CN117499185B - A method for estimating characteristic parameters of wireless signals with arbitrary symbol rate with high precision - Google Patents
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Abstract
Description
技术领域Technical Field
本发明属于无线通信技术领域,具体涉及一种高精度估计任意符号率无线信号特征参数的方法。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.
背景技术Background Art
无线通信是指多个节点间以电磁波为载体进行的远距离信息传输,已被广泛应用于各行各业,对人类社会产生了重大影响。在非协作无线通信的应用场景下,破解敌方发送的信号信息或信号指令在军事通信中意义重大,获取信号的关键特征参数对于电子对抗领域实施信号解调、监听、信号干扰等目的提供前提和基础,对截获的敌方信号关键特征参数的精确估计决定了电子对抗领域后续对信号的处理程度和质量。信号的关键参数通常有:符号率、载波频率、调制方式等,无一不对信号的解析起到关键作用。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.
循环谱估计能很好地利用信号的包络和统计信息,对信号的特征参数进行盲估计。传统的通信系统分析方法均假设已调信号是进过平稳随机过程产生的广义平稳信号,并以此来分析信号的特征参数,然而许多经过新型调制技术调制的信号并不都是广义平稳信号,而是循环平稳信号,传统信号的分析方法无法对循环平稳信号的特征参数进行精确估计。在循环谱理论中,当循环频率等于零时,循环平稳信号会退化为广义平稳随机信号,因此,循环谱估计是平稳随机过程分析的延拓,充分利用了信号的循环频域信息,提升了信号分析的广度和深度;并且,循环谱估计对噪声抑制明显,高斯白噪声通常视为平稳随机过程,只会影响循环频率等于零的截面,而不影响其它循环频率截面,提升了信号特征参数估计的精确度;虽然循环谱估计需要利用信号的二阶统计量信息,以及较高的抽样频率,使得理论计算复杂度极高,但利用循环谱估计快速实现算法,例如快速傅里叶变换累计算法FAM可以大大降低计算复杂度,并提升信号特征参数估计的精确程度。目前,无线信号特征参数盲估计的算法主要包括: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)瞬时时、频域法,”A.K.Nandi,E.E.Azzouz,“Automatic analogue modulationecognition[J],”Signal Processing,1995,46:211-222.公开了一种利用信号的时、频统计信息和功率谱来识别信号的调制方式,由于信号的包络、瞬时频率和瞬时相位包含了信号的调制信息,在10dB信噪比下,获取信号的调制方式精确度可达90%,但该方法由于没有充分利用信号的高阶统计信息,无法对信号的其它特征参数进行估计。(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)延迟相乘法,”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,”公开了一种利用信号的包络信息,将原信号和原信号的延时信号相乘,在一定条件下相乘信号的频谱信息会包含信号的码元速率信息,在奈奎斯特脉冲和矩形脉冲两种滤波器下实现信号的符号率估计,该方法计算量小,实时性高,但由于该方法仅利用了信号的小部分信息,无法对信号的特征参数进行高精度估计。(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)小波变换法,徐玉锋,彭志标,刘宝刚.基于小波变换的MPSK/QAM特征提取算法[J].科技信息(科学教研),2007(33):207+198.公开了一种利用信号的小波变换对信号进行特征参数的估计,小波变换本质上是利用信号的瞬态信息,对信号的包络突变非常敏感,对信号特征参数的估计精度也较高,但由于小波变换对信号的突变敏感,因此受噪声的干扰也极大,并且计算复杂度极高,实时性差。(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)循环谱估计法,W.A.Gardner,"Exploitation of spectral redundancy incyclostationary signals,"in IEEE Signal Processing Magazine,vol.8,no.2,pp.14-36,April 1991.公开一种利用调制信号循环平稳的特性从而求解循环谱,在循环谱上包含了信号的特征参数信息,且抗噪性能优越,识别率高,但该方法计算复杂度极高且大多数现有研究都只能估计整数符号率或符号率很大的情况,应用场景受限。(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.
综上所述,无线信号特征参数盲估计技术的缺点包括:估计精确度不够、特征参数的估计不够全面、计算复杂度高和不能对任意符号率进行估计的问题。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.
