CN111277526B

CN111277526B - Modulation identification method of constellation diagram identical signals based on compressed sensing

Info

Publication number: CN111277526B
Application number: CN202010133208.6A
Authority: CN
Inventors: 王伶; 段正祥; 张捷; 汪跃先; 杨欣; 张兆林; 谢坚; 陶明亮; 粟嘉; 韩闯; 宫延云
Original assignee: Northwestern Polytechnical University
Current assignee: Northwestern Polytechnical University
Priority date: 2020-03-01
Filing date: 2020-03-01
Publication date: 2021-06-11
Anticipated expiration: 2040-03-01
Also published as: CN111277526A

Abstract

The invention provides a modulation identification method for the same signal in a constellation diagram based on compressed sensing. By performing non-uniform sampling and rough reconstruction on the signal, and then using the spectral line quantity feature of the high-power spectrum of the signal, the second order of the signal is realized. quist frequency sampling, while realizing the signal identification in the signal set {QPSK, OQPSK, π/4‑DQPSK, 8PSK}. Due to the adoption of the technical means of compressing the signal quadratic spectrum, the present invention not only solves the technical problems of identifying between QPSK signals and OQPSK signals, and identifying between 8PSK signals and π/4-DQPSK signals, but also can effectively reduce the Sampling rate and number of sampling points.

Description

Modulation identification method of constellation diagram identical signals based on compressed sensing

Technical Field

The invention relates to the field of signal processing, in particular to a modulation identification method of a constellation diagram, which is suitable for signal identification in a signal set { QPSK, OQPSK, pi/4-DQPSK, 8PSK }.

Background

With the increase of communication devices and the increase of communication types, signal modulation methods are essential for realizing the intercommunication of multi-system signals. Modulation identification is a key technology between signal detection and signal demodulation, and in order to realize reliable, efficient and intelligent communication in a crowded electromagnetic spectrum environment, in a software radio and cognitive radio system, a receiving end needs to estimate information such as a modulation mode, a modulation parameter and the like of a received signal, so that intelligent receiving and demodulation of various modulated signals are realized.

The current modulation identification mode is mainly an identification method based on extracted features, and the extracted features mainly include the following: including instantaneous, statistical, and transform domain features of amplitude, frequency, and phase. At present, a digital modulation signal identification algorithm (DMRAs) which is a relatively effective identification characteristic method adopts key characteristic parameters such as instantaneous envelope, phase and frequency as the characteristics of modulation identification, has high calculation speed, obvious classification effect and is easy to realize in engineering, but does not have a corresponding characteristic extraction algorithm between signals with the same constellation diagram, such as identification between QPSK signals and OQPSK signals and identification between 8PSK signals and pi/4-DQPSK signals. Meanwhile, the method depends on a large amount of data, and brings huge pressure to the sampling frequency of the digital-analog converter and the storage capacity of a system under high-speed signals.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides a modulation identification method of constellation diagram identical signals based on compressed sensing. In order to solve the problem that partial signals cannot be identified and the ADC sampling frequency is high, the signal is subjected to non-uniform sampling and coarse reconstruction, and the number characteristic of spectral lines of a high-power spectrum of the signal is utilized, so that sub-Nyquist frequency sampling of the signal is realized, and signal identification in a signal set { QPSK, OQPSK, pi/4-DQPSK and 8PSK } is realized.

The technical scheme adopted by the invention for solving the technical problem comprises the following steps:

step 1: non-uniformly sampling a signal;

suppose that the required Nyquist sampling frequency of the signal is f_nyqThe sampling frequency of the digital-to-analog converter is f_ADCObtaining a compression ratio of the sample of

The relationship between the non-uniformly sampled signal and the nyquist sampled signal is represented as y ═ Ψ r, where y is the compressed sampled signal of dimension M × 1, r is the nyquist sampled signal of dimension N × 1, Ψ is the observation matrix of dimension M × N, Ψ is represented as

Wherein k is_j∈[1,ω],ψ_ijE psi, to get y [ j]＝r[ω(j-1)+k_j]；

Step 2: because QPSK signal, OQPSK signal and pi/4-DQPSK are four-phase shift modulation, the non-uniform sampling signal is subjected to fourth-order non-linear transformation to obtain y₄，y₄[j]＝(y[j])⁴，j＝0,1,...,M-1；

And step 3: carrying out coarse reconstruction on the four-order nonlinear transformation of the non-uniform sampling signal to obtain a fourth power spectrum u, wherein the coarse reconstruction method is that u is phi psi^Hy₄Where u is the Nx 1-dimensional reconstructed fourth power spectrum and Φ is the Nx N-dimensional Fourier transform basis, i.e. p-psi^Hy₄Performing Fourier transform; the fourth power spectrum of the signal is obtained by Fourier transform of the signal after fourth-order nonlinear transformation, i.e.

