Signal bandwidth estimation method for power spectral density function integration
By using the power spectral density function integral method, combined with fast Fourier transform and dynamic thresholding techniques, the contradiction between accuracy and complexity in signal bandwidth estimation is resolved, achieving high-precision signal bandwidth estimation with low complexity, which is suitable for satellite communication channels.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- XIAN INSTITUE OF SPACE RADIO TECH
- Filing Date
- 2025-12-18
- Publication Date
- 2026-04-17
AI Technical Summary
Existing signal bandwidth estimation methods present a trade-off between accuracy and algorithm complexity, making it difficult to achieve high-precision, low-complexity estimation, which limits their application, especially in the field of satellite electronic reconnaissance.
By employing the power spectral density function integral method, and combining fast Fourier transform, power spectral density distribution map smoothing filtering, and dynamic thresholding techniques with coarse and fine estimation steps, the signal and noise intervals are determined, achieving high-precision bandwidth estimation with low complexity.
It achieves high-precision signal bandwidth estimation with low computational complexity in satellite communication channels, and is applicable to bandwidth estimation of signal bandwidth greater than or equal to 1/2, thus avoiding estimation scheme failure.
Smart Images
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Abstract
Description
Technical Field
[0001] This invention belongs to the field of digital signal processing technology and relates to a method for estimating signal bandwidth by integrating the power spectral density function. Background Technology
[0002] Signal bandwidth estimation is a classic parameter estimation problem. As an important signal analysis method, it has a wide range of applications and significant value. Especially in the field of satellite electronic reconnaissance, effective and accurate bandwidth estimation can greatly assist subsequent signal processing or target signal downlink.
[0003] Most existing bandwidth estimation methods are based on the power spectrum of a signal, and common methods include autocorrelation methods, center of mass methods, energy concentration methods, energy integration methods, and power spectrum filtering. These methods are simple in principle and easy to implement, but their estimation accuracy is relatively poor. Methods based on power spectrum wavelet transform and power spectrum curve fitting have achieved better estimation results, but these methods are computationally complex and difficult to implement. Summary of the Invention
[0004] The technical problem solved by this invention is to overcome the contradiction between bandwidth estimation accuracy and algorithm complexity in existing estimation methods, and to provide a signal bandwidth estimation method based on the power spectral density function integral, which can achieve high-precision bandwidth estimation with low computational complexity.
[0005] The solution of the present invention is: A signal bandwidth estimation method based on the integration of the power spectral density function includes: (1) Perform a fast Fourier transform on the sampled signal according to the length of the signal, take the square of the modulus of the spectrum after the fast Fourier transform, convert the squared value into decibels, and obtain the power spectral density distribution map. (2) Calculate 2 M By integrating the power spectral density at each point, the slope variation curves for the forward and reverse directions are calculated. and positive slope change curve The point corresponding to the maximum value is a rough estimate of the upper limit. Reverse slope change curve The point corresponding to the maximum value is the lower limit coarse estimate. ; (3) Smooth the power spectral density distribution graph. The smoothed power spectral density distribution is defined as follows: , ~ This area has been identified as a signal zone, 1~ and ~2 M Defined as the noise floor region; when no broadband signal is present, the system measures... The mean is defined as TH0, the signal region. The mean minus 6 is defined as TH1, the noise floor region. The mean is defined as TH2. If TH2 ≥ TH1, then the signal threshold TH is set to TH0; otherwise, it is set to TH1. (4) To ~2 M A fine estimate of the upper limit of the signal is performed to obtain the upper limit fine estimate value. ; (5) To A fine estimate of the lower limit of the signal between ~1 is performed to obtain the fine estimate of the lower limit value. ; (6) Based on the upper limit precise estimate and lower limit precise estimate Calculate the actual signal bandwidth.
[0006] The beneficial effects of this invention compared to the prior art are: This invention employs logarithmic calculation of the power spectral density distribution function and smoothing filtering to reduce the impact of outliers on estimation accuracy; it rapidly determines the signal and noise intervals based on the change in the integral slope of the power spectral density distribution function; and it utilizes a dual-threshold scheme of dynamic and empirical thresholds, making it applicable to signals with bandwidths ≥ It provides bandwidth estimation at a ratio of 2 / 2 without causing the estimation scheme to fail. High-precision bandwidth estimation with low computational complexity is achieved. Attached Figure Description
[0007] Figure 1 This is a schematic diagram of a signal bandwidth estimation method based on the integration of the power spectral density function. Detailed Implementation
[0008] This invention provides a signal bandwidth estimation method based on power spectral density function integration, used for bandwidth estimation in satellite communication channels. This invention enables high-precision signal estimation with low complexity. The method first performs power spectral density integration, followed by coarse and fine estimations. Specifically: (1.1) Perform Fast Fourier Transform (FFT) on the sampled signal according to the length of the signal. The selection principle for the number of FFT points is that the number of FFT points is not less than the number of signal points raised to the power of 2. Take the square of the modulus value of the spectrum after FFT, and then convert the squared modulus value into decibels to obtain the power spectral density distribution map.
