CN109120562B - MFSK signal frequency estimation method based on spectrum accumulation matching - Google Patents

MFSK signal frequency estimation method based on spectrum accumulation matching Download PDF

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CN109120562B
CN109120562B CN201810883533.7A CN201810883533A CN109120562B CN 109120562 B CN109120562 B CN 109120562B CN 201810883533 A CN201810883533 A CN 201810883533A CN 109120562 B CN109120562 B CN 109120562B
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罗彪
马俊虎
廖红舒
甘露
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University of Electronic Science and Technology of China
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/0014—Carrier regulation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/10—Frequency-modulated carrier systems, i.e. using frequency-shift keying
    • H04L27/106—M-ary FSK
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2655—Synchronisation arrangements
    • H04L27/2689—Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation
    • H04L27/2695—Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation with channel estimation, e.g. determination of delay spread, derivative or peak tracking
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/0014—Carrier regulation
    • H04L2027/0024—Carrier regulation at the receiver end
    • H04L2027/0026—Correction of carrier offset
    • H04L2027/0032—Correction of carrier offset at baseband and passband

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Abstract

The invention belongs to the technical field of signal processing, and relates to an MFSK signal frequency estimation method based on spectrum accumulation matching. The invention firstly segments the non-partner received signal, performs Fast Fourier Transform (FFT), and gets the module to obtain the frequency spectrum. And correspondingly adding the first half elements of each section to obtain the data after accumulation processing. Then, M sections (M is a modulation system) are continuously taken from the accumulated data according to different intervals and starting points, and the maximum value of the vector obtained after the corresponding elements of the M sections are added is used as the element of the corresponding position of the matrix M. And finally, according to the position of the maximum value of the matrix M, obtaining the MFSK frequency modulation parameter. Compared with estimation methods based on wavelet transformation, short-time Fourier transformation and the like, the method has the advantages that the time-frequency analysis is not needed, the calculation amount is greatly reduced, the requirement on the length of received data is not high, and the method still has good performance under the condition of low signal-to-noise ratio.

