selected antenna elements for generating and beamforming different 0AM mode waves whereby one same antenna element (darkest shaded) is reused / shared for the different 0AM mode generations, according to various example embodiments of the first aspect of the present invention;FIG. 12 depicts a schematic drawing of a planar array of antenna elements with example antenna elements in the same layer or circle separated into multiple subsets to generate different 0AM modes, according to various example embodiments of the first aspect of the present invention;FIGs. 13 A and 13B depict two example planar phased array antenna designs / configurations (planar phased array 1 and planar phased array 2), according to various example embodiments of the first aspect of the present invention;FIGs. 14A and 14B show generated 0AM radiation pattern and wavefront of mode 0 with phased array 1 element in layer 0, according to various example embodiments of the first aspect of the present invention;FIGs. 15A to 15C show generated 0AM radiation pattern and wavefronts of modes +1 and -1 with phased array 1 elements in layer 1, according to various example embodiments of the first aspect of the present invention;FIGs. 16A to 16C show generated 0AM radiation pattern and wavefronts of modes +2 and -2 with phased array 1 element in layer 2, according to various example embodiments of the first aspect of the present invention;FIGs. 17A to 17C show generated 0AM radiation pattern and wavefronts of modes +3 and -3 with phased array 1 element in layer 2, according to various example embodiments of the first aspect of the present invention;FIGs. 18A to 18D show beamforming for the generated 0AM wave with phased array 1 elements in layer 1 and sensing the 0AM in different planes, according to various example embodiments of the first aspect of the present invention;FIGs. 19A to 19C show generated 0AM radiation pattern and wavefronts of modes +1 and -1 with phased array 2 elements e34, e45, e54 and e43, according to various example embodiments of the first aspect of the present invention;FIGs. 20A to 20D show generated 0AM radiation pattern and wavefronts of modes +1 and -1 with example non-circle antenna elements selection, according to various example embodiments of the first aspect of the present invention;FIGs. 21 A to 2 IF show generated 0AM wave with one-layer elements versus with two-layer elements, according to various example embodiments of the first aspect of the present invention;FIG. 22 illustrates an example directional misalignment of 0AM Tx and Rx, according to various first example embodiments of the second aspect of the present invention, FIG. 23 shows an example frame structure of RF-OAM communication system, according to various first example embodiments of the second aspect of the present invention;FIG. 24 shows estimates of distance error Epand azimuth angle error Eφthrough the gradient descent method;FIGs. 25A and 25B show an example deep learning (DL) model A and an example DL model B for distance error spestimation and azimuth angle error Eφestimation, respectively, according to various first example embodiments of the second aspect of the present invention;FIGs. 26A and 26B show RMSE versus SNR of distance error εpand azimuth angle error estimations through the DL / AI-based method, according to various first example embodiments of the second aspect of the present invention;FIG. 27 illustrates an example directional misalignment of 0AM Tx and Rx, according to various second example embodiments of the second aspect of the present invention,FIGs. 28A to 28D show the OAM wave generation and beam steering with a UPA (ℓ-1 OAM wave), according to various second example embodiments of the second aspect of the present invention;FIG. 29 shows an example frame structure of RF-OAM communication system, according to various second example embodiments of the second aspect of the present invention;FIGs. 30A to 30D show example DNN models designed for estimating errors εp, εφ, θrand φr, according to various second example embodiments of the second aspect of the present invention;FIG. 31 depicts a flow chart of an example method of OAM Tx-Rx direction alignment, according to various example embodiments of the second aspect of the present invention, FIGs. 32A to 32D show single mode detection degradation (SMDR) versus misalignment εpand mutual mode crosstalk (MMCR) versus misalignment εp, according to various example embodiments of the second aspect of the present invention; andFIGs. 33A to 33D show DL-based estimation results of θr, φr, εpand εφ, according to various example embodiments of the second aspect of the present invention.DETAILED DESCRIPTION

[0019] Various embodiments according to a first aspect of the present invention provide a method and a controller for multi-mode OAM wave generation and beamforming. Various embodiments according to a second aspect of the present invention provide a method and a system for OAM transmitter-receiver (Tx-Rx) directional alignment.

[0020] As discussed in the background, in RF applications without waveguide, the signal of an OAM wave may significantly change at different locations, and thus, the performance of OAM wave detection at the OAM receiver is location sensitive. Therefore, it is important to be able to effectively control OAM beams to desired directions. Furthermore, it is important to be able to simultaneously generate multiple modes of a multi-mode OAM wave to enhance communication capacity and sensing resolution. In this regard, various embodiments according to a first aspect of the present invention provide a method of OAM wave generation and beamforming, as well as a controller thereof, that seeks to overcome, or at least ameliorate, one or more deficiencies in conventional methods of OAM wave generation and / or beamforming, and more particularly, that is able to effectively generate a multi-mode OAM wave and beamform multiple modes of the multi-mode OAM wave to respective desired directions.

[0021] FIG. 1 depicts a schematic diagram of a method 100 of multi-mode 0AM wave generation and beamforming using a planar phased array antenna comprising a planar array of antenna elements, according to various embodiments of the first aspect of the present invention. The method 100 comprises, for each mode of a plurality of modes of a multi-mode 0 AM wave to be generated: selecting (at 106) a subset of antenna elements of the planar array of antenna elements for generating the mode of the multi-mode 0AM wave; applying (at 108), for each antenna element of the selected subset of antenna elements, a first phase shift to the antenna element, the first phase shift determined based on an index of the antenna element and the mode of the multi-mode 0AM wave for generating the mode of the multi-mode 0AM wave; and applying (at 110), for each antenna element of the selected subset of antenna elements, a second phase shift to the antenna element, the second phase shift determined based on the index of the antenna element and a beamforming direction defined for the mode of the multi-mode 0AM wave for beamforming the mode of 0AM wave to the beamforming direction defined therefor.

[0022] It will be appreciated by a person skilled in the art that a planar phased array antenna, comprising a planar array of antenna elements, as well as its operations / functions, is known in the art, and thus, it is not necessary to describe it in detail herein for clarity and conciseness. In addition, it will be appreciated by a person skilled in the art that the present invention is not limited to any specific or type of planar phased array antenna, as well as any specific size or dimensions thereof, and any planar phased array antenna may be employed or used as desired or as appropriate and is within the scope of the present invention, as long as the planar phased array antenna may be employed or used in the method 100 of multi-mode 0AM wave generation and beamforming for generating and beamforming a multi-mode 0AM wave according to various embodiments of the first aspect of the present invention.

[0023] In various embodiments of the first aspect of the present invention, the above-mentioned selecting (at 106) the subset of antenna elements for generating the mode of the multi-mode 0AM wave comprises: selecting one or more layers of antenna elements of the planar array of antenna elements for generating the mode of 0AM wave; and selecting, for each layer of the selected one or more layers of antenna elements, a plurality of antenna elements of the layer of antenna elements for inclusion in the subset of antenna elements for generating the mode of the multi-mode 0AM wave. Accordingly, one or more layers of antenna elements of the planar array of antenna elements may be selected for generating a mode of 0AM wave. Furthermore, the above-mentioned plurality of antenna elements of the layer of antenna elements may refer to the antenna elements in the layer of antenna elements that have beenselected. In various embodiments, a layer of antenna elements of the planar array refers to a set or collection of antenna elements along a geometrical shape (e.g., a closed shape) on the planar array. For example, the shape may be predefined. In various embodiments, as will be described later below and without limitation, for example, the shape may preferably be a circle (or generally a circle). In various embodiments, the subset of antenna elements for generating the mode of the multi-mode 0AM wave may be selected based on a layer parameter and an antenna element parameter defined for generating the mode of the multi-mode 0AM wave.

[0024] In various embodiments of the first aspect of the present invention, multiple layers of antenna elements of the planar array of antenna elements are selected for generating the mode of 0AM wave.

[0025] In various first embodiments of the first aspect of the present invention, the multiple layers of antenna elements of the planar array of antenna elements correspond to multiple concentric circles of antenna elements of the planar array of antenna elements having different radii.

[0026] In various first embodiments of the first aspect of the present invention, for two or more modes of the plurality of modes of the multi-mode 0AM wave, the two or more subsets of antenna elements respectively for generating the two or more modes of the plurality of modes are selected from common one or more layers of antenna elements of the planar array of antenna elements, and the two or more subsets of antenna elements selected respectively for generating the two or more modes of the plurality of modes are different groups (non-overlapping groups) of antenna elements of the planar array of antenna elements. In other words, the two or more subsets of antenna elements are selected from the same layer(s) of antenna elements and they do not overlap with each other.

[0027] In various second embodiments of the first aspect of the present invention, for two or more modes of the plurality of modes of the multi-mode 0AM wave, the two or more subsets of antenna elements respectively for generating the two or more modes of the multi-mode 0AM wave are respectively selected from two or more layers of antenna elements of the planar array of antenna elements, and for each pair of adjacent layers of the two or more layers of antenna elements, the two subsets of antenna elements respectively selected from the pair of adjacent layers share at least one common antenna element. In other words, the two or more subsets of antenna elements are respectively selected from two or more layers of antenna elements and every two adjacent layers thereof overlap with each other (sharing at least one common antenna element).

[0028] In various second embodiments of the first aspect of the present invention, for the above-mentioned each pair of adjacent layers corresponds to two circles of antenna elements of the planar array of antenna elements that intercept at the at least one common antenna element.

[0029] In various embodiments of the first aspect of the present invention, the index of the antenna element of the selected subset of antenna elements is with respect to a total number of antenna elements in the plurality of antenna elements of the layer of antenna elements at which the antenna element belongs to. In this regard, the first phase shift applied to the antenna element of the selected subset of antenna elements is determined further based on the total number of antenna elements in the plurality of antenna elements of the layer of antenna elements at which the antenna element belongs to. As an illustrative example and without limitation, for example, if the total number of antenna elements selected in the layer of antenna elements is 10 (i.e., the plurality of antenna elements of the layer of antenna elements has 10 antenna elements), each antenna element may be indexed from 1 to 10. Accordingly, in various embodiments, the index of the antenna element may also correspond to a count of the antenna element with respect to the total number of antenna elements in the plurality of antenna elements.

[0030] In various embodiments of the first aspect of the present invention, the beamforming direction defined for the mode of the multi-mode 0AM wave for beamforming the mode of OAM wave comprises an azimuth angle and an elevation angle. In this regard, the second phase shift applied to the antenna element of the selected subset of antenna elements is determined based on the azimuth angle and the elevation angle of the beamforming direction defined and further based on the total number of antenna elements in the plurality of antenna elements of the layer of antenna elements at which the antenna element belongs to.

[0031] FIG. 2 depicts a schematic block diagram of a controller 200 for controlling a planar phased array antenna comprising a planar array of antenna elements for multi-mode OAM wave generation and beamforming, according to various embodiments of the first aspect of the present invention, corresponding to the method 100 of multi-mode OAM wave generation and beamforming as described herein according to various embodiments of the first aspect of the present invention. The controller 200 comprises: at least one memory 202; and at least one processor 204 communicatively coupled to the at least one memory 202 and configured to, for each mode of a plurality of modes of a multi-mode OAM wave to be generated: select a subset of antenna elements of the planar array of antenna elements for generating the mode of the multi-mode OAM wave; apply, for each antenna element of the selected subset of antennaelements, a first phase shift to the antenna element, the first phase shift determined based on an index of the antenna element and the mode of the multi-mode 0AM wave for generating the mode of the multi-mode 0AM wave; and apply, for each antenna element of the selected subset of antenna elements, a second phase shift to the antenna element, the second phase shift determined based on the index of the antenna element and a beamforming direction defined for the mode of the multi-mode 0AM wave for beamforming the mode of 0AM wave to the beamforming direction defined therefor.

[0032] It will be appreciated by a person skilled in the art that the at least one processor 204 may be configured to perform various functions or operations through set(s) of instructions (e g., software modules) executable by the at least one processor 204 to perform various functions or operations. Accordingly, as shown in FIG. 2, the controller 200 may comprise: an antenna element selecting module (or an antenna element selecting circuit) 206 configured to, for each mode of a plurality of modes of a multi-mode 0AM wave to be generated, select a subset of antenna elements of the planar array of antenna elements for generating the mode of the multi-mode 0AM wave; a first phase shift applying module (or a first phase shift applying circuit) 208 configured to, for each mode of the plurality of modes of the multi-mode 0AM wave to be generated, apply, for each antenna element of the selected subset of antenna elements, a first phase shift to the antenna element, the first phase shift determined based on an index of the antenna element and the mode of the multi-mode 0AM wave for generating the mode of the multi-mode 0AM wave; and a second phase shift applying module (or a second phase shift applying circuit) 210 configured to, for each mode of the plurality of modes of the multi-mode 0AM wave to be generated, apply, for each antenna element of the selected subset of antenna elements, a second phase shift to the antenna element, the second phase shift determined based on the index of the antenna element and a beamforming direction defined for the mode of the multi-mode 0AM wave for beamforming the mode of 0AM wave to the beamforming direction defined therefor.

