A polarization state modulation method based on regular polyhedral constellation points
By designing a polarization state modulation method for constellation points on a Poincaré sphere, the problem of suboptimal constellation point distribution under high-order modulation is solved, improving spectral efficiency and noise immunity, and making it suitable for high-capacity wireless communication.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2026-03-26
- Publication Date
- 2026-07-07
AI Technical Summary
In existing polarization modulation techniques, the constellation point distribution is suboptimal under high-order modulation conditions, resulting in low spectral efficiency and failing to meet the requirements of high-capacity wireless communication.
A polarization state modulation method based on regular polyhedron constellation points is adopted. The polarization constellation points are designed on the Poincaré sphere by taking advantage of the geometric symmetry of regular polyhedra to maximize the geodesic distance between adjacent points. This method is combined with traditional modulation to achieve high-dimensional joint coding.
It improves noise immunity and spectrum utilization, making it suitable for high-capacity wireless communication scenarios with low signal-to-noise ratio, and enabling reliable joint high-dimensional data transmission.
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Figure CN122348879A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of wireless communication technology and relates to a polarization state modulation method based on regular polyhedral constellation points. Background Technology
[0002] With the development of wireless communication technology, the demand for high-capacity data transmission is increasing, leading to a growing scarcity of spectrum resources. To meet the high-dimensional modulation requirements of systems such as 5G / 6G, it is necessary to fully utilize the polarization state of electromagnetic waves as an additional information dimension. In existing technologies, polarization modulation has been preliminarily explored. For example, Polarization Shift Keying (PolSK) technology has been applied to optical communication and wireless scenarios to achieve polarization multiplexing and improve channel capacity. Based on a spatial electromagnetic field mathematical model, an innovative three-dimensional modulation framework utilizing signal amplitude, auxiliary polarization angle, and polarization phase difference angle has been proposed, integrating amplitude modulation and polarization modulation. From the perspective of RF power amplifier energy efficiency optimization, a joint modulation scheme combining polarization modulation and traditional amplitude and phase modulation has been developed.
[0003] While existing research has proposed various polarization modulation schemes, it has given little consideration to the optimal distribution of polarization constellation points on the Poincaré sphere, especially for higher-order modulation. Traditional PolSK techniques mainly include the following forms: Bi-state PolSK: using two orthogonal polarization states, such as left-handed and right-handed circular polarization, with each symbol carrying 1 bit of information; Quadri-state PolSK: using four polarization states, typically distributed at the equator or mutually orthogonal positions on the Poincaré sphere, with each symbol carrying 2 bits of information; and Poly-state PolSK: using even more polarization states, but traditional designs lack a systematic method to determine the optimal constellation point distribution. These shortcomings lead to low spectral efficiency in existing systems under high-capacity requirements, failing to meet the demands of future high-dimensional communications such as 6G. Summary of the Invention
[0004] To address the shortcomings of suboptimal constellation point distribution in existing polarization state modulation techniques, the present invention aims to provide a polarization state modulation method based on regular polyhedron constellation points. This method utilizes the geometric symmetry of regular polyhedra (such as regular tetrahedrons, regular octahedrons, etc.) to design polarization constellation points on a Poincaré sphere, maximizing the geodesic distance between adjacent points, thereby improving noise immunity and bit error rate threshold.
[0005] To achieve the above objectives, the present invention employs the following technical solution: A polarization state modulation method based on regular polyhedral constellation points includes: Based on the current channel quality, the polarization modulation order and the corresponding regular polyhedral constellation type are selected; for the original binary bit stream to be transmitted, the data rate is allocated according to the polarization modulation order and the preset conventional modulation order to obtain the conventional modulation bit stream and the polarization state modulation bit stream; conventional constellation mapping is performed on the conventional modulation bit stream to generate conventional modulation symbols. The polarization state is mapped using the polarization state modulation bitstream and the order of polarization modulation to obtain the corresponding polarization state description parameters, and the polarization weighting factor is determined. Polarization weighting fusion is performed based on the polarization weighting factor and the traditional modulation symbol to obtain the dual-channel high-dimensional modulation symbol to be transmitted; the dual-channel high-dimensional signal is preprocessed and then transmitted through an orthogonal dual-polarization antenna; The receiver receives radio frequency signals with horizontal and vertical polarization components through an orthogonal dual-polarized antenna; the two received signals are processed by radio frequency front-end to obtain the Jones vector representation of the baseband received signal; The Stokes parameters of the Jones vector representation of the baseband received signal are calculated; the Stokes parameters are inversely transformed to restore the polarization state parameters of the received signal; the estimated value of the polarization state modulated bit stream is output using the maximum likelihood decision, and combined with the estimated value of the traditional modulated bit stream, the original transmitted binary bit stream is recovered.
