An adaptive method and system for fast spatial spectrum estimation of multipath channels

Abstract

This invention provides an adaptive method and system for fast spatial spectrum estimation of multipath channels. The method includes: S1, using a linear uniform array as the receiving array, with the first element in the array as the reference element, deriving the broadband signal model and steering vector matrix received by the array; S2, constructing a fitness function, and using the dung beetle algorithm to search for the optimal fractional Fourier transform order of the received signal from the reference element; S3, performing the optimal fractional Fourier transform on the received signal of the array; S4, finding the coordinates (u) corresponding to the maximum value. p ,v p S5. Energy detection: Set a threshold for comparison. If the threshold is met, it indicates that the location of this point is a component of the multipath; otherwise, the algorithm ends. S6. Use the CLEAN algorithm to separate the multipath components. The center frequency of its narrowband filter is u. p S7. Use the MUSIC algorithm to estimate the incident angle of the multipath components; S8. Mask the strongest component among the current multipath components and return to repeat steps S4 to S7 until all components are estimated.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and more particularly to an adaptive method and system for fast spatial spectrum estimation of multipath channels. Background Technology

[0002] With the continuous development of communication technology, relying solely on a single antenna to extract and analyze the characteristics of received signals can no longer meet people's needs. Therefore, multiple antennas, i.e., antenna arrays, are used to analyze received signals. Compared with traditional single antennas, antenna arrays have greater gain, stronger anti-interference capabilities, and higher resolution, enabling research in areas such as beamforming, spatial spectrum estimation, source separation, and source number estimation. Array signal processing involves enhancing, denoising, and estimating parameters of the signals received by the array. Among these, spatial spectrum estimation, also known as Angle of Arrival (AOA) estimation, is an important branch of array signal processing, with wide applications in wireless communication, sonar, and physical layer security. In complex wireless environments, accurately and efficiently obtaining the angle information of signal sources through digital signal processing has always been a pressing problem for AOA estimation technology. With continuous research on broadband non-stationary signals, their characteristics such as resistance to Doppler attenuation, anti-interference, and low interception rate have been discovered, making AOA estimation of broadband signals a research hotspot.

[0003] In existing AOA estimation methods, the angles between arbitrary sources in the spatial domain can be well distinguished. However, after multiple reflections from obstacles such as buildings and mountains, the number of multipath components is uncertain, and the angles of arrival (AOA) between different components may be similar or the same. In this case, the multipath components are considered spatially dense signals. Furthermore, existing AOA estimation algorithms require an overdetermined condition, meaning the number of multipath components must be less than the number of antennas constituting the array. However, the number of multipath components is time-varying, often failing to meet this condition. This results in the multipath components in the array-received data not satisfying the low-rank condition, meaning the array manifold matrix is ​​not full-rank, leading to underdetermined conditions. Moreover, the multipath signals received by the array are a superposition of multiple broadband non-stationary signals with different frequencies, time delays, and amplitudes. Processing them using the fractional Fourier transform (FRFT) to find the optimal transform order involves relatively high computational costs. The dung beetle algorithm can significantly reduce this computational burden. Summary of the Invention

[0004] To address the problems in existing AOA estimation algorithms, such as the need to estimate a known number of signals, the inability to estimate spatially dense multipath components, the inability to estimate when the number of multipath components is greater than or equal to the number of array antennas, and the large computational cost of finding the optimal transform order when using fractional Fourier transform to process broadband multipath components, this invention can estimate signals with the same or similar angles when the number of multipath components is unknown, and can perform estimation under underdetermined conditions.

[0005] The technical means employed in this invention are as follows:

[0006] An adaptive fast spatial spectrum estimation method for multipath channels includes:

[0007] S1. Using a linear uniform array as the receiving array, with the first element in the array as the reference element, derive the broadband signal model and steering vector matrix received by the array.

[0008] S2. Construct a fitness function and use the dung beetle algorithm to search for the optimal fractional Fourier transform order of the received signal of the reference array element;

[0009] S3. Perform a fractional Fourier transform of the optimal order on the array received signal;

[0010] S4. Find the coordinates (u) corresponding to the maximum value. p ,v p );

[0011] S5. Energy detection, set threshold comparison, if... This indicates that the location of that point is a component of a multipath. The algorithm then ends;

[0012] S6. Using the CLEAN algorithm to separate multipath components, the center frequency of the narrowband filter is u. p The incident angle of the multipath component is estimated using the MUSIC algorithm.

