Fast DOA estimation method based on DFT in large-scale MIMO scene

Abstract

The invention discloses a fast direction of arrival (DOA) estimation method based on discrete Fourier transform (DFT) in a large scale multiple input multiple output (MIMO) scene, relates to the technical field of target positioning, and realizes fast DOA estimation through the DFT and Taylor series expansion. The method comprises the following steps: firstly, transmitting a detection signal to a target and receiving a target echo signal by using a large-scale MIMO array, and performing DFT on the received signal to obtain an initial DOA estimated value; then, performing first-order Taylor series expansion on the received signal at the initial DOA estimation value, and obtaining a difference value between the DOA value and the initial DOA estimation value by using a least square method; and finally, adding the difference value to the initial DOA estimation value to obtain an accurate DOA estimation value. According to the method, the characteristics of DFT, Taylor series expansion and a large-scale MIMO array are combined, so that the operations of spectrum peak search, covariance matrix construction and the like with relatively high calculation overhead are avoided, the DOA is quickly and accurately estimated, and engineering implementation is easy.

Description

Technical Field

[0001] The present invention relates to the technical field of target positioning, and particularly relates to a fast DOA estimation method based on DFT in a large-scale MIMO scenario. Background Art

[0002] Direction of Arrival (DOA) estimation refers to using the wave path difference of signals received by different array elements to estimate the azimuth of the signal source, which is an important research direction in the field of array signal processing and has broad application prospects in civil and military fields such as wireless communication, mobile communication, and navigation.

[0003] The performance of DOA estimation is mainly determined by the array aperture and the estimation algorithm. At present, the typical arrays used for DOA estimation are ULA (Uniform Linear Array), CLA (Coprime Linear Array), NLA (Nested Linear Array), and UCLA (Unfolded Coprime Linear Array). The CLA is composed of two sparse uniform sub-arrays. The element spacing of both sub-arrays is an integer multiple of half a wavelength and they are coprime, and the number of elements in the two sub-arrays is coprime. The NLA is composed of a uniform sub-array and a sparse uniform sub-array, and the element spacing of the sparse uniform sub-array is the array aperture of the uniform sub-array. Compared with the traditional uniform linear array, the CLA and NLA expand the array aperture, laying the foundation for improving the DOA estimation accuracy. Moreover, the ambiguity estimation problem caused by the expansion of the element spacing is suppressed by the coprime characteristics of the two sub-arrays, thus realizing DOA unambiguous estimation. In addition, large-scale MIMO arrays have rich element resources and strong spatial diversity, and have broad application prospects in the fields of target positioning and interference suppression. At present, the typical algorithms used for DOA estimation include subspace algorithms and compressive sensing algorithms, etc. Subspace algorithms use the array structure characteristics or spectral peak search to achieve DOA estimation, but cannot simultaneously improve the estimation effectiveness and reliability. Compressive sensing algorithms use the sparse characteristics of the target in space to achieve DOA estimation, but also need to search the spatial domain, so they cannot be effectively utilized in practice. At the same time, due to the large number of elements and the large scale of the array manifold in large-scale MIMO arrays, the computational complexity of using subspace algorithms or compressive sensing algorithms for DOA estimation is relatively high, and the computational efficiency is relatively low, and the potential of large-scale MIMO arrays in the field of target positioning cannot be fully exerted.

[0004] Therefore, it is necessary to propose a fast DOA estimation method to solve the above problems. Summary of the Invention

[0005] In view of the above deficiencies in the prior art, the present invention provides a fast DOA estimation method based on DFT in a large-scale MIMO scenario, which solves the problem that the existing subspace algorithms cannot achieve fast DOA estimation in a large-scale MIMO scenario, improves the efficiency of target positioning, and is beneficial to engineering practice.

[0006] To achieve the above object of the invention, the technical solution adopted by the present invention is as follows:

[0007] A DOA estimation method based on an unfolded co-prime nested array, comprising the following steps:

[0008] S1. Construct a large-scale MIMO array, send a probing signal, and receive the target echo signal;

[0009] S2. Construct a discrete Fourier transform normalization matrix, and perform a discrete Fourier transform on the received signal to obtain a discrete Fourier spectrum;

[0010] S3. Perform spectral search on the discrete Fourier spectrum to obtain an initial DOA estimate value;

[0011] S4. Perform a first-order Taylor series expansion on the discrete Fourier spectrum at the initial DOA estimate value to obtain a series-expanded discrete Fourier spectrum;

[0012] S5. Perform a least squares transformation on the series-expanded discrete Fourier spectrum to obtain the difference between the DOA value and the initial DOA estimate value;

[0013] S6. Add the initial DOA estimate value and the difference to obtain an accurate DOA estimate value.

