CN117499185B - A method for estimating characteristic parameters of wireless signals with arbitrary symbol rate with high precision - Google Patents

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

A method for estimating characteristic parameters of wireless signals with arbitrary symbol rate with high precision

Technical Field

The invention belongs to the technical field of wireless communications, and in particular relates to a method for estimating characteristic parameters of wireless signals with arbitrary symbol rates with high precision.

Background Art

Wireless communication refers to the long-distance information transmission between multiple nodes using electromagnetic waves as carriers. It has been widely used in all walks of life and has had a significant impact on human society. In the application scenario of non-cooperative wireless communication, cracking the signal information or signal instructions sent by the enemy is of great significance in military communications. Obtaining the key characteristic parameters of the signal provides the premise and basis for signal demodulation, monitoring, signal interference and other purposes in the field of electronic countermeasures. The accurate estimation of the key characteristic parameters of the intercepted enemy signal determines the subsequent degree and quality of signal processing in the field of electronic countermeasures. The key parameters of the signal are usually: symbol rate, carrier frequency, modulation mode, etc., all of which play a key role in the analysis of the signal.

Cyclic spectrum estimation can make good use of the envelope and statistical information of the signal to blindly estimate the characteristic parameters of the signal. Traditional communication system analysis methods all assume that the modulated signal is a wide-sense stationary signal generated by a stationary random process, and use this to analyze the characteristic parameters of the signal. However, many signals modulated by new modulation technologies are not wide-sense stationary signals, but cyclostationary signals. Traditional signal analysis methods cannot accurately estimate the characteristic parameters of cyclostationary signals. In cyclic spectrum theory, when the cyclic frequency is equal to zero, the cyclostationary signal will degenerate into a wide-sense stationary random signal. Therefore, cyclic spectrum estimation is an extension of the analysis of stationary random processes, which makes full use of the cyclic frequency domain information of the signal and improves the breadth and depth of signal analysis. In addition, cyclic spectrum estimation has obvious noise suppression. Gaussian white noise is usually regarded as a stationary random process, which only affects the section with cyclic frequency equal to zero, but not other cyclic frequency sections, thus improving the accuracy of signal characteristic parameter estimation. Although cyclic spectrum estimation requires the use of the second-order statistical information of the signal and a higher sampling frequency, which makes the theoretical calculation complexity extremely high, the use of cyclic spectrum estimation to quickly implement algorithms, such as the fast Fourier transform accumulation algorithm FAM, can greatly reduce the calculation complexity and improve the accuracy of signal characteristic parameter estimation. At present, the algorithms for blind estimation of wireless signal characteristic parameters mainly include:

(1) Instantaneous time and frequency domain method, A.K.Nandi, E.E.Azzouz, "Automatic analogue modulation ecology [J]," Signal Processing, 1995, 46: 211-222. discloses a method of using the time and frequency statistical information and power spectrum of the signal to identify the modulation mode of the signal. Since the envelope, instantaneous frequency and instantaneous phase of the signal contain the modulation information of the signal, the modulation mode of the signal can be obtained with an accuracy of 90% at a signal-to-noise ratio of 10 dB. However, since this method does not make full use of the high-order statistical information of the signal, it is unable to estimate other characteristic parameters of the signal.

(2) Delay multiplication method, "D.E.Reed and M.A.Wickert,"Minimization of detection ofsymbol-rate spectral lines by delay and multiply receivers,"in IEEETransactions on Communications,vol.36,no.1,pp.118-120,Jan.1988," discloses a method of using the envelope information of the signal to multiply the original signal and the delayed signal of the original signal. Under certain conditions, the spectrum information of the multiplied signal will contain the symbol rate information of the signal, and the symbol rate estimation of the signal can be realized under the Nyquist pulse and rectangular pulse filters. This method has low computational complexity and high real-time performance. However, since this method only uses a small part of the signal information, it is impossible to make a high-precision estimate of the characteristic parameters of the signal.

(3) Wavelet transform method, Xu Yufeng, Peng Zhibiao, Liu Baogang. MPSK/QAM feature extraction algorithm based on wavelet transform [J]. Science and Technology Information (Science and Technology Research), 2007(33):207+198. A method for estimating the characteristic parameters of a signal using the wavelet transform of the signal is disclosed. The wavelet transform essentially uses the transient information of the signal and is very sensitive to the sudden change of the signal envelope. The estimation accuracy of the signal characteristic parameters is also high. However, since the wavelet transform is sensitive to the sudden change of the signal, it is greatly affected by noise, and the computational complexity is extremely high, and the real-time performance is poor.