[0033] It will be appreciated by a person skilled in the art that the above-mentioned modules are not necessarily separate modules, and two or more modules may be realized by or implemented as one functional module (e g., a circuit or a software program) as desired or as appropriate without deviating from the scope of the present invention. For example, two or more of the antenna element selecting module 206, the first phase shift applying module 208 and the second phase shift applying module 210 may be realized (e.g., compiled together) as one executable software program (e g., software application or simply referred to as an “app”),which for example may be stored in the at least one memory 202 and executable by the at least one processor 204 to perform the corresponding functions or operations as described herein according to various embodiments of the present invention.

[0034] In various embodiments of the first aspect of the present invention, the controller 200 for controlling a planar phased array antenna for multi-mode 0AM wave generation and beamforming corresponds to the method 100 of multi-mode 0AM wave generation and beamforming using a planar phased array antenna as described hereinbefore with reference to FIG. 1, therefore, various operations, functions or steps configured to be performed by the least one processor 204 may correspond to various operations, functions or steps of the method 100 described hereinbefore according to various embodiments of the first aspect of the present invention, and thus need not be repeated with respect to the controller 200 for clarity and conciseness. In other words, various embodiments described herein in context of methods (e.g., the method 100 of multi-mode 0 AM wave generation and beamforming) are analogously valid for the corresponding systems or devices (e.g., the controller 200), and vice versa. For example, in various embodiments of the first aspect of the present invention, the at least one memory 202 may have stored therein the antenna element selecting module 206, the first phase shift applying module 208 and / or the second phase shift applying module 210, which respectively correspond to various operations, functions or steps of the method 100 of multi-mode 0AM wave generation and beamforming as described hereinbefore according to various embodiments of the first aspect of the present invention, which are executable by the at least one processor 204 to perform the corresponding operations, functions or steps as described herein.

[0035] As discussed in the background, although 0AM waves offer a promising path to increased spectrum efficiency by enabling multiplexing beyond traditional time, frequency and space division methods, effective 0AM multiplexing hinges on good alignment between transmitter (Tx) and receiver (Rx), which is challenging in radio frequency (RF). In particular, Tx-Rx directional misalignment will significantly affect RF-OAM performance. In this regard, various embodiments according to a second aspect of the present invention provide a method of 0AM Tx-Rx directional alignment, as well as a system thereof, that seeks to overcome, or at least ameliorate, one or more deficiencies in conventional methods of OAM-based wireless communications, and more particularly, for correcting or improving 0AM Tx-Rx directional alignment.

[0036] FIG. 3 depicts a schematic diagram of a method 300 of 0AM Tx-Rx directional alignment between an 0AM transmitter and an 0AM receiver, according to variousembodiments of the second aspect of the present invention. The 0AM receiver comprises a planar phased array antenna comprising a planar array of antenna elements. The method 300 comprises obtaining (at 306), from each antenna element of a plurality of antenna elements of a layer of antenna elements of the planar array of antenna elements of the 0AM receiver, a first phase value of a received signal of a first OAM wave of a first 0AM mode incident at the antenna element to obtain a set of first phase values of the received signals of the first OAM wave incident at the plurality of antenna elements of the layer of antenna elements, wherein the first OAM wave is transmitted from the OAM transmitter. That is, the OAM transmitter transmits the first OAM wave to the OAM receiver, and from each antenna element of the plurality of antenna elements of the layer of antenna elements, a first phase value of the received signal of the first OAM wave of the first OAM mode incident at the antenna element is obtained, thereby obtaining a set of first phase values of the received signals of the first OAM wave incident at the plurality of antenna elements of the layer of antenna elements. The method 300 further comprises predicting (at 308) a distance error between an intersection point of a transmitter beam axis (which may also be referred to as a transmitter emission axis) of the OAM transmitter at the planar array of antenna elements of the OAM receiver and a center of the planar array of antenna elements of the OAM receiver based on the set of first phase values of the received signals of the first OAM wave using a distance error machine learning model. In this regard, the distance error machine learning model is trained to predict the distance error based on the set of first phase values of the received signals of the first OAM wave. The method 300 further comprises predicting (at 310) an azimuth angle error associated with the distance error based on the set of first phase values of the received signals of the first OAM wave using an azimuth angle error machine learning model. In this regard, the azimuth angle error machine learning model is trained to predict the azimuth angle error based on the set of first phase values of the received signals of the first OAM wave. The method further comprises sending (at 312) transmitter beam axis error information based on the predicted distance error and the predicted azimuth angle error to the OAM transmitter for adjusting a transmitter beam axis (which may also be referred to as a transmitter emission axis) of the OAM transmitter for OAM transmitterreceiver directional alignment. For example, the transmitter beam axis error information may comprise the predicted distance error and the predicted azimuth angle error or may comprise information derived from the predicted distance error and the predicted azimuth angle error for adjusting the transmitter beam axis of the OAM transmitter for OAM transmitter-receiver directional alignment. For example, the transmitter beam axis error information may be sentfrom the 0AM receiver to the 0AM transmitter via any conventional wireless data communications known in the art as desired or as appropriate. After the 0AM transmitter receives the transmitter beam axis error information, the 0AM transmitter, or more particularly a controller thereof, may then adjust the transmitter beam axis based on the transmitter beam axis error information (e g, the predicted distance error and the predicted azimuth angle error).

[0037] As described hereinbefore in the first aspect of the present invention, in various embodiments, a layer of antenna elements of the planar array refers to a set or collection of antenna elements along a geometrical shape (e.g., a closed shape) on the planar array. For example, the shape may be predefined. In various embodiments, as will be described later below and without limitation, for example, the shape may preferably be a circle (or generally a circle).

[0038] In various embodiments of the second aspect of the present invention, the 0AM transmitter comprises a planar phased array antenna comprising a planar array of antenna elements. Furthermore, the above-mentioned adjusting the transmitter beam axis of the 0AM transmitter comprises adjusting a beamforming elevation angle parameter value and a beamforming azimuth angle parameter value associated with 0AM transmitter based on the transmitter beam axis error information (e g., based on the predicted distance error and the predicted azimuth angle error) for 0AM transmitter-receiver directional alignment.

[0039] In various embodiments of the second aspect of the present invention, the first 0 AM mode is 0AM mode 1 (+1 or -1).

[0040] In various embodiments of the second aspect of the present invention, the first 0AM wave of the first 0AM mode is transmitted from the 0AM transmitter without data payload.

[0041] In various embodiments of the second aspect of the present invention, the method 300 further comprises obtaining, from each antenna element of the plurality of antenna elements of the layer of antenna elements of the planar array of antenna elements of the 0AM receiver, a second phase value of a received signal of a second 0AM wave of a second 0AM mode incident at the antenna element to obtain a set of second phase values of the received signals of the second 0AM wave incident at the plurality of antenna elements of the layer of antenna elements, wherein the second 0AM wave is transmitted from the 0AM transmitter. The second 0AM mode and the first 0AM mode are different 0AM modes. That is, the 0AM transmitter transmits the second 0AM wave to the 0AM receiver, and from each antenna element of the plurality of antenna elements of the layer of antenna elements, a second phase value of the received signal of the second 0AM wave of the second 0AM mode incident at the antenna element is obtained, thereby obtaining a set of second phase values of the received signals ofthe second 0AM wave incident at the plurality of antenna elements of the layer of antenna elements. The method 300 further comprises predicting a beamforming elevation angle error of the 0 AM receiver based on the set of second phase values of the received signals of the second 0AM wave using a beamforming elevation angle error machine learning model. In this regard, the beamforming elevation angle error machine learning model is trained to predict the elevation angle error based on the set of second phase values of the received signals of the second 0AM wave. The method 300 further comprises predicting a beamforming azimuth angle error of the 0 AM receiver based on the set of second phase values of the received signals of the second 0AM wave using a beamforming azimuth angle error machine learning model. In this regard, the beamforming azimuth angle error machine learning model is trained to predict the beamforming azimuth angle error based on the set of second phase values of the received signals of the second 0AM wave. The method 300 further comprises adjusting a receiver beam axis (receiver beam facing the 0AM transmitter) of the 0AM receiver based on the predicted beamforming elevation angle error and the predicted beamforming azimuth angle error of the 0AM receiver for 0AM transmitter-receiver directional alignment.

[0042] In various embodiments of the second aspect of the present invention, the above-mentioned adjusting the receiver beam axis of the 0AM receiver comprises adjusting a beamforming elevation angle parameter value and a beamforming azimuth angle parameter value associated with 0AM receiver based on the predicted beamforming elevation angle error of the 0AM receiver and the predicted beamforming azimuth angle error for 0AM transmitterreceiver directional alignment.

[0043] It will be appreciated by a person skilled in the art that the “first” and “second” in the first 0AM wave and the second 0AM wave are used as a convenient way of distinguishing between the two 0AM waves and does not limit the order of transmission (or reception) of the two 0AM waves. That is, it is not necessary that the second 0AM wave is transmitted (and the related steps performed) after the first 0AM wave (and the related steps). For example, in various embodiments of the second aspect of the present invention, the second 0AM wave of the second OAM mode may be transmitted to the 0AM receiver (and the related steps performed) prior to the first OAM wave of the first OAM mode (and the related steps).

[0044] In various embodiments of the second aspect of the present invention, the second OAM mode is OAM mode 0.

[0045] In various embodiments of the second aspect of the present invention, the second 0AM wave of the second 0AM mode is transmitted from the 0AM transmitter without data payload.

[0046] In various embodiments of the second aspect of the present invention, the layer of antenna elements corresponds to a circle of antenna elements of the planar array of antenna elements of the 0AM receiver.

[0047] In various embodiments of the second aspect of the present invention, the method 300 further comprises: adjusting the transmitter beam axis of the 0AM transmitter based on the transmitter beam axis error information (e.g., the predicted distance error and the predicted azimuth angle error) for 0AM transmitter-receiver directional alignment; and controlling the 0AM transmitter to generate and beamform a multi-mode 0AM wave based on the adjusted transmitter beam axis of the 0AM transmitter. In various embodiments, the transmitter emission axis of the 0AM transmitter may be adjusted by adjusting a beamforming elevation angle parameter value and a beamforming azimuth angle parameter value associated with the 0AM transmitter based on the transmitter beam axis error information (e.g., the predicted distance error and the predicted azimuth angle error for 0AM transmitter-receiver directional alignment) for 0AM transmitter-receiver directional alignment.

[0048] In various embodiments of the second aspect of the present invention, the multimode 0AM wave is generated and beamformed according to the method 100 of multi-mode 0AM wave generation and beamforming as described hereinbefore according to various embodiments of the first aspect of the present invention. In this regard, as described in various embodiments of the first aspect of the present invention, to generate and beamform a multimode 0AM wave using a planar phased array antenna, for each mode of a plurality of modes of a multi-mode 0AM wave to be generated and for each antenna element of the selected subset of antenna elements, the first phase shift may be applied to the antenna element for generating the mode of the multi-mode 0AM wave and the second phase shift may be applied to the antenna element for beamforming the mode of 0AM wave to the beamforming direction defined therefor. In this regard, in various embodiments of the second aspect of the present invention, the first and second phase shift may be applied to the antenna element in addition to a phase shift applied to the antenna for adjusting the transmitter beam axis of the 0AM transmitter for 0AM transmitter-receiver directional alignment. In other words, the transmission beam steering phase shift for 0AM transmitter-receiver directional alignment and the multi-mode 0AM wave generation and beamforming phase shifts may be added together.

[0049] FIG. 4 depicts a schematic block diagram of a system 400 for 0AM transmitterreceiver directional alignment, according to various embodiments of the second aspect of the present invention, corresponding to the method 300 of 0AM transmitter-receiver directional alignment as described hereinbefore according to various embodiments of the second aspect of the present invention. The 0AM receiver comprises a planar phased array antenna comprising a planar array of antenna elements. The system comprises: at least one memory 402; and at least one processor 404 communicatively coupled to the at least one memory 402 and configured to: obtain, from each antenna element of a plurality of antenna elements of a layer of antenna elements of the planar array of antenna elements of the 0AM receiver, a first phase value of a received signal of a first 0AM wave of a first 0AM mode incident at the antenna element to obtain a set of first phase values of the received signals of the first 0AM wave incident the plurality of antenna elements of at the layer of antenna elements, wherein the first OAM wave is transmitted from the OAM transmitter; predict a distance error between an intersection point of a transmitter beam axis of the OAM transmitter at the planar array of antenna elements of the OAM receiver and a center of the planar array of antenna elements of the OAM receiver based on the set of first phase values of the received signals of the first OAM wave using a distance error machine learning model, the distance error machine learning model trained to predict the distance error based on the set of first phase values of the received signals of the first OAM wave; predict an azimuth angle error associated with the distance error based on the set of first phase values of the received signals of the first OAM wave using an azimuth angle error machine learning model, the azimuth angle error machine learning model trained to predict the azimuth angle error based on the set of first phase values of the received signals of the first OAM wave; and send transmitter beam axis error information based on the predicted distance error and the predicted azimuth angle error to the OAM transmitter for adjusting the transmitter beam axis of the OAM transmitter for OAM transmitter-receiver directional alignment.

