CN107135176B - Image domain communication signal modulation identification method based on fractional low-order cyclic spectrum - Google Patents

Abstract

The invention discloses a graph-domain communication signal modulation recognition method based on fractional low-order cyclic spectrum. Using the three-dimensional fractional low-order cyclic spectrum of the received signal, the modulated signal disturbed by the α-stable distributed noise is converted to the graph domain, and then the effective feature parameter row index sequence set can be extracted from the sparse adjacency matrix represented by the graph as the characteristic of the modulation type , according to the Hamming distance set of the row index sequence of the training signal and the received signal, to achieve a more stable and effective identification of the modulation type of the communication signal under the interference of α-stable distributed noise.

Description

Modulation recognition method of graph-domain communication signal based on fractional low-order cyclic spectrum

technical field

The invention belongs to the technical field of signal processing, and more specifically relates to a modulation recognition method of a graph-domain communication signal based on a fractional low-order cyclic spectrum.

Background technique

Automatic Modulation Classification (AMC), also known as communication signal modulation identification, can identify the modulation type of the received signal with little or no prior knowledge, and is an essential link between signal detection and demodulation. important step and is widely used in many military and civilian communications fields.

Classical automatic modulation classification (AMC) methods can generally be divided into two categories: (i) likelihood-based (LB) decision-theoretic methods and (ii) feature-based (FB) pattern recognition (PR) methods. However, LB's method inevitably has some shortcomings, such as lack of closed-form solutions, unbearably high computational complexity, and mismatched probability models. The performance of FB methods is not optimal, however they can be implemented very efficiently, therefore, many studies utilize different features and different classification algorithms to pursue the robust performance of FB methods.

It is worth noting that both the LB method and the FB method are applied on the assumption of a Gaussian noise channel, however, various studies have shown that in practical wireless communication channels, usually multiple access interference caused by distinct pulses , low-frequency atmospheric noise, electromagnetic interference, etc. These physical noises exhibit sharp impulsive properties and probability density distributions with heavy tails. According to the central limit theorem, these non-Gaussian distributed noises, which are the main error sources in wireless communication systems, can be modeled as α-stable distributed noises. In the channel where α-stable distributed noise appears, the performance of the traditional AMC method will deteriorate obviously.

Graph Domain-Based Automatic Modulation Classification (AMC _G ) introduces the AMC technique into the graph domain for the first time, and has achieved better performance than existing PR and LB-based decision-theoretic algorithms. However, this method is to map the second-order cyclic spectrum of the received signal to extract the features of the image domain. However, there are no second-order and higher-order statistics in α-stable distributed noise, so the existing AMC _G method is also invalid in α-stable distributed noise. Therefore, the new more stable and more effective method is suitable for α-stable AMC techniques for distributing noise are urgently to be discovered.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies of the prior art, and propose a graph-domain communication signal modulation identification method based on fractional low-order cyclic spectrum, so as to adapt to α-stable distribution noise and realize more stable and effective identification of communication signal modulation types .

In order to achieve the above-mentioned purpose of the invention, the present invention is based on the fractional low-order cyclic spectrum modulation recognition method for graph-domain communication signals, which is characterized in that it includes the following steps:

(1), feature extraction of modulation type training signal

1.1), graph-domain mapping based on fractional low-valence cyclic spectrum

For the noise-free training signal x ^k (t) of the kth type of modulation type, k=1,2,...,K, K is the type number of the modulation type; its sampling sequence is divided into L sections, and each section performs a graph domain mapping:

Using the FAM algorithm ((Fast Fourier transform) Accumulation Method): FFT accumulation algorithm, used to calculate the cyclic spectral density) to calculate the FLOCS (Fractional Low-Order Cyclic Spectrum, fractional low-order cyclic spectrum) of the l-segment training signal, and obtain the graph domain set :

in, h=1,2...H, which represents the time-domain smooth cycle periodogram corresponding to the cyclic frequency ε _h retained in the l segment of the training signal of the k-th modulation type, and extracts the H cyclic frequency ε _h corresponding to The adjacency matrix of the cycle periodogram is smoothed in the time domain, and the set of adjacency matrices is obtained:

Among them, the time-domain smoothing cycle periodogram is obtained according to the following method:

a1), normalize and quantize the calculated FLOCS, that is, the fractional low-order cyclic spectrum, and obtain a discrete fractional low-order cyclic spectrum with a maximum value of 1 Among them, ε is the cycle frequency, f is the frequency;