(4) Cyclic spectrum estimation method, W.A.Gardner, "Exploitation of spectral redundancy incyclostationary signals," in IEEE Signal Processing Magazine, vol.8, no.2, pp.14-36, April 1991. This paper discloses a method for solving the cyclic spectrum by utilizing the cyclostationary characteristics of the modulated signal. The cyclic spectrum contains the characteristic parameter information of the signal, and has excellent anti-noise performance and high recognition rate. However, this method has extremely high computational complexity and most existing studies can only estimate integer symbol rates or situations with very large symbol rates, which limits the application scenarios.

In summary, the disadvantages of the blind estimation technology of wireless signal characteristic parameters include: insufficient estimation accuracy, incomplete estimation of characteristic parameters, high computational complexity and inability to estimate arbitrary symbol rates.

Summary of the invention

In view of the above problems, an object of the present invention is to provide a method for estimating characteristic parameters of a wireless signal with arbitrary symbol rate with high precision.

The technical solution of the present invention to solve the above technical problems is as follows:

A method for estimating characteristic parameters of a wireless signal with arbitrary symbol rate with high precision comprises the following steps:

Step 1: Using the FAM algorithm, perform multi-rate linear interpolation on the signal to be detected and calculate the cyclic spectrum of the signal;

Step 2: extract the cyclic spectrum of the section f=0 to obtain the carrier frequency f _c of the signal to be detected;

Step 3, extract the cyclic spectrum of the cross section f=f _c , and use the spectrum peak search algorithm to find the spectrum line containing the symbol rate information; and calculate the absolute value of the cyclic frequency difference between two adjacent spectrum lines in the spectrum line containing the symbol rate information, and take the maximum value as a rough estimate of the symbol rate of the signal to be detected;

Step 4: According to the rough estimate of the symbol rate of the signal to be detected obtained in the previous step, select a suitable cyclic frequency search range, and make a fine estimate through quadratic linear interpolation to select the cyclic frequency value with the largest spectrum peak as the fine estimate a of the symbol rate of the signal to be detected;

Step 5, set the decision threshold, calculate the difference between the fine estimate of the symbol rate of the signal to be detected and the maximum absolute value of the difference between the cyclic frequencies of adjacent spectrum lines, if the difference is less than the decision threshold, output the fine estimate of the symbol rate a of the signal to be detected and the carrier frequency f _c , otherwise go to step 4 and reset the search range of the cyclic frequency.

Furthermore, the step 1 specifically includes the following steps:

Step 1.1, according to the definition of the cyclic spectral density function, when inputting the signal data to be measured, 0 of the signal data multiplied by an integer of 2 is added at the end of the signal to realize linear interpolation in the cyclic frequency domain;

Step 1.2: Use the FAM algorithm to calculate the cyclic spectrum of the signal to be measured. The calculation formula is:

where f is the frequency, b is the cyclic frequency, and X _T (f) is the Fourier transform of x(t), i.e. is the short-time Fourier transform of the input signal 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.

Furthermore, the step 2 specifically includes the following contents:

Since the signal to be measured has a carrier frequency component, the cyclic spectrum f=0 section of the signal to be measured is extracted, and the cyclic frequency b of the spectrum line where the secondary peak is located is obtained by spectrum peak search. The relationship between the cyclic frequency b and the carrier frequency is b=2f _c , and then the carrier frequency f _c is obtained.

Furthermore, the step 3 specifically includes the following contents:

Step 3.1, extract the cyclic spectrum f=f _c section, and use the spectrum peak search algorithm to find all the spectrum lines containing the symbol rate information in turn;

Step 3.2: Use the cyclic frequency corresponding to the secondary peak spectrum line as a rough estimate of the symbol rate of the signal to be detected. And calculate the absolute value of the cyclic frequency difference between two adjacent spectral lines _ai and _ai-1 , and take the maximum value as the first estimate of the symbol rate of the signal to be detected, that is, L is the total number of spectral lines searched, a ₀ =0.

Furthermore, the step 4 specifically includes the following contents:

Step 4.1: Get a rough estimate of the symbol rate of the signal to be detected Then, select the cycle frequency search range as Where Δa is the cycle frequency resolution;

Step 4.2, preprocess the input signal data, and the preprocessing method is one of the following two methods: keep the original cycle frequency resolution f _s /N unchanged, add more signal data multiplication zeros at the end of the input signal data, or reduce the original cycle frequency resolution f _s /N by increasing the number of data points of the input signal;

Step 4.3: Use the FAM algorithm to calculate the cross-sectional cycle frequency of the pre-processed input signal data f = f _c Cyclic spectrum within range;

Step 4.4, compare the cycle frequency The value of the spectrum line at each point in the range is taken, and the cycle frequency of the spectrum line corresponding to the maximum value is taken as the fine estimate of the symbol rate of the signal to be detected, that is,

Wherein, _fc is the carrier frequency of the signal to be detected, _fs is the sampling frequency for obtaining the signal to be detected, and N is the number of data points used to calculate the signal cyclic spectrum.

