CN110266354B - Signal receiving method of orbital angular momentum wireless communication system - Google Patents

Signal receiving method of orbital angular momentum wireless communication system Download PDF

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CN110266354B
CN110266354B CN201910508015.1A CN201910508015A CN110266354B CN 110266354 B CN110266354 B CN 110266354B CN 201910508015 A CN201910508015 A CN 201910508015A CN 110266354 B CN110266354 B CN 110266354B
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communication system
oam
phase modulation
receiving
beam phase
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CN110266354A (en
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陈睿
龙汶轩
李建东
邹敏强
杨彬
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Xidian University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/084—Equal gain combining, only phase adjustments
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/0848—Joint weighting
    • H04B7/0854—Joint weighting using error minimizing algorithms, e.g. minimum mean squared error [MMSE], "cross-correlation" or matrix inversion

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Abstract

The invention discloses a signal receiving method of an orbital angular momentum wireless communication system, which solves the problem that the prior art can not directly receive signals of an OAM communication system under the condition of misaligned receiving and transmitting ends. The implementation scheme is as follows: constructing an OAM communication system model; determining the coordinates of the circle center of the receiving end; constructing an equivalent channel matrix of an OAM communication system; constructing a wave beam phase modulation matrix of an OAM communication system and performing wave beam phase modulation at a receiving end; and detecting a received signal of the OAM communication system to obtain a multi-mode OAM received signal. The invention provides a beam phase modulation method when an azimuth angle and a pitch angle of a sending end of an OAM communication system coexist for the first time, and provides a received signal detection method of the OAM communication system based on amplitude detection. The invention can eliminate the intermode interference of the OAM channel under the condition of misalignment of the receiving and transmitting ends, realizes the accurate receiving of the signal information of the OAM communication system, and can be used for orbital angular momentum wireless communication.

Description

Signal receiving method of orbital angular momentum wireless communication system
Technical Field
The invention belongs to the technical field of wireless communication, and relates to a signal receiving method, in particular to a signal receiving method of an orbital angular momentum wireless communication system, which can be used for orbital angular momentum wireless communication.
Background
At present, the development of communication technology has led to the rapid rise of the demand of wireless spectrum resources, however, the traditional control of spectrum resources has led to the insufficiency of spectrum utilization, and the problem of insufficient spectrum resources is more and more serious. The dimensions of amplitude, frequency, phase and polarization state in the electromagnetic wave properties have been used for signal characterization to improve transmission capacity. On the existing basis, the channel capacity cannot be expanded by continuously adopting a mode of increasing the representation dimensionality of electromagnetic waves, and the spectrum efficiency can be further improved only by methods of spectrum compression, modulation rate improvement or modulation order improvement and the like. The orbital angular momentum OAM is a new transmission dimension, can transmit multiple channels of information at the same time in the same frequency band, can effectively solve the problem of shortage of spectrum resources, and has attracted wide attention at present.
One of the key technologies for constructing an OAM communication system is how to achieve accurate reception of OAM signals. The premise of accurate signal reception of the OAM communication system is perfect alignment between the transmit beam and the receive beam, which makes the beam phasing at the receiving end of the OAM communication system an emerging research direction in recent years. People have already carried on the preliminary study to the receiving end beam phasing method of OAM communication system, have already studied and carried on the beam phasing to the communication system when there is single pitch angle in sending end and receiving end, however, the relative position of sending end and receiving end is decided by sending end azimuth angle and pitch angle relative to receiving end together, the existing research result only utilizes the sending end to carry on the beam phasing to the pitch angle of receiving end, only can be used in OAM communication system under certain special circumstances, not suitable for OAM communication system under the general circumstances, have limitations. In addition, the OAM communication system must utilize a signal detection scheme suitable for the scene of orbital angular momentum communication to achieve signal reception at the receiving end, however, no report is yet made about the method for detecting the received signal of the OAM communication system at present, or the method is in a blank stage, the above beam phase modulation method has no versatility and no detection scheme, so that the practical application of the vortex electromagnetic wave in wireless communication is limited.
Disclosure of Invention
In view of the above-mentioned shortcomings of the prior art, an object of the present invention is to provide a signal receiving method for an orbital angular momentum wireless communication system with general applicability.
