CN115276693A - Multi-frequency-point multi-bandwidth identification method based on welch - Google Patents
Multi-frequency-point multi-bandwidth identification method based on welch Download PDFInfo
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- CN115276693A CN115276693A CN202211169175.6A CN202211169175A CN115276693A CN 115276693 A CN115276693 A CN 115276693A CN 202211169175 A CN202211169175 A CN 202211169175A CN 115276693 A CN115276693 A CN 115276693A
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
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- H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
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- H—ELECTRICITY
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Abstract
The invention provides a multi-frequency-point multi-bandwidth identification method based on welch, belonging to the technical field of communication, and the method comprises the following steps: acquiring a baseband signal to carry out welch power spectrum estimation to obtain a power spectrum Px of the point number of Fourier transform; performing m-order smooth filtering on the power spectrum Px, and performing m-order smooth filtering in reverse order to obtain a power spectrum Pz; segmenting the power spectrum Pz, and calculating a noise value and a full bandwidth threshold value; calculating the maximum value max and the corresponding index value of the power spectrum Pz and the 3db bandwidth threshold value, and judging the maximum value of the power spectrum Pz; obtaining a full-bandwidth right index value and a full-bandwidth left index value; solving a 3db bandwidth index difference; calculating a central frequency point and a 3db bandwidth; calculating the central frequency point and the 3db bandwidth of the secondary peak signal; and (4) moving the baseband signal received by the receiver backward by nfft, and estimating the next welch power spectrum. The invention realizes the identification of the central frequency point and the bandwidth of the signal under the condition of low signal-to-noise ratio.
Description
Technical Field
The invention relates to the technical field of communication, in particular to a multi-frequency-point multi-bandwidth identification method based on welch.
Background
The center frequency estimation and the bandwidth estimation mainly relate to a plurality of military and civil fields such as radar, sonar, navigation, communication, imaging, geological exploration, biomedical engineering and the like. In these fields, a receiver receives a plurality of different signals simultaneously within a reception bandwidth, and in the above fields, it is necessary to analyze such signals and extract a characteristic signal. Before extracting the characteristic signals, firstly, the estimation of the central frequency point and the bandwidth is carried out on the signals.
Regarding frequency estimation of a signal, frequency domain estimation methods include a periodogram method, a centroid method, wherein the periodogram method is a method based on maximum likelihood estimation, and a highest peak position of a periodogram is used as an estimation of a carrier frequency, and the method is suitable for a case where a carrier component exists and is not suitable for a case where a carrier is suppressed. The centroid method is suitable for frequency spectrum symmetric signals, and has a poor estimation effect on asymmetric signals. Therefore, the above method is not suitable for a scenario in which frequency point bandwidth calculation is performed on multiple signals within a reception bandwidth.
Conventional bandwidth estimation methods include a root mean square method, an autocorrelation method, a maximum entropy method, an energy concentration method, and the like. The bandwidth estimated by the methods is relatively low in precision and often cannot meet the requirements of practical application.
For the conditions of large interference and low signal-to-noise ratio, the existing method for estimating the bandwidth of the center frequency point is difficult to identify. The existing frequency point bandwidth calculation is based on the abundance of single signals and does not meet the processing of actual conditions. And for the multi-peak condition of mfsk (multi-system digital frequency modulation), the existing frequency point bandwidth mode identifies the multi-peak condition as a multi-frequency point, which is not in accordance with the reality.
Disclosure of Invention
Aiming at the problems in the prior art, the invention aims to provide a multi-frequency-point multi-bandwidth identification method based on welch, which realizes the identification of the central frequency point and the bandwidth of a signal under the condition of low signal-to-noise ratio.
