Low complexity frequency scanning lwa based on the idea of grouping fusion doa estimation method

Abstract

The application discloses a low-complexity frequency scanning LWA DOA estimation method based on a grouping fusion idea. The main beam direction of a leaky-wave antenna can be changed along with the change of a working frequency, so that the coverage of a radio signal is increased, and the energy consumption of equipment is effectively saved. Meanwhile, the application solves the DOA estimation problem of non-coherent signals and strongly correlated signals which can occur in a real scene. Compared with a traditional DOA estimation method, the method does not need array flow vector to be in a Vandermonde form, the calculation amount is greatly reduced compared with projection and other traditional methods, the required matrix dimension is low, and the implementation steps are simple. The method is not only suitable for single / multi-beam frequency scanning leaky-wave antennas, but also has generalizability for all frequency selection antennas.

Description

Technical Field

[0001] This invention relates to the fields of antenna technology, signal processing, and more specifically to a low-complexity frequency scanning LWA DOA estimation method based on the idea of ​​group fusion. Background Technology

[0002] Direction-of-arrival (DOA) estimation methods based on array signal processing are widely used in various fields such as sonar, radar, seismic surveying, and medicine. Traditional DOA estimation systems typically require a large number of complex radio frequency modules working together, including antenna arrays, radio frequency conversion channels, signal processing modules, etc., which makes the equipment too large, consumes too much energy, and is relatively expensive.

[0003] Leaky-wave antennas (LWAs), as a typical beam-scanning antenna, can change the direction of their main beam with the operating frequency, thereby increasing the coverage of radio signals, improving the frequency space reuse rate, and saving equipment energy.

[0004] In recent years, research on DOA estimation using LWA (Low-Range Waveguide) has achieved some results. However, most of these studies are based on electrically controlled beam scanning, requiring DC bias for each element, making the implementation process quite complex. Therefore, frequency-scanning leaky wave antennas (LWAs) have attracted much attention. Although there are feasible implementation schemes for DOA estimation of incoherent signals based on LWAs, how to use LWAs to solve the DOA estimation problem of strongly correlated signals that may occur in reality remains to be solved. Simply using subspace methods such as Multiple Signal Classification (MUSIC) algorithms for DOA estimation of correlated signals cannot achieve the desired results.

[0005] On the other hand, because the array manifold matrix of the LWA received signal is not in Vandermonde form, many DOA estimation methods cannot be applied. Transforming the LWA array manifold matrix into Vandermonde form using projection, then using preprocessing methods such as spatial smoothing to decoherentize, and finally obtaining the DOA through a subspace estimation algorithm is a viable solution. However, this method has high computational complexity and requires pre-determining the initial range of the incident signal based on techniques such as beamforming. Especially in DOA estimation of strongly correlated signals from multi-beam frequency-scanning leaky-wave antennas, the computational complexity of this method is extremely high, requiring the use of two-dimensional projection to barely complete.

[0006] Therefore, it is urgent to explore how to perform low-complexity DOA estimation for frequency-scanning leaky wave antennas. Summary of the Invention

[0007] The purpose of this invention is to solve the problem of DOA estimation for incoherent and strongly correlated signals, which is frequently encountered in existing technologies. It provides a low-complexity DOA estimation method for frequency-scanning loop wave antennas (LWAs) based on the grouping and fusion approach. This method transmits incoherent or strongly correlated signals, receives signals at different frequency bands using a single leaky wave antenna, groups the received signals at different frequencies for each LWA, and obtains the corresponding covariance matrix and array manifold vector. Finally, the DOA estimate is obtained using the MUSIC algorithm. This invention, while ensuring the accuracy of signal DOA estimation, fully utilizes the advantages of LWAs and significantly reduces computational complexity.

[0008] The objective of this invention can be achieved by adopting the following technical solutions:

[0009] A low-complexity frequency-scanning leaky-wave antenna DOA estimation method based on the idea of ​​group fusion is proposed. The DOA estimation method includes the following steps:

[0010] Transmitted signal: Narrowband signals are transmitted from different angles. After noise is superimposed during propagation, the transmitted signal is either an incoherent signal or a strongly correlated signal.

[0011] LWA received signal: There are R narrowband source signals from different directions θ1, θ2, ..., θ R The impact is directed onto a receiving array consisting of N leaky wave antennas of different frequencies. The leaky wave antenna is referred to as LWA below.