The invention relates to a signal receiving method of an orbital angular momentum wireless communication system, which is characterized by comprising the following steps:
(1) constructing an OAM communication system model: by two radii, each being RtAnd RrThe uniform circular array is used as a sending end and a receiving end of the OAM communication system, and a first coordinate system Z ' -X ' OY ' of the sending end is established by taking the circle center of the sending end as an original point and the plane where the sending array is located as an X ' OY ' plane at the sending end; at the receiving end, the circle center of the receiving end is used as the origin, and the plane where the receiving array is located is used as the plane
Figure BDA0002092482440000021
Plane establishment of receiving end coordinate system
Figure BDA0002092482440000022
The center of a sending end is positioned
Figure BDA0002092482440000023
The coordinates in the coordinate system are represented as
Figure BDA0002092482440000024
Wherein r is the distance between the center of the circle of the transmitting end and the center of the circle of the receiving end,
Figure BDA0002092482440000025
is the azimuth angle of the transmitting end, and alpha is the pitch angle of the transmitting end; transmitting end transmitting information signal vector s (l)
s(l)＝[s(l1),s(l2),…,s(lv),…,s(lV)]T,
Wherein, s (l)v) Information signals transmitted by different modes;
(2) determining the coordinates of the circle center of the receiving end: establishing a second coordinate system Z-XOY of the transmitting end by taking the circle center of the transmitting end as an origin and a plane parallel to the receiving array as XOY at the transmitting end, and expressing the coordinate of the circle center of the receiving end in the second coordinate system Z-XOY of the transmitting end as (r, theta, alpha) according to the angle relationship between the coordinate systems of the transmitting end and the receiving end, wherein theta is an included angle between an X axis and an X' axis, namely an azimuth angle of the circle center of the receiving end in the coordinate system Z-XOY;
(3) constructing an equivalent channel matrix of an OAM communication system: a second coordinate system Z-XO at the transmitting end by using the circle center of the receiving endCoordinates (r, theta, alpha) in Y, and constructing an equivalent channel matrix H of the OAM communication systemOAM＝[hOAM(u,v)]V×VWherein (u, v) indicates that the element is located in the equivalent channel matrix HOAMThe subscript V × V denotes an equivalent channel matrix HOAMIs a square matrix of V rows and V columns;
(4) constructing a wave beam phase modulation matrix of an OAM communication system: constructing a beam phase modulation matrix B to eliminate an equivalent channel matrix HOAMEach element hOAM(u, v) terms relating to the receiver azimuth angle θ and the pitch angle α;
(5) performing beam phase modulation on the OAM communication system: performing beam phase modulation on a receiving end of the OAM communication system by using a beam phase modulation matrix B to obtain an equivalent channel matrix H 'of the OAM communication system after the beam phase modulation'OAM；
(6) And (3) carrying out received signal detection on the OAM communication system: equivalent channel matrix H 'of OAM communication system after beam phase modulation'OAMPerforming Taylor expansion on each element in the wave beam to obtain an estimated value H of an equivalent channel matrix of the OAM communication system after the wave beam is modulatedeffUsing the matrix estimate HeffAmplitude detection is carried out at a receiving end to obtain a multi-mode OAM receiving signal
Figure BDA0002092482440000026
The invention realizes the positive alignment of the wave beams of the receiving and transmitting ends by carrying out the wave beam phase modulation matrix design at the receiving end, and simultaneously, the invention utilizes the estimated value H of the equivalent channel matrix of the OAM communication system after the wave beam phase modulationeffThe signal detection is carried out at the receiving end, the signal reception of the OAM communication system is realized for the first time, and a foundation is laid for the practical application of the OAM communication system.
Compared with the prior art, the invention has the following advantages:
1. realizing the beam phase modulation of a general OAM communication system: the invention provides an expression of a beam phase modulation matrix related to an azimuth angle and a pitch angle of a sending end, successfully realizes diagonalization of an equivalent channel matrix after beam phase modulation of an OAM communication system, and provides a method for beam phase modulation when the azimuth angle and the pitch angle of the sending end are any values in the OAM communication system.
2. And (3) reducing the complexity of the communication system: compared with the traditional MIMO communication system, the signal receiving scheme provided by the invention can directly detect the signal without channel estimation, so that the complexity of the OAM communication system for receiving the signal by applying the scheme is greatly reduced compared with the traditional MIMO system, and a foundation is laid for the practical application of the OAM communication system.
3. The method for detecting the received signal of the OAM communication system based on amplitude detection is firstly provided: compared with the traditional signal detection methods such as zero forcing detection, minimum mean square error detection and the like, the amplitude detection method provided by the invention has the advantages of smaller calculated amount and simpler realization.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
fig. 2 is a schematic diagram of an OAM communication system model used in the present invention;
FIG. 3 is a diagram illustrating an angle transformation relationship between coordinate systems of a transmitting end and a receiving end in the present invention;
fig. 4 shows the capacity of the system after beam-phasing by the method of the present invention under different snr conditions.
Fig. 5 shows the bit error rate of signal reception under different snr conditions by using the method proposed by the present invention.
Detailed Description
The embodiments and effects of the present invention are described in detail below with reference to the accompanying drawings.
Example 1
Because dimensions such as amplitude, frequency, phase, polarization state and the like in the plane electromagnetic wave attribute are used for signal representation, it is not practical to improve the capacity of a communication system by means of the existing signal modulation mode. OAM is used as a new transmission dimension, can effectively solve the problem of spectrum resource shortage, and has become a technical hotspot of future communication systems. One of the key points in constructing an OAM communication system is to achieve alignment between the transmitting and receiving ends of the OAM communication system. The existing OAM communication system receiving and transmitting end alignment technology can only realize the beam phase modulation when the transmitting end and the receiving end only have pitch angles, is not suitable for the OAM communication system under the general condition, and has limitation. In addition, a signal detection scheme suitable for an orbital angular momentum communication scene is also another key technology of an OAM communication system, however, research on a signal receiving detection method of the OAM communication system is still in a blank stage, so that practical application of vortex electromagnetic waves in wireless communication is limited. Therefore, the present invention develops research and exploration, and proposes a signal receiving method of an orbital angular momentum wireless communication system, referring to fig. 1, comprising the following steps:
(1) constructing an OAM communication system model: by a radius RtThe uniform circular array is used as a sending end of an OAM communication system, and the radius of the uniform circular array is RrThe uniform circular array of the OAM communication system is used as a sending end of the OAM communication system, and the uniform circular arrays of the sending end and the receiving end both comprise N array elements. And establishing a first coordinate system Z ' -X ' OY ' of the transmitting end by taking the circle center of the transmitting end as an original point and the plane where the transmitting array is located as an X ' OY ' plane at the transmitting end. At the receiving end, the circle center of the receiving end is used as the origin, and the plane where the receiving array is located is used as the plane
Figure BDA0002092482440000041
Plane establishment of receiving end coordinate system
Figure BDA0002092482440000042
The center of a sending end is positioned
Figure BDA0002092482440000043
The coordinates in the coordinate system are represented as
Figure BDA0002092482440000044
Wherein r is the distance between the center of the circle of the transmitting end and the center of the circle of the receiving end,
Figure BDA0002092482440000045
is the azimuth angle of the transmitting end, and alpha is the pitch angle of the transmitting end. Transmitting end transmitting information signal vector s (l)
s(l)＝[s(l1),s(l2),…,s(lv),…,s(lV)]T,
Wherein, s (l)v) Are information signals transmitted using different modalities.