[0009] The FFT number of points is not less than an integer power of 2 of the signal number of points, meaning that the FFT is performed based on the signal number N. M Fast Fourier Transform of Points, 2 M ≥N.
[0010] (1.2) In the rough estimate, the calculation of 2 M The power spectral density integral at point P, i.e., for any point P (P∈[1, 2], is calculated as follows: M The integral value at ]) It equals the cumulative power spectral density from point 1 to point P; after obtaining the power spectral density integral, calculate the slope change curves in the forward and reverse directions. and , and The value at the P-th point is: ; .
[0011] This is the integral value at the first point; For the 2nd M The integral value at each point.
[0012] (1.3) Find the slope change curves in the positive and negative directions. and The positions of the maximum values are obtained respectively. and These are the upper limit rough estimate and the lower limit rough estimate.
[0013] (1.4) Smooth the power spectral density distribution map to reduce the abrupt changes in power spectral density introduced by random values. The smoothed power spectral density distribution is defined as follows: , ~ This area has been identified as a signal zone, 1~ and ~2^M is defined as the noise floor region; when no broadband signal is present, the system measures... The mean is defined as TH0, the signal region. The mean minus 6 is defined as TH1, the noise floor zone. The mean is defined as TH2. If TH2 ≥ TH1, then the signal threshold TH is set to TH0; otherwise, it is set to TH1.
[0014] The length of the smoothing filter does not exceed 1 / 16 of the difference between the upper and lower coarse estimates. The smoothing filter is as follows: , In the formula, ceil(.) means rounding the data up.
[0015] (1.5) Precise estimation of the upper limit of the signal: with Starting from, in ~2 M The first step involves taking a sliding window with a width of 8 to represent the average value. ~ +7 consecutive 8 points If the mean is greater than the threshold TH, then continue the comparison. +1~ The relationship between the mean and the threshold is +8; this process continues until the mean is less than the threshold or the sliding window starts at 2. M Up to this point, the value at the starting point of the sliding window is the upper limit precise estimate. When taking 8 consecutive points as described above, if there are fewer than 8 points, use as many points as there are consecutive points.
[0016] (1.6) Precise estimation of the lower limit of the signal: Starting from, in The first step involves taking the mean value between ~1 and 8, using a sliding window with a width of 8. ~ -7 consecutive 8 points If the mean is greater than the threshold TH, then continue the comparison. -1~ The relationship between the mean and the threshold is calculated by applying this method until the mean is less than the threshold or the starting point of the sliding window is equal to 1. At this point, the value of the starting point of the sliding window is the precise estimate of the lower limit. When taking 8 consecutive points as described above, if there are fewer than 8 points, use as many points as there are consecutive points.
[0017] (1.7) Based on the upper and lower limits, the precise estimated value and The calculation method for converting to the actual signal bandwidth is as follows, where... The sampling rate of the signal.
[0018] , This invention enables bandwidth estimation of signals in satellite communication channels. First, a Fast Fourier Transform (FFT) is performed on the signal. The magnitude of the transformed signal is squared and then converted to fractions to obtain the power spectral density. The power spectral density is then integrated, and the extreme values of the slope changes of the integrated power spectrum are used to obtain coarse estimates of the upper and lower limits of the signal in the spectrum. Based on these coarse estimates, a power variation estimation is performed on the power spectral density to obtain a fine estimate. Finally, the true bandwidth of the signal is calculated based on the signal's sampling rate and the number of FFT points. This invention achieves high-precision bandwidth estimation with low computational complexity.
[0019] like Figure 1 As shown, the present invention provides a signal bandwidth estimation system for power spectral density function integral, including a power spectral density calculation module, a coarse estimation module, and a fine estimation module.
[0020] The power spectral density calculation module performs 2... M Fast Fourier Transform of Points, 2M ≥N, and take the square of the modulus of the spectrum after FFT, and then convert the squared modulus to fractional values; The coarse estimation module calculates the power spectral density integral from 1 to 2. M Find the maximum value of the changing slope, obtain a rough estimate of the upper limit of the broadband signal, and calculate the power spectral density integral from 2. M Find the lower limit rough estimate of the broadband signal by finding the maximum value of the slope of change to 1. The fine estimation module divides the spectrum into signal and noise regions based on the upper and lower limits of the signal obtained from the coarse estimation, determines the signal threshold, and then detects the edge of the signal region again. If the signal is above the threshold, it is considered a signal; if it is below the threshold, it is considered noise, thus obtaining the finely estimated signal region.
[0021] The parts of this invention not described in detail are common knowledge to those skilled in the art.