[0014] Further, the step S1 includes the following sub-steps:

[0015] S11. Construct a large-scale MIMO array;

[0016] S12. Send a probing signal and receive the target echo signal.

[0017] Further, in the step S11, the large-scale MIMO array adopts a ULA, the number of array elements is N, the element spacing is d = λ / 2, the transmitter and the receiver are co-located, and λ is the wavelength;

[0018] Further, the received target echo signal in the step S12 is:

[0019]

[0020] where is the array steering matrix, is the direction vector of the k-th target, θ kis the DOA value of the k-th target, K is the number of targets, s is the signal vector, and n is the noise vector. is the duplicate removal matrix, M = 2N - 1, is the duplicate removal array direction matrix.

[0021] Further, the step S2 includes the following sub-steps:

[0022] S21. Construct a discrete Fourier transform normalization matrix;

[0023] S22. Perform a discrete Fourier transform on the received signal to obtain a discrete Fourier spectrum.

[0024] Further, the discrete Fourier transform normalization matrix in the step S21 is constructed by the following formula:

[0025]

[0026] where the (p,q)-th element of the matrix F is

[0027] Further, the discrete Fourier transform is performed on the received signal in the step S22 to obtain a discrete Fourier spectrum expression:

[0028] y = Fx

[0029] Further, the step S3 performs a spectrum search on the discrete Fourier spectrum to obtain an initial DOA estimate value as:

[0030]

[0031] where, is the initial DOA estimate value, is the position where the maximum value of the discrete Fourier spectrum is located.

[0032] Further, in the step S4, the duplicate removal direction vector of the k-th target is expanded by the first-order Taylor series at the initial DOA estimate value to obtain the Taylor series expansion expression of:

[0033]

[0034] where, is the difference between the DOA value and the initial DOA estimate value;

[0035] The discrete Fourier spectrum is expanded by the first-order Taylor series at the initial DOA estimate value to obtain a series expansion discrete Fourier spectrum expression as:

[0036]

[0037] where, Λ = diag(ε1,..., ε K ), where α and β are intermediate variables and satisfy β = Λα.

[0038] Furthermore, step S5 performs a least squares variation on the series-expanded discrete Fourier spectrum to obtain:

[0039]

[0040] where + is for pseudo-inverse;

[0041] The expression for the difference between the DOA value and the initial DOA estimate is:

[0042] Λ = β. / α

[0043] where. / is vector point division.

[0044] Furthermore, step S6 adds the initial DOA estimate and the difference to obtain the accurate DOA estimate:

[0045]

[0046] The beneficial effects of the present invention are:

[0047] (1) Utilize a large-scale MIMO array to expand the array aperture, thereby bringing better DOA estimation performance;

[0048] (2) Combine DFT with Taylor series expansion to achieve fast DOA estimation while ensuring the DOA estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 is a flowchart of the fast DOA estimation method based on DFT in a large-scale MIMO scenario provided by an embodiment of the present invention;

[0050] Figure 2 is a schematic diagram of a large-scale MIMO array in an embodiment of the present invention:

[0051] Figure 3 is a discrete Fourier spectrum diagram in an embodiment of the present invention;

[0052] Figure 4 is a scatter plot of DOA estimation results in an embodiment of the present invention;

[0053] Figure 5 is a comparison diagram of computational complexity between an embodiment of the present invention and subspace-based algorithms. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0054] The following describes the specific embodiments of the present invention to facilitate the understanding of those skilled in the art of the present technology. It should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions made using the concept of the present invention are within the scope of protection.

[0055] As Figure 1 shown, in an embodiment of the present invention, a fast DOA estimation method based on DFT in a large-scale MIMO scenario includes the following steps:

[0056] S1. Construct a large-scale MIMO array, transmit a probing signal, and receive the target echo signal.