发明内容Summary of the invention
针对上述问题,本发明的目的是提供一种高精度估计任意符号率无线信号特征参数的方法。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.
本发明解决上述技术问题的技术方案如下:The technical solution of the present invention to solve the above technical problems is as follows:
一种高精度估计任意符号率无线信号特征参数的方法,包括以下步骤:A method for estimating characteristic parameters of a wireless signal with arbitrary symbol rate with high precision comprises the following steps:
步骤1、利用FAM算法,对待检测信号进行多倍率线性插值后计算得到信号的循环谱;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;
步骤2、提取f=0截面的循环谱,获取待检测信号的载波频率fc;Step 2: extract the cyclic spectrum of the section f=0 to obtain the carrier frequency f c of the signal to be detected;
步骤3、提取f=fc截面的循环谱,利用谱峰搜索算法找出含有符号率信息的谱线;并计算含有符号率信息的谱线中两两相邻谱线的循环频率差值的绝对值,并取其中的最大值作为待检测信号符号率的粗估计;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;
步骤4、根据上一步得到的待检测信号符号率的粗估计值,选取合适的循环频率搜索范围,通过二次线性插值精细估计,选取谱峰最大的循环频率值作为待检测信号符号率的精细估计值a;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;
步骤5、设置判决门限,计算待检测信号符号率的精细估计值和相邻谱线循环频率差值绝对值的最大值的差值,若差值小于判决门限则输出待检测信号的符号率的精细估计值a和载波频率fc,否则转到步骤4,并重新设置循环频率的搜索范围。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.
进一步的,所述步骤1具体包括以下步骤:Furthermore, the step 1 specifically includes the following steps:
步骤1.1、根据循环谱密度函数的定义,在输入待测信号数据时,在信号末尾补充2的整数次信号数据倍率的0,实现在循环频域的线性插值;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;
步骤1.2、采用FAM算法计算待测信号的循环谱,计算公式为: Step 1.2: Use the FAM algorithm to calculate the cyclic spectrum of the signal to be measured. The calculation formula is:
其中f是频率,b是循环频率,XT(f)是x(t)的傅里叶变换,即为输入待测信号x(n)的短时傅里叶变换,w(n)是数据窗,N是输入数据的总长度,M是短时傅里叶变换的长度。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.
进一步的,所述步骤2具体包括以下内容:Furthermore, the step 2 specifically includes the following contents:
由于待测信号有载波频率成分,则将待测信号的循环谱f=0截面提取,并利用谱峰搜索求其次峰所在谱线的循环频率b,循环频率b与载波频率的关系为b=2fc,进而得到得到载波频率fc。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.
进一步的,所述步骤3具体包括以下内容:Furthermore, the step 3 specifically includes the following contents:
步骤3.1、提取循环谱f=fc截面,利用谱峰搜索算法依次找出包含符号率信息在内的所有谱线;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;
步骤3.2、使用次峰谱线所对应的循环频率作为待检测信号符号率的粗估计值并计算两两相邻谱线ai和ai-1的循环频率差值的绝对值,取其最大值作为待检测信号符号率的首次估计值,即L是搜索出谱线的总个数,a0=0。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.
进一步的,所述步骤4具体包括以下内容:Furthermore, the step 4 specifically includes the following contents:
步骤4.1、得到待检测信号的符号率粗估计值后,选取循环频率搜索范围为其中Δa是循环频率分辨率;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;
步骤4.2、对输入信号数据进行预处理,预处理方法为以下两种方法之一:保持原始循环频率分辨率为fs/N不变,在输入信号数据末尾补充更多信号数据倍率的0,或减小原始循环频率分辨率fs/N,通过增加输入信号的数据点数;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;
步骤4.3、采用FAM算法计算通过预处理后的输入信号数据f=fc截面循环频率在范围内的循环谱;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;
步骤4.4、比较循环频率在范围内各点谱线的值,取最大值所对应谱线的循环频率作为待检测信号符号率的精细估计值,即 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,
其中,fc是待检测信号的载波频率,fs是获取待检测信号的抽样频率,N是用于计算信号循环谱的数据点数。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.