[0050] It will be appreciated by a person skilled in the art that the at least one processor 404 may be configured to perform various functions or operations through set(s) of instructions (e g., software modules) executable by the at least one processor 404 to perform various functions or operations. Accordingly, as shown in FIG. 4, the system 400 may comprise: a first phase value obtaining module (or a first phase value obtaining circuit) 406 configured to obtain, from each antenna element of a plurality of antenna elements of a layer of antenna elements of the planar array of antenna elements of the OAM receiver, a first phase value of a receivedsignal of a first 0AM wave of a first 0AM mode incident at the antenna element to obtain a set of first phase values of the received signals of the first 0AM wave incident at the plurality of antenna elements of the layer of antenna elements, wherein the first 0AM wave is transmitted from the 0AM transmitter; a distance error prediction module (or a distance error prediction circuit) 408 configured to predict a distance error between an intersection point of a transmitter beam axis of the 0AM transmitter at the planar array of antenna elements of the 0AM receiver and a center of the planar array of antenna elements of the 0AM receiver based on the set of first phase values of the received signals of the first 0AM wave using a distance error machine learning model, the distance error machine learning model trained to predict the distance error based on the set of first phase values of the received signals of the first 0AM wave; an azimuth angle error prediction module (or an azimuth angle error prediction circuit) 410 configured to predict an azimuth angle error associated with the distance error based on the set of first phase values of the received signals of the first 0AM wave using an azimuth angle error machine learning model, the azimuth angle error machine learning model trained to predict the azimuth angle error based on the set of first phase values of the received signals of the first 0AM wave; and a transmitter beam axis error information module (or a transmitter beam axis error information circuit) 412 configured to send transmitter beam axis error information based on the predicted distance error and the predicted azimuth angle error to the 0AM transmitter for adjusting the transmitter beam axis of the 0AM transmitter for 0AM transmitter-receiver directional alignment.

[0051] It will be appreciated by a person skilled in the art that the above-mentioned modules are not necessarily separate modules, and two or more modules may be realized by or implemented as one functional module (e.g., a circuit or a software program) as desired or as appropriate without deviating from the scope of the present invention. For example, two or more of the first phase value obtaining module 406, the distance error prediction module 408; the azimuth angle error prediction module 410; and the transmitter beam axis error information module 412 may be realized (e.g., compiled together) as one executable software program (e.g., software application or simply referred to as an “app”), which for example may be stored in the at least one memory 402 and executable by the at least one processor 404 to perform the corresponding functions or operations as described herein according to various embodiments of the present invention.

[0052] In various embodiments of the second aspect of the present invention, the system 400 for OAM transmitter-receiver directional alignment corresponds to the method 300 ofOAM transmitter-receiver directional alignment as described hereinbefore with reference to FIG. 3, therefore, according to various embodiments of the second aspect of the present invention, various operations, functions or steps configured to be performed by the least one processor 404 may correspond to various operations, functions or steps of the method 300 described hereinbefore according to various embodiments of the second aspect of the present invention, and thus need not be repeated with respect to the system 400 for clarity and conciseness. In other words, various embodiments described herein in context of methods (e.g., the method 300 of OAM transmitter-receiver directional alignment) are analogously valid for the corresponding systems or devices (e.g., the system 400), and vice versa. For example, in various embodiments of the second aspect of the present invention, the at least one memory 402 may have stored therein the first phase value obtaining module 406, the distance error prediction module 408; the azimuth angle error prediction module 410 and / or the transmitter beam axis error information module 412, which respectively correspond to various operations, functions or steps of the method 300 of OAM transmitter-receiver directional alignment as described hereinbefore according to various embodiments of the second aspect of the present invention, which are executable by the at least one processor 404 to perform the corresponding operations, functions or steps as described herein.

[0053] In various embodiments of the second aspect of the present invention, the system 400 further comprises: at least one second memory; and the at least one second processor communicatively coupled to the at least one second memory and configured to: adjust the transmitter beam axis of the OAM transmitter based on the transmitter beam axis error information for OAM transmitter-receiver directional alignment; and control the OAM transmitter to generate and beamform a multi-mode OAM wave based on the adjusted transmitter beam axis of the OAM transmitter.

[0054] A computing system, a controller, a microcontroller or any other system providing a processing capability may be provided according to various embodiments in the present invention. Such a system may be taken to include one or more processors and one or more computer-readable storage mediums. For example, the controller 200 and the system 400 described hereinbefore may each include at least one processor and at least one computer-readable storage medium (or memory) which are for example used in various processing carried out therein as described herein. A memory or computer-readable storage medium used in various embodiments may be a volatile memory, for example a DRAM (Dynamic Random Access Memory) or a non-volatile memory, for example a PROM (Programmable Read OnlyMemory), an EPROM (Erasable PROM), EEPROM (Electrically Erasable PROM), or a flash memory, e.g., a floating gate memory, a charge trapping memory, an MRAM (Magnetoresistive Random Access Memory) or a PCRAM (Phase Change Random Access Memory).

[0055] In various embodiments, a “circuit” may be understood as any kind of a logic implementing entity, which may be special purpose circuitry or a processor executing software stored in a memory, firmware, or any combination thereof. Thus, in an embodiment, a “circuit” may be a hard-wired logic circuit or a programmable logic circuit such as a programmable processor, e.g., a microprocessor (e.g., a Complex Instruction Set Computer (CISC) processor or a Reduced Instruction Set Computer (RISC) processor). A “circuit” may also be a processor executing software, e.g., any kind of computer program, e.g., a computer program using a virtual machine code, e.g., lava. Any other kind of implementation of various functions or operations may also be understood as a “circuit” in accordance with various other embodiments. Similarly, a “module” may be a portion of a system according to various embodiments in the present invention and may encompass a “circuit” as above, or may be understood to be any kind of a logic-implementing entity therefrom.

[0056] Some portions of the present disclosure may be explicitly or implicitly presented in tenns of algorithms and functional or symbolic representations of operations on data within a computer memory. These algorithmic descriptions and functional or symbolic representations are the means used by those skilled in the data processing arts to convey most effectively the substance of their work to others skilled in the art. An algorithm may be, and generally, conceived to be a self-consi stent sequence of steps leading to a desired result.

[0057] The present specification also discloses a system (e.g., which may also be embodied as one or more devices or apparatuses), such as the controller 200 (or a controlling system) or the system 400, for performing various operations, functions or steps of various methods described herein. Such a system may be specially constructed for the required purposes or may comprise a general purpose computer system selectively activated or reconfigured by a computer program stored in the computer system. In general, various algorithms that may be presented herein are not limited to being implemented or executed by any particular computer system. Alternatively, the construction of more specialized computer system to perform various operations, functions or steps of various methods described herein may be provided as desired or as appropriate without going beyond the scope of the present invention.

[0058] In addition, the present specification also at least implicitly discloses computer program(s) or software / functional module(s), in that it would be apparent to a person skilled inthe art that various operations, functions or steps of various methods described herein may be put into effect by computer code. The computer program(s) is not intended to be limited to any particular programming language and implementation thereof, and it will be appreciated by a person skilled in the art that a variety of programming languages and coding thereof may be used to implement the computer program(s). Moreover, the computer program(s) is not intended to be limited to any particular control flow as there are a variety of programming languages which can use different control flows. It will be appreciated by a person skilled in the art that a computer program may be stored on any computer-readable storage medium (non-transitory computer-readable storage medium), such as but not limited to, a magnetic disk, an optical disk or a memory chip. For example, a computer program stored on a computer-readable storage medium may be loaded and executed on a computer system to implement various operations, functions or steps of various methods described herein according to various embodiments of the present invention.

[0059] Accordingly, in various embodiments according to the first aspect of the present invention, there is provided a computer program product, embodied in one or more computer-readable storage mediums (non-transitory computer-readable storage medium), comprising instructions (e.g., the antenna element selecting module 206, the first phase shift applying module 208 and / or the second phase shift applying module 210) executable by one or more computer processors to perform the method 100 of multi-mode 0AM wave generation and beamforming as described hereinbefore with reference to FIG. 1 according to various embodiments of the first aspect of the present invention. Accordingly, various computer programs or software modules described herein may be stored in a computer program product receivable by a system therein, such as the controller 200 as shown in FIG. 2, for execution by at least one processor 204 of the controller 200 to perform various operations, functions or steps of various methods described herein according to various embodiments of the present invention.

[0060] Accordingly, in various embodiments according to the second aspect of the present invention, there is provided a computer program product, embodied in one or more computer-readable storage mediums (non-transitory computer-readable storage medium), comprising instructions (e g., the first phase value obtaining module 406, the distance error prediction module 408; the azimuth angle error prediction module 410 and / or the transmitter beam axis error information module 412) executable by one or more computer processors to perform the method 300 of 0AM transmitter-receiver directional alignment as described hereinbefore with reference to FIG. 3 according to various embodiments of the present invention of the secondaspect of the present invention. Accordingly, various computer programs or software modules described herein may be stored in a computer program product receivable by a system therein, such as the system 400 as shown in FIG. 2, for execution by at least one processor 404 of the system 400 to perform various operations, functions or steps of various methods described herein according to various embodiments of the present invention.

[0061] It will be appreciated by a person skilled in the art that various modules described herein (e.g., the antenna element selecting module 206, the first phase shift applying module 208 and / or the second phase shift applying module 210 for the controller 200 and the first phase value obtaining module 406, the distance error prediction module 408; the azimuth angle error prediction module 410 and / or the transmitter beam axis error information module 412 for the system 400) may be software module(s) realized by computer program(s) or set(s) of instructions executable by a computer processor to perform various functions or operations. Various modules described herein (e.g., the antenna element selecting module 206, the first phase shift applying module 208 and / or the second phase shift applying module 210 for the controller 200 and the first phase value obtaining module 406, the distance error prediction module 408; the azimuth angle error prediction module 410 and / or the transmitter beam axis error information module 412 for the system 400) may also be implemented as hardware module(s) being functional hardware unit(s) designed to perform various functions or operations. More particularly, in the hardware sense, a module is a functional hardware unit designed for use with other components or modules. For example, a module may be implemented using discrete electronic components, or it can form a portion of an entire electronic circuit such as an Application Specific Integrated Circuit (ASIC) or a Field Programmable Gate Array (FPGA). For example, in the case of the controller 200 being implemented as a FPGA, the memory 202 (e g., a non-volatile memory such as a flash memory) may store a configuration file for programming or configuring the FPGA (e.g., corresponding to the processor 204) to perform the method 100 of multi-mode 0AM wave generation and beamforming as described herein according to various embodiments of the first aspect of the present invention. Accordingly, the programmed or configured FPGA comprises the antenna element selecting module (as a circuit) 206, the first phase shift applying module (as a circuit) 208 and the second phase shift applying module 210 (as a circuit) configured to perform the method 100 of multi-mode 0AM wave generation and beamforming as described herein according to various embodiments of the first aspect of the present invention. Numerous other possibilities exist. It will also be appreciated by a person skilled in the art that a combination ofhardware and software modules may be implemented. Furthermore, various operations, functions or steps of various methods described herein may be performed in parallel rather than sequentially as desired or as appropriate (e g., as long as it does not render the method(s) inoperable or unsatisfactory for its intended purpose).

[0062] FIG. 5 depicts a schematic drawing of an 0AM transmitter 500 for multi-mode 0AM wave generation and beamforming, according to various embodiments of the first aspect of the present invention. The 0AM transmitter 500 comprises: a planar phased array antenna 510 comprising a planar array of antenna elements 514; and a controller 200 as described hereinbefore according to various embodiments of the first aspect of the present invention communicatively coupled to the planar phased array antenna 510 for controlling the planar phased array antenna 510 for multi-mode 0AM wave generation and beamforming.

[0063] FIG. 6 depicts a schematic drawing of an OAM-based wireless communication system 600, according to various embodiments of the second aspect of the present invention. The OAM-based wireless communication system 600 comprises: an 0AM transmitter 602 configured to generate and beamform multi-mode 0AM waves, the 0AM transmitter 602 comprising a planar phased array antenna 610 comprising a planar array of antenna elements 614; and an 0AM receiver 622 configured to receive and process the multi-mode 0AM waves from the 0AM transmitter 602, the 0AM receiver 622 comprising a planar phased array antenna 630 comprising a planar array of antenna elements 634. The 0AM receiver 622 comprises the at least one memory 402 and the at least one processor 404 of the system 400 as described hereinbefore according to various embodiments of the second aspect of the present invention communicatively coupled to the planar phased array antenna 630 and configured to perform 0AM transmitter-receiver directional alignment as described hereinbefore according to various embodiments of the second aspect of the present invention. In various embodiments, the 0AM transmitter 602 comprises the at least one second memory 642 and the at least one second processor 644 of the system 400 as described hereinbefore according to various embodiments of the second aspect of the present invention communicatively coupled to the planar phased array antenna 610 and configured to perform 0AM transmitter-receiver directional alignment as described hereinbefore according to various embodiments of the second aspect of the present invention. Accordingly, in various embodiments, a part of the system 400 for 0AM transmitter-receiver directional alignment may be implemented in the 0AM receiver 622 for generating and sending the transmitter beam axis error information (e.g., including the predicted distance error and the predicted azimuth angle error) and adjusting thereceiver beam axis of the 0AM receiver 622 based on the predicted beamforming elevation angle error and the predicted beamforming azimuth angle error of the 0AM receiver, and another part of the system 400 may be implemented in the 0AM transmitter 602 for adjusting the transmitter beam axis of the 0AM transmitter 602 based on the transmitter beam axis error information for 0AM transmitter-receiver directional alignment.