[0013] S7. Mask the strongest component among the current multipath components, and return to repeat steps S4 to S7 until all components are estimated.

[0014] Furthermore, step S1 also includes:

[0015] The transceiver local oscillator frequency error is modeled as a priori coefficient and introduced into the steering vector matrix.

[0016] Further, in step S2, the dung beetle algorithm is used to find the optimal order of the fractional Fourier transform, and the fitness function is obtained according to the following formula:

[0017]

[0018] Among them, F q [·] denotes the fractional-order Fourier transform operator, q denotes the order of the fractional-order Fourier transform, and x1(t) denotes the received signal of the reference array element. This represents the j-th part of the I initial values.

[0019] Further, in step S2, the search for the optimal transformation order of the fractional Fourier transform based on the dung beetle algorithm specifically includes:

[0020] S21. Randomly generate I initial values ​​in the search interval [0,2], represented as follows:

[0021]

[0022] Where lb = 0 is the lower limit of the search space, ub = 2 is the upper limit of the search space, and ξ is a uniformly distributed random number;

[0023] S22. Substituting the formula from step S21 into the fitness function, the result is as follows:

[0024]

[0025] Where X1(u) represents the fractional Fourier transform of the signal received by the reference array element;

[0026] Find the optimal and worst positions for initializing the transformation order, i.e., the maximum and minimum values, respectively, represented as:

[0027]

[0028]

[0029] S23. To simulate complex real-world scenarios, set a random number for the obstacle coefficient υ∈[0,1], specifically as follows:

[0030] When υ < 0.9, it is considered that there are no obstacles, and i pro The positional transformation of the dung beetle, i.e., the initial transformation order i pro The transformation occurs, represented as:

[0031]

[0032] in, Used to simulate natural conditions Indicates the deflection coefficient. Here, j represents the light intensity coefficient, and j represents the current iteration number. Indicates changes in light intensity, Indicates the j-th iteration i pro Location information of the dung beetle; to simulate a realistic natural scene, it is usually taken as... or These two values ​​are random; when When this occurs, it indicates that the environment has no impact on the dung beetle's path of movement. This indicates that the dung beetle encountered uneven terrain or other poor environmental conditions during its journey.

[0033] When 0.9 ≤ υ ≤ 1, an obstacle is considered to exist. At this time, the dung beetle needs to change its forward movement, and its position information is updated. That is, the step size of the transformation number changes, which is represented as:

[0034]

[0035] in, Rotate the dung beetle by an angle, when the angle The dung beetle's location will only be updated at that time;

[0036] The current optimal position, i.e., the current optimal transformation order, is denoted as...

[0037] S24, i pro After updating the transformation order, a new transformation interval needs to be locked, meaning the dung beetle chooses a suitable and safe area to lay its eggs. The upper and lower limits of the egg-laying area are then represented as follows:

[0038]

[0039] Among them, Lb egg Indicates the lower limit of the spawning area, Ub egg R represents the upper limit of the spawning area, and Lb and Ub represent the lower and upper limits of the preset transformation interval, respectively. R = 1 - j / J max J max Indicates the maximum number of iterations;

[0040] Dung beetles are strictly confined to laying their eggs within a new area, therefore, i egg The location information of the dung beetle's egg-laying location, i. egg The update of the order of the initial value change can be expressed as:

[0041]

[0042] Where κ1 and κ2 are one-dimensional random variables, and the two are independent of each other;

[0043] S25, the i that was conceived lar The small dung beetle needs to forage in the optimal foraging area, that is, for i lar The initial transformation order redefines the upper and lower limits, denoted as:

[0044]

[0045] Among them, B i Lb represents the optimal foraging location globally. lar and Ub lar These represent the lower and upper limits of the optimal foraging area, respectively; therefore, i lar The position of the dung beetle is updated, i. lar The update of the initial transformation order is represented as follows:

[0046]

[0047] in, Indicates the i-th lar The initial values ​​are the transformation order in the j-th iteration, ε1 represents a random number that follows a normal distribution, and ε2 is a random number ∈ (0,1).