[0012] Grouping of received signals: Grouping received signals of different frequencies in LWA;

[0013] Reconstructing the covariance matrix: Calculate the covariance matrix of each group of received signals, sum the covariance matrices of all groups and take the average value to obtain the reconstructed covariance matrix of the received signals;

[0014] Reconstructing the array manifold vector: Calculate the array manifold vector for each group of received signals, sum the array manifold vectors of all groups and take the average value to obtain the reconstructed array manifold vector corresponding to LWA;

[0015] The MUSIC algorithm estimates the DOA value: The MUSIC algorithm is used to estimate the reconstructed covariance matrix and the reconstructed array manifold vector to obtain the DOA value.

[0016] Furthermore, the N different frequencies of the leaky wave antenna are distributed at equal intervals. Here, the frequency-divided received signals are equivalent to the signals received by different array elements in a traditional array antenna. The difference is that there is no time delay when receiving signals at different frequencies, while there is a time delay in the different array elements of a traditional array antenna. These frequencies satisfy the following:

[0017] f = [f min ,fmin +Δf,...,f max -Δf,f max ]

[0018]

[0019] f min =f0-δ f / 2

[0020] f max =f0+δ f / 2

[0021] In the formula, f0 is the center frequency, δ f Where f is the frequency bandwidth used, Δf is the frequency sampling interval, and f max f is the maximum sampling frequency. min This is the minimum sampling frequency;

[0022] Divide all frequencies into Q groups, where q represents the total number of frequencies in each group, and Q = N / q. Use numbers 1, 2, ..., N to represent N different frequencies. The grouping of groups 1, 2, ..., Q is shown in the following numbers:

[0023] {1, Q+1, Q*2+1,…,Q*(q-1)+1}

[0024] {2, Q+2, Q*2+2,…,Q*(q-1)+2}

[0025] ...

[0026] {q, Q+q, Q*2+q,…,Q*(q-1)+Q}.

[0027] Furthermore, because the beam-scanning characteristics of leaky antennas facilitate the construction of multiple channels, no antenna array is required for signal reception; only the signal received by a single leaky antenna needs to be considered.

[0028] Y = AS + n

[0029] S is the signal emitted by the signal source, n is the noise during signal transmission, and A = [a(θ1), a(θ2), ..., a(θ)]. R [)] represents the array manifold vector corresponding to LWA, and the r-th incident angle θ r The corresponding guiding vector a(θ) r )for

[0030]

[0031] l represents the length of LWA, m forw and m back The harmonic order of the radiation at the forward and backward endpoints, k zmk and k0 are the first and second parameters for implementing the vector expression of the array manifold, respectively, m forw m back k zm The specific expressions for k0 are as follows:

[0032]

[0033]

[0034] k zm =β m -jα

[0035] k0=2πf / c

[0036] p is the spatial period of the modulation, c is the speed of light, and ε is the velocity of light. r It is a relative medium constant. The cutoff frequency, Let α be the width of the waveguide, α be the attenuation constant for leakage and loss, and β be the phase. m =β0 + 2πm / p, where β0 is the phase constant of the fundamental guided mode, and the harmonic order m ∈ [m back ,m forw ] is an integer.

[0037] Furthermore, inspired by traditional decoherence methods, which always group and smooth signals between different array elements, we consider grouping and fusing signals between different frequencies to attempt to partially recover the rank of the covariance matrix of the correlated signals. Let y be the signal obtained from the grouping into the i-th group. i Let i = 1, 2, ..., Q, and let R be the covariance matrix of the i-th group after grouping. i =E(y) i y i H Summing and averaging the covariance matrices of all groups yields the covariance matrix after reconstructing the received signal: The dimension of the covariance matrix is ​​reduced from (N×N) to (q×q) after reconstruction.

[0038] Furthermore, to maintain consistency with the dimensions after covariance matrix reconstruction in the previous step, and to utilize all information as much as possible while reducing computational cost, we adopt the same grouping method for the array manifold vectors. Let A be the array manifold vector in the i-th group after grouping. i , i = 1, 2, ..., Q, where, for array manifold vector A i Whether it is in Vandermonde form is not restricted. Summing and averaging the array manifold vectors of all groups, the reconstructed array manifold vector corresponding to LWA is obtained as follows:

[0039]

[0040] The array manifold vector dimension is reduced from (N×R) to (q×R) after reconstruction. The r-th incident angle θ r The corresponding reconstructed guide vector is a average (θ r ).