In order to achieve the purpose, the invention is realized by the following technical scheme:
a multi-frequency-point multi-bandwidth identification method based on welch comprises the following steps:
step 1: performing welch power spectrum estimation on a baseband signal with the length of N to obtain a power spectrum Px of the point number of Fourier transform;
step 2: performing m-order smoothing filtering on the power spectrum Px to obtain a power spectrum Py;
and step 3: performing m-order smoothing filtering on the power spectrum Py in a reverse order to obtain a power spectrum Pz;
and 4, step 4: segmenting the power spectrum Pz, and calculating a noise value noise and a full bandwidth threshold FullBwTH;
and 5: calculating a maximum value max of the power spectrum Pz and corresponding index values MaxInd and a 3db bandwidth threshold value ThreeBwTH, wherein ThreeBwTH = max/2, judging whether the maximum value max of the power spectrum Pz is smaller than a preset value, if so, turning to the step 10, otherwise, turning to the next step;
and 6: searching rightwards from the index value MaxInd according to the full-bandwidth threshold FULLBwTH to obtain a full-bandwidth right index value FullBwR, and searching rightwards from the index value MaxInd to obtain a full-bandwidth left index value FullBwL;
and 7: when the FullBwR and the FullBwL exist at the same time, obtaining a right index value ThreeBwR of the 3db bandwidth and a left index value ThreeBwL of the 3db bandwidth according to the 3db bandwidth threshold ThreeBwTH, and obtaining a 3db bandwidth index difference;
and 8: calculating a central frequency point and a 3db bandwidth according to a preset formula;
and step 9: setting Px in the interval of [ FullBwL, fullBwR ] as a noise value noise to calculate the central frequency point and the 3db bandwidth of the secondary peak signal;
step 10: the baseband signal received by the receiver is shifted back by nfft and the process goes to step 1 to calculate the next frequency spectrum.
Further, the step 1 specifically comprises:
taking the baseband signal received by the receiver each time
Performing welch power spectrum estimation on the data of the length to obtain
Power spectrum of a point
(ii) a Wherein the content of the first and second substances,
is the number of points in the fourier transform,
the number of segments in welch transformation is half of the data of each segment, and the length of each segment is equal to that of each segment
Number of stages is
。
Further, step 2 specifically comprises:
power spectrum by
To carry out
Smoothing of the order to obtain a power spectrum
；
Further, step 3 specifically comprises:
power spectrum is determined by
Performing m-order smoothing filtering on the reverse order to obtain a power spectrum
；
Further, step 4 specifically comprises:
the power spectrum obtained after smoothing
Is divided into
Segment per segment
Power spectrum of
Calculating the mean value
Minimum mean in segment as noise value
；
By the formula
A full bandwidth threshold is calculated, wherein,
is composed of
The center frequency point of the spectrum signal and the threshold value of bandwidth calculation.
Further, the step of judging whether the maximum max of the power spectrum Pz is smaller than a preset value specifically includes:
judging whether the maximum value max of the power spectrum Pz is smaller than
。
Further, step 6 includes:
searching rightward from the position of the index value MaxInd, and recording the previous index value of the index value which is firstly lower than the full bandwidth threshold FULLBwTH as the full bandwidth right index value FullBwR; and searching leftwards from the position of the index value MaxInd, and recording the next index value of the index values which are firstly lower than the full bandwidth threshold FULLBwTH as a full bandwidth left index value FullBwL.
Further, step 7 includes:
if the FullBwR and the FullBwL exist at the same time, calculating an index value of the 3db bandwidth, searching from the FullBwR to MaxInd to the left, finding out a first index value larger than ThreeBwTH, and recording as ThreeBwR; searching from FullBwR to MaxInd to the right, finding out the first index value larger than ThreeBwTH, and recording as ThreeBwL;
let fullbwwl =0, labeled flag = -1, if fullbwwl is not present;
let FullBwR = nfft-1, labeled flag =1, if FullBwR is not present;
obtaining a 3db bandwidth index difference ThreeBandInd according to a formula ThreeBandInd = ThreeBwR-ThreeBwL;
obtaining a left index difference deltaL of the full bandwidth 3db bandwidth according to a formula deltaL = ThreeBwL-FullBwL;
obtaining a full bandwidth 3db bandwidth right index difference deltaR according to a formula deltaR = FullBwR-ThreeBwR;
if deltaL/deltaR > 2, fullBwL = ThreeBwL-deltaR;
if deltaR/deltaL > 2, fullBwR = ThreeBwR + deltaL.