(2) Determining the coordinates of the circle center of the receiving end: establishing a second coordinate system Z-XOY of the transmitting end at the transmitting end by taking the circle center of the transmitting end as an origin and taking a plane parallel to the receiving array as XOY, and expressing the coordinate of the circle center of the receiving end in the second coordinate system Z-XOY of the transmitting end as (r, theta, alpha) according to the angular relationship between the coordinate systems of the transmitting end and the receiving end, wherein theta is an included angle between an X axis and an X' axis, namely an azimuth angle of the circle center of the receiving end in the coordinate system Z-XOY, and a pitch angle alpha and the circle center of the transmitting end are in the same angle
Figure BDA0002092482440000046
The pitch angles in the coordinate system are the same, namely the pitch angles of the circle centers of the transmitting and receiving ends in the two coordinate systems are the same. Compared with the existing OAM communication technology, the method establishes three coordinate systems at the transmitting end and the receiving end, and provides the coordinate of the circle center of the receiving end in the second coordinate system of the transmitting end by using the included angle between the first coordinate system of the transmitting end and the second coordinate system of the transmitting end, so that the relative position of the transmitting end and the receiving end is completely determined, in other words, the method determines the position of the receiving end relative to the transmitting end by using the azimuth angle and the pitch angle of the transmitting end for the first time.
(3) Constructing an equivalent channel matrix of an OAM communication system: constructing an equivalent channel matrix H of the OAM communication system by using coordinates (r, theta, alpha) of the circle center of the receiving end in a second coordinate system Z-XOY of the transmitting endOAM＝[hOAM(u,v)]V×VWherein (u, v) indicates that the element is located in the equivalent channel matrix HOAMLine u ofColumn V, subscript V × V denotes the equivalent channel matrix HOAMIs a square matrix of V rows and V columns.
(4) Constructing a wave beam phase modulation matrix of an OAM communication system: observing equivalent channel matrix H of OAM communication systemOAMIn the form of finding an equivalent channel matrix HOAMEach element hOAM(u, v) terms relating to receiver azimuth θ and elevation α result in HOAMInstead of a diagonal matrix, a beam-phase modulation matrix B is constructed to eliminate an equivalent channel matrix HOAMEach element hOAM(u, v) terms relating to the receiver azimuth angle θ and the pitch angle α. Compared with the prior OAM communication system which only can utilize the pitch angle of the sending end to perform beam phase modulation, the invention utilizes the azimuth angle and the pitch angle of the sending end to determine the beam phase modulation matrix of the OAM communication system, can realize the beam phase modulation when the sending end and the receiving end have the azimuth angle and the pitch angle at the same time, and is suitable for more common scenes.
(5) Performing beam phase modulation on the OAM communication system: performing beam phase modulation on a receiving end of the OAM communication system by using a beam phase modulation matrix B to obtain an equivalent channel matrix H 'of the OAM communication system after the beam phase modulation'OAM. Compared with the existing OAM wave beam phase modulation technology, the invention utilizes the wave beam phase modulation matrix related to the azimuth angle and the elevation angle of the sending end to perform wave beam phase modulation at the receiving end, breaks through the limitation that the prior art can only perform wave beam phase modulation when the elevation angle exists between the sending end and the receiving end, and realizes the diagonalization of the equivalent channel matrix of the OAM communication system in a common scene.
(6) And (3) carrying out received signal detection on the OAM communication system: equivalent channel matrix H 'of OAM communication system after beam phase modulation'OAMPerforming Taylor expansion on each element in the wave beam to obtain an estimated value H of an equivalent channel matrix of the OAM communication system after the wave beam is modulatedeffUsing the matrix estimate HeffAmplitude detection is carried out at a receiving end to obtain a multi-mode OAM receiving signal
Figure BDA0002092482440000051
Therefore, signal reception of the orbital angular momentum wireless communication system is completed. The invention provides a received signal detection method of an OAM communication system, which utilizes wavesIn addition, compared with traditional detection algorithms such as zero forcing detection, minimum mean square error detection and the like, the amplitude detection provided by the invention has lower calculation complexity, so that the practical application of the vortex electromagnetic wave in wireless communication becomes possible.
The invention provides an integral technical scheme of a signal receiving method of an orbital angular momentum wireless communication system.
The idea of the technical scheme of the invention is as follows: an OAM communication system is constructed by using uniform circular antenna array UCA, a beam phase modulation matrix is constructed by observing the form of an equivalent channel matrix of the OAM communication system, beam phase modulation is carried out at a receiving end to realize the alignment of the receiving and transmitting beam arrays of the OAM communication system, and then the amplitude detection is carried out on a received signal by using the estimated value of the equivalent channel matrix of the OAM communication system after the beam phase modulation to realize the accurate receiving of the signal.
The invention provides an expression of a beam phase modulation matrix related to the azimuth angle and the pitch angle of a sending end by observing the form of an equivalent channel matrix of an OAM communication system, provides a beam phase modulation method when the azimuth angle and the pitch angle exist between the sending end and a receiving end, and breaks through the limitation that the beam phase modulation can be carried out only when a single pitch angle exists at the sending end in the prior art. In addition, the invention provides a received signal detection method of the OAM communication system, which utilizes the estimated value of the equivalent channel matrix of the OAM communication system after the beam phase modulation to carry out amplitude detection on the received signal, thereby realizing the received signal detection of the receiving end of the OAM communication system.