In the FAM algorithm, the frequency resolution of FLOCS is Δf=f _s /N′, and the cycle frequency resolution Δα=1/Δt=f _s /N, where f _s is the sampling frequency and N′ is the data used for complex demodulation The number of points, N is the number of data points input within the Δt time, so the FLOCS calculated by the FAM algorithm is a matrix of (N'+1)×(2N+1);

a2), due to the symmetry of FLOCS, based on discrete fractional low-order loops The quarter-quadrants of create corresponding graph domain maps:

Define a stable cycle frequency ε _p , p=1,2...N, ε _p satisfies the condition:

Take the stable cycle frequency ε _p , the corresponding frequency value of p=1,2...N as the vertex, and get the vertex set:

Use the magnitude difference between two vertices as an edge to get a set of edges:

in:

In this way, the corresponding graph-domain mapping is obtained at each stable cycle frequency ε _p , and the smooth cycle-period graph in the instant domain is:

Delete the cyclic frequency whose fractional low-order cyclic spectrum is 0, and obtain the time-domain smooth cycle periodogram corresponding to H retained cyclic frequencies ε _h :

1.2), extraction of row index sequence

For each adjacency matrix l=1,2,...,L Extract the non-zero entries (elements) of the secondary diagonal directly above the main diagonal, and extract the row index sequence corresponding to these non-zero entries (elements) The principle of row index sequence extraction is as follows:

b1), check the non-zero values of the sub-diagonal, list the row indexes corresponding to these non-zero values, and arrange these row indexes in descending order according to the absolute value of these non-zero values, and then extract the row indexes in descending order ;

b2), if two or more non-zero entries have the same absolute value, extract the row index closest to the previously extracted row index, and discard the others;

b3), if two or more non-zero entries have the same absolute value and are the largest, select the largest row index, and discard the others;

In this way, L row index sequences corresponding to the cycle frequency ε _h are obtained, and the row index whose occurrence probability is greater than 95% in the L row index sequences is selected to form a stable row index sequence

For the training signal of the kth modulation type, extract H stable row index sequences with cyclic frequency ε _h to form a set of stable row index sequences: and as a characteristic of the k-th modulation type;

(2) Identification of communication signal modulation type

For the received signal, the characteristics of its modulation type are obtained according to the method of step (1), and the row index sequence set Among them, V is the number of retained cycle frequencies;

Calculate row index sequence set with the characteristics of the k-th modulation type The Hamming distance, get K Hamming distance k=1,2,...,K, and then find the minimum Hamming distance among them, and the corresponding modulation type is the modulation type of the received communication signal.

The purpose of the present invention is achieved like this.

In order to cope with α-stable distribution noise, the present invention is based on a fractional low-order cyclic spectrum image-domain communication signal modulation identification method. Using the three-dimensional fractional low-order cyclic spectrum of the received signal, the modulated signal disturbed by the α-stable distributed noise is converted to the graph domain, and then the effective feature parameter row index sequence set can be extracted from the sparse adjacency matrix represented by the graph as the characteristic of the modulation type , according to the Hamming distance set of the row index sequence of the training signal and the received signal, to achieve a more stable and effective identification of the modulation type of the communication signal under the interference of α-stable distributed noise.

Description of drawings

Fig. 1 is a functional block diagram of a specific embodiment of the application of the present invention.

Detailed ways

Specific embodiments of the present invention will be described below in conjunction with the accompanying drawings, so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when detailed descriptions of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

For the convenience of description, the relevant technical terms appearing in the specific implementation are explained first:

AMC (automatic modulation classification): automatic modulation classification;

FB (feature-based): based on statistical features

PR (pattern recognition): pattern recognition

LB (Likelihood-based influence): Based on the likelihood function

AMC _G (graph-based automatic modulation classification): graph domain automatic modulation classification;

PDF(probability density function): probability density function;

CF (characteristic function): characteristic function;

FLOCS(fractional low-order cyclic spectrum): Fractional low-order cyclic spectrum;

FLOC(fractional low-order correlation): Fractional low-order autocorrelation function;

FLOCC(fractional low-order cyclic correlation): Fractional low-order cyclic autocorrelation;

FAM (FFT (fast Fourier transform) accumulation method): FFT accumulation algorithm, used to calculate the cyclic spectral density;

BPSK (binary phase-shift keying): binary phase-shift keying;

QPSK (quadrature phase-shift keying): quadrature phase-shift keying;

OQPSK (offset quadrature phase-shift keying): offset quadrature phase-shift keying;

2FSK(binary frequency-shift keying): binary frequency shift keying;

4FSK(quadrature frequency-shift keying): quadrature frequency-shift keying;

MSK (minimum shift keying): minimum frequency shift keying;

1. α stable distribution

α-stable distribution, also known as non-Gaussian stable distribution and heavy-tailed distribution, is a generalized Gaussian distribution. This distribution model can accurately simulate the statistical characteristics of noise in the actual wireless communication environment.