[0048] S26, i ste The dung beetle is called a thief, i.e. ste The transformation order can be represented in another update form as follows:

[0049]

[0050] in, Indicates the i-th iteration of the j-th iteration. ste The transformation order of the initial values, μ1 is a constant, μ2 represents a random number, and it follows a normal distribution;

[0051] S27. Select the optimal order, expressed as:

[0052]

[0053] S28. Repeat steps S23 to S27 for J iterations to obtain the final optimal transformation order.

[0054] Furthermore, step S5 also includes:

[0055] The threshold is set based on the energy of the FRF domain noise.

[0056] Further, in step S6, it is necessary to calculate the covariance matrix of the multipath components in the FRF domain and perform eigenvalue decomposition on it, then construct the signal subspace and noise subspace, and utilize their orthogonality to construct the spatial spectral function, specifically including:

[0057] The p-th multipath component is incident on the array, which consists of M antennas with a spacing of d between them. The covariance matrix is ​​expressed as:

[0058] R(u,α)=E[X(u,α)X H (u,α)]

[0059] =A(u,α)E[S(u,α)S H (u,α)]A H (u,α)+E[N(u,α)N H (u,α)]

[0060] +A(u,α)E[S(u,α)N H (u,α)]+E[N(u,α)S H (u,α)]A H (u,α)

[0061] Where X(u,α) represents the fractional Fourier transform of the received signal, A(u,α) represents the steering vector matrix, S(u,α) represents the fractional Fourier transform of the source, and N(u,α) represents the fractional Fourier transform of the noise.

[0062] A(u,α)=[a1(u,α,θ1),a2(u,α,θ2),…,a P (u,α,θ P )]

[0063]

[0064] Among them, k, f0 and These represent the frequency modulation slope, initial frequency, and initial phase of the linear frequency modulated signal, respectively, τ. pm The time delay for the p-th component to reach the m-th array element;

[0065] Since the signal and noise are independent of each other, we have:

[0066] E[S(u,α)N H [u,α]=0

[0067] E[N(u,α)S H [u,α]=0

[0068] Therefore, the above formula for the covariance matrix can be expressed as:

[0069] R(u,α)=AE[S(u,α)S H (u,α)]A H +E[N(u,α)N H (u,α)]

[0070] =A(u,α)R S (u,α)A H (u,α)+σ 2 I

[0071] Where, σ 2 Noise power;

[0072] For multipath components s p After performing a fractional Fourier transform on (t), the energy is mainly concentrated in (u). p At position α), the energy at other positions can be ignored; therefore, the covariance matrix can be simplified to:

[0073] R(u p ,α)=A(u p ,α)R S (u p ,α)A H (u p ,α)+σ 2 I

[0074] Among them, R(u p ,α p The time-domain autocorrelation matrix is ​​replaced by the eigenvalue decomposition of the time-domain autocorrelation matrix, which can be expressed as:

[0075]

[0076] Among them, U S and U N These represent the signal subspace and noise subspace of the source signal in the FRF domain, respectively, Σ S and Σ N Let be the eigenvalues ​​corresponding to the signal subspace and noise subspace of the FRFT domain, respectively. Based on orthogonality, we can obtain:

[0077] R(u p ,α)U N (u p ,α)=A(u p ,α)R S (u p ,α)A H (u p ,α)+σ 2 U N (u p ,α)

[0078] =σ 2 U N (u p ,α)

[0079] We can obtain:

[0080] A(u p ,α)R S (u p ,α)A H (u p,α)U N (u p ,α)=0

[0081] Therefore, we can obtain:

[0082]

[0083] Among them, R S (u, α) is non-singular and full rank, therefore it has an invertible matrix, so the formula A(u) = ... p ,α)R S (u p ,α)A H (u p ,α)U N (u p ,α)=0 can be rewritten as:

[0084] A H (u p ,α)U N (u p ,α)=0

[0085] Therefore, we can obtain:

[0086]

[0087] Therefore, the spatial spectrum of the FRF domain MUSIC algorithm can be expressed as:

[0088]

[0089] This invention also provides an adaptive multipath channel fast spatial spectrum estimation system based on the above-mentioned adaptive multipath channel fast spatial spectrum estimation method, comprising: an array signal receiving module, an optimal order search module, a fractional-order Fourier transform module, an energy detection module, a multipath component separation module, and a spatial spectrum estimation module, wherein:

[0090] The array signal receiving module uses a uniform linear array to receive multipath components.

