Chirp signal direction of arrival estimation method based on fractional domain deconvolution beamforming

Abstract

The application discloses a chirp signal direction of arrival estimation method based on fractional domain deconvolution beam forming, and the method comprises the following steps: performing fractional order Fourier transform on array receiving signals by using optimal focusing order; generating fractional domain steering vectors according to array structure and optimal focusing order, and calculating beam forming output for all beam scanning directions; generating fractional domain array directivity patterns according to array structure and optimal focusing order, removing the influence of array spatial response by using deconvolution algorithm, and restoring real target spatial distribution; obtaining direction of arrival estimation results by peak searching based on the restored target spatial distribution; and realizing underwater detection and positioning based on the estimation results. The application realizes high-resolution direction of arrival estimation of a wideband chirp signal under the condition of a small aperture and low signal-to-noise ratio, and further realizes accurate detection and positioning of an underwater target.

Description

Technical Field

[0001] This invention relates to the field of array signal processing, and more particularly to a method for estimating the direction of arrival (DOA) of chirped signals based on fractional domain deconvolution beamforming. This invention improves the spatial resolution of underwater acoustic chirped signal DOA estimation. Background Technology

[0002] Chirped signals, as broadband non-stationary signals, possess large bandwidth and time width, and are widely used in underwater acoustic communication, topographic mapping, target detection, and other fields. Estimating their direction of arrival (DOA) is of significant practical value. The fractional Fourier transform (FFT), a fractional-domain representation of the signal after rotating the time-frequency coordinate axes counterclockwise around the origin by an arbitrary angle, is an excellent tool for chirped signal analysis. Fractional-domain beamforming focuses the chirped signal into the fractional domain using the FFT, and then uses narrowband beamforming to estimate the DOA, making it a highly effective method for chirped signal DOA estimation. However, its spatial resolution is limited by the array aperture, and it cannot distinguish nearby targets when the number of array elements is limited.

[0003] Deconvolution has been proven to be an effective method to improve the spatial resolution of beamforming without increasing the array aperture. Deconvolution beamforming treats the spatial spectrum as the convolution of the spatial response (also known as the "directivity pattern") of the receiving array to a point source target of unit intensity with the spatial distribution of the target energy. By weakening the influence of the array response through the deconvolution algorithm, the true spatial distribution of the target is restored, thereby achieving high-resolution estimation of the direction of arrival.

[0004] Most existing deconvolution beamforming methods are based on narrowband signal models, and there are no deconvolution beamforming methods for broadband signals, especially chirped signals. Summary of the Invention

[0005] This invention provides a method for estimating the direction of arrival (DOA) of chirped signals based on fractional-domain deconvolution beamforming. This invention achieves high-resolution DOA estimation of broadband chirped signals under conditions of small aperture and low signal-to-noise ratio, thereby enabling accurate detection and positioning of underwater targets. Details are described below:

[0006] A method for estimating the direction of arrival (DOA) of a chirped signal based on fractional-domain deconvolution beamforming, the method comprising:

[0007] A fractional Fourier transform is performed on the array received signal using the optimal focusing order; a fractional domain steering vector is generated based on the array structure and the optimal focusing order, and beamforming output is calculated for all beam directions;

[0008] Based on the array structure and the optimal focusing order, a fractional-domain array directional pattern is generated. The deconvolution algorithm is used to remove the influence of the array spatial response and restore the true target spatial distribution.

[0009] Based on the restored target spatial distribution, peaks are searched to obtain the direction of arrival estimation results; underwater detection and positioning are then achieved based on these estimation results.

[0010] Specifically, generating the fractional-domain array directional pattern based on the array structure and the optimal focusing order involves:

[0011] Spatial spectrum super-resolution optimization based on deconvolution is obtained by omitting the quadratic difference term of the time delay value and obtaining the optimized expression.

[0012] Based on the aforementioned expression, a complex directivity pattern is obtained, i.e., the chirping signal in the θ direction... Beam complex response at an angle.

[0013] The beneficial effects of the technical solution provided by this invention are:

[0014] 1. This invention is the first to realize fractional-domain deconvolution beamforming of broadband chirped signals. Based on fractional-domain beamforming, the direction of arrival (DOA) of the chirped signal after focusing is estimated through fractional Fourier transform, which greatly improves the DOA estimation performance under low signal-to-noise ratio conditions.

