A modulation method of OFDM satellite navigation signal based on phase jump

Abstract

This invention provides a modulation method for OFDM satellite navigation signals based on phase-hopping, the method comprising: S1, determining an initial discrete phase vector; S2, obtaining several clusters; S3, setting a random number rand∈(0,1), if rand<p1, randomly selecting one cluster from the several clusters and proceeding to S4; otherwise, randomly selecting two clusters from the several clusters and proceeding to S5; S4, obtaining an updated discrete phase vector based on the first subcarrier phase selection vector and proceeding to S6; S5, obtaining an updated discrete phase vector based on the second subcarrier phase selection vector and proceeding to S6; S6, using the discrete phase vector corresponding to the smaller of the two PAPR values ​​as the discrete phase vector output in the current loop; S7, obtaining the discrete phase vector output in the first loop; S8, obtaining the discrete phase vector output in the second loop; S9, obtaining the final discrete phase vector; S10, performing phase-hopping on each subcarrier of the original OFDM navigation signal vector to obtain the OFDM phase-hopping signal vector.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation technology, and in particular to a modulation method for OFDM satellite navigation signals based on phase skipping. Background Technology

[0002] Using Orthogonal Frequency Division Multiplexing (OFDM) technology in low-Earth orbit (LEO) satellite navigation signals offers advantages such as higher frequency bandwidth utilization and more flexible resource allocation. Traditional navigation signals are mostly constant envelope signals and largely use direct sequence spread spectrum, which differs significantly from OFDM modulation. To use OFDM technology on LEO satellites, the peak-to-average power ratio (PAPR) problem inherent in this technology must be addressed. While terrestrial wireless networks offer diverse methods for handling PAPR, satellite transmitter structures are difficult to modify and are typically power-limited. Furthermore, maintaining the accuracy of navigation signal service requires addressing the issue, making it impossible to use the PAPR handling methods employed in terrestrial wireless networks. Summary of the Invention

[0003] This invention provides a modulation method for OFDM satellite navigation signals based on phase skipping, addressing the technical problem of peak-to-average power ratio of OFDM navigation signals used in low-Earth orbit satellites.

[0004] This invention provides a modulation method for OFDM satellite navigation signals based on phase skipping, the method comprising:

[0005] S1. Determine the initial discrete phase vector for phase jumping;

[0006] S2. Perform k-means clustering on the initial discrete phase vectors to obtain several clusters;

[0007] S3. Set a random number rand∈(0,1). If rand<p1, then randomly select one cluster from several clusters and go to S4; otherwise, randomly select two clusters from several clusters and go to S5, where p1 is the probability of selecting one cluster.

[0008] S4. If rand < p 1c If the cluster center of the currently selected cluster is selected, then the cluster center of the selected cluster is used as the first subcarrier phase selection vector; otherwise, an individual is randomly selected from the currently selected cluster as the first subcarrier phase selection vector; based on the first subcarrier phase selection vector, the updated discrete phase vector is obtained, and the process is repeated in step S6, where p 1c The probability of selecting a cluster center for a given cluster;

[0009] S5. If rand < p 2c If the current clustering is successful, then the second subcarrier phase selection vector is obtained based on the cluster centers of the two currently selected clusters; otherwise, the second subcarrier phase selection vector is obtained by randomly selecting one individual from each of the two currently selected clusters. The updated discrete phase vector is then obtained based on the second subcarrier phase selection vector, and the process proceeds to S6, where p... 2c The probability of selecting the cluster center from the two clusters;

[0010] S6. Obtain the periodic synthesized sidelobe level of the periodic autocorrelation function of the OFDM original navigation signal vector. Under the constraint of minimizing the periodic synthesized sidelobe level of the periodic autocorrelation function of the OFDM original navigation signal vector, obtain the PAPR value of the OFDM original navigation signal vector based on the initial discrete phase vector; obtain the PAPR value of the OFDM original navigation signal vector based on the updated discrete phase vector; take the discrete phase vector corresponding to the smaller of the two PAPR values ​​as the discrete phase vector output in the current iteration.

[0011] S7. Take the discrete phase vector output in the current loop as the initial discrete phase vector, and repeat S2 to S6 until the number of loops in the first loop is reached, and obtain the discrete phase vector output in the first loop.

[0012] S8. Take the discrete phase vector output by the first loop as the initial discrete phase vector, and repeat S2 to S6 until the number of loops of the second loop is reached to obtain the discrete phase vector output by the second loop.