Example 2
The signal receiving method of the orbital angular momentum wireless communication system is the same as that of embodiment 1, wherein the step (3) is used for constructing an equivalent channel matrix H of the OAM communication systemOAMEach element h in (1)OAM(u, v) calculated by the following formula：
Figure BDA0002092482440000061
Wherein i is an imaginary unit,
Figure BDA0002092482440000062
is a constant coefficient, beta is a channel fading coefficient, N is the number of array elements at the transmitting and receiving ends, RrIs the radius of the receiving end circular array, RtThe radius of a transmitting end circular array is defined, k is a subcarrier used for transmitting signals, q is equal to n-m, m is an array element serial number of a receiving end circular array, n is an array element serial number of the transmitting end circular array, and t is equal to lu-lvRepresenting the difference of the modes used for signal transmission and signal reception,/vModality used for signalling,/uFor the mode of signal reception, (r, theta, alpha) is the coordinate of the center of the circle of the receiving end in the Z-XOY coordinate system.
The invention provides the quantitative representation of the equivalent channel matrix of the OAM communication system, converts the plane wave channel in the traditional communication system into the OAM channel carrying orbital angular momentum, expands the modulation mode of the transmitted signal, enables the transmitting and receiving ends to simultaneously transmit multi-channel information in the same frequency band, and can effectively solve the problem of frequency spectrum resource shortage.
Example 3
The signal receiving method of the orbital angular momentum wireless communication system is the same as that in the embodiment 1-2, wherein the wave beam phase modulation matrix B of the OAM communication system is constructed in the step (4), and is calculated by the following formula:
Figure BDA0002092482440000063
wherein b is a row vector of a wave beam phase modulation matrix of the OAM communication system,
Figure BDA0002092482440000064
Figure BDA0002092482440000065
i is OAM communication system beamThe N-dimensional full column vector of the phase modulation matrix.
The invention provides the beam phase modulation matrix related to the azimuth angle and the pitch angle of the sending end by the form of the equivalent channel matrix of the OAM communication system, lays a foundation for the positive alignment of the sending beam and the receiving beam, namely, the diagonalization of the equivalent channel matrix can be realized by utilizing the beam phase modulation matrix provided by the invention to carry out the beam phase modulation. The beam phase modulation method provided by the invention breaks through the limitation that the beam phase modulation can be carried out only when a single pitch angle exists at a sending end in the prior art, realizes the beam phase modulation under the condition that an azimuth angle and a pitch angle exist between the sending end and a receiving end, and lays a foundation for the signal reception of a general OAM communication system.
Example 4
The signal receiving method of the orbital angular momentum wireless communication system is the same as that in embodiments 1 to 3, wherein the equivalent channel matrix H 'of the wave beam modulated OAM communication system described in step (5)'OAMIs a diagonal matrix of which each diagonal element h'OAM(v, v) is represented as follows:
Figure BDA0002092482440000071
the invention utilizes the wave beam phase modulation matrix to carry out the wave beam phase modulation at the receiving end of the OAM communication system, eliminates the items related to the azimuth angle and the pitch angle of the sending end in the equivalent channel matrix, obtains the equivalent channel matrix of the OAM communication system after the wave beam phase modulation, realizes the diagonalization of the equivalent channel matrix of the OAM communication system, namely the sending wave beam and the receiving wave beam realize the alignment after the wave beam phase modulation is carried out on the wave beam by utilizing the method provided by the invention, and lays a foundation for the signal detection of the receiving end of the subsequent OAM communication system.
Example 5
The signal receiving method of the orbital angular momentum wireless communication system is the same as the embodiments 1 to 4, wherein the estimated value H of the equivalent channel matrix of the OAM communication system after the beam phase modulation is described in the step (6)effIs a diagonal matrix, each diagonal element h thereofeff(v, v) is represented as follows:
Figure BDA0002092482440000072
wherein, S is an estimated value H of an equivalent channel matrix of the OAM communication system after beam phase modulationeffThe coefficient of (a) is determined,
Figure BDA0002092482440000073
tau is an estimated value H of an equivalent channel matrix of the OAM communication system after beam phase modulationeffτ ═ min { | lv|,N-|lv|}。
The invention provides the quantitative calculation of the equivalent channel matrix estimated value in the received signal detection method of the OAM communication system, the amplitude detection is carried out on the received signal by utilizing the estimated value of the equivalent channel matrix of the OAM communication system after the beam phase modulation, the blank in the field of the received signal detection method of the OAM communication system is made up, in addition, compared with the traditional detection algorithms such as zero forcing detection, minimum mean square error detection and the like, the amplitude detection calculation provided by the invention is simpler and lower in complexity, and the practical application of the vortex electromagnetic wave in the wireless communication becomes possible.
A more detailed and complete example is given below to further illustrate the invention:
example 6
The signal receiving method of the orbital angular momentum wireless communication system is the same as the embodiments 1-5, and referring to fig. 1, the implementation steps of the embodiment are as follows:
step 1, constructing an OAM communication system model.
