CN117499185B - Method for estimating characteristic parameters of wireless signal with arbitrary symbol rate with high precision - Google Patents
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Abstract
The invention relates to a method for estimating the characteristic parameters of wireless signals with arbitrary symbol rate with high precision. For the second-order cyclostationary signal, the characteristic parameters of the received signal can be estimated efficiently by the cyclic spectrum estimation theory and the quick implementation algorithm thereof. According to the invention, the tail end of the input time domain signal data is subjected to multi-multiplying power zero filling, so that multi-multiplying power interpolation in a circulating frequency domain is realized, the resolution of the circulating frequency domain is improved, the accuracy of signal characteristic parameter estimation is improved, and the information that each discrete spectral line in a circulating spectrum contains symbol rate, carrier frequency and the like is fully utilized; when the symbol rate is further estimated finely, a proper search interval is selected for secondary linear interpolation to further improve the resolution of the cyclic spectrum, and whether the symbol rate is accurate or not is judged through comparison of the two estimates, so that fine estimation of the signal characteristic parameters of any symbol rate is realized.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a method for estimating wireless signal characteristic parameters of any symbol rate with high precision.
Background
Wireless communication is a long-distance information transmission between a plurality of nodes by using electromagnetic waves as a carrier, and has been widely used in various industries, and has a significant influence on human society. Under the application scene of non-cooperative wireless communication, the signal information or signal instruction sent by the cracking enemy is significant in the military communication, the key characteristic parameters of the acquired signals provide preconditions and foundations for the purposes of implementing signal demodulation, monitoring, signal interference and the like in the electronic countermeasure field, and the accurate estimation of the key characteristic parameters of the intercepted enemy signals determines the subsequent processing degree and quality of the signals in the electronic countermeasure field. The key parameters of the signal are typically: no symbol rate, carrier frequency, modulation scheme, etc., play a critical role in signal analysis.
The cyclic spectrum estimation can well utilize the envelope and statistical information of the signal to carry out blind estimation on the characteristic parameters of the signal. The conventional communication system analysis methods all assume that the modulated signal is a generalized stationary signal generated in a stationary random process, and analyze the characteristic parameters of the signal according to the generalized stationary signal, however, many signals modulated by the novel modulation technology are not generalized stationary signals, but cyclostationary signals, and the conventional signal analysis methods cannot accurately estimate the characteristic parameters of the cyclostationary signals. In the cyclic spectrum theory, when the cyclic frequency is equal to zero, the cyclic stationary signal is degraded into a generalized stationary random signal, so that cyclic spectrum estimation is a continuation of stationary random process analysis, cyclic frequency domain information of the signal is fully utilized, and the breadth and depth of signal analysis are improved; in addition, the cyclic spectrum estimation has obvious noise suppression, gaussian white noise is generally regarded as a stable random process, only the section with the cyclic frequency equal to zero is influenced, other cyclic frequency sections are not influenced, and the accuracy of signal characteristic parameter estimation is improved; although the cyclic spectrum estimation needs to use second order statistic information of the signal and higher sampling frequency, so that the theoretical calculation complexity is extremely high, the cyclic spectrum estimation is used for rapidly realizing an algorithm, such as a fast Fourier transform accumulation algorithm FAM, so that the calculation complexity can be greatly reduced, and the accuracy degree of signal characteristic parameter estimation is improved. Currently, the algorithm for blind estimation of the characteristic parameters of the wireless signals mainly comprises the following steps:
(1) The instantaneous and frequency domain method ,"A.K.Nandi,E.E.Azzouz,"Automatic analogue modulation ecognition[J],"Signal Processing,1995,46:211-222. discloses a method for identifying the modulation mode of a signal by utilizing the time-frequency statistical information and the power spectrum of the signal, and the accuracy of the modulation mode of the acquired signal can reach 90% under the signal-to-noise ratio of 10dB because the envelope, the instantaneous frequency and the instantaneous phase of the signal contain the modulation information of the signal.
