A fast direction of arrival estimation method based on dual FFT

Abstract

This invention provides a fast direction-of-arrival (DOA) estimation method based on dual FFTs, belonging to the field of array signal processing technology. The method first performs a first FFT on the array received data to obtain the phase difference of each channel at the point of maximum spectral amplitude, which is used to construct the array spatial sampling sequence. A second FFT is then performed on the spatial sampling sequence to obtain the direction-finding spatial spectrum. Finally, the signal's angle of arrival is determined based on the position of the spectrum peak. This dual FFT process achieves joint processing of the frequency and spatial domains of the array received signal, further improving the convergence speed and direction-finding accuracy of DOA estimation.

Description

Technical Field

[0001] The present invention relates to the technical field of array signal processing, and in particular to a fast direction of arrival estimation method based on double FFT. Background Art

[0002] Array signal processing is an extremely important branch of modern signal processing, and direction of arrival (DOA) estimation has long been considered a key research topic within this field. Traditional direction-finding methods, such as algorithms like MUSIC and ESPRIT, often require matrix operations like eigenvalue decomposition to achieve high spatial resolution, resulting in a significant computational burden. Traditional wavenumber-domain algorithms, while computationally efficient, suffer from low DF accuracy due to processing only a limited number of snapshots. This dialectical relationship between computational burden and accuracy in traditional DOA estimation algorithms limits their applicability and flexibility in engineering applications. Summary of the Invention

[0003] In view of this, the present invention proposes a fast direction of arrival estimation method based on dual FFT. The method has the characteristics of fast calculation speed and high direction finding accuracy.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is:

[0005] A fast direction of arrival estimation method based on dual FFT, characterized by comprising the following steps:

[0006] Step 1: Perform the first FFT processing of nFFT1 points on the array received data to transform the array received information from the time domain to the frequency domain;

[0007] Step 2: Locate the maximum spectrum amplitude position MaxPos1 and extract the phase of each receiving channel of the array at MaxPos1;

[0008] Step 3: Calculate the phase difference between each channel of the array based on the extracted phase, and construct the spatial sampling sequence accordingly:

[0009]

[0010] Where f is the signal frequency, d is the distance between adjacent elements in the array, and θ d is the angle of arrival of the signal to be estimated, c is the speed of light, M is the number of elements in the array, e is the base of the natural logarithm, and j is the imaginary unit;

[0011] Step 4: Perform a second FFT process of nFFT2 points on the spatial domain sampling sequence to obtain the spatial spectrum function P(θ);

[0012] Step 5: Locate the peak position MaxPos2 in the spatial spectrum function P(θ) and solve the signal's angle of arrival θ accordingly d :

[0013] θ d =acos[MaxPos2·c / (nFFT2·f·d)]

[0014] Where acos() is the arc cosine function.

[0015] Compared with the prior art, the present invention has the following advantages:

[0016] 1. Compared with the traditional wave number synthesis direction finding algorithm, the present invention can further improve the DOA estimation accuracy by increasing the number of second FFT processing points under the condition of limited sampling snapshot;

[0017] 2. Compared with the traditional beam-domain direction-finding algorithm, the present invention makes full use of limited sampling snapshot data, improves the construction accuracy of the spatial sampling sequence, and has higher direction-finding accuracy;

[0018] 3. Compared with the traditional spatial spectrum DOA estimation algorithm, the present invention does not require matrix decomposition and has a faster convergence speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is an overall flow chart of the method of the present invention.

[0020] Figure 2 This is the curve of direction finding accuracy of the method of the present invention and the traditional wavenumber domain algorithm changing with the signal-to-noise ratio.

[0021] Figure 3 This is the curve showing how the direction finding accuracy of the present invention changes as the number of points in the second FFT processing increases. DETAILED DESCRIPTION

[0022] The present invention will be described in further detail below with reference to the accompanying drawings.

[0023] A fast direction of arrival estimation method based on dual FFT includes the following steps:

[0024] Step 1: Perform the first FFT processing (nFFT1 point) on the array received data to transform the array received information from the time domain to the frequency domain;

[0025] Step 2: Locate the maximum spectrum amplitude position MaxPos1 and extract the phase of each receiving channel of the array at MaxPos1;

[0026] Step 3: Calculate the phase difference between each channel of the array based on the extracted phase, and construct the spatial sampling sequence accordingly:

[0027]

[0028] In the above formula, f is the signal frequency, d is the distance between adjacent array elements, and θ d is the angle of arrival of the signal to be estimated, c is the speed of light, and M is the number of elements in the array;

[0029] Step 4: Perform a second FFT process (nFFT2 points) on the spatial sampling sequence to obtain the spatial spectrum function P(θ);

[0030] Step 5: Locate the peak position MaxPos2 in the spatial spectrum function P(θ) and solve the angle of arrival of the signal accordingly:

[0031] θ d =acos[MaxPos2·c / (nFFT2·f·d)]

[0032] Where acos() is the arc cosine function.