Further, step 8 comprises:
judging whether the flag is 0, if not, turning to the step 5;
if the BandWidth is 0, calculating a center frequency FreCenter and a 3db BandWidth BandWidth according to the following formula;
wherein fs is the sampling rate.
Further, step 9 comprises:
and (5) setting Px in the index value of the full bandwidth [ FullBwL, fullBwR ] as a noise value noise, and skipping to the step 5 to calculate the central frequency point and the bandwidth of the secondary peak signal.
Compared with the prior art, the invention has the beneficial effects that:
1. the method has simple algorithm and easy realization, and realizes the identification of the central frequency point and the bandwidth of the signal under the condition of low signal-to-noise ratio.
2. The invention can correctly identify the center frequency point and the effective bandwidth thereof from mfsk.
3. The invention can identify the center frequency point and the bandwidth of the multi-frequency point multi-bandwidth signal.
Therefore, compared with the prior art, the invention has prominent substantive features and remarkable progress, and the beneficial effects of the implementation are also obvious.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a process flow diagram of an embodiment of the present invention.
FIG. 2 is a graph of fft spectra in accordance with an embodiment of the present invention.
Figure 3 is a welch smoothed spectrum graph of an embodiment of the invention.
FIG. 4 is an identification chart of the points of the 3db bandwidth of FIG. 3.
FIG. 5 is an identification chart of points of 3db bandwidth identified by 4fsk in accordance with an embodiment of the present invention.
FIG. 6 is a multi-frequency-point multi-bandwidth fft spectrogram in accordance with an embodiment of the present invention.
Fig. 7 is a multi-frequency-point multi-bandwidth welch smoothed spectrum diagram according to an embodiment of the invention.
Fig. 8 is a graphical representation of the identification of the bandwidth of the first frequency bin of fig. 7 at 3 db.
Fig. 9 is a graphical representation of the identification of the bandwidth of the second frequency bin 3db of fig. 7.
Fig. 10 is a graphical representation of the identification of the bandwidth of the third frequency bin of fig. 7 at 3 db.
Detailed Description
The following description of the embodiments of the present invention will be made with reference to the accompanying drawings.
As shown in fig. 1, the method for recognizing multiple frequency points and multiple bandwidths based on welch includes the following steps:
step 1: and (3) performing welch power spectrum estimation on the baseband signal with the length of N to obtain a power spectrum Px of the point number of Fourier transform.
The method specifically comprises the following steps: taking the baseband signal received by the receiver each time
Performing welch power spectrum estimation on the data of the length to obtain
Power spectrum of a point
(ii) a Wherein, the first and the second end of the pipe are connected with each other,
is the number of points in the fourier transform,
the number of segments in welch transformation is half of the data of each segment, and the length of each segment is equal to that of each segment
Number of stages is
。
Compared with the directly obtained power spectrum, the signal power spectrum obtained by the welch transformation in the step is a power spectrum obtained by windowing, segmenting and weighting, the power spectrum is smoother in representation, and the signal main lobe width can be more obvious. Moreover, some interference is filtered, so that the main lobe width is more accurate.
Step 2: and performing m-order smoothing filtering on the power spectrum Px to obtain a power spectrum Py.
Specifically, the power spectrum is corrected by the following formula
To carry out
Smoothing of the order to obtain a power spectrum
。
And step 3: and (4) performing m-order smoothing filtering on the power spectrum Py in a reverse order to obtain a power spectrum Pz.
Specifically, the power spectrum is expressed by
Performing m-order smoothing filtering in reverse order to obtain power spectrum
。
And 4, step 4: the power spectrum Pz is segmented and the noise value noise and the full bandwidth threshold fullbwhth are calculated.