[0064] It will be appreciated by a person skilled in the art that the terminology used herein is for the purpose of describing various embodiments only and is not intended to be limiting of the present invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and / or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0065] Any reference to an element or a feature herein using a designation such as “first”, “second” and so forth does not limit the quantity or order of such elements or features, unless stated or the context requires otherwise. For example, such designations may be used herein as a convenient way of distinguishing between two or more elements or instances of an element. Thus, a reference to first and second elements does not necessarily mean that only two elements can be employed, or that the first element must precede the second element, unless stated or the context requires otherwise. In addition, a phrase referring to “at least one of’ a list of items refers to any single item therein or any combination of two or more items therein.

[0066] In order that the present invention may be readily understood and put into practical effect, various example embodiments according to the first aspect and the second aspect of the present invention will be described hereinafter by way of examples only and not limitations. It will be appreciated by a person skilled in the art that the present invention may, however, be embodied in various different forms or configurations and should not be construed as limited to the example embodiments set forth hereinafter. Rather, these example embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the present invention to those skilled in the art.

[0067] A method of multi-mode 0AM (i.e., RF 0AM) wave generation and beamforming will now be described according to various example embodiments of the first aspect of the present invention.

[0068] OAM wave is a promising electromagnetic (EM) wave for multiplexing wireless communication signals as well as enhancing radar sensing resolution. OAM, which was first discovered and applied in optical fiber communication, is location sensitive. In RF applications having no waveguiding such as optical fiber, it is important to form the desired OAM beam to the desired direction. Moreover, effectively generating multiple modes of a multi-mode OAM wave is challenging. In this regard, various example embodiments of the first aspect of the present invention seek to address these two technical problems. In particular, various example embodiments of the first aspect of the present invention seek to simultaneously generate multiple modes of a multi-mode OAM wave with a planar phased array antenna and beamforming the multiple modes of the multi-mode OAM wave to respective desired directions Various design examples will be discussed later below to validate the method of multi-mode OAM wave generation and beamforming using a planar phased array antenna according to various example embodiments of the first aspect of the present invention.

[0069] An example method 700 of multi-mode OAM wave generation and beamforming using a planar phased array antenna will now be described with reference to FIG. 7 according to various example embodiments of the first aspect of the present invention. In particular, FIG.7 depicts a flow chart of the example method 700 of multi-mode OAM wave generation and beamforming.

[0070] At step 702, for each mode x of a plurality of modes of a multi-mode OAM wave to be generated, a subset of antenna elements of the planar array of antenna elements is selected for generating the mode x of the multi-mode OAM wave. In this regard, one or more layers of antenna elements of the planar array of antenna elements may be selected for generating the mode x of the multi-mode OAM wave; and for each layer of the selected one or more layers of antenna elements, a plurality of antenna elements Kn>. of the layer of antenna elements may be selected for inclusion in the subset of antenna elements for generating the mode x of the multimode OAM wave.

[0071] In various example embodiments of the first aspect of the present invention, each layer of the antenna element may correspond to a circle (or generally a circle) of antenna elements of the planar array of antenna elements. For example, to generate mode x OAM wave, where x E {0, ±1, ±2, }, select identical RF radiation elements forming Nxconcentric circles on the planar phased array, where NxE {1,2,3, ••• } and circle nxcomprises Knxselected antenna elements. For example, mode x OAM wave may be OAM mode +1 or mode -1. As an example illustration, FIG. 8 depicts a schematic drawing of a planar array of antennaelements with example selected antenna elements shown shaded for generating and beamforming a mode x 0AM wave. It will be appreciated by a person skilled in the art that the present invention is not limited to any particular or specific manner of selecting a subset of antenna elements of the planar array of antenna elements (including selecting one or more layers of antenna elements and for each layer, selecting a plurality of antenna elements of the layer of antenna elements) for generating a mode x of the multi-mode 0AM wave, which may be selected as desired or as appropriate without going beyond the scope of the present invention. For example, any available layer(s) may be selected for any mode. For example, for better resolution, outer layer(s) may be selected for higher mode 0AM wave generation, and inner layer(s) may be selected for lower mode 0AM wave generation.

[0072] At step 704, for each antenna element of the selected subset of antenna elements, a first phase shift is applied to the antenna element, which is determined based on an index k of the antenna element and the mode x of the multi-mode 0AM wave for generating the mode x of the multi-mode 0AM wave.

[0073] For example, for Knxselected antenna elements in selected circle nx, apply a first phase shifting to each antenna element k,k = 1 to Knx. For example, the first phase shifting applied to the fcthantenna element may be defined or determined as follows:Onxk= k2nx / Knx(Equation 1) For example, by applying the first phase shift to each k&selected antenna element on circle nxaccording to Equation (1), a mode x 0AM wave is generated by the selected antenna elements on circle nx. Accordingly, the index k of the antenna element of the selected subset of antenna elements is with respect to a total number Knxof antenna elements in the plurality of antenna elements of the layer of antenna elements at which the antenna element belongs to (e.g., k — 1 to Kn). As can be seen from Equation (1 ), the first phase shift applied to the antenna element of the selected subset of antenna elements is determined further based on the total number Knxof antenna elements in the plurality of antenna elements of the layer of antenna elements at which the antenna element belongs to. For example, in the case of mode 0, the first phase shift applied to all selected elements may be the same.

[0074] At step 706, for each antenna element of the selected subset of antenna elements, a second phase shift is applied to the antenna element, which is determined based on the index k of the antenna element and a beamforming direction defined for the mode x of the multi-mode OAM wave for beamforming the mode x of OAM wave to the beamforming direction defined therefor.

[0075] In various example embodiments of the first aspect of the present invention, the beamforming direction defined for the mode of the multi-mode 0AM wave for beamforming the mode of 0AM wave comprises an azimuth angle <pxand an elevation angle 6Xas illustrated in FIG 8. For example, to conduct beamforming for a mode x RF 0AM wave to a desired direction 3X, px(the elevation and azimuth angles, respectively), apply additional phase shifting (corresponding to the above-mentioned second phase shift) to the selected antenna elements in the selected circle nxfor mode x. For example, the additional (or second) phase shift for a selected antenna element k in a selected circle nxmay be defined or determined as follows:-j2n / Aansindxcos (<px--^-).bnxk= Ze 'Kn* (Equation 2) where arixis the radius of the circle nx, A is the wavelength of the RF signal. Accordingly, as can be seen from Equation (2), the second phase shift applied to the antenna element of the selected subset of antenna elements is determined based on the azimuth angle (pxand the elevation angle 9Xof the beamforming direction defined and further based on the total number Knxof antenna elements in the plurality of antenna elements of the layer of antenna elements at which the antenna element belongs to.

[0076] At step 708, it is determined whether all modes (or all desired modes) of the multimode OAM wave have been generated. If there is one or more remaining modes of the multimode 0AM wave to be generated and beamformed, the method 700 proceeds the next mode x by updating the mode parameter x to the next mode value and performs steps 702, 704, 706 and 708 based on the updated mode parameter value x. Furthermore, for the desired beamforming direction for the next mode x OAM wave, the beamforming direction parameters, e.g., elevation angle parameter 9Xand azimuth angle parameter <pxmay also be updated to the new elevation angle value and the new azimuth angle value. Therefore, for each mode x OAM wave to be generated and beamformed, the OAM mode x and the corresponding desired beamforming direction 0X, pxmay be updated to the respective new values and steps 702, 704, 706 and 708 are repeated until all desired OAM modes of the multi-mode OAM wave have been generated and the respective beamforming conducted for simultaneously generating multiple modes of the multi-mode OAM wave and beamforming the multiple modes of the multi-mode OAM wave to respective desired directions.

[0077] In various example embodiments of the first aspect of the present invention, the example method 700 of multi-mode OAM wave generation and beamforming using a planar phased array antenna has one or more of the following properties:• One 0AM mode can be generated with antenna elements in one circle or multiple concentric circles having different radii. The greater number of concentric circles used, the higher the antenna gain is (e.g., see FIG. 8). Accordingly, multiple layers of antenna elements of the planar array of antenna elements may be selected for generating the mode of 0AM wave.• The antenna elements selected as the sub-array generating a particular 0AM mode are also used to conduct beamforming of the generated 0AM mode wave to a desired direction (e g., see FIG 9) In particular, FIG 9 depicts a schematic drawing of a planer array of antenna elements with example selected antenna elements shown shaded for illustrating simultaneous 0AM wave generation and beamforming.• Different OAM modes generated can face the same or different directions through the beamforming step (e g., see FIG. 10). In particular, FIG. 10 depicts a schematic drawing of a planar array of antenna elements with example selected antenna elements shown shaded for illustrating beamforming different OAM mode waves to different directions.• One or more antenna elements can be reused for different OAM mode generations (partially overlapped) (e.g., see FIG. 11). In particular, for an antenna element having a total phase shift (i.e., sum of the first and second phase shifts determined according to the above Equation (1) and Equation (2)) determined that is the same for generating and beamforming different OAM mode waves, such an antenna element may be reused or shared in different layers (e.g., two different circles shown in FIG. 11) for generating and beamforming different OAM mode waves, respectively, and thus, such an antenna element may be selected or configured as an intersection point of the different layers. For example, two or more such antenna elements may thus be selected or configured as two or more intersection points of the different layers For example, FIG. 11 depicts a schematic drawing of a planar array of antenna elements with example selected antenna elements for generating and beamforming different OAM mode waves whereby one same antenna element (darkest shaded) is reused / shared for the different OAM mode generations. Accordingly, two or more subsets of antenna elements for generating the two or more OAM modes may be respectively selected from two or more layers of antenna elements and every two adjacent layers thereof overlap with each other (sharing at least one common antenna element).• All elements in one layer or circle can be separated into multiple subsets or groups to generate different modes of OAM waves (e g., see FIG. 12). In particular, FIG 12depicts a schematic drawing of a planar array of antenna elements with example antenna elements in the same layer or circle separated into multiple subsets to generate different 0AM modes (e g., lighter shaded antenna elements generate mode x and darker shaded antenna elements generate mode y) Accordingly, multiple 0AM modes can be obtained with antenna elements in a single circle by grouping antenna elements into multiple subsets generating different modes of 0AM waves, respectively. Accordingly, two or more subsets of antenna elements may be selected from the same layer(s) of antenna elements and they do not overlap with each other.• Each layer or circle of antenna elements may have different radius at different azimuth angles (with respect to the center of the circle), although large different radius at different azimuth angles may cause 0AM wave distortion.• The antenna elements distribution on a layer or circle can be uniform or non-uniform, although significantly non-uniform distribution of element can cause 0AM wave distortion Accordingly, for example, an 0AM wave may be generated with non- uniform and non-circle distributed antenna elements.

[0078] Various design examples will now be discussed to validate the method of multimode 0AM wave generation and beamforming using a planar phased array antenna according to various example embodiments of the first aspect of the present invention.

[0079] The example method 700 of generating multi-mode 0AM wave and corresponding beamforming is validated through example designs in EMPro. In this regard, two example planar phased array antennas of different types or configurations for generating RF 0AM and beamforming shown in FIGs. 13 A and 13B are evaluated as two example planar phased array antenna designs / configurations.

[0080] FIGs. 14A and 14B show generated 0AM radiation pattern and wavefront of mode 0 with phased array 1 element in layer 0 (beamforming direction is 6 — 0, p = 0, sensing plane [(1,1,15), (-1,-1, 15), (-1,1,15)] (defined by three points in space)). In particular, FIGs. 14A and 14B show the mode 0 generated. It is a common and non-twisted wave. It is not vortex wave. On the other hand, FIGs. 15A to FIG. 15C show the generated 0AM wave modes +1 and -1, respectively, using planar phased array type 1 with layer 1 elements, following the example method 700 of generating multi-mode 0AM wave. The twisted effect is clearly evident. In particular, FIGs. 15A to 15C show generated 0AM radiation pattern and wavefronts of modes + 1 and -1 with phased array 1 elements in layer 1 (beamforming direction is 6 = 0, <p = 0, sensing plane [(1,1,15), (-1,-1, 15), (-1,1,15)]).

[0081] FIGs. 16A to 16C and FIGs. 17A to 17C show modes ±2 and modes ±3 0AM wave, respectively, using elements on layer 2 of the phased array type 1. In particular, FIGs.16A to 16C show generated 0AM radiation pattern and wavefronts of modes +2 and -2 with phased array 1 element in layer 2 (beamforming direction is 6 = 0, p = 0, sensing plane [(1,1,15), (-1,-1, 15), (-1,1,15)]). FIGs. 17A to 17C show generated 0AM radiation pattern and wavefronts of modes +3 and -3 with phased array 1 element in layer 2 (beamforming direction is 6 = 0, <p = 0, sensing plane [(1,1,15), (-1,-1, 15), (-1,1,15)]).100821 FIGs. 18A to 18D show the beamforming for the generated 0AM wave with phased array 1 elements in layer 1 and sensing the 0AM in different planes according to the example method 700. In particular, FIGs. 18A and 18B are the radiation pattern comparison of different beamforming directions 0 = 0, cp = 0 versus 0 = 30°, <p = 0. It can be seen that the beamforming step in the example method 700 is able to clearly steer the radiation beam for the desired or defined beamforming direction. FIGs. 18C and 18B show the sensing results in two different sensing plane for the 0AM wave radiation steered to 6 = 30°, (p = 0. It can be seen that if sensing wave in the plane which is originally used to sense the wave generated in FIG.18 A, the sensed wave has siginificent distortion. While when sensing it in the phane slanting 0 = 30°, the sensed wave recovers to the normal mode 0AM wave. Therefore, this demonstrates the beamforming.