(2) The delay-phase multiplication ,"D.E.Reed and M.A.Wickert,"Minimization of detection of symbol-rate spectral lines by delay and multiply receivers,"in IEEE Transactions on Communications,vol.36,no.1,pp.118-120,Jan.1988," discloses a method for multiplying the original signal and the delay signal of the original signal by utilizing the envelope information of the signal, wherein the spectrum information of the multiplied signal can contain the code element rate information of the signal under a certain condition, and the symbol rate estimation of the signal is realized under two filters of Nyquist pulse and rectangular pulse.
(3) Wavelet transformation method Xu Yufeng, peng Zhibiao, liu Baogang, MPSK/QAM characteristic extraction algorithm based on wavelet transformation [ J ]. Technological information (scientific research), 2007 (33): 207+198. A method for estimating characteristic parameters of signal by wavelet transformation of signal is disclosed, the wavelet transformation is basically transient information of signal, is very sensitive to envelope mutation of signal, and has higher estimation accuracy of characteristic parameters of signal, but since wavelet transformation is sensitive to mutation of signal, interference of noise is also extremely high, and calculation complexity is extremely high and instantaneity is poor.
(4) The cyclic spectrum estimation method ,W.A.Gardner,"Exploitation of spectral redundancy in cyclostationary signals,"in IEEE Signal Processing Magazine,vol.8,no.2,pp.14-36,April 1991. discloses a method for solving a cyclic spectrum by utilizing the characteristic of cyclostationarity of a modulation signal, wherein the cyclic spectrum contains characteristic parameter information of the signal, has excellent noise immunity and high recognition rate, but the method has extremely high computational complexity, and most of the prior researches only can estimate the integer symbol rate or the condition that the symbol rate is very large, and has limited application scenes.
In summary, the drawbacks of the wireless signal characteristic parameter blind estimation technique include: the estimation accuracy is insufficient, the estimation of the characteristic parameters is not comprehensive enough, the calculation complexity is high, and the estimation of any symbol rate can not be performed.
Disclosure of Invention
In view of the foregoing, it is an object of the present invention to provide a method for estimating a characteristic parameter of a wireless signal with an arbitrary symbol rate with high accuracy.
The technical scheme for solving the technical problems is as follows:
A method for estimating characteristic parameters of a wireless signal at an arbitrary symbol rate with high accuracy, comprising the steps of:
Step 1, performing multi-multiplying power linear interpolation on a signal to be detected by using a FAM algorithm, and then calculating to obtain a cyclic spectrum of the signal;
Step2, extracting a circulating spectrum of f=0 section, and obtaining carrier frequency f c of a signal to be detected;
Step 3, extracting a circulating spectrum of f=f c section, and finding out spectral lines containing symbol rate information by using a spectral peak searching algorithm; calculating the absolute value of the cyclic frequency difference value of every two adjacent spectral lines in the spectral lines containing the symbol rate information, and taking the maximum value as the rough estimation of the symbol rate of the signal to be detected;
Step 4, selecting a proper cyclic frequency searching range according to the rough estimation value of the symbol rate of the signal to be detected obtained in the previous step, carrying out fine estimation through secondary linear interpolation, and selecting the cyclic frequency value with the largest spectral peak as a fine estimation value a of the symbol rate of the signal to be detected;
And 5, setting a judgment threshold, calculating a difference value between a fine estimated value of the symbol rate of the signal to be detected and a maximum value of the absolute value of the difference value of the cyclic frequencies of the adjacent spectral lines, outputting a fine estimated value a of the symbol rate of the signal to be detected and a carrier frequency f c if the difference value is smaller than the judgment threshold, otherwise, turning to the step 4, and resetting the searching range of the cyclic frequencies.
Further, the step 1 specifically includes the following steps:
step 1.1, according to the definition of a cyclic spectral density function, when signal data to be detected is input, 0 of the multiplying power of the signal data of an integral number of times of 2 is supplemented at the tail of the signal, and linear interpolation in a cyclic frequency domain is realized;
step 1.2, calculating a cyclic spectrum of a signal to be detected by adopting a FAM algorithm, wherein the calculation formula is as follows:
Where f is the frequency, b is the cyclic frequency, X T (f) is the Fourier transform of X (t), i.e For short-time fourier transform of input signal under test x (N), w (N) is the data window, N is the total length of the input data, and M is the length of the short-time fourier transform.