[0091] The optimal order search module uses the dung beetle algorithm to search for the optimal order of the fractional Fourier transform of the multipath components;

[0092] The fractional Fourier transform module performs a fractional Fourier transform on the array received signal with the optimal transform order.

[0093] The energy detection module sets a threshold to determine whether it is a multipath component;

[0094] The multipath component separation module uses CLEAN to separate multipath components of different intensities;

[0095] The spatial spectrum estimation module is used to estimate the incident angle information of each multipath component.

[0096] Compared with the prior art, the present invention has the following advantages:

[0097] 1. The adaptive multipath channel fast spatial spectrum estimation method provided by this invention can estimate signals with the same or similar angles when the number of multipath components is unknown, and can perform estimation under underdetermined conditions. Moreover, the algorithm has good resolution and improves algorithm performance.

[0098] 2. By using the method of the present invention, while ensuring search accuracy, the amount of computation when searching for the optimal transformation order of the fractional Fourier transform can be greatly reduced, thereby further improving the operation speed.

[0099] Based on the above reasons, this invention can be widely applied in fields such as array signal processing. Attached Figure Description

[0100] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0101] Figure 1 This is a flowchart of the method of the present invention.

[0102] Figure 2 A graph showing the relationship between the number of iterations and the optimal transformation order provided for embodiments of the present invention.

[0103] Figure 3(a) is a numerical graph of the dung beetle algorithm for each iteration of the present invention.

[0104] Figure 3(b) is a magnified view of a portion of Figure 3(a).

[0105] Figure 4 A comparison chart of the running time of the two-dimensional search and dung beetle algorithm provided in an embodiment of the present invention.

[0106] Figure 5 The fractional Fourier transform diagram of the reference antenna received signal provided in the embodiments of the present invention.

[0107] Figure 6 An angle of arrival estimation diagram for multipath components provided in an embodiment of the present invention.

[0108] Figure 7 This is a comparison chart of root mean square error provided in an embodiment of the present invention. Detailed Implementation

[0109] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0110] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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 some embodiments of the present invention, and not all embodiments. 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.

[0111] 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 scope of exemplary embodiments according to the invention. 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.

[0112] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described 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.

[0113] In the description of this invention, it should be understood that the orientation or positional relationship indicated by directional terms such as "front, back, up, down, left, right", "horizontal, vertical, horizontal" and "top, bottom" is generally based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing this invention and simplifying the description. Unless otherwise stated, these directional terms do not indicate or imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the scope of protection of this invention. The directional terms "inner" and "outer" refer to the inner and outer contours relative to the outline of each component itself.

[0114] For ease of description, spatial relative terms such as "above," "over," "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 besides the orientation of the device as described in the figures. For example, if the device in the figures is inverted, a device described as "above" or "above" 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.

[0115] 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.

[0116] like Figure 1 As shown, this invention provides an adaptive fast spatial spectrum estimation method for multipath channels, comprising:

[0117] S1. Using a linear uniform array as the receiving array, with the first element in the array as the reference element, derive the broadband signal model and steering vector matrix received by the array.

[0118] S2. Construct a fitness function and use the dung beetle algorithm to search for the optimal fractional Fourier transform order of the received signal of the reference array element;

[0119] S3. Perform a fractional Fourier transform of the optimal order on the array received signal;

[0120] S4. Find the coordinates (u) corresponding to the maximum value. p ,v p );

[0121] S5. Energy detection, set threshold comparison, if... This indicates that the location of that point is a component of a multipath. The algorithm then ends;

[0122] S6. Using the CLEAN algorithm to separate multipath components, the center frequency of the narrowband filter is u. p The incident angle of the multipath component is estimated using the MUSIC algorithm.

[0123] S7. Mask the strongest component among the current multipath components, and return to repeat steps S4 to S7 until all components are estimated.