[0006] Furthermore, based on the current channel quality, the order of polarization modulation and the corresponding regular polyhedral constellation type are selected, including: When the current SNR is less than the set lower limit of the signal-to-noise ratio threshold, select the order of polarization modulation. A regular tetrahedron; When the current SNR is greater than the set upper limit of the signal-to-noise ratio threshold, select the order of polarization modulation. A regular dodecahedron; When the current SNR is between the upper and lower limits of the preset signal-to-noise ratio threshold, select the order of polarization modulation. , , It can be a regular octahedron, a regular hexahedron, or a regular icosahedron.
[0007] Furthermore, data rate allocation is performed based on the polarization modulation order and a preset conventional modulation order, including: For the raw binary bit stream to be transmitted , before The bits are traditional modulation bit streams ;back Bit-polarized modulated bit stream ; , These are the polarization modulation order and the conventional modulation order, respectively.
[0008] Furthermore, polarization state mapping is performed using the polarization state modulation bitstream and the order of polarization modulation to obtain the corresponding polarization state description parameters, including: For polarization state modulated bit streams Map it to a set of polarized constellation points The corresponding polarized constellation point The constellation points are vertices of regular polyhedra embedded in the surface of a Poincaré sphere, and their values are determined according to the order of polarization modulation. Selecting the corresponding regular polyhedral constellation, its normalized vertex coordinates constitute the set of polarized constellation points. ; For the selected constellation point Perform parameter transformation to obtain the corresponding polarization state description parameters. The conversion relationship is as follows: and ; Polarization weighting factors include horizontal polarization branch weighting factors. and vertical polarization branch weighting factor : ; in, The imaginary unit; It is a natural constant.
[0009] Furthermore, the corresponding regular polyhedral constellation is selected based on the order of polarization modulation, including: When the order of polarization modulation When using a regular tetrahedral constellation, the vertex coordinates are... Represented as: ; when When using a regular octahedral constellation, the vertex coordinates are... Represented as: ; when At that time, a regular hexahedral constellation was used, with its vertex coordinates. Represented as: ; when At that time, the coordinates of the icosahedral constellation were used. Represented as: ; in, ; when At that time, a regular dodecahedral constellation was used, and its vertex coordinates were... After normalization, it is expressed as: .
[0010] Furthermore, polarization-weighted fusion is performed based on the polarization weighting factor and the traditional modulation symbol to obtain the dual-path high-dimensional modulation symbol to be transmitted, including: ; in, It is a dual-channel high-dimensional modulation symbol. For horizontally polarized branch baseband signals, For vertically polarized branch baseband signals; For the first The amplitude of a traditional modulation symbol; For the first The phase of a traditional modulation symbol, This is an additional phase.
[0011] Furthermore, the Jones vector representation of the baseband received signal is as follows:
[0012] in, and These are the baseband complex signals of the horizontal and vertical polarization branches at the receiving end, respectively. and These are mutually independent additive complex Gaussian white noise.
[0013] Furthermore, the Jones vector representation of the baseband received signal... Calculate its Stokes parameters : ; ; ; ; in, Represents the modulus of a complex number; By performing an inverse transform on the calculated Stokes parameters, the polarization state parameters of the received signal can be reconstructed. : ; .
[0014] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, it implements the polarization state modulation method based on regular polyhedral constellation points.