[0013] S9. Take the discrete phase vector output by the second loop as the initial discrete phase vector, and repeat S2 to S6 until the number of loops of the third loop is reached to obtain the discrete phase vector output by the third loop. Take the discrete phase vector output by the third loop as the final discrete phase vector.

[0014] S10. Based on the final discrete phase vector, the phase of each subcarrier of the original OFDM navigation signal vector is changed to obtain the OFDM phase-jumping signal vector.

[0015] Preferably, in S4 of the present invention, the updated discrete phase vector is obtained by the following formula:

[0016] θ new =θ select +ξ·N(μ,σ 2 )

[0017] In the formula, θ new For the updated discrete phase vector, θ select Let N(μ,σ) be the phase selection vector for the first subcarrier, ξ be the first weighting coefficient, and N(μ,σ) be the first subcarrier phase selection vector. 2Let σ be the Gaussian distribution function, μ be the mean, and σ be the mean. 2 Let Variance be the variance.

[0018] Preferably, in S5 of the present invention, the updated discrete phase vector is obtained by the following formula:

[0019] θ new =θ′ select +ξ·N(μ,σ 2 )

[0020] θ′ select =w1θ select_1 +w2θ select_2

[0021] In the formula, θ′ select The phase selection vector for the second subcarrier, θ select_1 θ select_2 w1 and w2 are the cluster centers of the two currently selected clusters or a randomly selected individual from each cluster, respectively, and the second and third weight coefficients are the second and third weight coefficients, respectively.

[0022] Preferably, the PAPR value of the original OFDM navigation signal vector is obtained by the following formula:

[0023]

[0024] in,

[0025] In the formula, PAPR is the PAPR value of the original OFDM navigation signal vector, b is the scaling factor, is a constant, X is the original OFDM navigation signal vector, H is the conjugate transpose, T is the transpose, N is the number of subcarriers, i, l, h are different subcarrier indices, and θ′[l] and θ′[h] are the discrete phases of the l-th and h-th subcarriers in the updated discrete phase vector.

[0026] Preferably, the OFDM phase-hopping signal vector is obtained by the following formula:

[0027] S PH =X⊙e θ

[0028] S PH =[s PH [0],s PH [1],...,s PH [N-1]

[0029] in,

[0030] In the formula, S PHLet X be the OFDM phase-hopping signal vector, θ be the original OFDM navigation signal vector, ⊙ be the final discrete phase vector, and s be the Hadamard product operation symbol. PH [k] represents the k-th OFDM phase-hopping signal in the OFDM phase-hopping signal vector, C[i] represents the ranging code of the ith subcarrier, θ[i] represents the discrete phase of the ith subcarrier in the final discrete phase vector, M represents the number of OFDM symbols, and N represents the number of subcarriers.

[0031] Preferably, the number of iterations in the first loop is equal to the number of OFDM symbols, the number of iterations in the second loop is equal to the total number of iterations, and the number of iterations in the third loop is equal to the number of uniform segments of the initial discrete phase vector within the range [0, 2π].

[0032] By applying the technical solution of this invention, the initial discrete phase vector is iteratively updated using the BSO algorithm to obtain the final discrete phase vector. Then, based on the final discrete phase vector, the phase of each subcarrier of the original OFDM navigation signal vector is changed to obtain the OFDM phase-hopping signal vector. Results show that this method significantly reduces the PAPR of the signal. Attached Figure Description

[0033] The accompanying drawings, which form part of this specification, are provided to further illustrate embodiments of the invention and, together with the textual description, explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0034] Figure 1 A flowchart of a modulation method for phase-hopping OFDM satellite navigation signals according to an embodiment of the present invention is shown;

[0035] Figure 2 A schematic diagram of the time-frequency structure of an OFDM navigation signal according to an embodiment of the present invention is shown;

[0036] Figure 3 A schematic diagram of PAPR curves obtained by the BSO algorithm under different subcarrier numbers provided in an embodiment of the present invention is shown.

[0037] Figure 4 A comparison diagram of the PAPR obtained from the original OFDM navigation signal and the OFDM phase-hopping signal when the number of subcarriers is 32, 64, 128, and 256, according to an embodiment of the present invention, is shown.

[0038] Figure 5 A schematic diagram of PAPR curves obtained under different iteration numbers according to an embodiment of the present invention is shown;

[0039] Figure 6 A schematic diagram of PAPR curves obtained under different phase jump bases according to an embodiment of the present invention is shown. Detailed Implementation

[0040] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0041] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0042] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0043] like Figure 1 As shown, this invention provides a modulation method for OFDM satellite navigation signals based on phase skipping, the method comprising:

[0044] S1. Determine the initial discrete phase vector for phase jumping;

[0045] S2. Perform k-means clustering on the initial discrete phase vectors to obtain several clusters;

[0046] S3. Set a random number rand∈(0,1). If rand<p1, then randomly select one cluster from several clusters and go to S4; otherwise, randomly select two clusters from several clusters and go to S5, where p1 is the probability of selecting one cluster.