Further, the step2 specifically includes the following:
And extracting a circulating spectrum f=0 section of the signal to be detected because the signal to be detected has carrier frequency components, and searching a spectrum peak to obtain a circulating frequency b of a spectral line where a secondary peak is located, wherein the relation between the circulating frequency b and the carrier frequency is b=2f c, so as to obtain the carrier frequency f c.
Further, the step3 specifically includes the following:
Step 3.1, extracting a section of a circulating spectrum f=f c, and sequentially finding out all spectral lines including symbol rate information by using a spectral peak searching algorithm;
Step 3.2, using the cyclic frequency corresponding to the sub-peak spectral line as the rough estimation value of the symbol rate of the signal to be detected And calculating the absolute value of the cyclic frequency difference between every two adjacent spectral lines a i and a i-1, taking the maximum value as the first estimated value of the symbol rate of the signal to be detected, namelyL is the total number of lines searched out, a 0 =0.
Further, the step4 specifically includes the following:
Step 4.1, obtaining a symbol rate rough estimation value of the signal to be detected Then, selecting the cyclic frequency search range asWhere Δa is the cyclic frequency resolution;
Step 4.2, preprocessing the input signal data, wherein the preprocessing method is one of the following two methods: the original cyclic frequency resolution is kept to be f s/N unchanged, 0 of more signal data multiplying power is supplemented at the tail of the input signal data, or the original cyclic frequency resolution f s/N is reduced, and the number of data points of the input signal is increased;
Step 4.3, calculating the cross-section circulation frequency of the preprocessed input signal data f=f3835 by adopting a FAM algorithm to obtain the frequency of the cross-section circulation of the preprocessed input signal data f=f c A cyclic spectrum within the range;
Step 4.4, comparing the cycle frequency at Taking the circulation frequency of the spectral line corresponding to the maximum value as the fine estimation value of the symbol rate of the signal to be detected, namely
Wherein f c is the carrier frequency of the signal to be detected, f s is the sampling frequency of the signal to be detected, and N is the number of data points used for calculating the signal cycle spectrum.
Further, the step 5 specifically includes the following:
Step 5.1, setting a judgment threshold r;
step 5.2, calculating Where a is a fine estimate of the symbol rate,Is the maximum value of the absolute value of the cyclic frequency difference value of the adjacent spectral lines;
Step 5.3, if a r > r, turning to step 4, and resetting the searching range of the circulating frequency; and if a r is less than or equal to r, outputting a fine estimated value a of the symbol rate of the signal to be detected and the carrier frequency f c.
The beneficial effects of the invention are as follows:
(1) The method provided by the invention can accurately estimate any symbol rate and carrier frequency under low signal-to-noise ratio, provides reliable characteristic parameters for demodulation and analysis of blind received signals, and has the advantage of reducing the calculation complexity of cyclic spectrum estimation. The cyclic spectrum estimation rapid implementation algorithm, namely the rapid Fourier accumulation algorithm, is adopted, the input signal data does not need to be the whole sampling frequency point number, and the cyclic spectrum can be estimated only by properly intercepting part of the signal data. And all module calculations of the cyclic spectrum estimation are almost based on the FFT algorithm, and the input data of all modules are supplemented to 2 n, so that the total calculation amount of the cyclic spectrum estimation can be effectively reduced.
(2) According to the invention, the tail end of the input time domain signal data is subjected to multi-multiplying power zero filling, so that multi-multiplying power interpolation in a circulating frequency domain is realized, the resolution of the circulating frequency domain is improved, the accuracy of signal characteristic parameter estimation is improved, and the information that each discrete spectral line in a circulating spectrum contains symbol rate, carrier frequency and the like is fully utilized. When the symbol rate is further estimated finely, a proper search interval is selected for secondary linear interpolation to further improve the resolution of the cyclic spectrum, and whether the symbol rate is accurate or not is judged through comparison of the two estimates, so that fine estimation of the signal characteristic parameters of any symbol rate is realized.