Furthermore, the step 5 specifically includes the following contents:

Step 5.1, set the decision threshold r;

Step 5.2: Calculation where a is a fine estimate of the symbol rate, It is the maximum absolute value of the difference between the cyclic frequencies of adjacent spectral lines;

Step 5.3: If a _r > r, go to step 4 and reset the search range of the cyclic frequency; if a _r ≤ r, output the fine estimation value a of the symbol rate of the signal to be detected and the carrier frequency f _c .

The beneficial effects of the present invention are:

(1) The method provided by the present invention can accurately estimate any symbol rate and carrier frequency under low signal-to-noise ratio, provide reliable characteristic parameters for demodulation and analysis of blind received signals, and has the advantage of reducing the computational complexity of cyclic spectrum estimation. By using the fast Fourier accumulation algorithm, a fast implementation algorithm for cyclic spectrum estimation, the input signal data does not have to be the entire sampling frequency point number, and only a portion of the signal data needs to be appropriately intercepted to estimate the cyclic spectrum. In addition, almost all module calculations of cyclic spectrum estimation are based on the FFT algorithm, and the input data of all modules are supplemented to ²ⁿ , which can effectively reduce the overall computational complexity of cyclic spectrum estimation.

(2) The present invention implements multi-rate interpolation in the cyclic frequency domain by multi-rate zero padding at the tail end of the input time domain signal data, thereby improving the resolution of the cyclic frequency domain, thereby improving the accuracy of signal characteristic parameter estimation, and making full use of the information such as symbol rate and carrier frequency contained in each discrete spectrum line in the cyclic spectrum. When further refining the symbol rate, a suitable search interval is selected for quadratic linear interpolation to further improve the resolution of the cyclic spectrum, and the symbol rate is judged by comparing the two estimates to determine whether it is accurate, thereby achieving a refined estimation of the characteristic parameters of the signal with any symbol rate.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 is a flow chart of an algorithm of the present invention;

FIG2 is a cross section of the f=0 cyclic spectrum of a rough estimate of the symbol rate in an embodiment;

FIG. 3 is a schematic diagram of a fast Fourier accumulation algorithm, which is a fast estimation algorithm for cyclic spectrum.

DETAILED DESCRIPTION

The principles and features of the present invention are described below in conjunction with specific embodiments. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

This embodiment provides a signal to be detected with a symbol rate of 327.58 Hz, a carrier frequency of f _c =2048 Hz, and a BPSK modulation mode, sets the signal-to-noise ratio SNR of the wireless channel to 10 dB, and the sampling frequency of the received signal to f _s =8000 Hz.

As shown in FIGS. 1 and 2 , the embodiment provides an algorithm flow chart for high-precision estimation of characteristic parameters of wireless signals at arbitrary symbol rates and a cyclic spectrum cross-section diagram for rough estimation of symbol rates in the embodiment, as follows:

1) At the receiving end, assume that the wireless signal receiver detects and receives an unknown modulated signal at a sampling frequency of _fs = 8000 Hz;

2) Based on the FAM algorithm, the cyclic spectrum of the signal is calculated after 16-fold linear interpolation;

3) Extract the cyclic spectrum of the section f=0 and obtain the carrier frequency f _c =2048 Hz of the signal to be detected;

4) Extract the cyclic spectrum of the f=f _c section and use the spectrum peak search algorithm to find the spectrum line containing the symbol rate information;

5) Calculate the absolute value of the cyclic frequency difference of each adjacent spectral line, and take the maximum value as a rough estimate of the symbol rate of the signal to be detected;

6) According to the rough estimate of the symbol rate of the signal to be detected, select a suitable cyclic frequency search range, and make a fine estimate through quadratic linear interpolation, and select the cyclic frequency value with the largest spectrum peak as the fine estimate of the symbol rate of the signal to be detected;

7) Compare the refined estimate of the symbol rate of the signal to be detected with the maximum absolute value of the difference between the cyclic frequencies of adjacent spectral lines, set a decision threshold, and output the symbol rate and carrier frequency of the signal to be detected if it is less than the decision threshold; otherwise, reset the search range of the cyclic frequency and search again.