[0057] Step S1 includes the following sub-steps:

[0058] S11. As Figure 2 shown, this large-scale MIMO array adopts a ULA, the number of array elements is N, the element spacing is d = λ / 2, the transmitter and the receiver are co-located, and λ is the wavelength;

[0059] S12. The transmitter sends an electromagnetic wave. Assuming there are K targets to be detected in the far field, the DOA value of each target is θ k , k = 1, 2,..., K, and the target echo signal received by the receiver is:

[0060]

[0061] Among them, is the array steering matrix, is the direction vector of the kth target, θ k is the DOA value of the kth target, K is the number of targets, s is the signal vector, n is the noise vector, is the de-duplication matrix, M = 2N - 1, is the de-duplication array steering matrix.

[0062] S2. Construct a discrete Fourier transform normalization matrix, and perform a discrete Fourier transform on the received signal to obtain a discrete Fourier spectrum.

[0063] Step S2 includes the following sub-steps:

[0064] S21. Construct a discrete Fourier transform normalization matrix:

[0065]

[0066] Among them, the (p, q)th element of the matrix F is

[0067] S22. Perform a discrete Fourier transform on the received signal to obtain a discrete Fourier spectrum:

[0068] y = Fx

[0069] S3. Perform a spectrum search on the discrete Fourier spectrum to obtain an initial DOA estimate value.

[0070] Performing a spectrum search on the discrete Fourier spectrum to obtain an initial DOA estimate value:

[0071]

[0072] where, is the initial DOA estimate value, is the position where the maximum value of the discrete Fourier spectrum is located.

[0073] S4. Perform a first-order Taylor series expansion on the discrete Fourier spectrum at the initial DOA estimate value to obtain a series-expanded discrete Fourier spectrum.

[0074] Perform a first-order Taylor series expansion on the direction vector for the k-th target at the initial DOA estimate value to obtain the Taylor series expansion expression of:

[0075]

[0076] where, is the difference between the DOA value and the initial DOA estimate value;

[0077] Perform a first-order Taylor series expansion on the discrete Fourier spectrum at the initial DOA estimate value to obtain the series-expanded discrete Fourier spectrum expression as:

[0078]

[0079] where, Λ = diag(ε1,..., ε K ), and α and β are intermediate variables and satisfy β = Λα.

[0080] S5. Perform a least squares variation on the series-expanded discrete Fourier spectrum to obtain the difference between the DOA value and the initial DOA estimate value.

[0081] Performing a least squares variation on the series-expanded discrete Fourier spectrum to obtain:

[0082]

[0083] where, + is for finding the pseudo-inverse;

[0084] The expression for the difference between the DOA value and the initial DOA estimate value is:

[0085] Λ = β. / α

[0086] where. / is the vector point division.

[0087] S6. The initial DOA estimate value is added to the difference to obtain the accurate DOA estimate value.

[0088] Adding the initial DOA estimate value to the difference to obtain the accurate DOA estimate value:

[0089]

[0090] The present invention will be further described below in conjunction with the simulation experiment results of MALTAB:

[0091] To evaluate the present invention, consider a large-scale MIMO array with the number of array elements at the transmitter and receiver both being N = 70, and the DOA values of K = 3 targets being θ1 = 30°, θ2 = 45°, and θ3 = 60° respectively.

[0092] Figure 3 This is the discrete Fourier spectrogram of the embodiment of the present invention, with the signal-to-noise ratio SNR = 10 dB. Observing Figure 3 It can be seen that peaks appear at the spectral lines of q1 = 60, q2 = 49, and q3 = 34, and respectively correspond to the DOA values of the three targets, indicating that the initial DOA estimate values of the targets can be effectively obtained through DFT, which is mainly due to the relatively large number of array elements in the large-scale MIMO array.

[0093] Figure 4 This is the scatter diagram of the DOA estimation results of the embodiment of the present invention, with the number of experiments T = 200 and the signal-to-noise ratio SNR = 10 dB. Observing Figure 4 It can be seen that the present invention can accurately obtain the DOA estimate values of all targets in each simulation experiment, which is mainly due to the large array aperture of the large-scale MIMO array. Figure 4 The results verify the reliability of the present invention in DOA estimation.