The OAM communication system in this example uses a UCA-based V-dimensional modal multiplexing communication system. Referring to fig. 2, the OAM communication system of the present invention uses an array element of N and radii of R respectively because of a simple structure and easy multiplexing of multi-modal vortex electromagnetic wavestAnd RrThe uniform circular antenna array UCA is used as a sending end and a receiving end of the system, and the number N of the receiving and sending antenna elements can be 4, 8, 16 and the like according to an actual common OAM communication system model. The transmitting end transmits an information signal vector s (l) ═ s (l)1),s(l2),…,s(lv),…,s(lV)]TWherein s (l)v) Is an information signal vector transmitted by different modes, and the mode lvAnd the number N of array elements at the transmitting and receiving ends needs to satisfy the relationship:
Figure BDA0002092482440000081
according to the actual common OAM communication system model, the mode l for transmitting and receiving signalsvCan be 0, ± 1, ± 2, ± 3, etc.; in actual communication, the positive alignment of a receiving end and a sending end is difficult to realize, and for convenience of analysis, the invention considers the condition that the sending end has non-parallel dislocation of an azimuth angle and a pitch angle relative to the receiving end as a conventional condition, so the invention continues to use an OAM communication non-parallel error model.
And step 2, determining the circle center coordinate of the transmitting end of the OAM communication system.
Referring to fig. 3, a transmitting end first coordinate system Z ' -X ' OY ' is established with a transmitting end circle center as an origin O, a plane where a transmitting end UCA is located as an X ' OY ' plane, a transmitting end second coordinate system Z-XOY is established with the transmitting end circle center as the origin O, a plane parallel to a receiving end UCA as an XOY plane, and a receiving end circle center as the origin
Figure BDA0002092482440000082
The receiving end UCA is located on the plane
Figure BDA0002092482440000083
Plane establishment of receiving end coordinate system
Figure BDA0002092482440000084
Coordinate system with transmitting end circle center at receiving end
Figure BDA0002092482440000085
Has the coordinates of
Figure BDA0002092482440000086
Wherein r is the distance between the center of the circle of the transmitting end and the center of the circle of the receiving end,
Figure BDA0002092482440000087
is the azimuth angle of the transmitting endAnd alpha is the pitch angle of the transmitting end, r is usually within the sight distance range according to the actual common OAM communication system model,
Figure BDA0002092482440000088
and alpha is usually in the range of [0 DEG, 10 DEG ]]As can be seen from fig. 2, the first,
Figure BDA0002092482440000089
the angle BOC ═ α, and as can be seen from the theory of triccosine, the angle between the X axis and the X' axis can be expressed as:
Figure BDA00020924824400000810
therefore, the center of the receiving end circle
Figure BDA00020924824400000811
The coordinates under the second coordinate system Z-XOY of the transmitting end are (r, theta, alpha), that is, the azimuth angle of the circle center of the receiving end in the second coordinate system Z-XOY of the transmitting end is theta, the pitch angle alpha of the circle center of the receiving end and the coordinate system of the circle center of the transmitting end in the receiving end are theta
Figure BDA00020924824400000812
The pitch angles in the coordinate system are the same, namely the pitch angles of the circle centers of the transmitting and receiving ends in the two coordinate systems are the same. The invention establishes three coordinate systems at the sending end and the receiving end together, wherein two coordinate systems are positioned at the sending end, and the other coordinate system is positioned at the receiving end. The method and the device utilize the included angle between the first coordinate system of the sending end and the second coordinate system of the sending end to determine the coordinate of the circle center of the receiving end in the second coordinate system of the sending end based on the three cosine theorem, so that the relative position between the sending end and the receiving end is completely determined, in other words, the position of the receiving end relative to the sending end is accurately described by the azimuth angle and the pitch angle of the sending end for the first time.
And 3, constructing an equivalent channel matrix of the OAM communication system.
An OAM communication system equivalent channel matrix is represented as:
HOAM＝FHFH, <1>
wherein, F is a Fourier matrix of the OAM communication system, and F is [ F ]H(l1),fH(l2),…,fH(lv),…,fH(lV)]H，
Figure BDA00020924824400000813
lvFor the mode used for signalling, H ═ Hm,n]N×NIs a fading matrix of the radio frequency channel in free space, each element H in Hm,nExpressed as:
Figure BDA0002092482440000091
where i is an imaginary unit, β is a free space radio frequency channel fading coefficient, k is 2 π f/c is the wavenumber, f is the frequency used, c is the speed of light in vacuum, dm,nThe distance between the nth (N is more than or equal to 1 and less than or equal to N) array element of the transmitting end UCA and the mth (N is more than or equal to 1 and less than or equal to N) array element of the receiving end UCA is represented by the following expression:
Figure BDA0002092482440000092
the invention constructs the equivalent channel matrix of the OAM communication system by utilizing the Fourier matrix of the OAM communication system, converts a plane wave channel in the traditional communication system into the OAM channel carrying orbital angular momentum, expands the modulation mode of a transmitted signal, and enables the OAM communication system to simultaneously transmit multi-channel information in the same frequency band.
And 4, constructing a beam phase modulation matrix according to the equivalent channel matrix of the OAM communication system.
Will be a formula<1>Medium equivalent channel matrix HOAMEach element h in (1)OAM(u, v) is expressed as:
Figure BDA0002092482440000093
wherein the content of the first and second substances,
Figure BDA0002092482440000094
is an equivalent channel matrix HOAMThe constant coefficient in (q) n-m represents the difference of the array element numbers of the transmitting and receiving ends, and t (l)u-lvRepresenting the difference of the modes used for signal transmission and signal reception,/vModality used for signalling,/uThe modality used for signal reception.