[0015] 2. This invention uses a deconvolution algorithm to remove the influence of fractional domain directivity patterns, restore the spatial distribution of target energy, and obtain high-resolution direction-of-arrival estimation results;

[0016] 3. The method proposed in this invention introduces deconvolution into the field of fractional domain array signal processing for the first time. Based on fractional domain beamforming, it uses the deconvolution algorithm to weaken the influence of array spatial response. While retaining the high noise resistance of fractional domain beamforming, it obtains a beamforming spatial spectrum with narrow main lobe and low side lobe characteristics.

[0017] 4. Compared with existing methods, the present invention significantly improves the spatial resolution of the direction of arrival estimation of broadband chirped signals without increasing the array aperture, especially under small aperture and low signal-to-noise ratio conditions, and achieves accurate underwater detection and positioning. Attached Figure Description

[0018] Figure 1 This is a flowchart of a method for estimating the direction of arrival (DOA) of chirped signals based on fractional-domain deconvolution beamforming.

[0019] Figure 2 This is a schematic diagram of the spatial spectrum of fractional-domain beamforming and the spatial spectrum of fractional-domain deconvolution beamforming for dual targets, with 10 array elements and a signal-to-noise ratio of 0 dB.

[0020] The chirped signal has a bandwidth of 1 kHz, a center frequency of 7.5 kHz, and a duration of 0.05 s. From Figure 2 As can be seen, the method proposed in this invention has the advantages of narrow main lobe and low side lobe, and has higher resolution, which can effectively distinguish nearby targets that cannot be distinguished by fractional-domain beamforming. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below.

[0022] Example 1

[0023] This invention proposes a method for estimating the direction of arrival (DOA) of chirped signals based on fractional-domain deconvolution beamforming. (See also...) Figure 1 The method includes the following steps:

[0024] 101: Acquire the array received signal and search for the optimal focusing order;

[0025] 102: Perform a fractional Fourier transform on the array received signal using the optimal focusing order;

[0026] 103: Generate fractional domain steering vectors based on array structure and optimal focusing order, and calculate beamforming output for all beam directions;

[0027] 104: Based on the array structure and the optimal focusing order, a fractional-domain array directional pattern is generated. The deconvolution algorithm is used to remove the influence of the array spatial response and restore the true target spatial distribution.

[0028] 105: Peak finding is performed based on the restored target spatial distribution to obtain the direction of arrival estimation results;

[0029] 106: Based on this estimation result, the mutual confusion of nearby underwater chirped signal targets can be effectively avoided, the target perception capability can be improved, and accurate underwater detection and positioning can be achieved.

[0030] Example 2

[0031] The following is combined Figures 1-2 The specific calculation formulas for the scheme in Example 1 will be further described below:

[0032] I. Fractional Domain Array Signal Model

[0033] Let f0 and μ be the start frequency and modulation frequency of the chirped signal, respectively. Define any chirped signal as:

[0034]

[0035] Assume s(t) is focused in the fractional domain at (α0, u0), where α0 is the counterclockwise rotation angle (in radians) of the signal axis and u0 is the peak position in the fractional Fourier transform spectrum. The expressions for α0 and u0 are:

[0036]

[0037] Therefore, the fractional Fourier transform value of s(t) in (α0, u0) can be expressed as:

[0038]

[0039] Suppose a chirped signal is incident from direction θ onto a uniform linear array with M elements. Then the signal received by the m-th element is s(t-τ). m ),in d is the time delay difference between the target signal propagating to the reference element and the m-th element, c is the speed of sound, and M is the number of elements.

[0040] Therefore, the received signal of the m-th element is:

[0041]

[0042] In equation (4), n m (t) represents the received noise of the m-th element, where the noise of each element is independent of the signal. It can be seen that the direction vector of the chirped signal is a function of frequency, and the classic single-frequency steering vector cannot achieve beamforming. Therefore, a frequency-independent steering vector needs to be derived in the fractional domain to achieve beamforming.

[0043] Let s(t-τ) m In the fractional domain, focus on (α) m ,u m If x m The value of (t) at this focal point is:

[0044]

[0045] in, The order of the fractional Fourier transform (α) m ≠ nπ and n∈Z), p m The fractional Fourier transform operator, where T is the duration of the chirped signal. Represents the received noise n m The fractional Fourier transform of s(t). When the signal s(t) is delayed, its initial frequency changes from f0 to f0-μτ. m However, its modulation frequency μ remains unchanged.