[0047] S4. If rand < p 1c If the cluster center of the currently selected cluster is selected, then the cluster center of the selected cluster is used as the first subcarrier phase selection vector; otherwise, an individual is randomly selected from the currently selected cluster as the first subcarrier phase selection vector; based on the first subcarrier phase selection vector, the updated discrete phase vector is obtained, and the process is repeated in step S6, where p 1c The probability of selecting a cluster center for a given cluster;

[0048] S5. If rand < p 2c If the current clustering is successful, then the second subcarrier phase selection vector is obtained based on the cluster centers of the two currently selected clusters; otherwise, the second subcarrier phase selection vector is obtained by randomly selecting one individual from each of the two currently selected clusters. The updated discrete phase vector is then obtained based on the second subcarrier phase selection vector, and the process proceeds to S6, where p... 2c The probability of selecting the cluster center from the two clusters;

[0049] S6. Obtain the periodic synthesized sidelobe level of the periodic autocorrelation function of the OFDM original navigation signal vector. Under the constraint of minimizing the periodic synthesized sidelobe level of the periodic autocorrelation function of the OFDM original navigation signal vector, obtain the PAPR value of the OFDM original navigation signal vector based on the initial discrete phase vector; obtain the PAPR value of the OFDM original navigation signal vector based on the updated discrete phase vector; take the discrete phase vector corresponding to the smaller of the two PAPR values ​​as the discrete phase vector output in the current iteration.

[0050] S7. Take the discrete phase vector output in the current loop as the initial discrete phase vector, and repeat S2 to S6 until the number of loops in the first loop is reached, and obtain the discrete phase vector output in the first loop.

[0051] S8. Take the discrete phase vector output by the first loop as the initial discrete phase vector, and repeat S2 to S6 until the number of loops of the second loop is reached to obtain the discrete phase vector output by the second loop.

[0052] S9. Take the discrete phase vector output by the second loop as the initial discrete phase vector, and repeat S2 to S6 until the number of loops of the third loop is reached to obtain the discrete phase vector output by the third loop. Take the discrete phase vector output by the third loop as the final discrete phase vector.

[0053] S10. Based on the final discrete phase vector, the phase of each subcarrier of the original OFDM navigation signal vector is changed to obtain the OFDM phase-jumping signal vector.

[0054] This invention employs the BSO algorithm to iteratively update the initial discrete phase vector, thereby obtaining the final discrete phase vector. Based on this final discrete phase vector, the phase of each subcarrier of the original OFDM navigation signal vector is changed to obtain the OFDM phase-hopping signal vector. Results show that this method significantly reduces the PAPR of the signal.

[0055] In this embodiment, the phase elements θ = [θ[0] θ[1] … θ[N-1]] superimposed on the signal are used as the optimization target. First, the optimization range needs to be determined. Since the values ​​to be optimized are all e... (·) The phase element is of the form θ, so the range of θ is [0, 2π], and individuals are divided into groups that are uniformly distributed within this range.

[0056] Before performing the discrete phase vector cyclic update, all variables and constants are first initialized, including the number of subcarriers N, the number of segments Size in the phase element range [0, 2π], the number of OFDM statistical symbols RunMax, the maximum number of iterations GenMax, the probability p1 of selecting a cluster, and the probability p of selecting the cluster center of a cluster. 1c The probability p of choosing the cluster center from the two clusters 2c .

[0057] According to one embodiment of the present invention, in S4 of the present invention, the updated discrete phase vector is obtained by the following formula:

[0058] θ new =θ select +ξ·N(μ,σ 2 )

[0059] In the formula, θ new For the updated discrete phase vector, θ select Let N(μ,σ) be the phase selection vector for the first subcarrier, ξ be the first weighting coefficient, and N(μ,σ) be the first subcarrier phase selection vector. 2 Let σ be the Gaussian distribution function, μ be the mean, and σ be the mean. 2 Let Variance be the variance.