First, the smoothed power spectrum is used
Is divided into
Segment per segment
Power spectrum of
Calculating the mean value
Minimum mean in segment as noise value
. Then, by the formula
A full bandwidth threshold is calculated, wherein,
is composed of
The center frequency point of the spectrum signal and the threshold value of bandwidth calculation.
And 5: and (3) calculating the maximum value max of the power spectrum Pz and the corresponding index value MaxInd and the bandwidth threshold ThreeBwTH of 3db, wherein ThreeBwTH = max/2, judging whether the maximum value max of the power spectrum Pz is smaller than a preset value, if so, turning to the step 10, otherwise, turning to the next step.
The specific step of judging whether the maximum value max of the power spectrum Pz is smaller than a preset value is as follows: judging whether the maximum value max of the power spectrum Pz is smaller than
。
And 6: and searching rightwards from the index value MaxInd according to the full bandwidth threshold FULLBwTH to obtain a full bandwidth right index value FullBwR, and searching rightwards from the index value MaxInd to obtain a full bandwidth left index value FullBwL.
Specifically, searching rightward from the position of the index value MaxInd, and finding the previous index value of the index value which is first lower than the full bandwidth threshold fullbwhth and recording the previous index value as the full bandwidth right index value fullbwhr; searching left from the position of the index value MaxInd, and recording the next index value of the index values which are firstly lower than the full bandwidth threshold fullbwwth as the full bandwidth left index value fullbwwl.
And 7: and when FullBwR and FullBwL exist at the same time, obtaining a right index value ThreeBwR of the 3db bandwidth and a left index value ThreeBwL of the 3db bandwidth according to the 3db bandwidth threshold ThreeBwTH, and obtaining a 3db bandwidth index difference.
If the FullBwR and the FullBwL exist at the same time, calculating an index value of the 3db bandwidth, searching from the FullBwR to MaxInd to the left, finding out a first index value larger than ThreeBwTH, and recording the index value as ThreeBwR; searching right from FullBwR to MaxInd, finding the first index value which is larger than ThreeBwTH and is marked as ThreeBwL. Let FullBwL =0 if FullBwL is not present, and flag = -1. Let FullBwR = nfft-1, labeled flag =1, if FullBwR is not present.
In the step, according to a formula ThreeBandInd = ThreeBwR-ThreeBwL, obtaining a 3db bandwidth index difference ThreeBandInd; obtaining a left index difference deltaL of the full bandwidth 3db bandwidth according to a formula deltaL = ThreeBwL-FullBwL; and solving the full bandwidth 3db bandwidth right index difference deltaR according to the formula deltaR = FullBwR-ThreeBwR.
Wherein, if deltaL/deltaR > 2, fullBwL = ThreeBwL-deltaR; if deltaR/deltaL > 2, fullBwR = ThreeBwR + deltaL.
And step 8: and calculating the central frequency point and the 3db bandwidth according to a preset formula.
Firstly, judging whether flag is 0, if not, turning to step 5.
If the BandWidth is 0, the center frequency FreCenter and the 3db BandWidth BandWidth are calculated according to the following formula.
Wherein fs is the sampling rate.
And step 9: and setting Px in the interval of [ FullBwL, fullBwR ] as a noise value noise to calculate the central frequency point and the 3db bandwidth of the secondary peak signal.
Specifically, px in the index value of the full bandwidth [ FullBwL, fullBwR ] is set as a noise value noise, and the step 5 is skipped to calculate the center frequency point and the bandwidth of the secondary peak signal.
Step 10: the baseband signal received by the receiver is shifted back by nfft and the process goes to step 1 to calculate the next frequency spectrum.