The model of α-stable distribution is the only model that satisfies the stability and the generalized central limit theorem. There is no unified and closed probability density function (PDF) for α-stable distribution, but it has a unified characteristic function (CF), and its characteristic function can be Expressed as:

ψ(u)=exp{jau-γ|u| ^α [1+jβsgn(u)ω(u,α)]} (9);

Among them, sgn(·) is a symbolic function. α(0<α≤2) is the characteristic index, which determines the degree of impulse characteristics of the distribution, the smaller the value of α, the thicker the tail of the corresponding distribution, so the more significant the impulse characteristics; β(-1≤β≤1) is The skew parameter is used to determine the degree of symmetry of the distribution; γ (γ>0) is the dispersion coefficient, also known as the scale parameter, which is a measure of the degree of dispersion of the sample from its mean, similar to the variance in the Gaussian distribution; α ( -∞<a<+∞) is the location parameter, corresponding to the mean or median of the stable distribution, and u is the random variable of the characteristic function.

When α=2, the α-stable distribution degenerates into a Gaussian distribution;

When α=1 and β=0, the stable distribution of α is Cauchy distribution;

When β=0, the α-stable distribution is a symmetric distribution about the mean α, and we call such a distribution a symmetric α-stable (SαS) distribution.

2. Fractional low-order cyclic spectrum (FLOCS) analysis

Since the modulated signal s(t) is polluted by noise n(t) that obeys an α-stable distribution, the received signal x(t) can be modeled as:

x(t)=s(t)+n(t) (11);

Among them, n(t) is the noise that obeys the SαS distribution. Since the noise of the α-stable distribution has significant spike characteristics and does not have second-order or higher-order statistics, the traditional AMC based on second-order or higher-order circular statistics The algorithm will be invalid in the noise of α-stable distribution, and the fractional low-order cyclic spectrum (FLOCS) obtained by nonlinear transformation of the received signal can effectively suppress the noise of α-stable distribution. Therefore, for the AMC technology, it can be obtained from the FLOCS of the received signal The corresponding information is extracted to identify the modulated signal.

Fig. 1 is a functional block diagram of a specific embodiment of the application of the present invention.

In this embodiment, the input data is modulated by the modulator in the transmitter to obtain the modulated signal s(t), and then the α-stable distributed noise n(t) mixed in the channel becomes the received signal x(t ).

First, in the automatic modulation classifier, the received signal x(t) is uniformly sampled at the sampling frequency F _s =1/T _s , and the fractional low-order autocorrelation function (FLOC) of the sampled discrete signal x(n) can be be marked as:

FLOC(n,m)=E{[x(n+m)] ^{b} [x ^* (n)] ^{b} } (12);

x(n) ^{b} = |x(n)| ^b-1 x ^* (n) (13);

Among them, formula (12) is the b-order nonlinear transformation of the scattered signal x(n), 0<b<α/2; E(·) is the expectation, and x ^* (n) is the conjugate of x(n). Then, the fractional low-order cyclic autocorrelation (FLOCC) of the signal is:

Among them, <·> represents the time average. It is worth noting that the b-order nonlinear transformation only changes the amplitude of the signal, but does not change the period information, so the cycle frequency defined under the second-order circular correlation is also suitable for the fractional low-order circular correlation; if b=1, FLOCC degenerates into second-order cyclic autocorrelation. FLOCS is the Fourier transform of FLOCC, which can be expressed as:

In fact, It can be estimated by using the time domain smoothing algorithm - FAM algorithm. For a given frequency f and cycle frequency ε, the time domain smooth cycle periodogram can be expressed by the following formula:

Where g(n) is a uniform weight function with a width of NT _s seconds, f ₁ and f ₂ are the center frequencies of the filters in the FAM algorithm, T _s is the sampling period, where f ₁ = f+α/2, f ₂ =f-α/2, X _T (r, f ₁ ) and X _T (r, f ₂ ) are complex demodulations of x(n), which can be calculated by the following formula.