[0083] FIGs. 19A to 19C show the modes ±2 0AM wave generation with phases array 2. There are just 4 elements in layer 1 around the center element used. In particular, FIGs. 19A to 19C show generated 0AM radiation pattern and wavefronts of modes +1 and -1 with phased array 2 elements e34, e45, e54 and e43 (beamforming direction is 0 = 0, <p = 0, sensing plane [(1,1,15), (-1,-1, 15), (-1,1,15)]).

[0084] FIGs. 20A to 20D show the effect when the antenna elements selected are not strictly on a circle with phased array 2. In particular, FIGs. 20A to 20D show the generated 0AM radiation pattern and wavefronts of modes +1 and -1 with non-circle antenna elements selection (beamforming direction is 0 = 0, <p — 0, sensing plane [(1,1,15), (-1,-1, 15), (-1,1,15)]). It can be seen that the desired 0AM modes can still be generated. However, distortion can be observed.

[0085] FIGs. 21A to 21F show the gain enhancement effect by increasing the number of layers for generating the same 0AM mode. In particular, FIGs. 21A to 21F show generated 0AM wave with one-layer elements versus with two-layer elements, (beamforming direction is 0 = 0, <p = 0, sensing plane [(1,1,15), (-1,-1, 15), (-1,1,15)]). Comparing the left-hand-sideresults, generating mode +1 with one- layer elements using phased array type 1, the right-hand-side results, which is with two-layer elements, show clearly high radiation gain. It can be observed through radiation pattern in FIG. 14D and the wavefront in FIG. 14E.

[0086] Accordingly, the example method 700 of multi-mode OAM wave generation and beamforming using a planar phased array antenna according to various embodiments of the first aspect of the present invention has various technical advantages, for example:• is able to generate any mode of OAM wave without hardware change.• is able to flexibly control the radiation direction and the generated OAM wave individually.• is able to simultaneously generate multiple modes of OAM wave and beamform these modes to different directions without hardware change.

[0087] A method of OAM (i.e., RF OAM) Tx-Rx directional alignment will now be described according to various first example embodiments of the second aspect of the present invention.

[0088] In a RF-OAM communication system, the transmitter (Tx) transmitting RF-OAM wave ideally should aim to a center of the RF-OAM receiver (Rx). Otherwise, the RF-OAM signal cannot be demodulated well or optimally. Accordingly, various first example embodiments of the second aspect of the present invention provide a method of OAM Tx-Rx directional alignment, and more particularly, more correcting or improving directional T-Rx misalignment.RF-OAM Receiver

[0089] The RF-OAM receiver may be implemented with a RF-OAM matched filter.Continuous OAM matched filter

[0090] In an ideal case, RF-OAM signal is demodulated by continuous matched filter. The continuous OAM matched filter is:rmg(f) = I rffe-i^dcp'—nf= I71xk{t)e^2nl’M<pOe-hP9d(pJ-Tlf71= xk(f)ej2nfd I e^ke-^d(p*-n(Equation 3)where g 6 {0, ±1, ±2, ••• } denotes the desired mode number for Rx matched filter. The output of the ideal matched filter is:(2nxk(fi)ej2nfct, ifk = g.., rw(t) = (0(Equation 4)

[0091] This means that with the ideal continuous matched filter and 0AM propagation axis aim to receiver matched filter centre, only the mode matched 0AM wave, k — g, can pass the matched filter and get a demodulated linear polarization RF signal. After that, one can apply the traditional down-convertor and analogue to digital convertor (ADC) to extract base-band data stream xk(t}- If the RF signal reaching the receiver has difference mode from the desired mode of the matched filter, including the linear polarization (k = 0) and all other 0AM mode (k g), the RF signal will be blocked by the 0AM mode matched filter completely.Discrete matched filter

[0092] When the 0AM matched filter comprises finite sensor elements, it may be represented as:hn5(0 = Z'=o r(t)e“7W= xfc(t)e727rfctE;=o (Equation 5) where I is the number of elements in the 0AM receiver, 0 < i < I — 1, is the discrete azimuth angle index around the propagation direction axis, and A = ^. An objective is to:XiZo ejlA^k~0^ = 0, V (fc - * 0 (Equation 6)

[0093] If I is multiple of 2max|fc|, and ( / < — g) #= 0,* _ -] I I -n7r£Z-1=£2maX|k|e;iA(z-fc) j2max|fc|-l= Q ( Ec|L|atj on 7)

[0094] Thus,,, jffc = gCnx(0 = (0 jf k* (Equation 8)

[0095] This means that if a discrete matched filter is applied and the number of sensor elements (antenna elements) is multiple of the twice of absolute of maximum mode number, and these sensors are uniformly distributed around the 0AM propagation axis, the same 0AM demodulation function as that as the continuous 0AM matched filter can be achieved. In general practice, the 0AM receiver is a discrete matched filter.

[0096] The above analysis is for that Tx transmission perfectly aims to the centre of Rx sensor plate. In existing applications, the Tx transmission axis may not aim to the centre of the receiver accurately, that is, there may be Tx-Rx directional misalignment as illustrated in FIG.22. In particular, FIG. 22 illustrates an example directional misalignment of 0AM Tx and Rx.

[0097] FIG. 22 shows that RF-OAM wave emitted by Tx reaches Rx with ep(the distance from the intersection point of Tx emission axis and the Rx sensor plane to the centre of Rx sensor, referred to herein as the distance error) and(the azimuth angle of (or associated with) the error distance sp). According to various first example embodiments of the second aspect of the present invention, a method of the Tx-Rx directional alignment is performed by estimating the distance error £pand the azimuth angle error s^, and adjust Tx emission direction (e g., a beamforming elevation angle parameter value and a beamforming azimuth angle parameter value) using beamforming function to compensate the distance error spand the azimuth angle error E^. In this regard, as will be described hereinafter, the beamforming elevation angle value 6 and the beamforming azimuth angle value p may be determined based on the distance error spand the azimuth angle errorrespectively. The Tx emission direction (which may also be referred to the transmitter beam axis) may then be adjusted based the beamforming elevation angle value 0 and the beamforming azimuth angle value <p by applying a phase shifting to antenna elements according to Equation (2) as described hereinbefore according to various example embodiments of the first aspect of the present invention.Close-Loop Tx-Rx Directional Alignment100981 An example frame structure of RF-OAM communication system according to various first example embodiments of the second aspect of the present invention is shown in FIG. 23. In pilot period, the 0AM transmitter (Tx) emits just a single 0AM mode (e.g., 0AM mode 1) without payload data for the Tx-Rx alignment as well as other communication estimations. At receiver side, the RF signal phases of received signals of the 0AM wave reaching to all sensors (antenna elements) located on the receiver sensor circle are analysed to estimate the distance error epand the azimuth angle error. Accordingly, the 0AM transmitter may transmit an 0AM wave of an 0AM mode to the 0AM receiver, and from each antenna element of a plurality of antenna elements of a layer of antenna elements of the planar array of antenna elements of the 0AM receiver, a phase value of the received signal of the 0AM wave of the 0AM mode incident at the antenna element is obtained, thereby obtaining a set of phase values of the received signals of the 0AM wave incident at the plurality of antenna elements of the layer of antenna elements. The estimated epand(denoted as epand s^) may then be communicated to the 0AM transmitter via any conventional wireless communications, such as linear wave wireless communications. After knowing Epand E^,, the 0AM transmittermay then adjust the transmission beam axis (emission direction) through beamforming function (e.g., by applying a phase shifting to antenna elements according to Equation (2) as described hereinbefore according to various example embodiments of the first aspect of the present invention). In various first example embodiments of the second aspect of the present invention, the beamforming elevation angle value may be defined as:9 = a tan y, (Equation 9) and the beamforming azimuth angle value is E^, that is:<p = E (Equation 10)

[0099] After the Tx and Rx are aligned based on Epand E(pestimation and compensations through beamforming, respectively, multi-mode 0AM transmission with data may then be carried out in payload period, such as according to the method 100 of 0AM wave generation and beamforming described hereinbefore according to various example embodiments of the first aspect of the present invention. In various first example embodiments of the second aspect of the present invention, the multiple modes of the OAM wave may be generated using respective sensor circles (concentric circles of antenna elements) which have the same center as that of the sensor circle(s) used to generate the mode 1 OAM wave used in the pilot period. Although an OAM wave of OAM mode 1 (mode +1 or -1) may preferably be used in the pilot period for ease of implementation, it will be appreciated by a person skilled in the art that the present invention is not limited to only utilizing an OAM wave of OAM mode 1 in the pilot period and other OAM mode may be utilized as appropriate, and in general, any OAM mode whose absolute value is smaller than N / 2, where N is the number of the antenna elements in the circle of antenna elements.

[0100] Let <pRxdenote the Rx signal phase along the receiver sensor circle shown FIG. 22. When Tx emission mode is mode 1 0AM wave in pilot period:( B(fp, Ep, R^ — E(p,if n > 0 ' / ’ / ?.■< = (Equation 11) (— B (<p, Ep, R) — Eq,, if — n < <p < 0 where _i I Sn+RcosGp) 1 _ B(ip, Ep, R^ — cos1.p: (Equation 12)\ R2+Sp2+2RSp cos(<p) Iwhere <p denotes the azimuth angle at the receiver senser plane. Epand Eipmay then be estimated based on pRx.

[0101] For example, an estimation cost function may be defined as:fc(.£p'£<p)=l (.(pRx ~ <p)2d< P■'-7T(Equation 13)

[0102] For example, if OAM receiver has / sensors along a circle uniformly,1—1fc(£p>£<p) = ^\<pRxi - 7T + t'A)2d<pi=l(Equation 14)

[0103] The estimates ofpand Erpmay then be:{EP, Etp) — arg min fc(£p, E^ (Equation 15)Recursive Gradient Descent Method

[0104] Equation (15) is a 2-dimension optimization problem. Since fc(£p, £<p) is convex, £pand E^can be obtained through gradient descent method. An example procedure is:

[0105] 1. Set initial values spk— 0, £(p = 0; set the learning factor a — 0.01 set the gradient step, 6 = 0.001 and the maximum residual error y.

[0106] 2 Associate with Tx to calculate gradientgk= WcOPfc.^fe) '[crc^fc+^J-cTc^pfe-^jy s (Equation 16) s where Epk— L * tan0Tk; EV— <pTk, and where 9Tkand <pTkare the Tx elevation and azimuth angles at the kth update, respectively, L is the distance between Tx and Rx.

[0107] 3. Update estimates of £p +1and E(p +1^Pk+1? Pkagk(Equation 17)fyk+l £<pk

[0108] If y > max kpfe+1- ' I i - terminate the procedure. The estimates of Epand EVare £pfc+1and EV k+1, respectively. Otherwise, k = k + 1, return to step 2.

[0109] FIG. 24 shows the estimates of spand E^ through the gradient descent method. (Ground truths of Epand Erpare 5 and 50 degrees, respectively. Number of sensor elements of OAM receiver, I — 8; receiving SNR=10dB). It can be seen that even by using a limited number of sensor elements in a circle, the misalignment parameters epand E^ can be estimated and compensated out.Artificial intelligence (Al) (or Machine learning model) based Method

[0110] Although the recursive gradient descent method is able to obtain / estimate £pand E^, the convergence is slow. There are more than a hundred of interactive iterations between the Tx and Rx to achieve the final estimations. To shorten the alignment period, a machine learning (e.g., deep learning (DL))-based process is applied. In particular, to address this technical problem, various first embodiments of the second aspect of the present invention estimate E and Sg, based on Al or DL (machine learning) models, which may be achieved through DL regression or classification. In the DL regression approach, a DL model may be used to fit the inverse function in Equation (14). Through that, the regression DL model may directly output continuous Epand £, estimates. However, the DL regression approach may need complicate DL hyperparameters and long learning curve. In contrast, the classification approach is more advantageous in terms of the model complexity and learning curve. The classification DL model outputs a limited or predefined number of classes for possible £pand £<pvalues. Since the combinations of different Epand £vis very large, various first embodiments of the second aspect of the present invention apply two DL models, A and B, to predict or estimate Epand £v, respectively.

[0111] FIGs. 25A and 25B show the two example DL models adopted. In particular, FIG.25A and 25B show an example DL model A and an example DL model B for distance error £pestimation and azimuth angle error E^, estimation, respectively. Both DL models A and B are deep neural networks (DNN) comprising four full connected layers with ReLu except last layer. Since the models are for classification, cross-entropy loss may be used.

[0112] The input of both DL models is:V = [<prx(0), ■■■, prx(jT eRlxl(Equation 18) where <prx(i) is the phase in degree of the received RF signal of the pilot 0AM wave at / the OAM sensors uniformly distributed on the receiver sensor circle. Accordingly, a distance error £pbetween an intersection point of a transmitter beam axis (which may also be referred to as a transmitter emission axis) of the OAM transmitter at the planar array of antenna elements of the OAM receiver and a center of the planar array of antenna elements of the OAM receiver may be predicted (or estimated) based on the set of phase values 'F of the received signals of the OAM wave (e.g., mode 1 OAM wave) using a distance error machine learning model (e.g., the DL model A). In this regard, the distance error machine learning model is trained to predictthe distance error based on the set of phase values 'P of the received signals of the 0AM wave. Furthermore, an azimuth angle errorassociated with the distance error spmay be predicted or estimated based on the set of phase values T7of the received signals of the 0AM wave using an azimuth angle error machine learning model (e.g., the DL model B). In this regard, the azimuth angle error machine learning model is trained to predict the azimuth angle error based on the set of phase values 'P of the received signals of the 0AM wave.