进一步的,所述步骤5具体包括以下内容:Furthermore, the step 5 specifically includes the following contents:
步骤5.1、设置判决门限r;Step 5.1, set the decision threshold r;
步骤5.2、计算其中a是符号率的精细估计,是相邻谱线循环频率差值绝对值的最大值;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;
步骤5.3、若ar>r则转到步骤4,并重新设置循环频率的搜索范围;若ar≤r则输出待检测信号的符号率的精细估计值a和载波频率fc。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 .
本发明的有益效果为:The beneficial effects of the present invention are:
(1)本发明提供方法可以在低信噪比下精确估计任意符号率和载波频率,为盲接收信号的解调与分析提供可靠的特征参数,具有降低循环谱估计计算复杂度的优点。采用循环谱估计快速实现算法——快速傅里叶累积算法,输入的信号数据不必是整个抽样频率点数,只需要适当截取部分信号数据即可估计循环谱。并且,循环谱估计的所有模块计算几乎都是基于FFT算法,将所有模块的输入数据均补充至2n,可以有效降低循环谱估计的总体计算量。(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)本发明通过在输入时域信号数据的尾端多倍率补零,实现在循环频域的多倍率插值,提高循环频域的分辨率,由此提高信号特征参数估计的精度,并且充分利用了循环谱中各个离散谱线包含符号率和载波频率等信息。在对符号率进一步精细估计时,选取合适的搜索区间进行二次线性插值进一步提高循环谱分辨率,通过两次估计的比对判断符号率是否精确,从而实现任意符号率信号特征参数的精细估计。(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.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1是本发明的算法的流程图;Fig. 1 is a flow chart of an algorithm of the present invention;
图2是实施例对符号率粗估计的f=0循环谱截面;FIG2 is a cross section of the f=0 cyclic spectrum of a rough estimate of the symbol rate in an embodiment;
图3是循环谱快速估计算法——快速傅里叶累积算法的原理图。FIG. 3 is a schematic diagram of a fast Fourier accumulation algorithm, which is a fast estimation algorithm for cyclic spectrum.
具体实施方式DETAILED DESCRIPTION
以下结合具体实施例对本发明的原理和特征进行描述,所举实例只用于解释本发明,并非用于限定本发明的范围。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.
本实施例提供一个符号率为327.58Hz,载波频率为fc=2048Hz,采用BPSK调制方式的待检测信号,设置无线信道的信噪比SNR=10dB,接收信号的采样频率fs=8000Hz。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.
如图1和2所示,实施例提供了任意符号率无线信号特征参数高精度估计的算法流程图和实施例符号率粗估计的循环谱截面图,具体如下: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)在接收端,假设无线信号接收机以抽样频率fs=8000Hz检测并接收到一段未知已调的信号;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)在FAM算法的基础上,进行16倍率线性插值后计算信号的循环谱;2) Based on the FAM algorithm, the cyclic spectrum of the signal is calculated after 16-fold linear interpolation;
3)提取f=0截面的循环谱,获取待检测信号的载波频率fc=2048Hz;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)提取f=fc截面的循环谱,利用谱峰搜索算法找出含有符号率信息的谱线;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)计算各相邻谱线的循环频率差值的绝对值,并取其最大值作为待检测信号符号率的粗估计;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)根据待检测信号符号率的粗估计值,选取合适的循环频率搜索范围,通过二次线性插值精细估计,选取谱峰最大的循环频率值作为待检测信号符号率的精细估计值;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)比较待检测信号符号率的精细估计值和相邻谱线循环频率差值绝对值的最大值,设置判决门限,若小于判决门限则输出待检测信号的符号率和载波频率,否则重新设置循环频率的搜索范围,重新搜索。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.
优选地,在FAM算法上进行16倍率线性插值计算待检测信号循环谱的过程为: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)根据循环谱密度函数的定义式截取0.2s的信号点数作为待测信号的输入数据N0=1600,即N0=fs×0.2=1600,再对输入数据补0至16倍率数据点数,即输入数据点数N=N0×16,实现在循环频域的线性插值;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)采用FAM算法计算待测信号的循环谱,计算公式可以表述为: b) The FAM algorithm is used to calculate the cyclic spectrum of the signal to be measured. The calculation formula can be expressed as:
其中f是频率,b是循环频率,XT(f)是x(t)的傅里叶变换,即为输入待测信号x(n)的短时傅里叶变换,w(n)是数据窗,N是输入数据的总长度,M是短时傅里叶变换的长度。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.