where a(r) is a tapered data window whose duration is T=N′T _s seconds, its width is the frequency resolution Δf of FLOCS, if a(r) is normalized, FLOCS can be determined by the time domain Smoothing the periodogram achieves unbiased estimation, as follows:

3. Graph Domain Mapping

Calculated using the FAM algorithm The magnitude of the 3D map is non-negative, and the calculated FLOCS is normalized and quantized to obtain a discrete fractional low-order cyclic spectrum with a maximum value of 1 In the FAM algorithm, the frequency resolution of FLOCS is Δf=f _s /N′, and the cycle frequency resolution Δα=1/Δt=f _s /N, where f _s is the sampling interval and N′ is the data used for complex demodulation The number of points, N is the number of data points input within Δt time. That is, the matrix of the FLOCS matrix (N'+1)×(2N+1) calculated by the FAM algorithm.

Due to the symmetry of FLOCS, for discrete spectrum A quarter-quadrant of the corresponding graph domain map is established. Define a stable cycle frequency ε _p , p=1,2...N, ε _p satisfies the condition:

Taking the frequency value corresponding to the stable cycle frequency as the vertex, set it as: Taking the magnitude difference between two vertices as an edge, set: q ₁ ,q ₂ =0,1,...,N′/2}, where:

So far, the corresponding image domain mapping can be obtained at each stable cycle frequency p=0,1,...,N, obviously the graph at each cycle frequency is cyclic, so the adjacency matrix of the corresponding graph can be extracted as a discriminative feature for different signals.

4. Extract features

Let the set of modulation types be in, Indicates the kth type of modulation type, k=1,2,...,K. In this embodiment, 6 types of modulation type signals can be identified, namely BPSK, 2FSK, 4FSK, QPSK, OQPSK, MSK, and for the noise-free kth modulation type training signal, its FLOCS can be calculated, according to Part 3 method to build a graph domain set.

Divide the sampling sequence of the training signal into L segments, and L times of graph domain mapping can be established. For each graph domain mapping, H graphs can be obtained. For the lth graph domain mapping, the set of graph domains can be expressed as in h=1,2...H, represents the graph corresponding to the cyclic frequency ε _h retained by the training signal of the kth modulation type, and the adjacency matrix set extracted from the corresponding graph is expressed as

Since FLOCS represents a weighted directed cycle in the graph domain, any adjacency matrix is a sparse matrix with the following properties

in, is the adjacency matrix The (u,v)th entry of , for each adjacency matrix Extract the non-zero entries of the sub-diagonal directly above the main diagonal of the adjacency matrix, and extract the row index sequence corresponding to these non-zero entries The principle of row index sequence extraction is as follows:

b1), check the non-zero values of the sub-diagonal, list the row indexes corresponding to these non-zero values, and arrange these row indexes in descending order according to the absolute value of these non-zero values, and then extract the row indexes in descending order ;

b2), if two or more non-zero entries have the same absolute value, extract the row index closest to the previously extracted row index, and discard the others;

b3), if two or more non-zero entries have the same absolute value and are the largest, select the largest row index, and discard the others;

In this way, L row index sequences corresponding to the cycle frequency ε _h are obtained, and the row index whose occurrence probability is greater than 95% in the L row index sequences is selected to form a stable row index sequence

For the training signal of the k-th modulation type, the stable row index sequence of H cycle frequency ε _h is extracted to form a set of stable row index sequences: and as a characteristic of the kth modulation type.

Note that these row index sequences do not have to have the same number of elements, since the length of each sequence is determined by the corresponding adjacency matrix determined by the non-zero elements of .

5. Identification of communication signal modulation type

For the received signal, follow the methods in Parts 3 and 4 to obtain the characteristics of its modulation type, and the set of row index sequences Among them, V is the number of retained cycle frequencies;

Calculate row index sequence set with the characteristics of the k-th modulation type The Hamming distance, get K Hamming distance k=1,2,...,K, and then find the minimum Hamming distance among them, and the corresponding modulation type is the modulation type of the received communication signal.

In this embodiment, as shown in Figure 1, the received signal x(t) is preprocessed and sent to the classifier to identify the modulation of the communication signal according to the method in Part 5 above, and the modulation type is sent to the demodulator , demodulate the preprocessed received signal according to the corresponding modulation type to obtain output data.