[0041] Furthermore, the rank deficiency of the covariance matrix is ​​improved after grouping. Since the array manifold vector is not in Vandermonde form, we substitute it into the MUSIC algorithm for DOA estimation. Substituting the reconstructed covariance matrix R... average and the reconstructed array manifold vector A average The MUSIC algorithm is used to obtain the estimated DOA value. The implementation process of the MUSIC algorithm is as follows:

[0042] The covariance matrix R after reconstructing the received signal average Perform eigenvalue decomposition into

[0043] R average =E s D s E s H +E n D n E n H

[0044] Where E s Let E be the signal subspace, where E n For the noise subspace, D s and D n The spatial spectrum function is constructed as follows, taking the eigenvalues ​​corresponding to the signal subspace and the noise subspace, respectively:

[0045]

[0046] By iterating through the range of values ​​for θ, P is obtained through spectral peak search. music The angle θ corresponding to the maximum value true This is the desired DOA value.

[0047] The present invention has the following advantages and effects compared with the prior art:

[0048] (1) Compared with other traditional antennas and phased arrays, the frequency-scanning LWA used in this invention utilizes beam scanning characteristics to construct multiple channels. This method requires smaller RF channel volume, has a wider application frequency range, and effectively saves equipment energy consumption. Compared with electrically controlled scanning LWA, which requires DC bias to each element, resulting in additional design complexity, frequency-scanning LWA is currently the most suitable choice for miniaturizing and reducing power consumption of DOA estimation equipment.

[0049] (2) The group fusion method proposed in this invention has a certain decoherence capability, and recovers the rank of the covariance matrix of a portion of the received signal by grouping. Experimental results show that it is still effective for strongly coherent signals with a coherence degree of 0.99.

[0050] (3) The DOA estimation method in this invention does not emphasize that the array manifold vector is in Vandermonde form; it only groups frequencies, which can be extended to all frequency-selective antennas. Traditional subspace methods require the array manifold vector to be in Vandermonde form if decoherence capability is required, which greatly limits the scope of application. The array manifold vector of single-beam frequency scanning LWA is also in non-Vandermonde form, and the number of beams corresponding to fixed frequencies is less than that of multi-beam LWA, resulting in lower experimental complexity. Therefore, it is also suitable for this scheme as a frequency-selective antenna.

[0051] (4) The group fusion method proposed in this invention reduces the dimension of the covariance matrix of the received signal from (N×N) to (q×q) after reconstruction. The dimension of the array manifold vector is reduced from (N×R) to (q×R) after reconstruction. As the matrix dimension decreases, the complexity is greatly reduced. Compared with the projection method, this scheme does not require initial angle estimation, the steps are simpler, the computational load is further reduced, and it is easy to apply in engineering. Attached Figure Description

[0052] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0053] Figure 1 This is a system block diagram of the low-complexity frequency scanning LWA DOA estimation method based on the idea of ​​group fusion disclosed in this invention;

[0054] Figure 2 This is a schematic diagram of signal grouping in this invention;

[0055] Figure 3 This is the normalized radiation pattern of a specified frequency of the multi-beam frequency scanning leaky antenna in Embodiment 1 of the present invention;

[0056] Figure 4This is the DOA estimation MUSIC pseudospectral diagram of a multi-beam frequency scanning leaky wave antenna based on the group fusion concept in Embodiment 1 of the present invention;

[0057] Figure 5 This is the normalized radiation pattern of a specified frequency of the single-beam frequency-scanning leaky antenna in Embodiment 2 of the present invention;

[0058] Figure 6 This is the MUSIC pseudospectral diagram of DOA estimation for a single-beam frequency scanning leaky wave antenna based on the group fusion concept in Embodiment 2 of the present invention. Detailed Implementation

[0059] 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, not all embodiments. 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.

[0060] Example 1

[0061] This embodiment discloses a low-complexity frequency-scanning multi-beam LWA DOA estimation method based on the grouping fusion concept, and the implementation block diagram is as follows: Figure 1 As shown, the specific steps include:

[0062] S1. Transmitted signal: Narrowband signals are transmitted from different angles. After noise is superimposed during propagation, the correlation of the transmitted signal is 0.99.