Drawings
FIG. 1 is a flow chart of an algorithm of the present invention;
fig. 2 is a f=0 cyclic spectrum cross section of the embodiment for a coarse estimation of symbol rate;
fig. 3 is a schematic diagram of a cyclic spectrum fast estimation algorithm, a fast fourier cumulative algorithm.
Detailed Description
The principles and features of the present invention are described below in connection with specific embodiments, examples of which are provided for illustration only and are not intended to limit the scope of the invention.
The embodiment provides a signal to be detected with a symbol rate of 327.58Hz, a carrier frequency of f c =2048 Hz, a BPSK modulation mode, a signal-to-noise ratio snr=10 dB of a wireless channel, and a sampling frequency f s =8000 Hz of a received signal.
As shown in fig. 1 and 2, the embodiment provides an algorithm flow chart for high-precision estimation of characteristic parameters of wireless signals with arbitrary symbol rate and a cyclic spectrum cross-section chart for rough estimation of symbol rate, which are specifically as follows:
1) At the receiving end, the wireless signal receiver is assumed to detect and receive a section of unknown modulated signal at the sampling frequency f s =8000 Hz;
2) On the basis of the FAM algorithm, calculating the cyclic spectrum of the signal after 16-multiplying power linear interpolation;
3) Extracting a circulating spectrum of f=0 section, and obtaining carrier frequency f c =2048 Hz of a signal to be detected;
4) Extracting a circulating spectrum of f=f c section, and finding out spectral lines containing symbol rate information by using a spectral peak searching algorithm;
5) Calculating the absolute value of the cyclic frequency difference value of each adjacent spectral line, and taking the maximum value as the rough estimation of the symbol rate of the signal to be detected;
6) Selecting a proper cyclic frequency searching range according to the rough estimation value of the symbol rate of the signal to be detected, finely estimating through secondary linear interpolation, and selecting the cyclic frequency value with the maximum spectral peak as the fine estimation value of the symbol rate of the signal to be detected;
7) Comparing the fine estimated value of the symbol rate of the signal to be detected with the maximum value of the absolute value of the cyclic frequency difference value of the adjacent spectral lines, setting a judgment threshold, outputting the symbol rate and the carrier frequency of the signal to be detected if the judgment threshold is smaller than the judgment threshold, otherwise resetting the searching range of the cyclic frequency, and searching again.
Preferably, the process of performing 16-rate linear interpolation on the FAM algorithm to calculate the cyclic spectrum of the signal to be detected is as follows:
a) Defined by cyclic spectral density functions Intercepting the signal point number of 0.2s as input data N 0 =1600 of the signal to be detected, namely N 0＝fs multiplied by 0.2=1600, and then supplementing the input data with 0 to 16 multiplying power data point numbers, namely the input data point number N=N 0 multiplied by 16, so as to realize linear interpolation in a circulating frequency domain;
b) The FAM algorithm is adopted to calculate the cyclic spectrum of the signal to be measured, and the calculation formula can be expressed as follows:
Where f is the frequency, b is the cyclic frequency, X T (f) is the Fourier transform of X (t), i.e For short-time fourier transform of input signal under test x (N), w (N) is the data window, N is the total length of the input data, and M is the length of the short-time fourier transform.