[0015] A computer-readable storage medium storing a computer program; when executed by a processor, the computer program implements the polarization state modulation method based on regular polyhedral constellation points.
[0016] Compared with the prior art, the present invention has the following technical features: This invention achieves polarization state modulation with optimized distribution on the Poincaré sphere using regular polyhedral constellation points. This maximizes geodesic distance to improve noise immunity and spectral efficiency, making it suitable for high-capacity wireless communication scenarios with low signal-to-noise ratios and enabling reliable joint high-dimensional data transmission. Attached Figure Description
[0017] Figure 1 It is a polarized constellation structure based on regular polyhedra (tetrahedron, octahedron, hexahedron, icosahedron and dodecahedron in sequence); Figure 2 These are the simulation results of the polarization modulation symbol error rate in the embodiments of the present invention; Figure 3 These are the simulation results of the polarization modulation bit error rate in the embodiments of the present invention; Figure 4 This refers to the bit error rate of the regular polyhedral constellation and the random constellation in the embodiments of the present invention; Figure 5 This refers to the spectral efficiency of polarization modulation and conventional modulation in the embodiments of the present invention. Detailed Implementation
[0018] This invention provides a polarization state modulation method based on regular polyhedral constellation points. The core of this method lies in the design of a regular polyhedral constellation on a Poincaré sphere, combined with traditional modulation to achieve high-dimensional joint coding. This invention carries more bit information through higher-order polarization states, achieving joint high-dimensional modulation by combining traditional PSK / QAM modulation, significantly improving spectral efficiency through a significant increase in the total order. A spherical noise model based on the Von Mises-Fisher distribution is established, and the symbol error rate expression is derived to ensure reliability. An analytical coordinate expression is provided to facilitate hardware standardization and supports adaptive order selection; lower orders are used for reliability scenarios, while higher orders are used for high-capacity requirements. By achieving the above objectives, this invention provides an innovative modulation paradigm for high-capacity wireless communication systems, alleviates the spectrum crisis, and promotes the development of the Internet of Things, vehicle-to-everything (V2X) communication, and satellite communication.
[0019] In the technical solution of this invention, the transmitting end adaptively selects the order of the regular polyhedron constellation according to the channel quality, divides the bit stream to be transmitted into two paths, one path is modulated in a conventional manner, and the other path is modulated based on the polarization state of the selected regular polyhedron vertex constellation. The two paths are then fused and transmitted through a dual-polarized antenna. The receiving end then recovers the original bit stream from the received signal through joint processing.
[0020] Step 1: Adaptive constellation order selection, bit stream segmentation, and traditional modulation symbol generation.
[0021] Step 1.1: Perform adaptive decision-making based on the current channel quality assessment parameters (such as signal-to-noise ratio SNR) to determine the order of polarization modulation. And the corresponding regular polyhedral constellation type; the determination method is: When the current channel quality is low (e.g., SNR is less than the set lower limit of the signal-to-noise ratio threshold), select a low-cost regular polyhedron (e.g., (a regular tetrahedron) to utilize its maximum minimum distance characteristic to ensure transmission reliability; When the current channel quality is high (e.g., when the SNR is greater than the set upper limit of the signal-to-noise ratio threshold), a higher-order regular polyhedron (e.g., a regular dodecahedron or a regular icosahedron) is selected to pursue higher spectral efficiency. When the current channel quality is at a moderate level (such as SNR between the upper and lower limits of the preset signal-to-noise ratio threshold), a mid-order regular polyhedron (such as a regular hexahedron or a regular octahedron) is selected to balance reliability and efficiency.
[0022] The upper and lower limits of the signal-to-noise ratio threshold are set according to actual needs or experience, for example, they can be 5dB and 15dB.
[0023] This step is designed considering the distinct performance trade-offs exhibited by different modulation orders in polarization modulation systems. Low-order modulation, such as tetrahedral configurations, while having lower spectral efficiency, offers excellent reliability, making it particularly suitable for applications with limited signal-to-noise ratios and stringent transmission reliability requirements. Mid-order modulation, employing hexahedral or octahedral constellations, achieves a good balance between spectral efficiency and reliability, providing a compromise for most moderately complex communication systems. High-order modulation, using complex geometries such as icosahedrons or dodecahedrons, achieves very high spectral efficiency but places more stringent demands on channel quality. Its rate advantage is only realized in high signal-to-noise ratio environments, making it suitable for high-quality channel applications with extremely high transmission rate requirements.