Description

MFSK signal frequency estimation method based on spectrum accumulation matching
Technical Field
The invention belongs to the technical field of signal processing, and relates to an MFSK signal frequency estimation method based on spectrum accumulation matching.
Background
Multi-system frequency shift keying (MFSK) has good anti-multipath delay characteristics, and has been widely used in short-wave and ultra-short-wave radio stations and underwater acoustic communication channels in recent years. The accurate modulation parameter blind estimation of the signal is a necessary link for the non-cooperative receiver to complete signal matching identification and blind demodulation, and is also an important content in spectrum monitoring and communication countermeasure. At present, a great deal of research is carried out on the problem of blind reception of the MFSK signal, including modulation identification, symbol rate, symbol synchronization information of the signal, and signal demodulation based on the research, but the literature for directly estimating the frequency information is not abundant. The current main methods are peak clustering based estimation methods, time frequency analysis based estimation methods and all-digital phase-locked loops based estimation methods.
The method based on peak clustering mainly estimates the clustering center as the modulation frequency of the MFSK signal after obtaining the signal spectrum. However, the clustering algorithm needs to manually give some parameters such as initial clustering centers of the clustering numbers in advance, and the parameters are very subjective and difficult to determine manually without prior knowledge. And the effect is not good under the condition of low signal-to-noise ratio.
The time-frequency analysis-based method obtains the time-frequency variation waveform of the MFSK signal through wavelet transformation or short-time Fourier transformation (STFT), obtains a symbol hopping time pulse after differential transformation, extracts a timing component of the symbol hopping time pulse, estimates the symbol rate, performs symbol synchronization, and then obtains carrier frequency information. However, the process of extracting the local frequency change time in the signal by wavelet transform to obtain the symbol rate and the jump time has larger error and poor anti-noise performance under low signal-to-noise ratio, and simultaneously the wavelet transform scale has larger influence on the result. Short-time Fourier transform is one of the most common time-frequency analysis tools, and a signal time-frequency graph can be obtained by reasonably selecting transformed parameters, so that the related parameters of the signal are estimated. However, due to the limitation of the Heisenberg inaccuracy measuring principle, the short-time fourier transform has contradiction between time-frequency resolutions, so that the parameter estimation precision is greatly influenced by the time-frequency diagram resolution, and the parameters of the short-time fourier transform are not easy to select. Under blind receiving conditions, the determination of the time-frequency diagram parameters is difficult because the signal parameters are unknown.
Compared with time-frequency analysis, the method based on the all-digital phase-locked loop has smaller required data volume, and the method provides tracking results of signal amplitude, frequency and instantaneous phase based on the change of the locked signal tracked by the improved digital phase-locked loop (EPLL). However, the method mainly aims at the demodulation of the MFSK signal, and the estimation of the frequency mainly depends on the frequency tracking signal, so that the method is difficult to realize in non-cooperative communication and cannot be widely applied.
Disclosure of Invention
The invention aims to provide a method for accurately estimating the frequency information of an MFSK signal under the condition of blind reception. The invention mainly analyzes by utilizing the characteristic that the MFSK signal modulation frequency increment is fixed through the frequency spectrum of the signal. Compared with a time-frequency analysis method, the method does not need a time-frequency diagram; compared with mountain peak clustering, the method is more accurate, better in anti-noise performance and still small in estimation error under low signal-to-noise ratio.
The technical scheme adopted by the invention is as follows:
a MFSK signal frequency estimation method based on spectrum accumulation matching is characterized in that Fast Fourier Transform (FFT) is conducted on non-cooperative received signal segments to obtain spectrums and accumulate the spectrums, and searching is conducted according to an MFSK modulation system after spectrum accumulation processing by utilizing the characteristic that modulation intervals are fixed. If the frequency intervals are matched, the MFSK signal spectrum energy peaks correspond, the accumulated value is the maximum, and the accumulated maximum values in an interval before the initial modulation frequency at the search starting point are the same. The method comprises the following steps:
s1, setting some non-partner to receive the signal as
Figure BDA0001755038680000021
Where N is the signal length. Determining number of segments
Figure BDA0001755038680000022
Data to be recorded
Figure BDA0001755038680000023
Divided into K segments, where L is the length of each segment of data,
Figure BDA0001755038680000024
represents rounding down to obtain a segmented data vector si
si＝{y(i-1)L+1，y(i-1)L+2，…，yiL}，i＝1，2，…，K；
S2, pair SiFFT to obtain frequency spectrum wi；
S3, pair { wiThe first half elements of K, i 1, …, are summed according to equation (1) to give a vector spec,
Figure BDA0001755038680000025
s4, setting the search variable Δ f to 1;
s5, operating according to the formula (2) and determining the matrix PΔf(f, t) wherein f is 1,2, …, L/2-M · Δ f, t is 1,2, …, Δ f, M is a known modulation scale;
Figure BDA0001755038680000026
s6, finding out the matrix P according to the formula (3)ΔfThe maximum value of each row, and stored in the matrix M (af, f),
M(Δf，f)＝maxPΔf(f,: formula (3)
S7, judgment
Figure BDA0001755038680000027
If yes, Δ f ═ Δ f +1, and S5, S6 are repeated; if not, go to step S8;
s8, searching the row-column position (g) corresponding to the maximum value in M (delta f, f)d，hd) D is 1, …, D, M modulation frequencies of the MFSK signal are estimated by equation (4),
Figure BDA0001755038680000031
wherein M is 0, …, M-1.
The method has the advantages that under the condition that only the MFSK signal category is known, the signal spectrum is intelligently searched, the modulation frequency is accurately estimated, time-frequency diagram analysis is not needed in the estimation process, the calculated amount and the parameter influence are greatly reduced, and the signal-to-noise ratio influence is small; providing accurate a priori knowledge for subsequent demodulation.
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FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a diagram illustrating normalized root mean square error of frequency estimation under different SNR conditions in example 1 of the present invention;
fig. 3 shows normalized root mean square error of frequency estimation under different snr conditions in embodiment 2 of the present invention.
Detailed Description
The technical solution of the present invention will be further explained with reference to the accompanying drawings and examples.
Example 1
The purpose of this embodiment is to estimate the center frequency and frequency increment of different 4FSK signals under different signal-to-noise ratio scenarios, and the verification method of the present invention can realize accurate estimation of the frequency information of the 4FSK signals. In this embodiment, the length of the simulated signal is N-62500, the sampling rate is Fs-6250 Hz, the symbols are randomly generated, the symbol rate is 125Baud, and the center frequency of the signal modulation is f02000Hz, 300Hz for the data frequency difference Af, and 1 step in the in-band signal-to-noise ratio from-5 dB to 10 dB. According to the invention:
s1, the received signal is { y1，y2，…，yNDividing the data into 10 segments, and each segment length L6250 to obtain
Figure BDA0001755038680000032
S2, for each data SiPerforming FFT to obtain wi，i＝1，2，…，10；
S3, pair { wiThe first half elements of K, i 1, …, are summed as follows to give a vector spec,
Figure BDA0001755038680000041
s4, setting the search variable Δ f to 1;
s5, continuously taking 4 vector segments with length Δ f from f on spec, calculating according to the following formula, and determining matrix PΔf(f, t) wherein f is 1,2, …, 3125-4 Δ f, t is 1,2, …, Δ f;
Figure BDA0001755038680000042
s6, finding out the matrix P according to the following formulaΔfThe maximum value of each row, and stored in the matrix M (af, f),
M(Δf，f)＝maxPΔf(f，：)
s7, judgment
Figure BDA0001755038680000043
If yes, Δ f ═ Δ f +1, and S5, S6 are repeated; if not, go to step S8;
s8, searching the row-column position (g) corresponding to the maximum value in M (delta f, f)d，hd) D is 1, …, D, the frequency increment and center frequency estimate of the 4FSK signal are estimated by the following formula,
Figure BDA0001755038680000044
the monte carlo test was repeated 100 times per signal-to-noise ratio, and its performance was measured by Normalized Root Mean Square Error (NRMSE) of frequency increment and center frequency estimate:
Figure BDA0001755038680000045
Figure BDA0001755038680000046
the resulting frequency increment and the normalized root mean square error of the center frequency estimate are shown in fig. 2.
Example 2
The purpose of this embodiment is to estimate the center frequency and frequency increment of 2FSK and 8FSK signals under different signal-to-noise ratio scenarios, and verify the estimation performance of the method of the present invention. In this embodiment, the length of the simulated signal is 40000, the sampling rate is Fs 8000Hz, symbols are randomly generated, the symbol rate is 160Baud, and the center frequency of the signal modulation is f02000Hz, data frequency difference Δ f 300Hz, in-band signal-to-noise ratio steps 1 from 0dB to 10 dB. According to the examples1 in the same manner 100 trials were performed and the resulting normalized root mean square estimation error is shown in figure 3.
The result shows that the method provided by the invention can accurately estimate the MFSK signal frequency information, and especially can still realize accurate estimation at low signal-to-noise ratio. And the normalized root mean square error of the frequency increment estimation of the 4FSK signal is less than-16 dB at 1dB, and the normalized root mean square error of the central frequency estimation is less than-24%. The frequency increment estimation normalization root mean square error of the 8FSK signal is less than-16 dB at 2dB, the center frequency estimation normalization root mean square error is less than-22 dB, and the estimation performance of the 2FSK signal is better. The time-frequency graph without signals shows that the method can directly solve the estimation problem of the MFSK frequency modulation parameters on the frequency domain.