[0060] According to one embodiment of the present invention, in S5 of the present invention, the updated discrete phase vector is obtained by the following formula:

[0061] θ new =θ′ select +ξ·N(μ,σ 2 )

[0062] θ′ select =w1θ select_1 +w2θ select_2

[0063] In the formula, θ′ select The phase selection vector for the second subcarrier, θ select_1 θ select_2 w1 and w2 are the cluster centers of the two currently selected clusters or a randomly selected individual from each cluster, respectively, and the second and third weight coefficients are the second and third weight coefficients, respectively.

[0064] According to one embodiment of the present invention, the PAPR value of the original OFDM navigation signal vector is obtained by the following formula:

[0065]

[0066] in,

[0067] In the formula, PAPR is the PAPR value of the original OFDM navigation signal vector, b is the scaling factor, is a constant, X is the original OFDM navigation signal vector, H is the conjugate transpose, T is the transpose, N is the number of subcarriers, i, l, h are different subcarrier indices, θ′[l] and θ′[h] are the discrete phases of the l-th and h-th subcarriers in the updated discrete phase vector, and θ′[l] and θ′[h] are elements in the phase vector of X generated during the expansion of the formula.

[0068] The constraint in the above equation is that the periodic synthesized sidelobe level of the periodic autocorrelation function of the OFDM original navigation signal vector is minimized. The periodic synthesized sidelobe level (PISL) of the periodic autocorrelation function of the OFDM original navigation signal vector is obtained by the following equation. x :

[0069]

[0070] In the formula, n∈[-(N-1),N-1],n≠0, n is the signal vector index, and X[n] is the nth frequency domain signal of the original OFDM navigation signal vector. Let X[n] be the autocorrelation function of the nth period of the original OFDM navigation signal vector. To optimize the PISL performance of the signal, this value should be as small as possible. Therefore, we should set |X[n]| = 1 and use it as a constraint in the signal design process.

[0071] The OFDM navigation signal vector will occupy the entire bandwidth within the available frequency band and will also occupy all available time slots. The time-frequency structure of the signal vector is as follows: Figure 2 As shown, the OFDM navigation signal vector consists of a ranging code of length M×N, where M is the number of OFDM symbols and N is the number of subcarriers. The ranging code is divided into M segments, and each segment is placed on an OFDM symbol in the order of subcarrier indices [1,N].

[0072] Each OFDM symbol (i.e., each OFDM navigation signal) can be represented as:

[0073]

[0074] Phase-skipping modulation jumps the phase on each subcarrier. Let the discrete phase vector for phase skipping on an OFDM symbol be θ = [θ[0] θ[1] … θ[N-1]]. Then the OFDM phase-skipping signal can be expressed as:

[0075]

[0076] The OFDM phase-hopping signal vector is obtained using the following formula:

[0077] S PH =X⊙e θ

[0078] S PH =[s PH [0],s PH [1],...,s PH [N-1]

[0079] in,

[0080] In the formula, S PH Let X be the OFDM phase-hopping signal vector, θ be the original OFDM navigation signal vector, ⊙ be the final discrete phase vector, and s be the Hadamard product operation symbol. PH [k] represents the k-th OFDM phase-hopping signal in the OFDM phase-hopping signal vector, C[i] represents the ranging code of the ith subcarrier, θ[i] represents the discrete phase of the ith subcarrier in the final discrete phase vector, M represents the number of OFDM symbols, and N represents the number of subcarriers.

[0081] According to one embodiment of the present invention, the number of iterations of the first layer loop is the number of OFDM symbols, the number of iterations of the second layer loop is the total number of iterations, and the number of iterations of the third layer loop is the number of uniform segments of the initial discrete phase vector in the range [0, 2π].

[0082] In summary, this invention provides a modulation method for OFDM satellite navigation signals based on phase-hopping. It employs the BSO algorithm to iteratively update the initial discrete phase vector, thereby obtaining the final discrete phase vector. Then, based on the final discrete phase vector, it performs phase-hopping on each subcarrier of the original OFDM navigation signal vector to obtain the OFDM phase-hopping signal vector. Results show that this method significantly reduces the PAPR of the signal, specifically as follows: Figures 3-6 As shown.

[0083] For ease of description, spatial relative terms such as "above," "on top of," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation beyond the orientation of the device as described in the figures. For example, if the device in the figures were inverted, a device described as "above" or "on top of" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.

[0084] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.