Based on the method, the invention can embody the following advantages after practical use:
fig. 2 is a frequency spectrum diagram of a signal with a signal-to-noise ratio of-15 db and a 4fsk signal directly drawn in the fft mode, and it can be seen in fig. 2 that a useful signal is completely submerged in noise, and it is impossible to identify a center frequency point and a bandwidth by using the frequency spectrum diagram. Fig. 3 is a frequency spectrum graph drawn after steps 1 to 3 of the method, and four peak points of useful bandwidth and 4fsk can be clearly seen, which illustrates that the problem of identifying the center frequency point and the bandwidth under the condition of low signal-to-noise ratio can be well solved by the processing of the method. The dot in fig. 4 is the position of the 3db bandwidth identified by the method, and the corresponding center frequency dot and bandwidth can be obtained according to step 8.
The method is particularly suitable for the case of mfsk, and a general algorithm can easily identify 4fsk as 4 frequency points as shown in fig. 5, and the method is characterized in that the method adopted in step 6 and step 7 can correctly identify the center frequency point and the effective bandwidth thereof from mfsk. The dot in fig. 5 is the position of the 3db bandwidth identified by the present invention, and the corresponding center frequency point and bandwidth are obtained according to step 8.
The method is characterized in that the central frequency point and the bandwidth of a multi-frequency-point multi-bandwidth signal can be identified, as shown in fig. 6, the method is a frequency spectrum diagram which is formed by three modulation modes of 2ask, 4fsk and 16qam and is directly drawn by adopting a fft mode. At low signal-to-noise ratios, the multi-frequency point multi-bandwidth signal main lobe of fig. 6 is less visible. Fig. 7 is a spectrum diagram after steps 1 to 3 in the method of the present invention, which clearly shows the outline of the multi-frequency-point multi-bandwidth signal. The dots in fig. 8 mark the location of the 3db bandwidth of the highest signal; the dot in fig. 9 marks the position of the 3db bandwidth of the second high signal; the position of the 3db bandwidth of the third highest signal is marked by the dot in fig. 10, which should be 4fsk as can be seen from the presence of 4 peaks in fig. 10. And (4) obtaining corresponding central frequency points and bandwidths for all the signals according to the step (8).
Therefore, the method is simple to implement, low in complexity, effective in identifying the frequency point bandwidths of various modulation modes, and also suitable for the multi-peak condition of mfsk.
The invention is further described with reference to the accompanying drawings and specific embodiments. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention can be made by those skilled in the art after reading the teaching of the present invention, and these equivalents also fall within the scope defined by the present application.
Claims (10)
1. A multilink multi-point multi-bandwidth identification method based on welch is characterized by comprising the following steps:
step 1: performing welch power spectrum estimation on a baseband signal with the length of N to obtain a power spectrum Px of the point number of Fourier transform;
step 2: performing m-order smoothing filtering on the power spectrum Px to obtain a power spectrum Py;
and 3, step 3: performing m-order smoothing filtering on the power spectrum Py in a reverse order to obtain a power spectrum Pz;
and 4, step 4: segmenting the power spectrum Pz, and calculating a noise value noise and a full bandwidth threshold FullBwTH;
and 5: calculating a maximum value max of the power spectrum Pz and corresponding index values MaxInd and a 3db bandwidth threshold value ThreeBwTH, wherein ThreeBwTH = max/2, judging whether the maximum value max of the power spectrum Pz is smaller than a preset value, if so, turning to the step 10, otherwise, turning to the next step;
step 6: searching rightwards from the index value MaxInd according to the full-bandwidth threshold FULLBwTH to obtain a full-bandwidth right index value FullBwR, and searching rightwards from the index value MaxInd to obtain a full-bandwidth left index value FullBwL;
and 7: when the FullBwR and the FullBwL exist at the same time, obtaining a right index value ThreeBwR of the 3db bandwidth and a left index value ThreeBwL of the 3db bandwidth according to the 3db bandwidth threshold ThreeBwTH, and obtaining a 3db bandwidth index difference;
and step 8: calculating a central frequency point and a 3db bandwidth according to a preset formula;
and step 9: setting Px in the interval of [ FullBwL, fullBwR ] as a noise value noise to calculate the central frequency point and the 3db bandwidth of the secondary peak signal;
step 10: and (4) shifting the baseband signal received by the receiver back by nfft, and turning to the step 1 to calculate the next frequency spectrum.