[0063] S2, LWA received signal: Three narrowband source signals from different directions [θ1,θ2,θ3]=[10°,-20.25°,-10.25°] strike the receiving array composed of 200 leaky antennas of different frequencies. Then the signal received by a single leaky antenna is Y=AS+n.

[0064] S is the signal emitted by the signal source, n is the noise during signal transmission, A = [a(θ1), a(θ2), a(θ3)] is the array manifold vector corresponding to LWA, and the r-th incident angle θ r The corresponding guiding vector a(θ) r )for

[0065] In the formula, l = 20cm represents the length of LWA, m forw and m back The harmonic orders radiated at the forward and backward endpoints, m in a multi-beam frequency-scanning leaky antenna. forw -m back+1 = 5. k zm k and k0 are the first and second parameters, respectively, for implementing the vector expression of the array manifold. The relative medium constant ε r =2.94, waveguide width a = 3.5mm, attenuation constant α / k0 = 0.01. Center frequency f0 = 26.5GHz for 200 different frequencies, frequency bandwidth δ f =2GHz, frequency sampling interval Δf = 0.01GHz, maximum sampling frequency f max =27.5GHz, minimum sampling frequency f min =25.5GHz. The normalized radiation pattern for a specified frequency using a multi-beam frequency-scanning leaky antenna is shown below. Figure 3 As shown.

[0066] S3. Grouping received signals: Group the received signals of different frequencies in LWA.

[0067] Taking the total number of frequencies used in LWA as N = 200, and the total number of frequencies in each group as q = 50 as an example, there are a total of Q = 4 groups. The numbers 1, 2, ..., 200 represent 200 different frequencies respectively. The numbers of groups 1, 2, 3, and 4 are as follows:

[0068] S4. Reconstructing the Covariance Matrix: Calculate the covariance matrix for each group of received signals, sum the covariance matrices of all groups, and take the average to obtain the reconstructed covariance matrix of the received signals. Let y be the signal obtained from the i-th group. i Let i = 1, 2, 3, 4, and let R be the covariance matrix of the i-th group after grouping. i =E(y) i y i H Summing and averaging the covariance matrices of all groups yields the covariance matrix after reconstructing the received signal: The dimension of the covariance matrix was reduced from (200×200) to (50×50) after reconstruction.

[0069] S5. Reconstructing the Array Manifold Vector: Calculate the array manifold vector for each group of received signals, sum the array manifold vectors of all groups, and take the average to obtain the reconstructed array manifold vector corresponding to LWA. Let A be the array manifold vector of the i-th group after grouping. i , i = 1, 2, 3, 4, where, for array manifold vector A i Whether it is in Vandermonde form is not restricted. Summing and averaging the array manifold vectors of all groups, the reconstructed array manifold vector corresponding to LWA is obtained as follows:

[0070]

[0071] The array manifold vector dimension was reduced from (200×3) to (50×3) after reconstruction. The r-th incident angle θ r The corresponding reconstructed guide vector is a average (θ r ).

[0072] S6. Estimating DOA using the MUSIC algorithm: The DOA value is obtained by estimating the reconstructed covariance matrix and the reconstructed array manifold vector using the MUSIC algorithm. The specific implementation process of the MUSIC algorithm is as follows:

[0073] The covariance matrix R after reconstructing the received signal average Perform eigenvalue decomposition into

[0074] R average =E s D s E s H +E n D n E n H

[0075] Where E s Let E be the signal subspace, where E n For the noise subspace, D s and D n These are the eigenvalues ​​corresponding to the signal subspace and the noise subspace, respectively.

[0076] The spatial spectral function is constructed as follows:

[0077] By iterating through the range of values ​​for θ, P is obtained through spectral peak search. music The angle θ corresponding to the maximum value true This is the desired DOA value, such as... Figure 4 As shown. Note that if the rank of the transmitted signal covariance matrix is ​​3, then the matrix dimension of the corresponding eigenvalues ​​in the noise subspace decreases from 200×197 before reconstruction to 50×47 after reconstruction. The r-th incident angle θ r The corresponding guiding vector matrix dimension was reduced from (200×1) to (50×1) after reconstruction, greatly reducing the computational complexity.