The last summation term in equation <2> is defined as:
Figure BDA0002092482440000095
it is apparent that ζ (0,0,0) is 1 when α is 0, θ is 0, and t is 0, ζ (0,0, t) is 0 when α is 0, θ is 0, and t is not equal to 0, and ζ (α, θ, t) is not equal to 0 when α is not equal to 0 or θ is not equal to 0. Based on the above discussion, to ensure the equivalent channel matrix HOAMThe non-diagonal elements in (1) are constantly zero, and the beam phase modulation matrix is designed as follows:
Figure BDA0002092482440000101
wherein b is a row vector of a wave beam phase modulation matrix of the OAM communication system,
Figure BDA0002092482440000102
Figure BDA0002092482440000103
i is an N-dimensional full-column vector of a wave beam phase modulation matrix of the OAM communication system. Observation formula<2>In the form of an equivalent channel matrix of a medium OAM communication system, the invention determines an item which causes the equivalent channel matrix to be a non-diagonal matrix, and provides a beam phase modulation matrix related to the azimuth angle and the pitch angle of a transmitting end on the basis of the item, thereby laying a foundation for the positive alignment of a transmitting beam and a receiving beam, namely realizing the diagonalization of the equivalent channel matrix by utilizing the beam phase modulation matrix provided by the invention to carry out the beam phase modulation.
And 5, performing beam phase modulation on the receiving end.
Performing beam phase modulation on a receiving end by using a formula <3>, and expressing an equivalent channel matrix after the beam phase modulation of the OAM communication system as follows:
H′OAM＝(B⊙F)HFU；
wherein, H'OAMIs a V multiplied by V diagonal matrix, each diagonal element h'OAM(v, v) is expressed as:
Figure BDA0002092482440000104
according to the invention, the wave beam phase modulation matrix is utilized at the receiving end of the OAM communication system to carry out the wave beam phase modulation, so that the item causing the matrix non-diagonalization in the equivalent channel matrix is successfully eliminated, the equivalent channel matrix of the OAM communication system after the wave beam phase modulation is obtained, the positive alignment of the sending wave beam and the receiving wave beam of the OAM communication system is realized, the problem that the OAM communication system cannot normally communicate under the non-aligned condition is solved, the system reachable rate and the system capacity of the OAM communication system under the non-aligned condition are greatly improved, and a good foundation is laid for the practical application of the OAM communication system.
And 6, determining an estimated value of an equivalent channel matrix of the OAM communication system after the wave beam phase modulation.
According to Taylor expansion
Figure BDA0002092482440000105
Will be a formula<4>Takk unfolding, expressed as:
Figure BDA0002092482440000106
Figure BDA0002092482440000111
ignoring the higher order infinitesimal term in equation <5>, it is approximately expressed as:
Figure BDA0002092482440000112
wherein, S is an estimated value H of an equivalent channel matrix of the OAM communication system after beam phase modulationeffThe coefficient of (a) is determined,
Figure BDA0002092482440000113
according to an actual common OAM communication system model, S is usually close to 0, and tau is an estimated value H of an equivalent channel matrix of the OAM communication system after beam phase modulationeffτ ═ min { | lv|,N-|lvIn an actual OAM communication system, the value of tau is determined by the mode l used for sending signalsvAnd the number N of array elements at the transmitting/receiving end is determined by using a formula<6>Obtaining an estimated value H of an equivalent channel matrix of the OAM communication system after beam phase modulationeff. The invention utilizes Taylor expansion to give quantitative calculation of the equivalent channel matrix estimation value of the OAM communication system, and lays a foundation for the received signal detection of the receiving end of the OAM communication system.
And 7, carrying out amplitude detection on the received signal.
After the receiving end completes the beam phase modulation, the signal vector required for the receiving end to perform amplitude detection is expressed as:
y(l)＝(B⊙F)HFU·s(l)+n(l), <7>
wherein y (l) ═ y (l)1),y(l2),…,y(lv),…,y(lV)]TFor the signals of different modes of amplitude detection required by the receiving end, n (l) is an additional noise vector under each mode.
Estimation value H of equivalent channel matrix of OAM communication system after utilizing wave beam phase modulationeffDirect pair formula<7>And (3) amplitude detection is carried out:
Figure BDA0002092482440000114
obtained
Figure BDA0002092482440000115
Is receivingAn estimate of the signal. Therefore, accurate receiving of OAM communication system signals can be achieved. In an actual OAM communication system, the accuracy of the received signal is in communication with the mode l used in the OAM communication systemvThe factors such as the signal-to-noise ratio of the system are related, and as the diffusion of waves in free space propagation is severe when the mode of vortex electromagnetic waves is high, the OAM communication system generally adopts 0, ± 1, ± 2 modes for communication in order to reduce the error rate of the OAM communication system. The invention utilizes the estimated value of the equivalent channel matrix of the OAM communication system after the wave beam phase modulation to carry out amplitude detection on the received signal, successfully obtains the estimated value of the transmitted signal at the receiving end, realizes the accurate receiving of the transmitted signal of the OAM communication system, makes up the blank of the field of the method for detecting the received signal of the OAM communication system, and in addition, compared with the traditional detection algorithms such as zero forcing detection, minimum mean square error detection and the like, the amplitude detection provided by the invention is simpler in calculation and lower in complexity, thereby enabling the practical application of the vortex electromagnetic wave in wireless communication to be possible.
The invention provides an expression of a beam phase modulation matrix related to an azimuth angle and a pitch angle of a sending end, successfully realizes diagonalization of an equivalent channel matrix after beam phase modulation of an OAM communication system, and provides a method for beam phase modulation when the azimuth angle and the pitch angle of the sending end are any values in the OAM communication system. In addition, the invention provides a method for carrying out amplitude detection at the receiving end of the OAM communication system by utilizing the estimated value of the equivalent channel, compared with the traditional signal detection methods such as zero forcing detection, minimum mean square error detection and the like, the amplitude detection method provided by the invention has the advantages of smaller calculated amount and simpler realization, makes up the blank of the OAM communication system in the field of signal receiving and detection, and enables the practical application of the OAM communication system to be possible.