Claims
1. A method of signal bandwidth estimation by integration of a power spectral density function, characterized by, include: (1) Perform a fast Fourier transform on the sampled signal according to the length of the signal, take the square of the modulus of the spectrum after the fast Fourier transform, and then convert the squared value into decibels to obtain the power spectral density distribution map. (2) Calculate the power spectrum density integral of 2 points M , and calculate the forward and reverse slope change curves after the power spectrum density integral , the maximum value of the forward slope change curve corresponds to the upper limit of the rough estimate value , the maximum value of the reverse slope change curve corresponds to the lower limit of the rough estimate value ; (3) Smooth the power spectral density distribution graph. The smoothed power spectral density distribution is defined as follows: , ~ This area has been identified as a signal zone, 1~ and ~2 M Defined as the noise floor region; when no broadband signal is present, the system measures... The mean is defined as TH0, the signal region. The mean minus 6 is defined as TH1, the noise floor region. The mean is defined as TH2. If TH2 ≥ TH1, then the signal threshold TH is set to TH0; otherwise, it is set to TH1. (4) To ~2 M A fine estimate of the upper limit of the signal is obtained by performing a fine estimate of the upper limit. ; (5) To A fine estimate of the lower limit of the signal between ~1 is performed to obtain the fine estimate of the lower limit value. ; (6) Based on the upper limit precise estimate and lower limit precise estimate Calculate the actual signal bandwidth.
2. The signal bandwidth estimation method based on the power spectral density function integration according to claim 1, characterized in that, The number of points of the fast Fourier transform is selected according to the following principle: according to the number of points N of the signal, perform a 2 M point fast Fourier transform, 2 M ≥N.
3. The signal bandwidth estimation method based on the power spectral density function integral according to claim 1, characterized in that, Calculate 2 in the rough estimate M The power spectral density integral at point P, where the integral value at point P is... It equals the cumulative power spectral density from point 1 to point P, where P∈[1, 2]. M ].
4. The signal bandwidth estimation method based on the power spectral density function integration according to claim 3, characterized in that, Positive slope change curve The value at the P-th point is: ； This is the integral value at the first point; Reverse slope change curve The value at the P-th point is: For the 2nd M The integral value at each point.
5. The signal bandwidth estimation method based on the power spectral density function integration according to claim 1, characterized in that, right ~2 M The upper limit of the signal between the given ranges is precisely estimated using the following method: by Starting from, in ~2 M The first step involves taking a sliding window with a width of 8 to represent the average value. ~ +7 consecutive 8 points If the mean is greater than the threshold TH, then continue the comparison. +1~ The relationship between the mean and the threshold is +8; this process continues until the mean is less than the threshold or the sliding window starts at 2. M Up to this point, the value at the starting point of the sliding window is the upper limit precise estimate. When taking 8 consecutive points as described above, if there are fewer than 8 points, use as many points as there are consecutive points.
6. The signal bandwidth estimation method based on the power spectral density function integral according to claim 1, characterized in that, The lower limit of the signal between ~1 is precisely estimated using the following method: by Starting from, in The first step involves taking the mean value between ~1 and 8, using a sliding window with a width of 8. ~ -7 consecutive 8 points If the mean is greater than the threshold TH, then continue the comparison. -1~ The relationship between the mean and the threshold is calculated by applying this method until the mean is less than the threshold or the starting point of the sliding window is equal to 1. At this point, the value of the starting point of the sliding window is the precise estimate of the lower limit. When taking 8 consecutive points as described above, if there are fewer than 8 points, use as many points as there are consecutive points.
7. The signal bandwidth estimation method based on the power spectral density function integral according to claim 1, characterized in that, Actual signal bandwidth The calculation formula is as follows: ， in The sampling rate of the signal.
8. The signal bandwidth estimation method based on the power spectral density function integration according to claim 1, characterized in that, Smoothing filters are used, and the length of the smoothing filter does not exceed 1 / 16 of the difference between the upper and lower bound coarse estimates.
9. The signal bandwidth estimation method based on the power spectral density function integration according to claim 8, characterized in that, The smoothing filter is: ， In the formula, ceil(.) means rounding the data up.
10. A signal bandwidth estimation system based on the power spectral density function integral, characterized in that: It includes a power spectral density calculation module, a coarse estimation module, and a fine estimation module, wherein: The power spectrum density calculation module performs 2 M point fast Fourier transform on the sampling signal according to the point number N of the signal, M ≥N, and takes the square of the modulus value of the frequency spectrum after the fast Fourier transform, then converts the modulus square value into decibel value to obtain a power spectrum density distribution diagram; The coarse estimation module calculates 2. M By integrating the power spectral density at each point, the slope variation curves for the forward and reverse directions are calculated. and positive slope change curve The point corresponding to the maximum value is a rough estimate of the upper limit, and the curve shows the change in the reverse slope. The point corresponding to the maximum value is a rough estimate of the lower limit; The fine estimation module divides the spectrum into signal and noise regions based on the upper and lower limit coarse estimates obtained from the coarse estimation module, and determines the signal threshold. Based on the signal threshold, the edge of the signal region is detected to obtain the finely estimated signal region, and thus the true signal bandwidth is obtained.