优选地,当得到待检测信号的循环谱后,在循环频域提取待检测信号的载波频率和符号率特征参数,过程为: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.由于待测信号有载波频率成分,则将待测信号的循环谱f=0截面提取,并利用谱峰搜索求其次峰所在谱线的循环频率,该循环频率与载波频率的关系为b=2fc=4096;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.得到载波频率fc=2048,然后提取循环谱f=2048截面,利用谱峰搜索算法,设置搜索阈值大于0.02的谱峰,依次找出包含符号率信息在内的所有谱线,包括a∈{-1310,-982.9,-655.3,-327.1,0,327.6,655.8,982.9};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.使用次峰谱线所对应的循环频率作为待检测信号符号率的粗估计值并计算相邻谱线的循环频率差值的绝对值{|ai-ai-1}={327.1,327.6,328.2,327.1,327.6,328.2,327.1},取其最大值作为待检测信号符号率的首次估计值,即 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,
优选地,当得到待检测信号符号率的粗估计值后,经过二次线性插值进一步对符号率精细估计的过程包括: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)得到待检测信号的符号率粗估计值后,选取循环频率搜索范围在[327.6-5×fs/N0,327.6+5×fs/N0],其中Δa=fs/N0=5是循环频率分辨率;(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)对输入信号数据进行预处理,以达到提高循环谱分辨率的效果。共有两种方案:其一,保持原始循环频率分辨率为fs/N不变,在输入信号数据末尾补充更多信号数据倍率的0;其二,减小原始循环频率分辨率fs/N,通过增加输入信号的数据点数。(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.
在本实施例中采取方法一,将输入数据的尾端补充一倍的0,即N=1600×16×2增加输入信号的数据量;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)采用FAM算法计算通过预处理后的输入信号数据f=2048截面循环频率在[327.6-5×fs/N0,327.6+5×fs/N0]范围内的循环谱。(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)比较循环频率在[327.6-5×fs/N0,327.6+5×fs/N0]范围内各点谱线的值,取最大值所对应谱线的循环频率作为待检测信号符号率的精细估计值,即 (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,
其中,fc是待检测信号的载波频率2048Hz,fs是获取待检测信号的抽样频率8000Hz,N是用于计算信号循环谱的数据点数N=1600×16×2。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.
优选地,当得到待检测信号符号率的精细估计值和相邻谱线循环频率差值绝对值的最大值后,设置判决门限进行比较后输出的过程包括: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.设置判决门限r=fsN0=8000/1600=5;a. Set the decision threshold r = fsN0 = 8000/1600 = 5;
b.计算其中a是符号率的精细估计,是相邻谱线循环频率差值绝对值的最大值;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.若ar>r则重新设置循环频率的搜索范围,重新搜索;若ar≤r则输出待检测信号的符号率的精细估计值a和载波频率。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.
本实施例中因此输出精细估计符号率的值a=327.58以及载波频率值fc=2048。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.
综上所述,本发明提供的任意符号率无线信号特征参数高精度估计的算法,通过在输入时域信号数据的尾端多倍率补零,实现在循环频域的多倍率插值,提高循环频域的分辨率,由此提高信号特征参数估计的精度,并且充分利用了循环谱中各个离散谱线包含符号率和载波频率等信息。在对符号率进一步精细估计时,选取合适的搜索区间进行二次线性插值进一步提高循环谱分辨率,通过两次估计的比对判断符号率是否精确,从而实现任意符号率信号特征参数的精细估计,并且算法的各个模块和整个计算过程都是基于FFT算法,不必采用整个fs数据,只需利用少部分信号数据计算即可。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.
以上所述仅为本发明的较佳实施例,并不用以限制本发明,凡在本发明的精神和原则之内,所作的任何修改、等同替换、改进等,均应包含在本发明的保护范围之内。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.
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