[0046] Therefore, α m and um It can be represented as:

[0047]

[0048] Substituting equation (6) into equation (5), and replacing f0,μ with α0,u0, then X m (α m ,u m It can be transformed into the following form:

[0049]

[0050] in, For frequency-independent fractional-domain directivity coefficients, A(τ) m Transforming this into a form with θ as the variable yields:

[0051]

[0052] Where θ is the direction of arrival of the signal wave.

[0053] II. Fractional-Domain Beamforming

[0054] From the form of equation (8), the guiding vector in the fractional domain can be defined as:

[0055]

[0056]

[0057] in, For the m-th array element in Angular guide vector, The superscript (·) represents the spatial scanning angle. T This represents the transpose of a matrix.

[0058] The output of fractional-domain beamforming can be obtained from this:

[0059]

[0060] In equation (11), X = [X1(α1,u1),X2(α2,u2),…,X M (α M ,u M )] T It is a fractional-domain signal snapshot matrix, composed of the fractional-order Fourier transform peaks of the signals received by each array element.

[0061] in, The beamforming output represents noise, indicated by the superscript (·). H Represents conjugate transpose, N m (α m ,um ) represents the fractional-domain snapshot of the received noise of the m-th element, α m and u m These represent the focusing order and focusing position of the m-th element receiving the chirped signal, respectively.

[0062] Beamforming output of chirped signal It is represented as:

[0063]

[0064] Among them, A m (θ) is the direction vector of the wave coming from the m-th element in the θ direction, and S(α0,u0) is the value of the chirped signal at the focal point.

[0065] Then the spatial spectrum of fractional domain beamforming It can be given by the following formula, where the peak value corresponds to The value is the DOA estimation result of fractional domain beamforming.

[0066]

[0067] in, The fractional-domain beamforming output is used to generate the received signal from the array.

[0068] III. Spatial Spectral Super-Resolution Optimization Based on Deconvolution

[0069] In equation (12), the second difference term of the time delay value It is inversely proportional to the square of the speed of sound, so its value is very small and can be neglected.

[0070] Equation (12) can then be transformed into:

[0071]

[0072] For a chirped signal focused on (α0, u0) in the fractional domain, the complex directivity pattern can be obtained according to equation (14), that is, the chirped signal in the θ direction is... Beam complex response at angle:

[0073]

[0074] Let the true value of the direction of arrival (ROA) of the chirped signal be ψ, then its spatial distribution can be defined as:

[0075] D(θ)=S(α0,u0)δ(cosθ-cosψ) (16)

[0076] δ(cosθ-cosψ)=0,cosθ≠cosψ,∫δ(cosθ-cosψ)dcosθ=1 (17)

[0077] Due to directional patterns yes The function, i.e. Fractional domain beamforming output of the target signal It can be represented as the integral of the product of the complex directivity pattern of the array to the chirped signal and the spatial distribution of the target signal over all target angles θ, i.e.:

[0078]

[0079] Where D(θ) is the spatial distribution of the chirped signal. If equation (18) is considered as a function of the cosine of the angle, it can be rewritten in convolution form:

[0080]

[0081] Therefore, in the known and Under the premise that D(cosθ) can be restored by deconvolution, the deconvolution of equation (19) is transformed into the sparse constraint optimization problem shown in equation (20).

[0082]

[0083] in, These are the fractional-domain beamforming output vector and the target signal spatial distribution vector, respectively. and The discretized representation of Y. λ∈R are the coefficients of the regularization term. P ∈C G×G The complex directivity pattern matrix for fractional-domain beamforming is defined as follows:

[0084] Y P =[Y P (θ ri |θ ci )] G×G (twenty one)

[0085] Where G represents the total number of discrete angles in space. These represent the row and column indices of the matrix, [θ1, θ2, ..., θ]. G ] represents a discrete set of spatial angles. Equation (21) is solved using MFISTA (Monotonic Fast Iterative Shrinking Threshold Algorithm), the specific process of which is shown below:

[0086] MFISTA algorithm:

[0087] Input: Fractional domain beamforming; Output Y S Complex directional pattern Y P Regularization coefficient λ, number of iterations Niter Initial value of iteration

[0088] Output: Estimated spatial distribution of the target signal

[0089] Step 1: Set the initial value of the intermediate variable in the iteration to l1 = 1.