The technical effect of the present invention is further explained by simulation and data thereof as follows:
example 7
The signal receiving method of the orbital angular momentum wireless communication system is the same as that of embodiments 1 to 6.
Simulation conditions are as follows:
the number N of UCA array elements at a receiving end is 9, a subcarrier f used for transmitting signals is 9.024GHz, a corresponding k is 189, the modes used for transmitting and receiving the signals are l-2, -1, …,0, …,2, and the azimuth angle of the transmitting end is
Figure BDA0002092482440000121
Is 7 degrees and the pitch angle alpha of the transmitting end is 7 degrees.
Simulation content:
simulation 1, under the condition that the signal-to-noise ratio is [0dB,30dB ], the scheme provided by the invention is used for performing beam phase modulation at a receiving end, the achievable rate result of the OAM communication system is shown in fig. 4, and fig. 4 shows the capacity of the system after the beam phase modulation is performed by using the method provided by the invention under the condition of different signal-to-noise ratios.
In fig. 4, the abscissa is the signal-to-noise ratio of the receiving end of the OAM communication system, the ordinate is the reachable rate of the OAM communication system, the square frame line at the lower part is the reachable rate when the OAM communication system is not beam-phased under the case that the communication mode is 5 hours misalignment, the plus line at the lower part is the reachable rate when the OAM communication system is not beam-phased under the case that the communication mode is 4 hours misalignment, the circle line at the upper part is the reachable rate of the OAM communication system under the case that the communication mode is 5 hours alignment, the triangle line at the upper part is the reachable rate of the OAM communication system under the case that the communication mode is 4 hours alignment, the cross line at the upper part is the reachable rate of the OAM communication system after beam-phased by the proposed method under the case that the OAM communication mode is 5 hours misalignment, and the star line at the upper part is the reachable rate after beam-phased by the proposed method under the case that the OAM communication system is 4 hours misalignment. Compared with the square frame line and the plus sign line at the lower part of the figure 4, the reachable rates of the cross sign line and the star sign line are obviously improved and are very close to those of the circle line and the triangle line, which shows that after the method provided by the invention is used for carrying out the wave beam phase modulation on the OAM communication system, the reachable rate of the OAM communication system is obviously improved under the conditions of different signal-to-noise ratios, and is close to the reachable rate of the OAM communication system under the condition that the receiving and transmitting ends are aligned, and the effectiveness of the wave beam phase modulation method provided by the invention is proved. The invention can well solve the problem of beam alignment of the transmitting and receiving ends of the OAM communication system by utilizing the beam phase modulation.
Example 8
The signal receiving method of the orbital angular momentum wireless communication system is the same as the embodiments 1 to 6, and the simulation conditions are the same as the embodiment 7.
Simulation 2, under the condition that the signal-to-noise ratio is [0dB,30dB ], the proposed scheme is used for signal detection at the receiving end, the error rate of the received signal of the OAM communication system is as shown in fig. 5, and fig. 5 is the error rate of the signal reception under the condition of different signal-to-noise ratios by using the method proposed by the present invention.
In fig. 5, the abscissa is the signal-to-noise ratio of the receiving end of the OAM communication system, the ordinate is the error rate of the OAM communication system, the asterisk line is the error rate when the OAM communication system communicates by using 5 modes under the condition of positive alignment, the plus sign line is the error rate when the OAM communication system communicates by using 4 modes under the condition of positive alignment, the box line is the error rate of the receiving end after performing beam phase modulation and received signal detection by using the method provided by the present invention for the OAM communication system that communicates by using 5 modes under the condition of non-positive alignment, and the circle line is the error rate of the receiving end after performing beam phase modulation and received signal detection by using the method provided by the present invention for the OAM communication system that communicates by using 4 modes under the condition of non-positive alignment. As can be seen from fig. 5, the asterisk line and the square frame line are almost overlapped, the difference between the plus line and the circle line is very small under the condition of low signal-to-noise ratio, and the plus line and the circle line are also close to overlap under the condition of high signal-to-noise ratio, which shows that after the beam phase modulation method provided by the present invention is used to perform the beam phase modulation on the OAM communication system, the bit error rate of the system is very close to the bit error rate of the OAM communication system under the condition that the transceiving end is aligned, and the effectiveness of the beam phase modulation method provided by the. Meanwhile, the asterisk line, the square line, the plus sign line and the circle line are all less than 0.1 at 0dB and are continuously reduced along with the increase of the abscissa, which shows that the error rate of the OAM communication system is kept at a lower value under the condition of low signal-to-noise ratio, and the error rate is continuously reduced along with the increase of the signal-to-noise ratio, when the error rate is reduced, the error rate is reduced along with the increase of the signal-to-noise ratioWhen the signal-to-noise ratio is 30dB, the error rate of the OAM communication system reaches 10-2Therefore, the method for detecting the received signals can accurately restore the transmitted signals at the receiving end, and realizes the accurate communication of the OAM communication system.
In summary, the signal receiving method of the orbital angular momentum wireless communication system disclosed by the invention solves the problem that the prior art cannot directly receive the signal of the OAM communication system under the condition of misaligned receiving and transmitting ends. The implementation scheme is as follows: constructing an OAM communication system model; determining the coordinates of the circle center of the receiving end; constructing an equivalent channel matrix of an OAM communication system; constructing a wave beam phase modulation matrix of an OAM communication system and performing wave beam phase modulation at a receiving end; and detecting a received signal of the OAM communication system to obtain a multi-mode OAM received signal. The invention provides a beam phase modulation method when an azimuth angle and a pitch angle of a sending end of an OAM communication system coexist for the first time, and provides a received signal detection method of the OAM communication system based on amplitude detection for the first time. The invention can eliminate the intermode interference of the OAM channel under the condition of misalignment of the receiving and transmitting ends, realizes the accurate receiving of the signal information of the OAM communication system, and can be used for orbital angular momentum wireless communication.