[0085] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A modulation method for a phase-switching based OFDM satellite navigation signal, characterized in that, The method comprises: S1, determining an initial discrete phase vector for phase hopping; S2, performing a kmeans clustering operation on the initial discrete phase vector to obtain a plurality of clusters; S3, setting a random number rand∈(0,1), if rand S4, if rand 1c , then the cluster center of the currently selected one cluster is taken as the first subcarrier phase selection vector; otherwise, a individual is randomly selected from the currently selected one cluster as the first subcarrier phase selection vector; an updated discrete phase vector is obtained based on the first subcarrier phase selection vector, and the process goes to S6, wherein p 1c is the probability of selecting the cluster center of one cluster; S5、if rand < p 2c then obtaining the second subcarrier phase selection vector based on the cluster centers of the two clusters selected currently; otherwise, obtaining the second subcarrier phase selection vector based on a random individual selected from the two clusters selected currently; obtaining the updated discrete phase vector based on the second subcarrier phase selection vector, and going to S6, wherein, p 2c is the probability of selecting the cluster center of the two clusters. S6, obtaining a periodic comprehensive sidelobe level of a periodic autocorrelation function of an OFDM original navigation signal vector, obtaining a PAPR value of the OFDM original navigation signal vector based on the initial discrete phase vector under the constraint condition that the periodic comprehensive sidelobe level of the periodic autocorrelation function of the OFDM original navigation signal vector is the lowest, obtaining a PAPR value of the OFDM original navigation signal vector based on the updated discrete phase vector, and taking the discrete phase vector corresponding to the smaller value of the two PAPR values as the discrete phase vector output in the current cycle; S7, taking the discrete phase vector output in the current cycle as the initial discrete phase vector, and repeating S2-S6 until the cycle number of the first layer cycle is reached, to obtain a discrete phase vector output in the first layer cycle; S8, taking the discrete phase vector output in the first layer cycle as the initial discrete phase vector, and repeating S2-S6 until the cycle number of the second layer cycle is reached, to obtain a discrete phase vector output in the second layer cycle; S9, taking the discrete phase vector output in the second layer cycle as the initial discrete phase vector, and repeating S2-S6 until the cycle number of the third layer cycle is reached, to obtain a discrete phase vector output in the third layer cycle, and taking the discrete phase vector output in the third layer cycle as the final discrete phase vector; S10, performing phase hopping on each subcarrier of the OFDM original navigation signal vector based on the final discrete phase vector, to obtain an OFDM hopping signal vector.

2. The method of claim 1, wherein, In S4, the updated discrete phase vector is obtained by the following formula: θ new = θ select + ξ · N(μ, σ 2 ) In the formula, θ new is an updated discrete phase vector, θ select is a first subcarrier phase selection vector, ξ is a first weight coefficient, N(μ,σ 2 ) is a Gaussian distribution function, μ is a mean value, and σ 2 is a variance.

3. The method of claim 2, wherein, In S5, the updated discrete phase vector is obtained by the following formula: θ new = θ' select + ξ · N(μ, σ 2 ) θ' select = w1θ select_1 + w2θ select_2 In the formula, θ′ select is a second subcarrier phase selection vector, θ select_1 , θ select_2 are respectively a cluster center of each of two clusters currently selected or a randomly selected individual of each of two clusters, and w1 and w2 are respectively a second and third weight coefficient.

4. The method of claim 1, wherein, The PAPR value of the OFDM original navigation signal vector is obtained by the following formula: wherein l=0,1,...,N-1 h=0,1,...,N-1 k=0,1,...,M-1 In the formula, PAPR is the PAPR value of the OFDM original navigation signal vector, b is a proportional coefficient, is a constant, X is the OFDM original navigation signal vector, H is a conjugate transpose, T is a transpose, N is the number of subcarriers, i, l, and h are different subcarrier indexes, θ′[l] and θ′[h] are the discrete phases of the lth and hth subcarriers in the updated discrete phase vector, and M is the number of OFDM symbols.

5. The method of claim 1, wherein, The OFDM hopping signal vector is obtained by the following formula: S PH = X e θ S PH = [s PH [0], s PH [1],..., s PH [N-1]] wherein In the formula, S PH is an OFDM hopping signal vector, X is an OFDM original navigation signal vector, θ is a final discrete phase vector, is a Hadamard product operator symbol, s PH is the kth OFDM hopping signal in the OFDM hopping signal vector, C[i] is a ranging code of the ith subcarrier, θ[i] is a discrete phase of the ith subcarrier in the final discrete phase vector, M is the number of OFDM symbols, and N is the number of subcarriers.

6. The method of claim 1, wherein, The cycle number of the first layer cycle is the number of OFDM symbols, the cycle number of the second layer cycle is the total number of iterations, and the cycle number of the third layer cycle is the number of uniform segmentation of the initial discrete phase vector in the range of [0, 2π].

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