[0113] For example, he DL model estimating Epoutputs an instant estimate of Epthrough an integer number, X, from 0 to 99, for example:. rO.1% / ?, ifX < 99 „.£P=I > 10 / ? if X = 99(EquatlOn 19)where R is the radius of the Rx receiver sensor circle Accordingly, in this example, the DL model is configured to classify the error range of p into 100 classes. It will be appreciated by a person skilled in the art that the number of classes may be configured as desired or as appropriate.

[0114] For example, the DL model estimating Eg, also outputs an instant estimate of Eg, in degree through an integer number, Y, from 0 to 359, for example:,p— Y — 180 (Equation 20) Accordingly, in this example, Eg, range is configured as [-180, 180] for covering 360 degrees.

[0115] In experiments, 100K *P samples with random Epand Eg, in signal to noise ratio (SNR) 30dB were generated to train the DL models A and B. In the training section, the batch size was set as 500, epoch was 500, the learning rate was 0.0001, and the other detailed hyperparameters are marked in FIGs 25A and 25B.

[0116] After the training, other 10KlP samples with random epand Eg, are generated in different signal to noise ratio (SNR) from 0 dB to 30 dB to validate the DL estimation. The estimation results of Epand Eg, are shown in FIGs. 26A and 26B, respectively. In these example implementations, I was selected as 4 and 12, respectively. FIGs. 26A and 26B show RMSE versus SNR of Epand estimations through the DL / ALbased method. It can be seen that £pand E<p are estimated in one step in the DL / ALbased method. Therefore, the DL / ALbased method is more effective than the gradient descent method In the DL / ALbased method, larger I, the number of Rx sensors, leads to better root mean square error (RMSE) performance for Epand EVestimations in low signal to noise ratio (SNR) environment. However, larger 1 also means higher hardware complexity and high power consumption.

[0117] After epandare estimated, Epand Eipmay be communicated to 0AM transmitter (Tx) by the 0AM receiver (Rx) through wireless communications such as linear polarization wireless communications. Tx may then compensate for £pandaccording to Equations (9) and (10). Accordingly, transmitter beam axis error information (e.g., comprising the predicted distance error spand the predicted azimuth angle error Etfl) may be sent to the 0AM transmitter for adjusting a transmitter beam axis of the 0AM transmitter for 0AM Tx-Rx directional alignment. For example, the transmitter beam axis error information may comprise the predicted distance error spand the predicted azimuth angle error E^ or may comprise information derived from the predicted distance error Epand the predicted azimuth angle error £<p for adjusting the transmitter beam axis of the 0AM transmitter for 0AM Tx-Rx directional alignment. After the 0AM transmitter receives the transmitter beam axis error information, the OAM transmitter, or more particularly a controller thereof, may then adjust the transmitter beam axis based on the transmitter beam axis error information (e.g., the predicted distance error and the predicted azimuth angle error). In this regard, to generate and beamform a multimode OAM wave using a planar phased array antenna, for each mode of a plurality of modes of a multi-mode OAM wave to be generated and for each antenna element of the selected subset of antenna elements, a first phase shift may be applied to the antenna element for generating the mode of the multi-mode OAM wave (e.g., as described hereinbefore according to Equation (1)) and a second phase shift may be applied to the antenna element for beamforming the mode of OAM wave to the beamforming direction defined therefor (e.g., as described hereinbefore according to Equation (2)). In this regard, in various example embodiments of the second aspect of the present invention, the first and second phase shift may be applied to the antenna element in addition to a phase shift applied to the antenna for adjusting the transmitter beam axis of the OAM transmitter for OAM Tx-Rx directional alignment. In other words, the transmission beam steering phase shift for OAM Tx-Rx directional alignment and the multi-mode OAM wave generation and beamforming phase shifts may be added together.

[0118] In various first example embodiments of the second aspect of the present invention, in the payload period, all OAM modes transmitted including the pilot OAM mode are coaxial, and all OAM modes received including the pilot OAM mode are coaxial too Thus, multi-mode OAM Tx-Rx directions are advantageously aligned.

[0119] A method of OAM (i.e., RF OAM) Tx-Rx directional alignment will now be described according to various second example embodiments of the second aspect of the present invention.

[0120] As explained hereinbefore, 0AM EM waves offer a promising path to increased spectrum efficiency by enabling multiplexing beyond traditional time, frequency, and space division methods. However, effective 0AM multiplexing hinges on good alignment between Tx and Rx, which is challenging in RF. In this regard, various second example embodiments of the second aspect of the present invention quantitatively assesses the impact of Tx-Rx misalignment on RF-OAM detection and multiplexing, demonstrating the critical need for accurate alignment. In particular, a DL-based (or machine learning (ML)-based) solution or method is provided for misalignment correction, of which numerical results demonstrate the DL-based method is both fast and accurate.

[0121] 0AM EM waves are promising in providing high-capacity wireless communications. It has attracted huge interest. In relation to 0AM wave generation, various multi-mode RF-OAM generators were reported with metamaterial, four-feed circular patch antenna, single port PIN diodes control and uniform circular array (UCA), respectively. In relation to RF-OAM systems, comparison of RF-OAM and conventional multiple input and multiple input (MIMO) system in wireless communications have shown that RF-OAM multiplexing achieves higher channel capacity than that of the typical MIMO system.

[0122] RF-OAM is a good candidate for next generation wireless communication systems, since the additional 0AM multiplexing besides traditional time, frequency and space divisions leads to higher spectrum utilization rate However, this potential rests on the basis of good alignment between the Tx and the Rx. Directional misalignment can significantly affect RF-OAM performance.

[0123] The 0AM misalignment problem and its deep learning solution are quantitatively studied. In this regard, various second example embodiments of the second aspect of the present invention:• generate OAM wave with the uniform planar array (UPA) widely used in wireless communication systems. It is more general than UCA.• quantitatively analyze mutual mode crosstalk and single mode degradation caused by Tx-Rx directional misalignment.• propose and validate a DL-based solution for directional misalignment estimation and correction. It is fast (with a single snapshot signal) and effective.RF-OAM SYSTEM MODELING

[0124] An RF-OAM system with mathematical representations for 0AM signal transmission, reception and beam steering will now be described according to various second example embodiments of the second aspect of the present invention.RF-OAM Tx|00125| RF-OAM waves with different modes may be generated by activating subsets of a large-scale UPA panel to form multiple coaxial UCAs. All modes of RF-OAM wave carry respective data streams. The emitted multi-mode RF-OAM wave is:s(t) = Ykxk(F)ei^nfct+<p, >, (Equation 21) where k E {0, ±1, ±2, } is the mode number of 0AM wave, xfc(t) is the data stream carried by 0 AM wave mode k, ip E [— it, n) is the azimuth angle around the propagation direction axis, fcis the carrier frequency.RF-OAMRx

[0126] The RF-OAM Rx can be implemented with RF-OAM matched filter.

[0127] Continuous 0AM matched filter. As described hereinbefore, in an ideal case, RF-OAM signal is demultiplexed by continuous matched filter. The continuous 0AM matched filter may be expressed as:= xk(f) ej27TM e;,pfce ~j(p9dtp (Equation 22)where g G {0, ±1, ±2, ••• } denotes the desired mode number for the RF-OAM match filter. The output of the ideal matched filter is:,, (2nxk(t)ej27Tlf iffc = g= [Q(Equation 2J)

[0128] This means that only the input mode k matching designed mode g can pass through the matched filter and get a linear polarization RF signal. After that, one can apply traditional radio receiver to extract base-band data stream xk( ). The other modes of 0AM wave will be blocked by the matched filter completely.

[0129] Discrete matched filter: When the 0 AM matched filter consists of finite sensor elements, it can be expressed as: / -i1 = 0—xfc(t)e;2JT^ctSLoe',lA('fc 9i(Equation 24) where I is the number of sensor elements in the OAM receiver, 0 < i < I — 1, is the discrete azimuth angle index around the propagation direction axis, and A =An objective is to:£i=o = 0, V ( / c — g) 0 (Equation 25)

[0130] If / is multiple of 2max|fc|, and (fc — g) 0,1_. nnJ / -1ejt^k-g)=^2max|k|ejiA(x-fc) ^2max|fc|-i= Q(Equation 26)

[0131] Thus,f / ej27T / Ct if / , _ grmx(t) = 'f, f (Equation 27)

[0132] This means that if the number of sensor elements meet the requirement above, the same OAM demultiplexing as that as the continuous OAM matched filter can be achieved.

[0133] However, above analysis is for that Tx transmission perfectly aims to the centre of Rx sensor plate. In existing applications, the Tx transmission axis may not aim to the centre of the Rx accurately. Tx-Rx misalignment of OAM Tx and Rx is shown in FIG. 27.

[0134] FIG. 27 shows that RF-OAM wave emitted by Tx reaches Rx with errors sp(the distance from the intersection of Tx emission axis and the Rx plane to the centre of Rx sensor) and £<fJ(the azimuth angle for Ep). Moreover, Rx sensor plane may not perfectly face the incident wave. It includes elevation and azimuth errors 9rand <pr, respectively. In this regard, various second example embodiments of the second aspect of the present invention performs misalignment correction by estimating the errors£p, 0rand <pr, and then compensate 0rand (prby Rx beam steering, correct errors Epand Eg, through Tx beam steering. Accordingly, in various second example embodiments of the second aspect of the present invention, in addition to Tx-Rx directional alignment based on estimating and correcting errors Epand EVthrough Tx beam steering as described hereinbefore according to various first example embodiments of the second aspect of the present invention, 0rand <prare estimated and corrected based on Rx beam steering for steering the Rx beam facing the transmitter to correct the Rx beam axis as the Rx sensor plane may not perfectly face the incident OAM wave from the transmitter. In this regard, the Rx beam axis may be adjusted by adjusting a beamforming elevation angle parameter value and a beamforming azimuth angle parameter value associated with receiver based on the predicted beamforming elevation angle error 9rof the OAM receiver and the predicted beamforming azimuth angle error <prfor OAM transmitterreceiver directional alignment.RF-OAM Beam Steering

[0135] To conduct beamforming for mode x to the desired direction 9X, <px, the elevation and azimuth angles, respectively, additional phase shift may be applied to antenna elements of circles 1 to Nx. The additional phase shift for antenna element k (k = 0,1, ■■■, Kn— 1) in circle nxis as follows:j2Tt / ^RTnsln6xcosbnxk— ZeKn* (Equation 28) where Rmxis the radius of the circle array nxin the Tx array penal, / Lis the wavelength of the RF signal. Knxis the the number of elements on circular array nx, and z(-) denotes the phase whithin [— n, n) of the signal. FIGs. 28A to 28D show the 0AM wave generation and beam steering with a UPA (f- l 0AM wave).Tx-Rx Directional Alignment

[0136] The effects of directional misalignment of 0AM will now be analyzed followed by a method of 0AM Tx-Rx direction alignment according to various second example embodiments of the second aspect of the present invention.Effects of Tx-Rx directional misalignment

[0137] First, the Rx phase distortion due to misalignment is described. Let (pRxdenote the Rx signal phase along the receiver circle shown FIG. 27.

[0138] Ideally, when the incident wave is perpendicular to Rx sensor plane,. ( kB(<p, c0, R) - c„, if n > 0<pRx\t=k = (Equation 29)(— kB{(p, Ep, R) — E<p, if - 7T < (p < 0where£?(<p, Ep, R) = cos-11 Ep+fi cosO) \ (Equation 30)\ R2+Ep2+2R?p cos(<p) Ip denotes the azimuth angle at the receiver senser plane, k denotes 0AM mode number

[0139] In more general case, the incident wave is not perpendicular to Rx plane. In this case,<PRx\t=k = + ^ / ^TnxsmercOs «pr-<p) (Equation 31) where 9rEf— |, |) and <prE [““<“) are the elevation azimuth angles of the incident wave of Rx. Field of view (FoV) of Rx is assumed to be 120° Thus, 0AM matched filter output in the condition of misalignment may be expressed as:Ik^g— xfc(t)e^2’r- / ’ctJ027rej< PRx^=ke~ja<pd(p. (Equation 32)

[0140] The single mode degradation rate (SMDR) may be defined as:IW=>9 2TT 2»r \ / Accordingly, Sgrepresents a parameter for quantitively indicating how serious the 0AM mode degrades.

[0141] The mutual mode crosstalk rate (MMCR) from mode k to mode g may be defined as:=IW \fr^^e-^d<p\k^9 \rg^g\ ^ne>ll,Rxk=ge-jg<pd(p^ (Equation 34)

[0142] Accordingly, Mk^grepresents a parameter for quantitively indicating how serious the 0AM mode is interfered by the other 0AM modes.