Claims (3)

1. A signal receiving method of an orbital angular momentum wireless communication system is characterized by comprising the following steps:
(1) constructing an OAM communication system model: by two radii, each being RtAnd RrThe uniform circular array is used as a sending end and a receiving end of the OAM communication system, and a first coordinate system Z ' -X ' OY ' of the sending end is established by taking the circle center of the sending end as an original point and the plane where the sending array is located as an X ' OY ' plane at the sending end; at the receiving end, the circle center of the receiving end is used as the origin, and the plane where the receiving array is located is used as the plane
Figure FDA0002966431930000011
Plane establishment of receiving end coordinate system
Figure FDA0002966431930000012
Coordinate system with the center of circle of the transmitting end at the receiving end
Figure FDA0002966431930000013
The coordinates in (A) are expressed as
Figure FDA0002966431930000014
Wherein r is the distance between the center of the circle of the transmitting end and the center of the circle of the receiving end,
Figure FDA0002966431930000015
is the azimuth angle of the transmitting end, and alpha is the pitch angle of the transmitting end; transmitting end transmitting information signal vector s (l)
s(l)＝[s(l1),s(l2),…,s(lv),…,s(lV)]T,
Wherein, s (l)v) Information signals transmitted by different modes;
(2) determining the coordinates of the circle center of the receiving end: establishing a second coordinate system Z-XOY of the transmitting end by taking the circle center of the transmitting end as an origin and a plane parallel to the receiving array as XOY at the transmitting end, and expressing the coordinate of the circle center of the receiving end in the second coordinate system Z-XOY of the transmitting end as (r, theta, alpha) according to the angle relationship between the coordinate systems of the transmitting end and the receiving end, wherein theta is an included angle between an X axis and an X' axis, namely an azimuth angle of the circle center of the receiving end in the coordinate system Z-XOY;
(3) constructing an equivalent channel matrix of an OAM communication system: constructing an equivalent channel matrix H of the OAM communication system by using coordinates (r, theta, alpha) of the circle center of the receiving end in a second coordinate system Z-XOY of the transmitting endOAM＝[hOAM(u,v)]v×vWherein (u, v) indicates that the element is located in the equivalent channel matrix HOAMThe subscript V × V denotes an equivalent channel matrix HOAMIs a square matrix of V rows and V columns;
constructing equivalent channel matrix H of OAM communication systemOAMEach element h in (1)OAM(u, v) calculated by the following formula:
Figure FDA0002966431930000016
wherein i is an imaginary unit,
Figure FDA0002966431930000017
is a constant coefficient, beta is a channel fading coefficient, N is the number of array elements at the transmitting and receiving ends, RrAnd RtThe radius of the transmitting and receiving end circular array, k the subcarrier used for transmitting signal, q is n-m, m, n is the array element number of the transmitting and receiving end circular array, t is lu-lvRepresenting the difference of the modes used for signal transmission and signal reception,/vModality used for signalling,/uThe mode used for signal receiving, (r, theta, alpha) is the coordinate of the circle center of the receiving end in a second coordinate system Z-XOY of the transmitting end;
(4) constructing a wave beam phase modulation matrix of an OAM communication system: constructing a beam phase modulation matrix B to eliminate an equivalent channel matrix HOAMEach element hOAM(u, v) terms relating to the receiver azimuth angle θ and the pitch angle α;
constructing a wave beam phase modulation matrix B of the OAM communication system, and calculating by the following formula:
Figure FDA0002966431930000021
wherein b is a row vector of a wave beam phase modulation matrix of the OAM communication system,
Figure FDA0002966431930000022
Figure FDA0002966431930000023
i is an N-dimensional full-column vector of a wave beam phase modulation matrix of the OAM communication system;
(5) performing beam phase modulation on the OAM communication system: performing beam phase modulation on a receiving end of the OAM communication system by using a beam phase modulation matrix B to obtain an equivalent channel matrix H 'of the OAM communication system after the beam phase modulation'OAM；
(6) And (3) carrying out received signal detection on the OAM communication system: equivalent channel matrix H 'of OAM communication system after beam phase modulation'OAMEach element in (1) carries out TaiPerforming lux expansion to obtain an estimated value H of an equivalent channel matrix of the OAM communication system after beam phase modulationeffUsing the matrix estimate HeffAmplitude detection is carried out at a receiving end to obtain a multi-mode OAM receiving signal
Figure FDA0002966431930000027
2. The signal receiving method of orbital angular momentum wireless communication system according to claim 1, wherein the equivalent channel matrix H 'of the beam-modulated OAM communication system in step (5)'OAMIs a diagonal matrix of which each diagonal element h'OAM(v, v) is represented as follows:
Figure FDA0002966431930000024
3. the signal receiving method of an orbital angular momentum wireless communication system according to claim 1, wherein the estimated value H of the equivalent channel matrix of the beam-modulated OAM communication system in step (6)effIs a diagonal matrix, each diagonal element h thereofeff(v, v) is represented as follows:
Figure FDA0002966431930000025
wherein, S is an estimated value H of an equivalent channel matrix of the OAM communication system after beam phase modulationeffThe coefficient of (a) is determined,
Figure FDA0002966431930000026
tau is an estimated value H of an equivalent channel matrix of the OAM communication system after beam phase modulationeffτ ═ min { | lv|,N-|lv|}。
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