Wherein

Representation fourier

Representing a fourier transform;

and 4, step 4: finding out the positions of 3 maximum spectrum peaks of the signal fourth power spectrum u, and recording the positions as F_max＝{f_m1,f_m2,f_m3In which | u (f)_m1)|≥|u(f_m2)|≥|u(f_m3)|；

And 5: will y₄The average is divided into two sections of M/2 multiplied by 1 dimensional vector y_4，1And y_4，2Constructing a new N/2 XN/2-dimensional discrete Fourier basis phi_N/2Simultaneously, the M × N-dimensional observation matrix Ψ is divided into 4 parts of 4M/2 × N/2 dimensions as follows:

step 6: two slices u are obtained₁And u₂The fourth power spectrum of (A) is: u. of₁＝Φ_N/2Ψ₁ ^Hy_4，1，u₂＝Φ_N/2Ψ₄ ^Hy_4，2；

And 7: look for u separately₁And u₂Position F where maximum 3 spectral peaks are located_max,1＝{f_m1,1,f_m2,1,f_m3,1And F_max,2＝{f_m1,2,f_m2,2,f_m3,2In which u₁(f_m1,1)≥u₁(f_m2,1)≥u₁(f_m3,1)，u₂(f_m1,2)≥u₂(f_m2,2)≥u₂(f_m3,2)；

And 8: union set F_max,o＝F_max,1∪F_max,2；

And step 9: find the intersection F_max,a＝F_max∩F_max,o；

Step 10: to obtain F_max,aNumber of middle element N_r；

If N is present_rIf the number is 0, the modulation mode of the output identification result is 8 PSK; if N is present_r1, outputting an identification result in an OQPSK modulation mode; if N is present_r3, outputting the identification result, wherein the modulation mode is QPSK; if N is present_rStep 11 is entered for 2;

step 11: if N is present_rIs 2, judge

Whether the output identification result is greater than the threshold eta or not, if so, outputting the identification result with a QPSK modulation mode; if the output identification result is less than or equal to eta, the modulation mode of the output identification result is pi/4-DQPSK.

The invention has the advantages that the technical means of compressed sensing of the signal fourth power spectrum is adopted, so that the technical problems of identification between QPSK signals and OQPSK signals and identification between 8PSK signals and pi/4-DQPSK signals are solved, and the sampling rate and the number of sampling points can be effectively reduced.

Drawings

FIG. 1 is a flow chart of the spectral peak detection algorithm under the compression framework of the present invention.

FIG. 2 is a non-uniform sampling schematic diagram of the present invention.

FIG. 3 is a timing diagram of the sample and hold module of the present invention.

FIG. 4 is a timing diagram of a non-uniform sampling system according to the present invention.

FIG. 5 is a coarse reconstructed quartile spectrum of different signals according to the present invention.

FIG. 6 is a graph of the recognition probability of different signals at compression ratio 4 according to the present invention.

Detailed Description

The present invention is further illustrated by the following examples in conjunction with the drawings, and the present invention includes but is not limited to the following examples, which specifically include the following steps:

step 1: non-uniformly sampling a signal;

Wherein k is_j∈[1,ω],ψ_ijE psi, to get y [ j]＝r[ω(j-1)+k_j]；

Wherein

Representing a fourier transform;

and 4, step 4: finding out the positions of 3 maximum spectrum peaks of the signal fourth power spectrum u, and recording the positions as F_max＝{f_m1,f_m2,f_m3In which | u (f)_m1)|≥u|(f_m2)|≥|u(f_m3)|；

And 7: look for u separately₁And u₂Position F where maximum 3 spectral peaks are located_max,1＝{f_m1,1,f_m2,1,f_m3,1And F_max,2＝{f_m1,2,f_m2,2,f_m3,2In which | u₁(f_m1,1)|≥|u₁(f_m2,1)|≥|u₁(f_m3,1)|，|u₂(f_m1,2)|≥|u₂(f_m2,2)|≥|u₂(f_m3,2)|；