[0124] In a specific implementation, as a preferred embodiment of the present invention, step S1 further includes:

[0125] The transceiver local oscillator frequency error is modeled as a priori coefficient and introduced into the steering vector matrix.

[0126] In specific implementation, as a preferred embodiment of the present invention, such as Figure 2 Figures 3 and 4 show the relationship between the number of iterations and the optimal transformation order, as well as the numerical graph and local magnified view of each iteration of the dung beetle algorithm. In step S2, the dung beetle algorithm is used to find the optimal transformation order of the fractional Fourier transform. The fitness function is obtained according to the following formula:

[0127]

[0128] Among them, F q [·] denotes the fractional-order Fourier transform operator, q denotes the order of the fractional-order Fourier transform, and x1(t) denotes the received signal of the reference array element. This represents the j-th part of the I initial values.

[0129] In a specific implementation, as a preferred embodiment of the present invention, individuals within a dung beetle population play different roles, including: producers, egg masses, larvae, and thieves, each denoted by a size i. pro i egg i lar and i ste Then population I j =i pro +i egg +i lar +i ste .like Figure 4 The figure shows a comparison of the running time of the two-dimensional search and the dung beetle algorithm. In step S2, the search for the optimal transformation order based on the fractional Fourier transform using the dung beetle algorithm specifically includes:

[0130] S21. Randomly generate I initial values ​​in the search interval [0,2], represented as follows:

[0131]

[0132] Where lb = 0 is the lower limit of the search space, ub = 2 is the upper limit of the search space, and ξ is a uniformly distributed random number;

[0133] S22. Substituting the formula from step S21 into the fitness function, the result is as follows:

[0134]

[0135] Where X1(u) represents the fractional Fourier transform of the signal received by the reference array element.

[0136] Find the optimal and worst positions for initializing the transformation order, i.e., the maximum and minimum values, respectively, represented as:

[0137]

[0138]

[0139] S23. To simulate complex real-world scenarios, set a random number for the obstacle coefficient υ∈[0,1], specifically as follows:

[0140] When υ < 0.9, it is considered that there are no obstacles, and i pro The positional transformation of the dung beetle, i.e., the initial transformation order i pro The transformation occurs, represented as:

[0141]

[0142] in, Used to simulate natural conditions Indicates the deflection coefficient. Here, j represents the light intensity coefficient, and j represents the current iteration number. Indicates changes in light intensity, Indicates the j-th iteration i pro The location information of the dung beetle; the selection of each parameter in the above formula is very important for the algorithm's search capability and convergence speed. In this embodiment, in order to simulate a real natural scene, the parameters are usually selected as follows: or These two values ​​are random; when When this occurs, it indicates that the environment has no impact on the dung beetle's path of movement. This indicates that the dung beetle encountered uneven terrain or other poor environmental conditions during its journey.

[0143] When 0.9 ≤ υ ≤ 1, an obstacle is considered to exist. At this time, the dung beetle needs to change its forward movement, and its position information is updated. That is, the step size of the transformation number changes, which is represented as:

[0144]

[0145] in, Rotate the dung beetle by an angle, when the angle The dung beetle's location will only be updated at that time;

[0146] The current optimal position, i.e., the current optimal transformation order, is denoted as...

[0147] S24, i pro After updating the transformation order, a new transformation interval needs to be locked, meaning the dung beetle chooses a suitable and safe area to lay its eggs. The upper and lower limits of the egg-laying area are then represented as follows:

[0148]

[0149] Among them, Lb egg Indicates the lower limit of the spawning area, Ub egg R represents the upper limit of the spawning area, and Lb and Ub represent the lower and upper limits of the preset transformation interval, respectively. R = 1 - j / J max J max Indicates the maximum number of iterations;

[0150] Dung beetles are strictly confined to laying their eggs within a new area, therefore, i egg The location information of the dung beetle's egg-laying location, i. egg The update of the order of the initial value change can be expressed as:

[0151]

[0152] Where κ1 and κ2 are one-dimensional random variables, and the two are independent of each other;

[0153] S25, the i that was conceived lar The small dung beetle needs to forage in the optimal foraging area, that is, for i lar The initial transformation order redefines the upper and lower limits, denoted as:

[0154]

[0155] Among them, B i Lb represents the optimal foraging location globally. lar and Ub lar These represent the lower and upper limits of the optimal foraging area, respectively; therefore, i lar The position of the dung beetle is updated, i. larThe update of the initial transformation order is represented as follows:

[0156]

[0157] in, Indicates the i-th lar The initial values ​​are the transformation order in the j-th iteration, ε1 represents a random number that follows a normal distribution, and ε2 is a random number ∈ (0,1).