Claims (1)

1. A frequency estimation method of a multi-system frequency shift keying (MFSK) signal based on spectrum accumulation matching sets the type of a known signal, and is characterized by comprising the following steps:
s1, setting the non-cooperative party to receive the signal as
Figure FDA0002753221860000011
Wherein N is the signal length; determining number of segments
Figure FDA0002753221860000012
Data to be recorded
Figure FDA0002753221860000013
Divided into K segments, where L is the length of each segment of data,
Figure FDA0002753221860000014
represents rounding down to obtain a segmented data vector si：
si＝{y(i-1)L+1,y(i-1)L+2,…,yiL},i＝1,2,…,K；
S2, pair SiFFT to obtain frequency spectrum wi；
S3, pair { wiThe first half element of K is expressed asAdding according to formula 1 to obtain a vector spec:
Figure FDA0002753221860000015
s4, setting a search variable Δ f to 1;
s5, determining matrix P according to formula 2△f(f, t) wherein f is 1,2, …, L/2-M. Δ f, when Δ f is 1, t is Δ f, when Δ f is 1>When 1, t is 1,2, …, Δ f, M is a known modulation system;
Figure FDA0002753221860000016
s6, finding out the matrix P according to the formula 3△fThe maximum value of each row and stored in the matrix M (Δ f, f):
M(△f,f)＝maxP△f(f,: formula 3)
S7, judgment
Figure FDA0002753221860000017
If yes, determining that the delta f is delta f +1, and repeating the steps S5 and S6; if not, go to step S8;
s8, searching for the row-column position (g) corresponding to the maximum value in M (Deltaf, f)d,hd) D is 1, …, D, M modulation frequencies of the MFSK signal are estimated from equation 4,
Figure FDA0002753221860000018
wherein M is 0, …, M-1.
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