[0024] Step 1.2, for the raw binary bit stream to be transmitted According to the determined and preset traditional modulation order Data rate allocation is performed to obtain two parallel bit substreams: a conventional modulation bitstream. and polarization state modulated bit stream ;in, It is a binary sequence after source coding and channel coding; the total order of joint modulation is The number of bits that each joint modulation symbol can carry is .
[0025] That is, for an input bit sequence Perform bit allocation to obtain the first bit. Bit and after Bit That is, before Bits are mapped to traditional modulation symbols, and then... Bits are mapped to polarization state vectors. Traditional modulation sections can use PSK or QAM modulation to generate complex signal symbols, i.e.,... Converted to complex sign; the polarization modulation part then converts... The data is mapped to polarization constellation points, generating weighting factors for the horizontal and vertical polarization branches. These two parts of information are combined by polarization weighting units to form a complete high-dimensional modulated signal, which is finally transmitted through an orthogonal dual-polarization antenna.
[0026] Step 1.3, for traditional modulation bitstreams Perform traditional constellation mapping (such as PSK or QAM modulation) to generate traditional modulation symbols. : ; in, For the first The amplitude of a traditional modulation symbol; For the first The phase of a traditional modulation symbol, For additional phase; The imaginary unit; It is a natural constant.
[0027] In step 1, the transmitting end first performs source coding and channel coding on the bit stream, and then the encoded binary sequence bit stream is distributed through the data rate allocation unit. It is divided into two parts, among which Used for traditional modulation, while Used for polarization state modulation. The allocation ratio depends on system parameters; in this embodiment, the number of symbols transmitted by conventional modulation per unit time is set equal to the number of symbols transmitted by polarization state modulation. Each polarization state is associated with a conventional modulation constellation, thus expanding the constellation dimension.
[0028] Step 2, modulate the bit stream according to the polarization state. and a definite order Perform polarization state mapping to obtain the corresponding polarization state description parameters. And determine the polarization weighting factor. Among them, The auxiliary polarization angle has a range of values. ; The polarization phase difference angle has a range of values. .
[0029] In this step, the following optimization criteria are followed when designing the polarization state constellation: Minimum distance maximization principle: The distance between adjacent constellation points should be as large as possible to improve the system's noise immunity; Symmetry principle: The constellation structure should have good symmetry to facilitate encoding and decoding; Mathematical processing convenience: Vertex coordinates have precise analytical expressions, eliminating the need for numerical optimization; Standardized design: Based on a clear geometric structure, it facilitates standardized engineering implementation.
[0030] Based on these principles, a design method is proposed that utilizes the vertices of regular polyhedra embedded in the Poincaré sphere as polarization constellation points. A regular polyhedron is a highly symmetrical geometric solid in three-dimensional space, where all faces are congruent regular polygons and all vertices are equidistant from the center. According to Euclidean geometry, there exist regular tetrahedrons, regular hexahedrons (cubes), regular octahedrons, regular dodecahedrons, and regular icosahedrons in three-dimensional space. Mapping the vertices of these five regular polyhedra onto the Poincaré sphere constructs polarization constellation point sets of different orders; the details are as follows: Step 2.1, modulate the bit stream according to the polarization state. Map it to the corresponding polarized constellation point The mapping refers to... The binary values are mapped one-to-one to the set of polarized constellation points. A specific constellation point in the constellation; the specific mapping rules are to be set by the user, as long as the binary bit values correspond to the constellation points respectively; as follows: The constellation points of the polarization state mapping are designed based on the principles of minimum distance maximization, symmetry, mathematical convenience, and normalization; specifically, they are the vertices of regular polyhedra embedded in the Poincaré sphere. The polarization modulation order is determined accordingly. Selecting the corresponding regular polyhedral constellation, its normalized vertex coordinates constitute the set of polarized constellation points. Specifically: when At that time, a regular tetrahedral constellation is used, with 4 vertices corresponding to 4 polarization states; each symbol can carry Bit information, its vertex coordinates Represented as: ; These points are uniformly distributed on the Poincaré sphere, and the minimum geodesic distance between any two points is: ; The tetrahedral structure achieves the theoretically optimal minimum distance under a 4-point configuration, making it an ideal choice for low-complexity polarization modulation.