[0158] S26, i ste The dung beetle is called a thief, i.e. ste The transformation order can be represented in another update form as follows:

[0159]

[0160] in, Indicates the i-th iteration of the j-th iteration. ste The transformation order of the initial values, μ1 is a constant, μ2 represents a random number, and it follows a normal distribution;

[0161] S27. Select the optimal order, expressed as:

[0162]

[0163] S28. Repeat steps S23 to S27 for J iterations to obtain the final optimal transformation order. For example... Figure 5 The figure shown is a fractional Fourier transform diagram of the signal received by the reference antenna.

[0164] In a specific implementation, as a preferred embodiment of the present invention, step S5 further includes:

[0165] The threshold is set based on the energy of the FRF domain noise.

[0166] In specific implementation, as a preferred embodiment of the present invention, such as Figure 6 The image shows the angle of arrival estimation diagram for the multipath components. Figure 7 The image shows a comparison of root mean square errors. In step S6, the covariance matrix of the multipath components in the FRF domain needs to be calculated and its eigenvalues ​​decomposed. Then, a signal subspace and a noise subspace are constructed. Using their orthogonality, a spatial spectral function is constructed, specifically including:

[0167] The p-th multipath component is incident on the array, which consists of M antennas with a spacing of d between them. The covariance matrix is ​​expressed as:

[0168] R(u,α)=E[X(u,α)X H (u,α)]

[0169] =A(u,α)E[S(u,α)S H (u,α)]A H (u,α)+E[N(u,α)N H (u,α)]

[0170] +A(u,α)E[S(u,α)N H (u,α)]+E[N(u,α)S H (u,α)]A H (u,α)

[0171] Where X(u,α) represents the fractional Fourier transform of the received signal, A(u,α) represents the steering vector matrix, S(u,α) represents the fractional Fourier transform of the source, and N(u,α) represents the fractional Fourier transform of the noise.

[0172] A(u,α)=[a1(u,α,θ1),a2(u,α,θ2),…,a P (u,α,θ P )]

[0173]

[0174] Among them, k, f0 and These represent the frequency modulation slope, initial frequency, and initial phase of the linear frequency modulated signal, respectively, τ. pm Let be the time delay for the p-th component to reach the m-th array element.

[0175] Since the signal and noise are independent of each other, we have:

[0176] E[S(u,α)N H [u,α]=0

[0177] E[N(u,α)S H [u,α]=0

[0178] Therefore, the above formula for the covariance matrix can be expressed as:

[0179] R(u,α)=AE[S(u,α)S H (u,α)]A H +E[N(u,α)N H (u,α)]

[0180] =A(u,α)R S (u,α)A H (u,α)+σ 2 I

[0181] Where, σ 2 Noise power;

[0182] For multipath components s p After performing a fractional Fourier transform on (t), the energy is mainly concentrated in (u). p At position α), the energy at other positions can be ignored; therefore, the covariance matrix can be simplified to:

[0183] R(u p ,α)=A(u p ,α)R S (u p ,α)A H (u p ,α)+σ 2 I

[0184] Among them, R(u p The time-domain autocorrelation matrix is ​​replaced by α, and its eigenvalue decomposition can be expressed as:

[0185]

[0186] Among them, U S and U N These represent the signal subspace and noise subspace of the source signal in the FRF domain, respectively, Σ S and Σ N Let be the eigenvalues ​​corresponding to the signal subspace and noise subspace of the FRFT domain, respectively. Based on orthogonality, we can obtain:

[0187] R(u p ,α)U N (u p ,α)=A(u p ,α)R S (u p ,α)A H (u p ,α)+σ 2 U N (u p ,α)