[0033] The main working process of this method includes: performing a first FFT on the array received data to obtain the spectral information of the received signal, extracting the phase of each array channel at the point of maximum spectral amplitude, and then calculating the phase difference between each channel and the reference channel from the phase information to construct a spatial sampling snapshot sequence of the array. The spatial sampling sequence is then subjected to a second FFT to obtain the spatial direction-finding spatial spectrum. Finally, the correspondence between the peak position of the spatial spectrum and the signal's angle of arrival is used to estimate the signal's direction of arrival. Based on the array received signal, this method combines the spatial characteristics of the received signal affected by the array structure with the signal's own spectral characteristics. It also exploits the similarity between the array spatial sampling snapshot model and the FFT multiplier to achieve rapid and accurate estimation of the source's direction of arrival.

[0034] In this method, nFFT1 is determined based on the system hardware and software resources, and nFFT2 can be determined based on the accuracy requirements and operating speed of subsequent data processing. The two do not need to be equal (they can be equal or unequal) and can be flexibly set separately.

[0035] Here's a more specific example:

[0036] Reference Figure 1 , a fast direction of arrival estimation method based on double FFT, comprising the following steps:

[0037] Step 1: Perform the first FFT processing (nFFT1 point) on the array received data to transform the array received information from the time domain to the frequency domain;

[0038] Step 2: Locate the maximum spectrum amplitude position MaxPos1 and extract the phase of each receiving channel of the array at MaxPos1;

[0039] Step 3: Calculate the phase difference between each channel of the array based on the extracted phase, and construct the spatial sampling sequence accordingly:

[0040]

[0041] In the above formula, f is the signal frequency, d is the distance between adjacent array elements, and θ d is the angle of arrival of the signal to be estimated, c is the speed of light, and M is the number of elements in the array;

[0042] Considering that the FFT transformation formula is:

[0043]

[0044] Therefore, the array spatial domain sampling snapshot sequence can be organized into the following form:

[0045]

[0046] In the above formula, Corresponding to k in the FFT transformation formula, we can obtain the corresponding relationship between the spatial spectrum peak and the signal arrival angle after FFT processing of the array spatial domain sampling:

[0047] θ d =acos[k·c / (N·f·d)]

[0048] Step 4: Perform a second FFT process (nFFT2 points) on the spatial sampling sequence to obtain the spatial spectrum function P(θ);

[0049] Step 5: Locate the peak position MaxPos2 in the spatial spectrum function P(θ) and solve the angle of arrival of the signal accordingly:

[0050] θ d =acos[MaxPos2·c / (nFFT2·f·d)]

[0051] Where acos() is the arc cosine function.

[0052] The above method is simulated and verified as follows:

[0053] Simulation conditions: A uniform linear array with 16 elements is used, the spacing d between adjacent elements is half a wavelength, and the signal frequency is 1800 MHz. The trend of direction finding accuracy changes under different conditions is simulated.

[0054] The simulation results are as follows Figure 2 、 Figure 3 shown.

[0055] pass Figure 2It can be seen that under different signal-to-noise ratios, the fast DOA estimation method based on dual FFT has significantly improved direction-finding accuracy compared to the traditional wavenumber domain direction-finding algorithm. In addition, since the traditional beam domain algorithm only uses one snapshot for DOA estimation, the direction-finding accuracy does not increase significantly with the improvement of signal-to-noise ratio. However, the fast DOA estimation method based on dual FFT makes full use of the limited sampling snapshots of the array through the first FFT processing. Therefore, as the signal-to-noise ratio increases, the direction-finding accuracy also increases and gradually remains stable, reflecting better DOA estimation performance. Figure 3 It can be seen that when the number of array sampling snapshots is limited, the number of second FFT processing points can be increased by zero-padding method to enhance the algorithm's spatial resolution and further improve the direction finding accuracy.

[0056] In summary, the present invention first performs a first FFT on the array's received data to obtain the phase difference of each channel at the point of maximum spectral amplitude, which is used to construct the array's spatial sampling sequence. A second FFT is then performed on the spatial sampling sequence to obtain the direction-finding spatial spectrum. Finally, the signal's angle of arrival is determined based on the position of the spectrum peak. This dual FFT process achieves joint processing of the array's received signals in both the frequency and spatial domains, further improving the convergence speed of direction-of-arrival estimation and the accuracy of direction-finding.

Claims

1. A fast direction of arrival estimation method based on dual FFT, characterized in that: The following steps are involved: Step 1: Perform the first FFT processing of nFFT1 points on the array received data to transform the array received information from the time domain to the frequency domain; Step 2: Locate the maximum spectrum amplitude position MaxPos1 and extract the phase of each receiving channel of the array at MaxPos1; Step 3: Calculate the phase difference between each channel of the array based on the extracted phase, and construct the spatial sampling sequence accordingly: Where f is the signal frequency, d is the distance between adjacent elements in the array, and θ d is the angle of arrival of the signal to be estimated, c is the speed of light, M is the number of elements in the array, e is the base of the natural logarithm, and j is the imaginary unit; Step 4: Perform a second FFT process of nFFT2 points on the spatial domain sampling sequence to obtain the spatial spectrum function P(θ); Step 5: Locate the peak position MaxPos2 in the spatial spectrum function P(θ) and solve the signal's angle of arrival θ accordingly d : i d =acos[MaxPos2·c / (nFFT2·f·d)] Where acos() is the arc cosine function.

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