[0031] when At that time, a regular octahedral constellation is used, with 6 vertices corresponding to 6 polarization states; each symbol can carry Bit information, its vertex coordinates It can be represented as: ; when At that time, a hexahedral / cubic constellation is used, with 8 vertices corresponding to 8 polarization states; each symbol can carry Bit information, its vertex coordinates It can be represented as: ; The cube provides an intuitive and easy-to-implement polarization modulation technique, and each symbol can encode an integer number of bits.
[0032] when At that time, an icosahedral constellation was used, with 12 vertices corresponding to 12 polarization states; each symbol can carry... Bit information, its vertex coordinates It's quite complex and involves the golden ratio. , can be represented as: ; These coordinates are then normalized to unit vectors to ensure that all points lie on the Poincaré sphere.
[0033] when At that time, a regular dodecahedral constellation was used, with 20 vertices corresponding to 20 polarization states, and each symbol could carry... Bit information; the dodecahedron offers extremely high spectral efficiency, but also places higher demands on channel conditions, and its vertex coordinates... Through the golden ratio Represented as: ; These coordinates need to be normalized to unit vectors.
[0034] Step 2.2, for the selected constellation points Perform parameter transformation to obtain the corresponding polarization state description parameters. The conversion relationship is as follows: and .
[0035] Step 2.3, describing the polarization state parameters Calculate the polarization weighting factor to obtain the horizontal polarization branch weighting factor. and vertical polarization branch weighting factor : ; in, and Used to distribute the amplitude of the two signals. Used to introduce the phase difference between the vertical polarization branch and the horizontal polarization branch. .
[0036] Step 3: High-dimensional modulation signal synthesis and transmission.
[0037] For traditional modulation symbols and polarization weighting factor Polarization-weighted fusion is performed to obtain the dual-path high-dimensional modulation symbols to be transmitted. : ; in, For horizontally polarized branch baseband signals, This is the baseband signal of the vertically polarized branch.
[0038] For dual-channel high-dimensional modulation symbols The two baseband signals included and The signal undergoes up-conversion and power amplification in the RF front-end processing to obtain two RF signals. Finally, these two RF signals are transmitted from the horizontal and vertical polarization channels respectively through orthogonal dual-polarized antennas. The two transmitted signals couple into an electromagnetic wave with a specific polarization state in the far-field space. This polarization state is related to the bit stream. Unique correspondence.
[0039] This invention combines traditional modulation with polarization-state modulation, adding an independent polarization dimension in addition to the traditional amplitude / phase dimension, thus constructing a high-dimensional modulation signal space. This joint coding method effectively improves the system's spectral efficiency and data transmission rate without increasing bandwidth.
[0040] Step 4: Signal reception and preprocessing at the receiving end.
[0041] The receiver receives signals through an orthogonal dual-polarized antenna, receiving both horizontal and vertical polarization components of the radio frequency (RF) signals. The two RF signals are then subjected to RF front-end processing such as down-conversion and analog-to-digital conversion to obtain the Jones vector representation of the baseband received signal. :
[0042] in, and These are the baseband complex signals of the horizontal and vertical polarization branches at the receiving end, respectively. and These are mutually independent additive complex Gaussian white noise.
[0043] In this step, the polarization modulation receiver needs to recover the original data bits from the received waveform. First, it receives the signal through a polarization antenna. After RF front-end processing such as down-conversion and analog-to-digital conversion, it obtains the baseband signals of the horizontal and vertical polarization components. The receiving system mainly consists of two processing units: a polarization state identification unit and a conventional demodulation unit. The polarization state identification unit recovers the polarization state information by calculating Stokes parameters, while the conventional demodulation unit extracts the amplitude and phase information of the signal.