[0143] Ideally, SMDR, and MMCR should always be 1 and 0, respectively. However, due to misalignment, SMDR is <1 and MMCR is > 0. It will be show numerically how SMDR and MMCR change along with £pincreasing in next Section with some examples.DL-based Tx-Rx alignment

[0144] Theoretically, for estimating £p, £tp, 9rand pr, the cost function may be represented as:fc^P, £ 9r> < Pr} = O*j°Rxk=i - <p)2d< P (Equation 35)

[0145] If 0AM receiver comprises 1 sensors along a circle uniformly,fc^p’£ Sr,(Pr) = S^i(< PRxlr=i ~n+ i&)2d<p (Equation 36)

[0146] Then, the estimates may be expressed as:(Ep. E^ier^r ) arg min fc(£p, £„, 6r, <pr~) (Equation 37)EP>E< P 9r,<pr,

[0147] Equation (37) is a 4-dimension optimization problem, and thus, its maximum likelihood solution would be very complex.

[0148] Various second example embodiments of the second aspect of the present invention employ machine learning (e.g., DL) to address the above technical problem, and more particularly, provide a machine learning method or approach to find a relationship between the misalignment and received signal phase combinations, for example, without modelling error and complex analytical formula. Four parameter estimations can be sorted as classification problems, respectively. (0r, (pr) can be estimated with two deep neuro network (DNN) models when Tx emits mode 0 0AM wave, while {£p, £ip} can be estimated with other two DNN models when Tx emits mode 1 0AM wave. An example frame structure for the RF-OAM communication system according to various second example embodiments of the second aspectof the present invention is shown in FIG. 29. In Pilot 1 period, RF signal phases of received signals of the incident 0AM wave reaching all sensors (antenna elements) located on the receiver sensor circle are analysed to estimate 6r, pr) and then conduct corresponding compensation through Rx beam steering. Similarly, in Pilot 2 period, {sp, ) are estimated in Rx. Although 0AM wave of 0AM mode 0 may preferably be used in the pilot period 1 and 0AM wave of 0AM mode 1 may preferably be used in the pilot period 2 for ease of implementation, it will be appreciated by a person skilled in the art that the present invention is not limited to only utilizing an 0AM wave of 0AM mode 0 in the pilot period 1 and an 0AM wave of OAM mode 1 in the pilot period 2 and that other 0AM modes may be utilized as appropriate.

[0149] Accordingly, in pilot period 1, the OAM transmitter may transmit an OAM wave of an OAM mode (e g., mode 0 OAM wave) to the OAM receiver, and from each antenna element of the plurality of antenna elements of the layer of antenna elements of the planar array of antenna elements of the OAM receiver, a phase value of the received signal of the OAM wave of the OAM mode incident at the antenna element is obtained, thereby obtaining a set of phase values of the received signals of the OAM wave incident at the plurality of antenna elements of the layer of antenna elements. In pilot period 2, the OAM transmitter may transmit another OAM wave of another OAM mode (e.g., mode 1 OAM wave) to the OAM receiver, and from each antenna element of a plurality of antenna elements of a layer of antenna elements of the planar array of antenna elements of the OAM receiver, a phase value of the received signal of said another OAM wave of said another OAM mode incident at the antenna element is obtained, thereby obtaining another set of phase values of the received signals of said another OAM wave incident at the plurality of antenna elements of the layer of antenna elements.

[0150] The estimated {sp, E<P) may then be fed back to the OAM transmitter (Tx), and the correction for (sp, E,,, ) may be performed through Tx beam steering. The beamforming elevation angle value is:6 — atan(Ep / L), (Equation 38) and azimuth angle value is EV, that is:p = E, (Equation 39)

[0151] After the Tx and Rx are aligned through Tx and Rx beam steering, respectively, multi-mode OAM transmission with data may then be carried out in the payload period. The multiple mode OAM waves have their respective sensor circles which are coaxial with the sensor circles used in the pilot periods. The misalignment detection and correction may beperiodically conducted. An example method of 0AM Tx-Rx direction alignment according to various second example embodiments of the second aspect of the present invention is shown in FIG. 31 for continuous misalignment estimation and correction followed by multi-mode 0AM communications.

[0152] FIG. 30A to 30D show example DNN models designed All example models comprise four full connected layers with ReLu activations except the last layer. Since the models are for classifications, cross-entropy loss function is used.

[0153] The inputs of all DL models are:= [<jW0)k=i> ■" >< PRxU)\i=iV £ R'xl(Equation 40) where (pRxt) denotes the phase in degree of the received signal of the pilot OAM waves at ith element of the OAM Rx. There are I elements uniformly distributed on the Rx sensor circle. Accordingly, a beamforming elevation angle error 6rof the OAM receiver may be predicted (or estimated) based on the set of phase values T of the received signals of the OAM wave (e.g., mode 0 OAM wave) using a beamforming elevation angle error machine learning model (e.g., Model A below). A beamforming azimuth angle error <prof the OAM receiver may be predicted (or estimated) based on the set of phase values 'F of the received signals of the OAM wave (e g., mode 0 OAM wave) using a beamforming azimuth angle error machine learning model (e.g., Model B below). A distance error Epbetween an intersection point of a transmitter beam axis (which may also be referred to as a transmitter emission axis) of the OAM transmitter at the planar array of antenna elements of the OAM receiver and a center of the planar array of antenna elements of the OAM receiver may be predicted (or estimated) based on the set of phase values 4’ of the received signals of said another OAM wave (e g., mode 1 OAM wave) using a distance error machine learning model (e.g., Model C below). Furthermore, an azimuth angle error £rpassociated with the distance error spmay be predicted or estimated based on the set of phase values f of the received signals of said another OAM wave (e.g., mode 1 OAM wave) using an azimuth angle error machine learning model (e g., Model D below).

[0154] For example, Model A delivers an instant 6r(in degree) every frame through an integer number,from 0 to 119, which means incident wave elevation angle in degree:— 60 (Equation 41)

[0155] Accordingly, in this example, 0rrange is configured as [-60, 60] for covering 120 degrees.

[0156] Model B delivers one prper frame (in degree) by an integer number, X2, from 0 to 179, which may be expressed as:<pr= X2— 90 (Equation 42) Accordingly, in this example, (prrange is configured as [-90, 90] for covering 180 degrees.

[0157] Model C estimates sponce per frame by an integer number, X3, from 0 to 99, which may be expressed as:„ (-0.1X3R, if X < 99= I > 10B lf% = 99 (Equation 4j) where R is the radius of the Rx sensor circle for pilot.Accordingly, in this example, the DL model is configured to classify the error range of p into 100 classes.

[0158] Model D estimates Eponce per frame (in degree) through an integer number, X4, from 0 to 359, which may be expressed as:= X4— 180 (Equation 44) Accordingly, in this example, E^ range is configured as [-180, 180] for covering 360 degrees.

[0159] 100K samples with random sp,6r, prand signal to noise ratio (SNR) of 30dB are generated to train the DL models. In the training section, the batch size was set as 500, the number of epochs was 500, the learning rate was 0.0001, and the other detailed hyperparameters are indicated in FIG. 30A to 30D.Numerical ResultsThe misalignment between Tx and Rx affecting 0AM wave detection will now be numerically shown in terms of single mode detection degradation and mutual mode interference. After that, the performance of the alignment method will be evaluated.|00160| When the incident wave is perpendicular to Rx plane, the single mode detection degradation versus misalignment Epis shown in FIG. 32A. It can be seen that 0AM detection degrades along with misalignment Epincreasing. Higher modes are more sensitive to the misalignment. Mutual mode crosstalk is shown in FIG. 32B 0AM modes are no longer orthogonal to each other when Tx does not aim to Rx centre well. The mutual mode interference also increases along with Epincreasing. If the incident wave is not perpendicular to Rx planes, the degradations are more serious. FIGs. 32C and 32D show SMDR and MMCR, respectively, when ()r— 10°, pr= 5° It can be seen that higher modes suffer from larger degradations in both SMDR and MMCR. This shows that keeping Tx-Rx aligned is important for 0AM wave transmission.

[0161] To validate the DNN models of the DL-based method for misalignment correction, new 10K samples with random sp, EV, 6rand prand random SNR from 0 to 30 dB weregenerated. The DL -based estimation results are shown in FIGs. 33A to 33D. In the example implementations, / was 4 and 12, respectively. Ep, E^, 6rand <prWQVQ estimated within one frame. It is effective. It can be seen that larger / , the number of Rx sensors, leads to better root mean square error (RMSE) performance for all estimations in low SNR environment. However, larger / means higher hardware complexity and higher power consumption.

[0162] After 6r(pr, £pand Eg,, are estimated, the compensation and correction are conducted on Rx and Tx sides, respectively, within the same frame as presented before. The DL-based method for misalignment estimation and correction is advantageously with a single snapshot signal, hence fast compared to the existing multiple-snapshot solution.

[0163] The impact of Tx-Rx misalignment in a RF-OAM communication system has been discussed. Results show that misalignment significantly degrades single-mode 0AM detection and increases inter-mode crosstalk. To address this technical problem, various second embodiments of the present invention provide a fast and effective DL-based method for misalignment estimation and correction, of which numerical results confirm to be both fast and accurate.

[0164] While embodiments of the invention have been particularly shown and described with reference to specific embodiments, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the scope of the invention as defined by the appended claims. The scope of the invention is thus indicated by the appended claims and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced.

Claims

CLAIMS1. A method of multi-mode orbital angular momentum (0AM) wave generation and beamforming using a planar phased array antenna comprising a planar array of antenna elements, the method comprising, for each mode of a plurality of modes of a multi-mode 0 AM wave to be generated:selecting a subset of antenna elements of the planar array of antenna elements for generating the mode of the multi-mode 0AM wave;applying, for each antenna element of the selected subset of antenna elements, a first phase shift to the antenna element, the first phase shift determined based on an index of the antenna element and the mode of the multi-mode 0AM wave for generating the mode of the multi-mode 0AM wave; andapplying, for each antenna element of the selected subset of antenna elements, a second phase shift to the antenna element, the second phase shift determined based on the index of the antenna element and a beamforming direction defined for the mode of the multi-mode 0AM wave for beamforming the mode of 0AM wave to the beamforming direction defined therefor.

2. The method according to claim 1, wherein said selecting the subset of antenna elements for generating the mode of the multi-mode 0AM wave comprises:selecting one or more layers of antenna elements of the planar array of antenna elements for generating the mode of 0AM wave; andselecting, for each layer of the selected one or more layers of antenna elements, a plurality of antenna elements of the layer of antenna elements for inclusion in the subset of antenna elements for generating the mode of the multi-mode 0AM wave.

3. The method according to claim 2, wherein multiple layers of antenna elements of the planar array of antenna elements are selected for generating the mode of 0AM wave.

4. The method according to claim 3, wherein the multiple layers of antenna elements of the planar array of antenna elements correspond to multiple concentric circles of antenna elements of the planar array of antenna elements having different radii.

5. The method according to any one of claims 2 to 4, wherein for two or more modes of the plurality of modes of the multi-mode 0AM wave,the two or more subsets of antenna elements respectively for generating the two or more modes of the plurality of modes are selected from common one or more layers of antenna elements of the planar array of antenna elements, andthe two or more subsets of antenna elements selected respectively for generating the two or more modes of the plurality of modes are different groups of antenna elements of the planar array of antenna elements.

6. The method according to claim 2, wherein for two or more modes of the plurality of modes of the multi-mode 0AM wave,the two or more subsets of antenna elements respectively for generating the two or more modes of the multi-mode 0AM wave are respectively selected from two or more layers of antenna elements of the planar array of antenna elements, andfor each pair of adjacent layers of the two or more layers of antenna elements, the two subsets of antenna elements respectively selected from the pair of adjacent layers share at least one common antenna element.

7. The method according to claim 6, wherein said each pair of adjacent layers corresponds to two circles of antenna elements of the planar array of antenna elements that intercept at the at least one common antenna element.

8. The method according to any one of claims 2 to 7, whereinthe index of the antenna element of the selected subset of antenna elements is with respect to a total number of antenna elements in the plurality of antenna elements of the layer of antenna elements at which the antenna element belongs to, andthe first phase shift applied to the antenna element of the selected subset of antenna elements is determined further based on the total number of antenna elements in the plurality of antenna elements of the layer of antenna elements at which the antenna element belongs to.

9. The method according to claim 8, whereinthe beamforming direction defined for the mode of the multi-mode 0AM wave for beamforming the mode of 0AM wave comprises an azimuth angle and an elevation angle, andthe second phase shift applied to the antenna element of the selected subset of antenna elements is determined based on the azimuth angle and the elevation angle of the beamforming direction defined and further based on the total number of antenna elements in the plurality of antenna elements of the layer of antenna elements at which the antenna element belongs to.

10. A controller for controlling a planar phased array antenna comprising a planar array of antenna elements for multi-mode orbital angular momentum (0AM) wave generation and beamforming, the controller comprising:at least one memory; andat least one processor communicatively coupled to the at least one memory and configured to, for each mode of a plurality of modes of a multi-mode 0AM wave to be generated:select a subset of antenna elements of the planar array of antenna elements for generating the mode of the multi-mode OAM wave;apply, for each antenna element of the selected subset of antenna elements, a first phase shift to the antenna element, the first phase shift determined based on an index of the antenna element and the mode of the multi-mode OAM wave for generating the mode of the multi-mode OAM wave; andapply, for each antenna element of the selected subset of antenna elements, a second phase shift to the antenna element, the second phase shift determined based on the index of the antenna element and a beamforming direction defined for the mode of the multi-mode OAM wave for beamforming the mode of OAM wave to the beamforming direction defined therefor.