2. The welch-based multi-frequency-point multi-bandwidth identification method according to claim 1, wherein the step 1 specifically comprises:
taking the baseband signal received by the receiver each time
Performing welch power spectrum estimation on the data of the length to obtain
Power spectrum of a point
(ii) a Wherein the content of the first and second substances,
is the number of points in the fourier transform,
the number of segments in welch transformation is half of the data of each segment, and the length of each segment is equal to that of each segment
Number of stages is
。
3. The welch-based multi-frequency-point multi-bandwidth identification method according to claim 2, wherein the step 2 is specifically:
power spectrum by
To carry out
Smoothing of the order to obtain a power spectrum
；
4. The welch-based multi-frequency-point multi-bandwidth identification method according to claim 3, wherein the step 3 is specifically as follows:
power spectrum is determined by
Performing m-order smoothing filtering in reverse order to obtain power spectrum
；
5. The welch-based multi-frequency-point multi-bandwidth identification method according to claim 4, wherein the step 4 is specifically:
the power spectrum obtained after smoothing
Is divided into
Segment per segment
Power spectrum of
Calculating the mean value
Minimum mean in segment as noise value
；
By the formula
A full bandwidth threshold is calculated, wherein,
is composed of
The center frequency point of the spectrum signal and the threshold value of bandwidth calculation.
6. The welch-based multi-frequency-point multi-bandwidth identification method according to claim 5, wherein the determining whether the maximum value max of the power spectrum Pz is smaller than a preset value specifically comprises:
judging whether the maximum value max of the power spectrum Pz is smaller than
。
7. The welch-based multi-frequency-point multi-bandwidth identification method according to claim 6, wherein the step 6 comprises:
searching rightward from the position of the index value MaxInd, and finding the previous index value of the index value which is lower than the full bandwidth threshold FULLBwTH for the first time and recording the previous index value as the full bandwidth right index value FullBwR; searching left from the position of the index value MaxInd, and recording the next index value of the index values which are firstly lower than the full bandwidth threshold fullbwwth as the full bandwidth left index value fullbwwl.
8. The welch-based multi-frequency-point multi-bandwidth identification method according to claim 7, wherein the step 7 comprises:
if the FullBwR and the FullBwL exist at the same time, calculating an index value of the 3db bandwidth, searching from the FullBwR to MaxInd to the left, finding out a first index value larger than ThreeBwTH, and recording as ThreeBwR; searching from FullBwR to MaxInd to the right, finding the first index value which is larger than ThreeBwTH and recording as ThreeBwL;
let fullbwwl =0, labeled flag = -1, if fullbwwl is not present;
let FullBwR = nfft-1, marked as flag =1, if FullBwR is not present;
obtaining a 3db bandwidth index difference ThreeBandInd according to a formula ThreeBandInd = ThreeBwR-ThreeBwL;
obtaining a left index difference deltaL of the full bandwidth 3db bandwidth according to a formula deltaL = ThreeBwL-FullBwL;
obtaining a full bandwidth 3db bandwidth right index difference deltaR according to a formula deltaR = FullBwR-ThreeBwR;
if deltaL/deltaR > 2, fullBwL = ThreeBwL-deltaR;
if deltaR/deltaL > 2, fullBwR = ThreeBwR + deltaL.
9. The welch-based multi-frequency-point multi-bandwidth identification method according to claim 8, wherein the step 8 comprises:
judging whether the flag is 0, if not, turning to the step 5;
if the BandWidth is 0, calculating a center frequency FreCenter and a 3db BandWidth BandWidth according to the following formula;
wherein fs is the sampling rate.
10. The welch-based multi-frequency-point multi-bandwidth identification method according to claim 9, wherein the step 9 comprises:
and (5) setting Px in the index value of the full bandwidth [ FullBwL, fullBwR ] as a noise value noise, and skipping to the step 5 to calculate the central frequency point and the bandwidth of the secondary peak signal.
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