[0044] Step 5: Polarization state identification and demodulation.
[0045] Step 5.1, Jones vector representation of the baseband received signal Calculate its Stokes parameters : ; ; ; ; in, Represents the modulus of a complex number.
[0046] Step 5.2: Perform an inverse transform on the calculated Stokes parameters to reconstruct the polarization state parameters of the received signal. : ; ; Step 5.3, regarding the restored polarization state parameters Combine it with the set of points of a regular polyhedron constellation. Perform maximum likelihood comparison and determine the polarization state modulation bitstream. The estimated value .
[0047] Step 6, signal demodulation and recovery.
[0048] Jones vector representation for baseband received signals The amplitude and phase information are extracted; this can be achieved by merging or processing the two signals separately to obtain an estimate of the traditional modulation symbol. Regarding the estimated value Perform conventional demodulation (such as PSK / QAM demodulation) corresponding to the transmitter, and output the conventional modulated bit stream. The estimated value ; Based on the estimated value and estimated value The bits are merged according to the segmentation order at the transmitting end to recover the original transmitted binary bit stream. The entire demodulation process makes full use of the joint information from the polarization domain and the traditional domain, effectively improving system performance.
[0049] Explanation of the principle: 1. Polarization states and Poincaré's theory of spherical description.
[0050] The polarization state of an electromagnetic wave is determined by the orthogonal components of the electric field vector. For along... A monochromatic plane wave propagating along an axis, The instantaneous electric field at time t can be expressed as: ,in and It is a unit vector. and It is the electric field component.
[0051] The Jones vector is a commonly used tool for describing fully polarized waves; it contains the amplitude and phase information of the two orthogonal components of the electric field. For a frequency of... A monochromatic plane wave, whose Jones vector is expressed as:
[0052] in and These represent the amplitudes of the horizontal and vertical components, respectively. and For the corresponding phase; It is a natural constant. The unit is the imaginary unit. Through parameter transformation, the auxiliary polarization angle can be used. and polarization phase difference This is used to represent the Jones vector.
[0053] The Stokes parameters provide an alternative way to describe the polarization state. For a fully polarized wave, the four Stokes parameters can be represented as: ; ; ; ; in Indicates the total intensity of the wave. , and Together, they describe the polarization state. By using normalized Stokes parameters, a one-to-one correspondence can be established between the polarization state and the points on the Poincaré sphere.
[0054] Normalized Stokes parameters These points form a unit sphere, which is called the Poincaré sphere; each point on the sphere uniquely corresponds to a polarization state.
[0055] 2. The geometric principles of regular polyhedral constellation design.
[0056] To quantify the merits of constellation designs, two points on the surface of a Poincaré sphere are introduced. and The geodesic distance between them is used as a metric: ; in, Indicates two points The inner product of coordinates; a key indicator in constellation design is the minimum distance. .
[0057] Regular polyhedra, due to their high symmetry and uniform distribution of vertices on a sphere, serve as ideal templates for polarized constellations. Their vertex coordinates have precise analytical solutions, and they can achieve the theoretically optimal minimum distance for that number of vertices, satisfying four criteria: maximizing minimum distance, symmetry, ease of mathematical processing, and standardized design. The key parameters of different regular polyhedra are shown in the table below: Table 1. Parameters of different regular polyhedral polarization constellations
[0058] Bit error rate performance analysis: The polarization modulation signal points are distributed on a unit Poincaré sphere. Let the set of constellation points be: , where each point satisfy Therefore, bit error rate analysis needs to take into account the geometric characteristics of the spherical surface.
[0059] When noise affects the received signal, points on the sphere will shift from their original positions, and the bit error rate is mainly determined by the minimum distance (geodesic distance) between constellation points. In the spherical coordinate system, assuming the distribution of noise-affected receiving points on the sphere follows a Von Mises-Fisher distribution, this is a simulation of the Gaussian distribution on the sphere:
[0060] in It sends polarized constellation points. It is a concentration parameter, which is directly proportional to the signal-to-noise ratio; It is the receiving polarization constellation point.