As shown in Figure 1, the present invention converts the modulated signal disturbed by α-stable distributed noise to the graph domain by calculating the fractional low-order cyclic spectrum FLOCS, and then obtains the characteristics of the modulation type training signal through graph domain mapping and feature extraction, and then Carry out graph-domain classification based on features to achieve more stable and effective identification of communication signal modulation types under α-stable distributed noise interference.

Although the illustrative specific embodiments of the present invention have been described above, so that those skilled in the art can understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, As long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are included in the protection list.

Claims (1)

1. A graph-domain communication signal modulation identification method based on fractional low-order cyclic spectrum, is characterized in that, comprises the following steps: (1), feature extraction of modulation type training signal 1.1), graph-domain mapping based on fractional low-order cyclic spectrum For the noise-free training signal x ^k (t) of the kth type of modulation type, k=1,2,...,K, K is the type number of the modulation type; its sampling sequence is divided into L sections, and each section performs a graph domain mapping: The FAM algorithm ((Fast Fourier transform Accumulation Method): FFT accumulation algorithm, used to calculate the cyclic spectral density) is used to calculate the FLOCS (Fractional Low-Order Cyclic Spectrum, fractional low-order cyclic spectrum) of the l-segment training signal, and the image domain set is obtained: in, Represent the time-domain smooth cycle periodogram corresponding to the cycle frequency ε _h corresponding to the retained cycle frequency ε h of the training signal of the k-th type of modulation type, and extract the adjacency matrix of the time-domain smooth cycle cycle graph corresponding to H cycle frequencies ε _h , Get a set of adjacency matrices: Among them, the time-domain smoothing cycle periodogram is obtained according to the following method: a1), normalize and quantize the calculated FLOCS, that is, the fractional low-order cyclic spectrum, and obtain a discrete fractional low-order cyclic spectrum with a maximum value of 1 In the FAM algorithm, the frequency resolution of FLOCS is Δf=f _s /N′, and the cycle frequency resolution Δα=1/Δt=f _s /N, where f _s is the sampling frequency and N′ is the data used for complex demodulation The number of points, N is the number of data points input within the Δt time, so the FLOCS calculated by the FAM algorithm is a matrix of (N'+1)×(2N+1); a2), due to the symmetry of FLOCS, based on discrete fractional low-order loops The quarter-quadrants of create corresponding graph domain maps: Define a stable cycle frequency ε _p , p=1,2...N, ε _p satisfies the condition: Take the stable cycle frequency ε _p , the corresponding frequency value of p=1,2...N as the vertex, and get the vertex set: Use the magnitude difference between two vertices as an edge to get a set of edges: in: In this way, the corresponding graph-domain mapping is obtained at each stable cycle frequency ε _p , and the smooth cycle-period graph in the instant domain is: Delete the cyclic frequency whose fractional low-order cyclic spectrum is 0, and obtain the time-domain smooth cycle periodogram corresponding to H retained cyclic frequencies ε _h : 1.2), extraction of row index sequence For each adjacency matrix Extract the non-zero entries of the secondary diagonal directly above the main diagonal, and extract the sequence of row indices corresponding to these non-zero entries The principle of row index sequence extraction is as follows: b1), check the non-zero values of the sub-diagonal, list the row indexes corresponding to these non-zero values, and arrange these row indexes in descending order according to the absolute value of these non-zero values, and then extract the row indexes in descending order ; b2), if two or more non-zero entries have the same absolute value, extract the row index closest to the previously extracted row index, and discard the others; b3), if two or more non-zero entries have the same absolute value and are the largest, select the largest row index, and discard the others; In this way, L row index sequences corresponding to the cycle frequency ε _h are obtained, and the row index whose occurrence probability is greater than 95% in the L row index sequences is selected to form a stable row index sequence For the training signal of the kth modulation type, extract H stable row index sequences with cyclic frequency ε _h to form a set of stable row index sequences: and as a characteristic of the k-th modulation type; (2) Identification of communication signal modulation type For the received signal, the characteristics of its modulation type are obtained according to the method of step (1), and the row index sequence set Among them, V is the number of retained cycle frequencies; Calculate row index sequence set with the characteristics of the k-th modulation type The Hamming distance, get K Hamming distance Then find the minimum Hamming distance among them, and the corresponding modulation type is the modulation type of the received communication signal.