11. The controller according to claim 10, wherein said select the subset of antenna elements for generating the mode of the multi-mode OAM wave comprises:selecting one or more layers of antenna elements of the planar array of antenna elements for generating the mode of OAM wave; andselecting, for each layer of the selected one or more layers of antenna elements, a plurality of antenna elements of the layer of antenna elements for inclusion in the subset of antenna elements for generating the mode of the multi-mode OAM wave.

12. The controller according to claim 11, wherein multiple layers of antenna elements of the planar array of antenna elements are selected for generating the mode of OAM wave13. The controller according to claim 12, wherein the multiple layers of antenna elements of the planar array of antenna elements correspond to multiple concentric circles of antenna elements of the planar array of antenna elements having different radii.

14. The controller according to any one of claims 11 to 13, wherein for two or more modes of the plurality of modes of the multi-mode 0AM wave,the two or more subsets of antenna elements respectively for generating the two or more modes of the plurality of modes are selected from common one or more layers of antenna elements of the planar array of antenna elements, andthe two or more subsets of antenna elements selected respectively for generating the two or more modes of the plurality of modes are different groups of antenna elements of the planar array of antenna elements.

15. The controller according to claim 11, wherein for two or more modes of the plurality of modes of the multi-mode 0AM wave,the two or more subsets of antenna elements respectively for generating the two or more modes of the multi-mode 0AM wave are respectively selected from two or more layers of antenna elements of the planar array of antenna elements, andfor each pair of adjacent layers of the two or more layers of antenna elements, the two subsets of antenna elements respectively selected from the pair of adjacent layers share at least one common antenna element.

16. The controller according to claim 15, wherein said each pair of adjacent layers corresponds to two circles of antenna elements of the planar array of antenna elements that intercept at the at least one common antenna element.

17. The controller according to any one of claims 11 to 16, whereinthe index of the antenna element of the selected subset of antenna elements is with respect to a total number of antenna elements in the plurality of antenna elements of the layer of antenna elements at which the antenna element belongs to, andthe first phase shift applied to the antenna element of the selected subset of antenna elements is determined further based on the total number of antenna elements in the plurality of antenna elements of the layer of antenna elements at which the antenna element belongs to.

18. The controller according to claim 17, whereinthe beamforming direction defined for the mode of the multi-mode 0AM wave for beamforming the mode of 0AM wave comprises an azimuth angle and an elevation angle, and the second phase shift applied to the antenna element of the selected subset of antenna elements is determined based on the azimuth angle and the elevation angle of the beamforming direction defined and further based on the total number of antenna elements in the plurality of antenna elements of the layer of antenna elements at which the antenna element belongs to.

19. An orbital angular momentum (0AM) transmitter for multi-mode 0AM wave generation and beamforming, comprising:a planar phased array antenna comprising a planar array of antenna elements; and a controller according to any one of claims 10 to 18 communicatively coupled to the planar phased array antenna for controlling the planar phased array antenna for multi-mode 0AM wave generation and beamforming.

20. A method of orbital angular momentum (0AM) transmitter-receiver directional alignment between an 0AM transmitter and an 0AM receiver, the 0AM receiver comprising a planar phased array antenna comprising a planar array of antenna elements, the method comprising:obtaining, from each antenna element of a plurality of antenna elements of a layer of antenna elements of the planar array of antenna elements of the 0AM receiver, a first phase value of a received signal of a first OAM wave of a first 0AM mode incident at the antenna element to obtain a set of first phase values of the received signals of the first OAM wave incident at the plurality of antenna elements of the layer of antenna elements, wherein the first OAM wave is transmitted from the OAM transmitter;predicting a distance error between an intersection point of a transmitter beam axis of the OAM transmitter at the planar array of antenna elements of the OAM receiver and a center of the planar array of antenna elements of the OAM receiver based on the set of first phase values of the received signals of the first OAM wave using a distance error machine learningmodel, the distance error machine learning model trained to predict the distance error based on the set of first phase values of the received signals of the first 0AM wave;predicting an azimuth angle error associated with the distance error based on the set of first phase values of the received signals of the first 0AM wave using an azimuth angle error machine learning model, the azimuth angle error machine learning model trained to predict the azimuth angle error based on the set of first phase values of the received signals of the first 0AM wave; andsending transmitter beam axis error information based on the predicted distance error and the predicted azimuth angle error to the 0AM transmitter for adjusting a transmitter beam axis of the 0AM transmitter for 0AM transmitter-receiver directional alignment.

21. The method according to claim 20, whereinthe 0AM transmitter comprises a planar phased array antenna comprising a planar array of antenna elements, andsaid adjusting the transmitter beam axis of the 0AM transmitter comprises adjusting a beamforming elevation angle parameter value and a beamforming azimuth angle parameter value associated with 0AM transmitter based on the transmitter beam axis error information for 0AM transmitter-receiver directional alignment.

22. The method according to claim 20 or 21, wherein the first 0AM mode is 0AM mode 1.

23. The method according to any one of claims 20 to 22, wherein the first 0AM wave of the first 0AM mode is transmitted from the 0AM transmitter without data payload.

24. The method according to any one of claims 20 to 23, further comprising:obtaining, from each antenna element of the plurality of antenna elements of the layer of antenna elements of the planar array of antenna elements of the 0AM receiver, a second phase value of a received signal of a second 0AM wave of a second 0 AM mode incident at the antenna element to obtain a set of second phase values of the received signals of the second 0AM wave incident at the plurality of antenna elements of the layer of antenna elements, wherein the second 0AM wave is transmitted from the 0AM transmitter;predicting a beamforming elevation angle error of the 0AM receiver based on the set of second phase values of the received signals of the second 0AM wave using a beamforming elevation angle error machine learning model, the beamforming elevation angle error machine learning model trained to predict the elevation angle error based on the set of second phase values of the received signals of the second 0 AM wave;predicting a beamforming azimuth angle error of the 0AM receiver based on the set of second phase values of the received signals of the second 0AM wave using a beamforming azimuth angle error machine learning model, the beamforming azimuth angle error machine learning model trained to predict the beamforming azimuth angle error based on the set of second phase values of the received signals of the second 0AM wave; andadjusting a receiver beam axis of the 0AM receiver based on the predicted beamforming elevation angle error and the predicted beamforming azimuth angle error of the 0AM receiver for 0AM transmitter-receiver directional alignment.

25. The method according to claim 24, wherein said adjusting the receiver beam axis of the 0AM receiver comprises adjusting a beamforming elevation angle parameter value and a beamforming azimuth angle parameter value associated with 0AM receiver based on the predicted beamforming elevation angle error and the predicted beamforming azimuth angle error of the 0AM receiver for 0AM transmitter-receiver directional alignment.

26. The method according to claim 24 or 25, wherein the second 0AM mode is 0AM mode 0.

27. The method according to any one of claims 24 to 26, wherein the second 0AM wave of the second 0AM mode is transmitted from the 0AM transmitter without data payload.

28. The method according to any one of claims 20 to 27, wherein the layer of antenna elements corresponds to a circle of antenna elements of the planar array of antenna elements of the 0AM receiver.

29. The method according to any one of claims 20 to 28, further comprises:adjusting the transmitter beam axis of the 0AM transmitter based on the transmitter beam axis error information for 0AM transmitter-receiver directional alignment; andcontrolling the 0AM transmitter to generate and beamform a multi-mode 0AM wave based on the adjusted transmitter beam axis of the 0AM transmitter.

30. The method according to claim 29, wherein the multi-mode 0AM wave is generated and beamformed according to any one of claims 1 to 9.

31. A system for orbital angular momentum (0AM) transmitter-receiver directional alignment between an 0AM transmitter and an 0AM receiver, the 0AM receiver comprising a planar phased array antenna comprising a planar array of antenna elements, the system comprising:at least one memory; andat least one processor communicatively coupled to the at least one memory and configured to:obtain, from each antenna element of a plurality of antenna elements of a layer of antenna elements of the planar array of antenna elements of the 0AM receiver, a first phase value of a received signal of a first 0AM wave of a first 0AM mode incident at the antenna element to obtain a set of first phase values of the received signals of the first 0AM wave incident at the plurality of antenna elements of the layer of antenna elements, wherein the first OAM wave is transmitted from the 0AM transmitter;predict a distance error between an intersection point of a transmitter beam axis of the OAM transmitter at the planar array of antenna elements of the OAM receiver and a center of the planar array of antenna elements of the OAM receiver based on the set of first phase values of the received signals of the first OAM wave using a distance error machine learning model, the distance error machine learning model trained to predict the distance error based on the set of first phase values of the received signals of the first OAM wave;predict an azimuth angle error associated with the distance error based on the set of first phase values of the received signals of the first OAM wave using an azimuth angle error machine learning model, the azimuth angle error machine learning model trained to predict the azimuth angle error based on the set of first phase values of the received signals of the first OAM wave; andsend transmitter beam axis error information based on the predicted distance error and the predicted azimuth angle error to the OAM transmitter for adjusting a transmitter beam axis of the OAM transmitter for OAM transmitter-receiver directional alignment.

32. The system according to claim 31, whereinthe 0AM transmitter comprises a planar phased array antenna comprising a planar array of antenna elements, andsaid adjusting the transmitter beam axis of the 0 AM transmitter comprises adjusting a beamforming elevation angle parameter value and a beamforming azimuth angle parameter value associated with 0AM transmitter based on the transmitter beam axis error information for 0AM transmitter-receiver directional alignment.

33. The system according to claim 31 or 32, wherein the first 0AM mode is 0AM mode 1.

34. The system according to any one of claims 31 to 33, wherein the first 0 AM wave of the first 0AM mode is transmitted from the 0AM transmitter without data payload.

35. The system according to any one of claims 31 to 34, wherein the at least one processor is further configured to:obtain, from each antenna element of the plurality of antenna elements of the layer of antenna elements of the planar array of antenna elements of the 0AM receiver, a second phase value of a received signal of a second 0AM wave of a second 0AM mode incident at the antenna element to obtain a set of second phase values of the received signals of the second 0AM wave incident at the plurality of antenna elements of the layer of antenna elements, wherein the second 0AM wave is transmitted from the 0AM transmitter;predict a beamforming elevation angle error of the 0AM receiver based on the set of second phase values of the received signals of the second 0AM wave using a beamforming elevation angle error machine learning model, the beamforming elevation angle error machine learning model trained to predict the elevation angle error based on the set of second phase values of the received signals of the second 0AM wave;predict a beamforming azimuth angle error of the 0AM receiver based on the set of second phase values of the received signals of the second 0AM wave using a beamforming azimuth angle error machine learning model, the beamforming azimuth angle error machine learning model trained to predict the beamforming azimuth angle error based on the set of second phase values of the received signals of the second 0AM wave; andadjust a receiver beam axis of the 0AM receiver based on the predicted beamforming elevation angle error and the predicted beamforming azimuth angle error of the 0AM receiver for 0AM transmitter-receiver directional alignment.

36. The system according to claim 35, wherein said adjust the receiver axis of the 0AM receiver comprises adjusting a beamforming elevation angle parameter value and a beamforming azimuth angle parameter value associated with 0AM receiver based on the predicted beamforming elevation angle error and the predicted beamforming azimuth angle error of the 0AM receiver for 0AM transmitter-receiver directional alignment.

37. The system according to claim 35 or 36, wherein the second 0AM mode is 0AM mode 0.

38. The system according to any one of claims 35 to 37, wherein the second 0AM wave of the second 0AM mode is transmitted from the 0AM transmitter without data payload.

39. The system according to any one of claims 31 to 38, wherein the layer of antenna elements corresponds to a circle of antenna elements of the planar array of antenna elements of the 0AM receiver.

40. The system according to any one of claims 31 to 39, further comprising:at least one second memory; andthe at least one second processor communicatively coupled to the at least one second memory and configured to:adjust the transmitter beam axis of the 0AM transmitter based on the transmitter beam axis error information for 0AM transmitter-receiver directional alignment; andcontrol the 0AM transmitter to generate and beamform a multi-mode 0AM wave based on the adjusted transmitter beam axis of the OAM transmitter.

41. The system according to claim 40, wherein the multi-mode OAM wave is generated and beamformed according to any one of claims 1 to 9.

42. An orbital angular momentum (OAM)-based wireless communication system comprising:an OAM transmitter configured to generate and beamform multi-mode 0AM waves, the OAM transmitter comprising a planar phased array antenna comprising a planar array of antenna elements; andan OAM receiver configured to receive and process the multi-mode OAM waves from the OAM transmitter, the OAM receiver comprising a planar phased array antenna comprising a planar array of antenna elements, whereinthe OAM receiver comprises the at least one memory and the at least one processor of the system according to any one of claims 31 to 39 communicatively coupled to the planar phased array antenna of the OAM receiver and configured to perform OAM transmitter-receiver directional alignment43. The OAM-based wireless communication system according to claim 42, wherein the OAM transmitter comprises the at least one second memory and the at least one second processor of the system according to claim 40 communicatively coupled to the planar phased array antenna of the OAM transmitter and configured to perform OAM transmitter-receiver directional alignment.

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