[0188] =σ 2 U N (u p ,α)

[0189] We can obtain:

[0190] A(u p ,α)R S (u p ,α)A H (u p ,α)U N (u p ,α)=0

[0191] Therefore, we can obtain:

[0192]

[0193] Among them, R S (u, α) is non-singular and full rank, therefore it has an invertible matrix, so the formula A(u) = ... p ,α)R S (u p ,α)A H (u p ,α)U N (u p ,α)=0 can be rewritten as:

[0194] A H (u p ,α)U N (u p ,α)=0

[0195] Therefore, we can obtain:

[0196]

[0197] Therefore, the spatial spectrum of the FRF domain MUSIC algorithm can be expressed as:

[0198]

[0199] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention 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 or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An adaptive fast spatial spectrum estimation method for multipath channels, characterized in that, include: S1. Using a linear uniform array as the receiving array, with the first element in the array as the reference element, derive the broadband signal model and steering vector matrix received by the array. S2. Construct a fitness function and use the dung beetle algorithm to search for the optimal fractional Fourier transform order of the received signal of the reference array element; S3. Perform a fractional Fourier transform of the optimal order on the array received signal; S4. Find the coordinates corresponding to the maximum value. ; S5. Energy detection, setting threshold. Comparison, if This indicates that the location of that point is a component of a multipath. The algorithm then ends; S6. Using the CLEAN algorithm to separate multipath components, the center frequency of the narrowband filter is: The MUSIC algorithm is used to estimate the incident angle of the multipath components; the covariance matrix of the multipath components in the FRF domain is calculated and its eigenvalues ​​are decomposed; then, a signal subspace and a noise subspace are constructed, and the spatial spectrum function is constructed using their orthogonality. The spatial spectrum representation of the FRF domain MUSIC algorithm is as follows: in, This represents the guiding vector matrix of the array in the FRF domain; Represents the noise subspace matrix; S7. Mask the strongest component among the current multipath components, and return to repeat steps S4 to S7 until all components are estimated.

2. The adaptive multipath channel fast spatial spectrum estimation method according to claim 1, characterized in that, Step S1 also includes: The transceiver local oscillator frequency error is modeled as a priori coefficient and introduced into the steering vector matrix.

3. The adaptive multipath channel fast spatial spectrum estimation method according to claim 1, characterized in that, In step S2, the dung beetle algorithm is used to find the optimal order of the fractional Fourier transform, and the fitness function is obtained according to the following formula: in, This represents a fractional Fourier transform operator. q This indicates the order of the fractional Fourier transform. This indicates that the reference array element receives the signal. Indicates in I The first initial value is divided into the first... j Each part.

4. The adaptive multipath channel fast spatial spectrum estimation method according to claim 1, characterized in that, In step S2, the search for the optimal transformation order of the fractional Fourier transform based on the dung beetle algorithm specifically includes: S21, within the search interval Randomly generated I An initial value is represented as: in, As the lower bound of the search space, This is the upper limit of the search space. These are uniformly distributed random numbers; S22. Substituting the formula from step S21 into the fitness function, the result is as follows: in, This represents the fractional Fourier transform of the signal received by the reference array element; Find the optimal and worst positions for initializing the transformation order, i.e., the maximum and minimum values, respectively, represented as: S23. To simulate complex real-world scenarios, set the obstacle coefficient. The random number is as follows: when At that time, they thought there were no roadblocks. The positional transformation of the dung beetle, i.e., the initial transformation order. The transformation occurs, represented as: in, Used to simulate natural conditions Indicates the deflection coefficient. This is the light intensity coefficient. j Indicates the current iteration number. Indicates changes in light intensity, Indicates the first j Second iteration Location information of the dung beetle; to simulate a realistic natural scene, [the following information is taken]. , , or These two values ​​are random; when When this occurs, it indicates that the environment has no impact on the dung beetle's path of movement. This indicates that the dung beetle encountered an uneven road surface during its journey. when When the dung beetle perceives an obstacle, it needs to change its movement pattern, updating its position information. This means the step size of the transformation number changes, represented as: in, Rotate the dung beetle by an angle, when the angle The dung beetle's location will only be updated at that time; The current optimal position, i.e., the current optimal transformation order, is denoted as... S24, After updating the transformation order, a new transformation interval needs to be locked, meaning the dung beetle chooses a suitable and safe area to lay its eggs. The upper and lower limits of the egg-laying area are then represented as follows: in, Indicates the lower limit of the spawning area. Indicates the upper limit of the spawning area. and These represent the lower and upper limits of the preset transformation interval, respectively; , Indicates the maximum number of iterations; Dung beetles are strictly confined to laying their eggs within a new area, therefore... Information on the location where a dung beetle lays its eggs, i.e. The update of the order of initial value change is expressed as: in, and Let be a one-dimensional random variable, and the two are independent of each other; S25, born from The dung beetle needs to forage in the optimal foraging area, that is, it needs to... The initial transformation order redefines the upper and lower limits, denoted as: in, This indicates the optimal foraging location globally. and These represent the lower and upper limits of the optimal foraging area, respectively; therefore, The location of the dung beetle is updated, that is... The update of the initial transformation order is represented as follows: in, Indicates the first The initial value at the th ... j The transformation order of the next iteration This represents a random number that follows a normal distribution. Random numbers; S26, Yes Dung beetles are called thieves, that is... The transformation order can be represented in another update form as follows: in, Indicates the first j The second iteration The transformation order of initial values, For a constant value, This represents a random number that follows a normal distribution. S27. Select the optimal order, expressed as: S28, proceed J Repeat steps S23 to S27 in the next iteration to obtain the final optimal transformation order.