[0090] Step 2: From i=1 to N iter Repeat steps 3 through 6;

[0091] Step 3: Calculate the potential update value based on the shrinkage threshold function.

[0092] Step 4: Determine whether to update based on the gradient descent principle.

[0093] Step 5: Update intermediate values

[0094] Step 6: Update intermediate values

[0095] Step 7: Loop terminates, output the estimated spatial distribution of the target signal.

[0096] in, This represents the estimated spatial distribution of the target signal at the i-th iteration. i ,y i ,z i Y is the intermediate value of the i-th iteration, which has no physical meaning. L is the iteration step size. P The largest eigenvalue of the covariance matrix.

[0097] Among them, the shrinkage threshold function S in step 3 λ / L (x) for any x = [x1, x2, ..., x G ] T ∈C G Defined as:

[0098]

[0099] In step 3, z i =S λ / L (·) is a vector function whose independent variable takes the value of In formula (22), x represents the independent variable and gives S. λ / L The mapping relationship of (·).

[0100] The spatial distribution estimate of the target signal is obtained by deconvolution of equation (19) using MFISTA. Then, the spatial spectrum formed by the fractional-domain deconvolution beam can be expressed as:

[0101]

[0102] like Figure 2 As shown, when two adjacent chirped sources exist simultaneously, the fractional-domain beamforming spatial spectrum only exhibits a single significant peak, failing to effectively detect both targets, and exhibits high sidelobes. Fractional-domain deconvolution beamforming effectively reduces the main lobe width and sidelobe height, effectively distinguishing two adjacent targets. The final DOA estimate in this embodiment of the invention is P. DFrFB The peak value in.

[0103] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of a preferred embodiment, and the sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0104] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for estimating the direction of arrival (DOA) of a chirped signal based on fractional-domain deconvolution beamforming, characterized in that, The method includes: A fractional Fourier transform is performed on the array received signal using the optimal focusing order; a fractional domain steering vector is generated based on the array structure and the optimal focusing order, and beamforming output is calculated for all beam scanning directions; Based on the array structure and the optimal focusing order, a fractional-domain array directional pattern is generated. The deconvolution algorithm is used to remove the influence of the array spatial response and restore the true target spatial distribution. Based on the restored target spatial distribution, peaks are searched to obtain the direction of arrival estimation results; underwater detection and positioning are then achieved based on these estimation results.

2. The method for estimating the direction of arrival (DOA) of a chirped signal based on fractional-domain deconvolution beamforming according to claim 1, characterized in that, The specific steps for generating the fractional-domain array directional pattern based on the array structure and optimal focusing order are as follows: Based on deconvolution spatial spectrum super-resolution optimization, the quadratic difference term of the time delay value is omitted to obtain the optimized beamforming output expression; Based on the optimized expression, a complex directional pattern is obtained, i.e. directional chirping signals in Beam complex response at an angle.

3. The method for estimating the direction of arrival (DOA) of a chirped signal based on fractional-domain deconvolution beamforming according to claim 2, characterized in that, The complex beam response is: ； in, This represents the counterclockwise rotation angle of the signal axis. This represents the peak position in the fractional Fourier transform spectrum. For the spacing between array elements, For the speed of sound, The number of array elements.

4. The method for estimating the direction of arrival (DOA) of a chirped signal based on fractional-domain deconvolution beamforming according to claim 3, characterized in that, The deconvolution algorithm is used to remove the influence of the array spatial response, restoring the true target spatial distribution as follows: Fractional domain beamforming output of the target signal Represented as the product of the complex directivity pattern of the array to the chirped signal and the spatial distribution of the target signal over all target angles. The integral, that is: ； in, For the spatial distribution of the chirped signal, let the true value of the chirped signal direction of arrival be... ,but: ； ； in, Let be the impulse function; transform the integral into a convolution expression, i.e.: ； Restoring by deconvolution This is transformed into a sparse-constrained optimization problem: ； in, These are the fractional-domain beamforming output vector and the target signal spatial distribution vector, respectively. and Discretized representation, is the coefficient of the regularization term.

5. The method for estimating the direction of arrival of a chirped signal based on fractional-domain deconvolution beamforming according to claim 4, characterized in that, The complex directivity pattern matrix for fractional-domain beamforming: ； in, Represents the total number of discrete angles in space. These represent the row index and column index of the matrix, respectively. It represents a discrete set of spatial angles.

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