[0061] For constellation points Its decision-making area Defined as: ; When sending constellation points When the receiving point falls within the wrong decision region, a demodulation error occurs, and the symbol error rate is: ; in It is the area element on the surface of a sphere.
[0062] because The integral becomes:
[0063] In a spherical modulation system, after matched filtering and symbol rate sampling, the noise variance on each Cartesian coordinate is: ,in This is the one-sided noise power spectral density, and T is the symbol period. After normalizing T=1, .
[0064] Concentration parameters With signal-to-noise ratio The relationship is: ,in This is the definition of symbolic signal-to-noise ratio.
[0065] Due to the perfect symmetry of the regular polyhedron, the conditional sign error rate is equal at all constellation points: ; Consider Using a coordinate system centered at the center, under the assumption of symmetry: ; in It is the geodesic distance, corresponding to the angle of the decision boundary, satisfying: ; Simplifying, we get: ; when Sometimes, We can obtain: ; In the modulation technique of regular polyhedral polarized constellation points, it is assumed that all constellation points are transmitted with equal probability: ; The average symbol error rate is: ; Due to the symmetry of regular polyhedra: ; The final average symbol error rate is: ; for Dot constellations, each symbol carries For bits, under the condition of independent errors and uniform distribution, the bit error rate is: .
[0066] In theory The spectral efficiency of the point constellation is: ; Considering the impact of bit error rate, the actual spectral efficiency is: .
[0067] Figure 2 The simulation results of the symbol error rate based on the proposed polarization modulation technique using regular polyhedra are compared with the theoretical analysis. The simulation results agree well with the derived theoretical formulas, verifying the accuracy of the theoretical analysis. Figure 3 A comparison of the bit error rate performance of various regular polyhedral polarization modulation techniques is presented. To verify the advantages of constellation design based on regular polyhedra compared to randomly distributed constellation points, Figure 4 The bit error rate performance of regular polyhedral constellations and random constellations with the same number of constellation points was compared. The random constellation was constructed by randomly generating a corresponding number of points on the Poincaré sphere. Each random constellation experiment was repeated 3 times and the average value was taken. Figure 5 The paper compares the effective spectral efficiency of different modulation techniques under various signal-to-noise ratio conditions; where effective spectral efficiency is defined as the actual information transmission rate after considering the influence of bit error rate. The simulation results show that this invention achieves polarization state modulation with optimized distribution on a Poincaré sphere using regular polyhedral constellation points, which can maximize geodesic distance to improve noise immunity and spectral efficiency.
[0068] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.
Claims
1. A method of polarization state modulation based on regular polyhedral star points, characterized by, include: The polarization modulation order and the corresponding regular polyhedral constellation type are selected based on the current channel quality. For the original binary bit stream to be transmitted, the data rate is allocated according to the polarization modulation order and the preset conventional modulation order to obtain the conventional modulation bit stream and the polarization state modulation bit stream. Traditional modulation bitstreams are mapped using traditional constellations to generate traditional modulation symbols. The polarization state is mapped using the polarization state modulation bitstream and the order of polarization modulation to obtain the corresponding polarization state description parameters, and the polarization weighting factor is determined. Polarization weighting fusion is performed based on the polarization weighting factor and the traditional modulation symbol to obtain the dual-channel high-dimensional modulation symbol to be transmitted; the dual-channel high-dimensional signal is preprocessed and then transmitted through an orthogonal dual-polarization antenna; The receiver receives radio frequency signals with horizontal and vertical polarization components through an orthogonal dual-polarized antenna; The two received signals are processed by radio frequency front-end to obtain the Jones vector representation of the baseband received signal; The Stokes parameters of the Jones vector representation of the baseband received signal are calculated; the Stokes parameters are inversely transformed to restore the polarization state parameters of the received signal; the estimated value of the polarization state modulated bit stream is output using the maximum likelihood decision, and combined with the estimated value of the traditional modulated bit stream, the original transmitted binary bit stream is recovered.