Preferably, after a cyclic spectrum of the signal to be detected is obtained, extracting characteristic parameters of carrier frequency and symbol rate of the signal to be detected in a cyclic frequency domain, wherein the process is as follows:
1. As the signal to be measured has carrier frequency components, extracting the section f=0 of the cyclic spectrum of the signal to be measured, and searching for the cyclic frequency of the spectral line where the secondary peak is located by utilizing the spectral peak, wherein the relation between the cyclic frequency and the carrier frequency is b=2f c =4096;
2. Obtaining carrier frequency f c =2048, extracting a circular spectrum f=2048 section, setting a spectrum peak with a search threshold value larger than 0.02 by using a spectrum peak search algorithm, and sequentially finding all spectral lines including symbol rate information, including a epsilon-1310, -982.9, -655.3, -327.1,0,327.6,655.8,982.9;
3. Using the cyclic frequency corresponding to the sub-peak spectral line as a rough estimate of the symbol rate of the signal to be detected And calculating the absolute value of the cyclic frequency difference of adjacent spectral lines { |a i-ai-1 } = {327.1,327.6,328.2,327.1,327.6,328.2,327.1}, taking the maximum value as the first estimated value of the symbol rate of the signal to be detected, namely
Preferably, after obtaining the rough estimation value of the symbol rate of the signal to be detected, the process of further estimating the symbol rate through secondary linear interpolation comprises the following steps:
(1) Obtaining a symbol rate rough estimation value of a signal to be detected Then, selecting a cyclic frequency search range of [327.6-5 xf s/N0,327.6+5×fs/N0 ], wherein Δa=f s/N0 =5 is cyclic frequency resolution;
(2) Preprocessing the input signal data to achieve the effect of improving the resolution of the cyclic spectrum. There are two schemes: firstly, keeping the original cyclic frequency resolution as f s/N unchanged, and supplementing 0 of more signal data multiplying power at the tail of input signal data; secondly, the original cyclic frequency resolution f s/N is reduced by increasing the number of data points of the input signal.
In the present embodiment, a first method is adopted, in which the tail end of the input data is complemented by 0 which is one time, namely, n=1600×16×2 increases the data amount of the input signal;
(3) The FAM algorithm is used to calculate the cyclic spectrum of the f=2048 cross-section cyclic frequency of the input signal after preprocessing in the range of [327.6-5 xf s/N0,327.6+5×fs/N0 ].
(4) Comparing the values of the spectral lines of each point with the cyclic frequency within the range of [327.6-5 xf s/N0,327.6+5×fs/N0 ], taking the cyclic frequency of the spectral line corresponding to the maximum value as the fine estimated value of the symbol rate of the signal to be detected, namely
Where f c is the carrier frequency 2048hz of the signal to be detected, f s is the sampling frequency 8000hz of the signal to be detected, N is the number of data points n=1600×16×2 used to calculate the signal cycle spectrum.
Preferably, after obtaining the fine estimated value of the symbol rate of the signal to be detected and the maximum value of the absolute value of the cyclic frequency difference value of the adjacent spectral lines, the process of setting a decision threshold for comparison and outputting comprises the following steps:
a. Setting a decision threshold r=f sN0 =8000/1600=5;
b. Calculation of Where a is a fine estimate of the symbol rate,Is the maximum value of the absolute value of the cyclic frequency difference value of the adjacent spectral lines;
c. If a r is larger than r, resetting the searching range of the cyclic frequency, and searching again; and if a r is less than or equal to r, outputting a fine estimated value a of the symbol rate of the signal to be detected and the carrier frequency.
In the present embodimentThe value a= 327.58 of the fine estimated symbol rate and the carrier frequency value f c =2048 are thus output.
In summary, the algorithm for high-precision estimation of the characteristic parameters of the wireless signal with any symbol rate provided by the invention realizes multi-rate interpolation in the cyclic frequency domain by multi-rate zero padding at the tail end of the input time domain signal data, improves the resolution of the cyclic frequency domain, thereby improving the precision of estimation of the characteristic parameters of the signal, and fully utilizing the information such as symbol rate, carrier frequency and the like contained in each discrete spectral line in the cyclic spectrum. When the symbol rate is further estimated finely, a proper search interval is selected for secondary linear interpolation to further improve the cyclic spectrum resolution, whether the symbol rate is accurate is judged through comparison of the two estimates, so that fine estimation of signal characteristic parameters of any symbol rate is realized, all modules of the algorithm and the whole calculation process are based on the FFT algorithm, the whole f s data is not needed, and only a small part of signal data is needed to be used for calculation.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (1)
1. A method for estimating characteristic parameters of a wireless signal at an arbitrary symbol rate with high accuracy, comprising the steps of:
Step 1, performing multi-multiplying power linear interpolation on a signal to be detected by using a FAM algorithm, and then calculating to obtain a cyclic spectrum of the signal;
the step1 specifically comprises the following steps:
step 1.1, according to the definition of a cyclic spectral density function, when signal data to be detected is input, 0 of the multiplying power of the signal data of an integral number of times of 2 is supplemented at the tail of the signal, and linear interpolation in a cyclic frequency domain is realized;
step 1.2, calculating a cyclic spectrum of a signal to be detected by adopting a FAM algorithm, wherein the calculation formula is as follows:
Where f is the frequency, b is the cyclic frequency, X T (f) is the Fourier transform of X (t), i.e For short-time fourier transform of input signal to be measured x (N), w (N) is a data window, N is the total length of input data, and M is the length of short-time fourier transform;
Step2, extracting a circulating spectrum of f=0 section, and obtaining carrier frequency f c of a signal to be detected;
the step 2 specifically comprises the following steps:
As the signal to be detected has carrier frequency components, extracting a circulating spectrum f=0 section of the signal to be detected, and searching a spectrum peak to obtain a circulating frequency b of a spectral line where a secondary peak is located, wherein the relation between the circulating frequency b and the carrier frequency is b=2f c, so as to obtain a carrier frequency f c;
Step 3, extracting a circulating spectrum of f=f c section, and finding out spectral lines containing symbol rate information by using a spectral peak searching algorithm; calculating the absolute value of the cyclic frequency difference value of every two adjacent spectral lines in the spectral lines containing the symbol rate information, and taking the maximum value as the rough estimation of the symbol rate of the signal to be detected;
The step 3 specifically comprises the following steps:
Step 3.1, extracting a section of a circulating spectrum f=f c, and sequentially finding out all spectral lines including symbol rate information by using a spectral peak searching algorithm;
Step 3.2, using the cyclic frequency corresponding to the sub-peak spectral line as the rough estimation value of the symbol rate of the signal to be detected And calculating the absolute value of the cyclic frequency difference between every two adjacent spectral lines a i and a i-1, taking the maximum value as the first estimated value of the symbol rate of the signal to be detected, namelyL is the total number of lines searched out, a 0 =0;
Step 4, selecting a proper cyclic frequency searching range according to the rough estimation value of the symbol rate of the signal to be detected obtained in the previous step, carrying out fine estimation through secondary linear interpolation, and selecting the cyclic frequency value with the largest spectral peak as a fine estimation value a of the symbol rate of the signal to be detected;
Step 4 specifically includes the following:
Step 4.1, obtaining a symbol rate rough estimation value of the signal to be detected Then, selecting the cyclic frequency search range asWhere Δa is the cyclic frequency resolution;
Step 4.2, preprocessing the input signal data, wherein the preprocessing method is one of the following two methods: the original cyclic frequency resolution is kept to be f s/N unchanged, 0 of more signal data multiplying power is supplemented at the tail of the input signal data, or the original cyclic frequency resolution f s/N is reduced, and the number of data points of the input signal is increased;
Step 4.3, calculating the cross-section circulation frequency of the preprocessed input signal data f=f3835 by adopting a FAM algorithm to obtain the frequency of the cross-section circulation of the preprocessed input signal data f=f c A cyclic spectrum within the range;
Step 4.4, comparing the cycle frequency at Taking the circulation frequency of the spectral line corresponding to the maximum value as the fine estimation value of the symbol rate of the signal to be detected, namely
Wherein f c is the carrier frequency of the signal to be detected, f s is the sampling frequency of the signal to be detected, and N is the number of data points for calculating the signal cycle spectrum;
step 5, setting a judgment threshold, calculating the difference between the fine estimation value of the symbol rate of the signal to be detected and the maximum value of the absolute value of the difference between the cyclic frequencies of the adjacent spectral lines, if the difference is smaller than the judgment threshold, outputting the fine estimation value a of the symbol rate of the signal to be detected and the carrier frequency f c, otherwise, turning to step 4, and resetting the searching range of the cyclic frequency;
the step 5 specifically comprises the following steps:
Step 5.1, setting a judgment threshold r;
step 5.2, calculating Where a is a fine estimate of the symbol rate,Is the maximum value of the absolute value of the cyclic frequency difference value of the adjacent spectral lines;
Step 5.3, if a r > r, turning to step 4, and resetting the searching range of the circulating frequency; and if a r is less than or equal to r, outputting a fine estimated value a of the symbol rate of the signal to be detected and the carrier frequency f c.
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