5. The adaptive multipath channel fast spatial spectrum estimation method according to claim 1, characterized in that, Step S5 further includes: The threshold is set based on the energy of the FRF domain noise.

6. The adaptive multipath channel fast spatial spectrum estimation method according to claim 1, characterized in that, In step S6, the covariance matrix of the multipath components in the FRF domain is calculated and its eigenvalues ​​are decomposed. Then, a signal subspace and a noise subspace are constructed. Using their orthogonality, a spatial spectral function is constructed, specifically including: No. p Multiple path components are incident on the array, and the receiving array consists of... M It consists of several antennas, with a spacing between the antennas being [missing information]. d The covariance matrix is ​​expressed as: in, Represents the fractional Fourier transform of the received signal. Represents the guiding vector matrix. Represents the fractional Fourier transform of the information source. The fractional Fourier transform representing noise; in, k , and These represent the frequency modulation slope, initial frequency, and initial phase of the linear frequency modulated signal, respectively. For the first p The component reaches the first m The latency of each array element; Since the signal and noise are independent of each other, we have: Therefore, the above formula for the covariance matrix is ​​expressed as: in, Noise power; For multipath components After performing a fractional Fourier transform, the energy is mainly concentrated in At point 1, energy is negligible elsewhere; therefore, the covariance matrix simplifies to: in, The time-domain autocorrelation matrix is ​​replaced, and its eigenvalue decomposition is expressed as: in, and These are the signal subspace and noise subspace of the source signal in the FRF domain, respectively. and The eigenvalues ​​corresponding to the signal subspace and noise subspace in the FRFT domain are respectively obtained based on orthogonality: get: Therefore, we get: in, Since it is non-singular and full-rank, it has an invertible matrix, hence the formula... Rewritten as: Therefore, we get: Therefore, the spatial spectrum of the FRF domain MUSIC algorithm is represented as: 。 7. An adaptive multipath channel fast spatial spectrum estimation system based on the adaptive multipath channel fast spatial spectrum estimation method according to any one of claims 1-6, characterized in that, include: The system includes an array signal receiving module, an optimal order search module, a fractional-order Fourier transform module, an energy detection module, a multipath component separation module, and a spatial spectrum estimation module, among which: The array signal receiving module uses a uniform linear array to receive multipath components. The optimal order search module uses the dung beetle algorithm to search for the optimal order of the fractional Fourier transform of the multipath components; The fractional Fourier transform module performs a fractional Fourier transform on the array received signal with the optimal transform order. The energy detection module sets a threshold to determine whether it is a multipath component; The multipath component separation module uses CLEAN to separate multipath components of different intensities; The spatial spectrum estimation module is used to estimate the incident angle information of each multipath component.

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