[0078] In summary, this embodiment can achieve DOA estimation of strongly correlated signals using multi-beam frequency scanning LWA with relatively low computational cost. The DOA estimation of strongly correlated signals in this embodiment can be extended to DOA estimation of incoherent signals, and multi-beam frequency scanning LWA can be extended to all frequency scanning antennas.

[0079] Example 2

[0080] This embodiment discloses a low-complexity frequency-scanning single-beam LWA DOA estimation method based on the idea of ​​group fusion, and the implementation block diagram is as follows. Figure 1 As shown, the specific steps include:

[0081] S1. Transmitted signal: Narrowband signals are transmitted from different angles. After noise is superimposed during propagation, the correlation of the transmitted signal is 0.55.

[0082] S2, LWA received signal: Three narrowband source signals from different directions [θ1,θ2,θ3]=[10°,-20.25°,-10.25°] strike the receiving array composed of 200 leaky antennas of different frequencies. Then the signal received by a single leaky antenna is Y=AS+n.

[0083] S is the signal emitted by the signal source, n is the noise during signal transmission, A = [a(θ1), a(θ2), a(θ3)] is the array manifold vector corresponding to LWA, and the r-th incident angle θ r The corresponding guiding vector a(θ) r )for

[0084]

[0085] The parameter definitions differ slightly from those in Example 1, as detailed below. l = 20cm represents the length of LWA, m forw and m back The harmonic orders radiated at the forward and backward endpoints, m in a single-beam frequency-scanning leaky antenna. forw -m back +1 = 2. k zm k and k0 are the first and second parameters, respectively, for implementing the vector expression of the array manifold. The relative medium constant ε r =10.2, waveguide width a = 3.5mm, attenuation constant α / k0 = 0.01. Center frequency f0 = 29.2GHz for 200 different frequencies, frequency bandwidth δ f =5GHz, frequency sampling interval Δf = 0.05GHz, maximum sampling frequency f max =34.4GHz, minimum sampling frequency f min =24GHz. The normalized radiation pattern of a single-beam frequency-scanning leaky antenna at a specified frequency is shown below. Figure 5 As shown.

[0086] S3. Grouping received signals: Group the received signals of different frequencies in LWA.

[0087] Taking the total number of frequencies used in LWA as N = 200, and the total number of frequencies in each group as q = 50 as an example, there are a total of Q = 4 groups. The numbers 1, 2, ..., 200 represent 200 different frequencies respectively. The numbers of groups 1, 2, 3, and 4 are as follows:

[0088] S4. Reconstructing the Covariance Matrix: Calculate the covariance matrix for each group of received signals, sum the covariance matrices of all groups, and take the average to obtain the reconstructed covariance matrix of the received signals. Let y be the signal obtained from the i-th group. i Let i = 1, 2, 3, 4, and let R be the covariance matrix of the i-th group after grouping. i =E(y) i y i H Summing and averaging the covariance matrices of all groups yields the covariance matrix after reconstructing the received signal: The dimension of the covariance matrix was reduced from (200×200) to (50×50) after reconstruction.

[0089] S5. Reconstructing the Array Manifold Vector: Calculate the array manifold vector for each group of received signals, sum the array manifold vectors of all groups, and take the average to obtain the reconstructed array manifold vector corresponding to LWA. Let A be the array manifold vector of the i-th group after grouping. i , i = 1, 2, 3, 4, where, for array manifold vector A i Whether it is in Vandermonde form is not restricted. Summing and averaging the array manifold vectors of all groups, the reconstructed array manifold vector corresponding to LWA is obtained as follows:

[0090]

[0091] The array manifold vector dimension was reduced from (200×3) to (50×3) after reconstruction. The r-th incident angle θ r The corresponding reconstructed guide vector is a average (θ r ).

[0092] S6. Estimating DOA using the MUSIC algorithm: The DOA value is obtained by estimating the reconstructed covariance matrix and the reconstructed array manifold vector using the MUSIC algorithm. The specific implementation process of the MUSIC algorithm is as follows:

[0093] The covariance matrix R after reconstructing the received signal average Perform eigenvalue decomposition into

[0094] R average =E s D s E s H+E n D n E n H

[0095] Where E s Let E be the signal subspace, where E n For the noise subspace, D s and D n These are the eigenvalues ​​corresponding to the signal subspace and the noise subspace, respectively.