Preferably, the process of calculating the cyclic spectrum of the signal to be detected by performing 16-fold linear interpolation on the FAM algorithm is as follows:

a) According to the definition of cyclic spectral density function The signal points of 0.2s are intercepted as the input data N ₀ =1600 of the signal to be measured, that is, N ₀ =f _s ×0.2=1600, and then the input data is supplemented with 0 to 16 times the data points, that is, the input data points N=N ₀ ×16, to achieve linear interpolation in the cyclic frequency domain;

b) The FAM algorithm is used to calculate the cyclic spectrum of the signal to be measured. The calculation formula can be expressed as:

where f is the frequency, b is the cyclic frequency, and X _T (f) is the Fourier transform of x(t), i.e. is the short-time Fourier transform of the input signal 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 the cyclic spectrum of the signal to be detected is obtained, the carrier frequency and symbol rate characteristic parameters of the signal to be detected are extracted in the cyclic frequency domain, and the process is:

1. Since the signal to be measured has a carrier frequency component, the cyclic spectrum f=0 section of the signal to be measured is extracted, and the cyclic frequency of the spectrum line where the secondary peak is located is obtained by using the spectrum peak search. The relationship between the cyclic frequency and the carrier frequency is b=2f _c =4096;

2. Get the carrier frequency f _c = 2048, then extract the cyclic spectrum f = 2048 section, use the spectrum peak search algorithm, set the search threshold greater than 0.02 spectrum peak, and find all spectrum lines containing symbol rate information in turn, including a∈{-1310,-982.9,-655.3,-327.1,0,327.6,655.8,982.9};

3. Use the cyclic frequency corresponding to the secondary peak spectrum as a rough estimate of the symbol rate of the signal to be detected And calculate the absolute value of the cyclic frequency difference of adjacent spectral lines {|a _i -a _i-1 } = {327.1, 327.6, 328.2, 327.1, 327.6, 328.2, 327.1}, and take the maximum value as the first estimate of the symbol rate of the signal to be detected, that is,

Preferably, after obtaining a rough estimate of the symbol rate of the signal to be detected, the process of further refining the symbol rate by quadratic linear interpolation includes:

(1) Obtain a rough estimate of the symbol rate of the signal to be detected Then, the cycle frequency search range is selected to be [327.6-5×f _s /N ₀ ,327.6+5×f _s /N ₀ ], where Δa＝f _s /N ₀ ＝5 is the cycle frequency resolution;

(2) Preprocess the input signal data to improve the resolution of the cyclic spectrum. There are two solutions: first, keep the original cyclic frequency resolution at f _s /N unchanged, and add more signal data multipliers of 0 at the end of the input signal data; second, reduce the original cyclic frequency resolution f _s /N by increasing the number of data points of the input signal.

In this embodiment, method 1 is adopted to add double 0s to the tail of the input data, that is, N=1600×16×2 to increase the data volume of the input signal;

(3) The FAM algorithm is used to calculate the cyclic spectrum of the preprocessed input signal data f=2048 with the cyclic frequency in the range of [327.6-5×f _s /N ₀ ,327.6+5×f _s /N ₀ ].

(4) Compare the values of the spectrum lines at each point in the range of [327.6-5× _fs / _N0 , 327.6+5× _fs / _N0 ], and take the cycle frequency of the spectrum line corresponding to the maximum value as the fine estimate of the symbol rate of the signal to be detected, that is,

Wherein, _fc is the carrier frequency of the signal to be detected, 2048 Hz, _fs is the sampling frequency of the signal to be detected, 8000 Hz, and N is the number of data points used to calculate the cyclic spectrum of the signal, N=1600×16×2.

Preferably, after obtaining the fine estimation value of the symbol rate of the signal to be detected and the maximum absolute value of the difference between the cyclic frequencies of adjacent spectral lines, the process of setting the decision threshold for comparison and outputting includes:

a. Set the decision _threshold r = _fsN0 = 8000/1600 = 5;

b. Calculation where a is a fine estimate of the symbol rate, It is the maximum absolute value of the difference between the cyclic frequencies of adjacent spectral lines;

c. If a _r > r, reset the search range of the cyclic frequency and search again; if a _r ≤ r, output the refined estimate a of the symbol rate of the signal to be detected and the carrier frequency.

In this embodiment Therefore, the value of the fine estimated symbol rate a=327.58 and the carrier frequency value f _c =2048 are output.

In summary, the algorithm for high-precision estimation of characteristic parameters of wireless signals with arbitrary symbol rates provided by the present 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 accuracy of signal characteristic parameter estimation, and fully utilizes the information such as symbol rate and carrier frequency contained in each discrete spectrum line in the cyclic spectrum. When further estimating the symbol rate, a suitable search interval is selected for quadratic linear interpolation to further improve the resolution of the cyclic spectrum, and the symbol rate is determined by comparing the two estimates to determine whether it is accurate, thereby realizing a fine estimation of the characteristic parameters of the signal with arbitrary symbol rate, and each module of the algorithm and the entire calculation process are based on the FFT algorithm, and it is not necessary to use the entire _fs data, and only a small part of the signal data needs to be used for calculation.

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 principle of the present invention should be included in the protection scope of the present 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.