[0094] Figure 5 This is the comparison diagram of the computational complexity between the embodiment of the present invention and subspace-based algorithms. Among them, the DOA search range of the MUSIC algorithm is Δθ = 180°, the search step is θ d = 0.01°, and the number of snapshots is L = 200. Observing Figure 5 It can be seen that the computational complexity of the present invention is lower than that of the MUSIC algorithm and the ESPRIT algorithm, which is mainly due to the fact that the present invention avoids computationally expensive operations such as spectral peak search and covariance matrix construction, and realizes fast DOA estimation only through DFT and Taylor series expansion. Figure 5The results verify the effectiveness of the present invention in DOA estimation.

[0095] In summary, the present invention expands the array aperture by means of a large-scale MIMO array, thereby bringing better DOA estimation performance. At the same time, by combining DFT with Taylor series expansion, it avoids computationally expensive operations such as spectral peak search and covariance matrix construction, and realizes fast DOA estimation only through DFT and Taylor series expansion on the premise of ensuring the DOA estimation accuracy, which is more suitable for rapid target positioning.

Claims

1. A fast DOA estimation method based on DFT in a massive MIMO scenario, characterized in that: The following steps are involved: S1, build a large-scale MIMO array, send detection signals and receive target echo signals; S2, constructing a discrete Fourier transform normalization matrix, performing discrete Fourier transform on the received signal to obtain a discrete Fourier spectrum; S3, performing spectrum search on the discrete Fourier spectrum to obtain an initial DOA estimate; S4, performing a first-order Taylor series expansion on the discrete Fourier spectrum at the initial DOA estimation value to obtain a series expanded discrete Fourier spectrum; S5, performing least square transformation on the series expansion discrete Fourier spectrum to obtain the difference between the DOA value and the initial DOA estimate; S6. The initial DOA estimate is added to the difference to obtain an accurate DOA estimate.

2. The fast DOA estimation method based on DFT in a massive MIMO scenario according to claim 1, characterized in that: The step S1 comprises the following sub-steps: S11. The massive MIMO array uses ULA, the number of array elements is N, the array element spacing is d = λ / 2, the transmitter and the receiver are co-located, and λ is the wavelength; S12, the transmitting end sends electromagnetic waves, and the receiving end receives the target echo signal: in, is the array direction matrix, is the direction vector of the kth target, θ k is the DOA value of the kth target, K is the number of targets, s is the signal vector, n is the noise vector, is the deduplication matrix, M = 2N-1, is the deduplication array direction matrix.

3. The fast DOA estimation method based on DFT in a massive MIMO scenario according to claim 2, characterized in that: The step S2 comprises the following sub-steps: S21. Construct the discrete Fourier transform normalized matrix: Among them, the (p,q)th element of the matrix F is S22. Perform discrete Fourier transform on the received signal to obtain a discrete Fourier spectrum: y=Fx 4. The DFT-based fast DOA estimation method in a massive MIMO scenario according to claim 3, characterized in that: In step S3, the initial DOA estimation value is obtained by performing spectrum search on the discrete Fourier spectrum: in, is the initial DOA estimate, is the location of the maximum value of the discrete Fourier spectrum.

5. The DFT-based fast DOA estimation method in a massive MIMO scenario according to claim 4, characterized in that: The step S4 removes the duplicate direction vector of the kth target at the initial DOA estimate. Do a first-order Taylor series expansion and we get The Taylor series expansion expression of is: in, is the difference between the DOA value and the initial DOA estimate; Perform a first-order Taylor series expansion on the discrete Fourier spectrum at the initial DOA estimate, and the series expansion discrete Fourier spectrum expression is: in, Λ=diag(ε1,...,ε K ), α and β are intermediate variables and satisfy β=Λα.

6. The DFT-based fast DOA estimation method in a massive MIMO scenario according to claim 5, characterized in that: In step S5, the series expansion discrete Fourier spectrum is subjected to least square transformation to obtain: in, +For pseudo-rebellion; The difference between the DOA value and the initial DOA estimate is expressed as: Λ=β. / α Among them, . / is vector dot division.

7. The fast DOA estimation method based on DFT in a massive MIMO scenario according to claim 6, characterized in that: In step S6, the initial DOA estimate is added to the difference to obtain a precise DOA estimate:

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