[0096] The spatial spectral function is constructed as follows:

[0097] By iterating through the range of values ​​for θ, P is obtained through spectral peak search. music The angle θ corresponding to the maximum value true This is the desired DOA value, such as... Figure 6 As shown. Note that if the rank of the transmitted signal covariance matrix is ​​3, then the matrix dimension of the corresponding eigenvalues ​​in the noise subspace decreases from 200×197 before reconstruction to 50×47 after reconstruction. The r-th incident angle θ r The corresponding guiding vector matrix dimension was reduced from (200×1) to (50×1) after reconstruction, greatly reducing the computational complexity.

[0098] In summary, this embodiment can achieve DOA estimation of strongly correlated signals using single-beam frequency scanning LWA with relatively low computational cost.

[0099] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A low-complexity frequency-scanning LWA DOA estimation method based on the idea of ​​group fusion, characterized in that, The DOA estimation method includes the following steps: Transmitted signal: Narrowband signals are transmitted from different angles. After noise is superimposed during propagation, the transmitted signal is either an incoherent signal or a strongly correlated signal. LWA received signal: Yes A narrowband source signal comes from different directions Impacted by A receiving array composed of leaky antennas of different frequencies, hereinafter referred to as LWA; the leaky antennas... A distribution of different frequencies at equal intervals, satisfying: ， ， ， ， In the formula, For the center frequency, For the frequency bandwidth used, The frequency sampling interval, The maximum sampling frequency, This is the minimum sampling frequency; Divide all frequencies into Group, This represents the total frequency of each group after grouping, where Using serial numbers 1, 2, ... They represent Different frequencies, number 1, 2, ... The groups are grouped as follows: ， ， ……， ； The signal received by a single leaky antenna is , The signal emitted by the signal source. Noise during signal transmission Let LWA be the array manifold vector, the first... Angle of incidence Corresponding guide vector for: ， Represents the length of LWA, and The harmonic orders of the radiation at the forward and backward endpoints, and These are the first and second parameters that implement the vector expression of the array manifold. , , and The specific expression is as follows: ， ， ， ， For the spatial period of modulation, At the speed of light, It is a relative medium constant. The cutoff frequency, The width of the waveguide, The attenuation constant for leakage and loss, phase , The phase constant of the fundamental guided mode and the harmonic order are given. It is an integer; Grouping of received signals: Grouping received signals of different frequencies in LWA; Reconstructing the covariance matrix: Calculate the covariance matrix of each group of received signals, sum the covariance matrices of all groups and take the average value to obtain the reconstructed covariance matrix of the received signals; Reconstructing the array manifold vector: Calculate the array manifold vector for each group of received signals, sum the array manifold vectors of all groups and take the average value to obtain the reconstructed array manifold vector corresponding to LWA; The MUSIC algorithm is used to estimate the DOA value: the MUSIC algorithm is used to reconstruct the covariance matrix. and the reconstructed array manifold vector The DOA value is estimated; the implementation process of the MUSIC algorithm is as follows: The covariance matrix after reconstructing the received signal Perform eigenvalue decomposition into , in Let be the signal subspace, where For the noise subspace, and The spatial spectrum function is constructed as follows, taking the eigenvalues ​​corresponding to the signal subspace and the noise subspace, respectively: , exist The range of values ​​is traversed, and the peaks are searched to obtain the result. Angle corresponding to the maximum value This is the desired DOA value.

2. The DOA estimation method for low-complexity frequency scanning LWA based on the grouping fusion idea as described in claim 1, characterized in that, let... Grouping to obtain the first Group signal is , The first group after Group covariance matrix The covariance matrices of all groups are summed and averaged to obtain the covariance matrix after reconstructing the received signal. for: , covariance matrix The dimension is After reconstruction, it was reduced to .

3. The DOA estimation method for low-complexity frequency-scanning LWA based on the grouping fusion idea as described in claim 1, characterized in that, Let the grouping result be the first... Group array manifold vector , Among them, for array manifold vectors Whether it is in Vandermonde form is not restricted. Summing and averaging the array manifold vectors of all groups, the reconstructed array manifold vector corresponding to LWA is obtained as follows: ， Array manifold vector dimension from After reconstruction, it was reduced to , No. Angle of incidence The corresponding reconstructed guide vector is .

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