2. The method of claim 1, wherein the regular polygonal star constellation points are defined by a regular polygonal star constellation point set, and the regular polygonal star constellation point set is defined by a regular polygonal star constellation point set formula. Based on the current channel quality, the order of polarization modulation and the corresponding regular polyhedral constellation type are selected, including: selecting an order of polarization modulation when a current SNR is less than a set SNR threshold lower limit a regular tetrahedron; When the current SNR is greater than the set upper limit of the signal-to-noise ratio threshold, select the order of polarization modulation. A regular dodecahedron; When the current SNR is between the upper and lower limits of the preset signal-to-noise ratio threshold, select the order of polarization modulation. , , It can be a regular octahedron, a regular hexahedron, or a regular icosahedron.
3. The polarization state modulation method based on regular polyhedral constellation points according to claim 1, characterized in that, Data rate allocation is performed based on the polarization modulation order and a preset conventional modulation order, including: For the raw binary bit stream to be transmitted , before The bits are from a traditional modulated bit stream. ;back Bit-polarized modulated bit stream ; , These are the polarization modulation order and the conventional modulation order, respectively.
4. The polarization state modulation method based on regular polyhedral constellation points according to claim 1, characterized in that, Polarization state mapping is performed using the polarization state modulation bitstream and the order of polarization modulation to obtain the corresponding polarization state description parameters, including: For polarization state modulated bit streams Map it to a set of polarized constellation points The corresponding polarized constellation point The constellation points are vertices of regular polyhedra embedded in the Poincaré sphere, determined according to the order of polarization modulation. Selecting the corresponding regular polyhedral constellation, its normalized vertex coordinates constitute the set of polarized constellation points. ; For the selected constellation point Perform parameter transformation to obtain the corresponding polarization state description parameters. The conversion relationship is as follows: and ; Polarization weighting factors include horizontal polarization branch weighting factors. and vertical polarization branch weighting factor : ； in, The imaginary unit; It is a natural constant.
5. The polarization state modulation method based on regular polyhedral constellation points according to claim 1, characterized in that, The corresponding regular polyhedral constellation is selected based on the order of polarization modulation, including: When the order of polarization modulation When using a regular tetrahedral constellation, the vertex coordinates are... Represented as: ； when When using a regular octahedral constellation, the vertex coordinates are... Represented as: ； when At that time, a regular hexahedral constellation was used, with its vertex coordinates. Represented as: ； when At that time, the coordinates of the icosahedral constellation were used. Represented as: ； in, ; when At that time, a regular dodecahedral constellation was used, and its vertex coordinates were... After normalization, it is expressed as: 。 6. The polarization state modulation method based on regular polyhedral constellation points according to claim 1, characterized in that, Polarization weighting fusion is performed based on the polarization weighting factor and the traditional modulation symbol to obtain the dual-path high-dimensional modulation symbol to be transmitted, including: ； in, It is a dual-channel high-dimensional modulation symbol. For horizontally polarized branch baseband signals, For vertically polarized branch baseband signals; For the first The amplitude of a traditional modulation symbol; For the first The phase of a traditional modulation symbol, This is an additional phase.
7. The polarization state modulation method based on regular polyhedral constellation points according to claim 1, characterized in that, The Jones vector representation of the baseband received signal is as follows: in, and These are the baseband complex signals of the horizontal and vertical polarization branches at the receiving end, respectively. and These are mutually independent additive complex Gaussian white noises.
8. The polarization state modulation method based on regular polyhedral constellation points according to claim 1, characterized in that, Jones vector representation of baseband received signal Calculate its Stokes parameters : ； ； ； ； in, The modulus of a complex number; By performing an inverse transform on the calculated Stokes parameters, the polarization state parameters of the received signal can be reconstructed. : ； 。 9. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that, When the processor executes a computer program, it implements the polarization state modulation method based on regular polyhedral constellation points as described in any one of claims 1-8.
10. A computer-readable storage medium storing a computer program; characterized in that, When the computer program is executed by the processor, it implements the polarization state modulation method based on regular polyhedral constellation points as described in any one of claims 1-8.