And 8: union set F_max,o＝F_max,1∪F_max,2；

And step 9: find the intersection F_max,a＝F_max∩F_max,o；

Step 10: to obtain F_max,aNumber of middle element N_r；

step 11: if N is present_rIs 2, judge

The invention also provides a method for reducing the residual carrier frequency f by using a filtered frequency_c0.5GHz, symbol rate f_bFor example, 1GHz unknown modulation signal. Assuming receiver equivalent naphthaleneNyquist sampling frequency f_nyq4GHz, sampling compression ratio omega 4A/D converter actual sampling frequency

Number of sampled symbols N_symbol4096, as shown in fig. 1, the present invention provides a modulation recognition based on compressed sensing, and the specific embodiment is as follows:

the method comprises the following steps: the signal is sampled by non-uniform sampling to obtain a 4096 x 1-dimensional sampling value y, and a system schematic diagram is shown in fig. 2. The whole system consists of a clock generation module, a sampling and holding module and a data acquisition module 3. And the clock generation module is responsible for generating two clocks, namely an ADC sampling clock and a non-uniform clock. The non-uniform clock is generated by a string of pseudo-random binary codes satisfying the nyquist frequency, wherein the output clock is high when the pseudo-random code is 1, and low when the pseudo-random code is 0, there is only one falling edge all the time in one ADC sampling clock period, and the pseudo-random code is also set to 1 when the next ADC sampling clock rising edge comes, i.e. the pseudo-random code is in the form of '… 11100 …'. The function of the sample and hold block is to collect the signal at the time when the falling edge of the non-uniform clock arrives and hold it until the next rising edge of the non-uniform clock arrives, while the analog signal can freely pass through when the clock signal is high, as shown in fig. 3. The data acquisition module samples the signal from the sample-and-hold module according to the ADC sampling clock. The whole process is described as shown in fig. 4, it can be seen that although the sampling clock of the ADC is far lower than the nyquist sampling frequency, the actual acquired signal is non-uniformly sampled according to the nyquist frequency by the sample-and-hold module, and the equivalent observation matrix is Ψ with 4096 × 16384 dimensions, where Ψ can be expressed as

Wherein k is_j∈[1,4],ψ_ij∈Ψ。

Step two: solving the fourth power of each value of the non-uniform sampling signal to obtain y₄。

Step three: by the formula u-phi psi^Hy₄The roughly reconstructed fourth power spectrum is obtained, the 16384 × 16384-dimensional fourier transform base Φ can be obtained by performing fourier transform on the unit matrix of the corresponding dimension, and the roughly reconstructed spectra of different signals are shown in fig. 5.

Step four: finding out the positions of 3 maximum spectrum peaks of the signal fourth power spectrum u, and recording the positions as F_max＝{f_m1,f_m2,f_m3In which | u (f)_m1)|≥|u(f_m2)|≥|u(f_m3)|。

Step five: will y₄Is divided into two 2048 multiplied by 1 dimensional vectors y on average_4，1And y_4，2Constructing a new 8192X 8192 dimensional discrete Fourier base phi_N/2Simultaneously, the 4096 × 16384-dimensional observation matrix Ψ is divided into 4 portions of 4 2048 × 8192 dimensions as follows:

step six: two slices u are obtained₁And u₂The fourth power spectrum of (A) is: u. of₁＝Φ_N/2Ψ₁ ^Hy_4，1，u₂＝Φ_N/2Ψ₄ ^Hy_4，2。

Step seven: look for u separately₁And u₂Position F where maximum 3 spectral peaks are located_max,1＝{f_m1,1,f_m2,1,f_m3,1And F_max,2＝{f_m1,2,f_m2,2,f_m3,2In which | u₁(f_m1,1)|≥|u₁(f_m2,1)|≥|u₁(f_m3,1)|，|u₂(f_m1,2)|≥|u₂(f_m2,2)|≥|u₂(f_m3,2)|。

Step eight: union set F_max,o＝F_max,1∪F_max,2。

Step nine: find the intersection F_max,a＝F_max∩F_max,o。

Step ten: to obtain F_max,aNumber of middle element N_r。

If N is present_rIf the number is 0, the modulation mode of the output identification result is 8 PSK; if N is present_r1, outputting an identification result in an OQPSK modulation mode; if N is present_rAnd 3, outputting the identification result, wherein the modulation mode is QPSK. If N is present_rStep eleven was performed for 2.

Step eleven: if N is present_rIs judged as 2

If the eta is larger than the threshold eta, the eta is 1.8, and if the eta is larger than 1.8, the modulation mode of the output identification result is QPSK; and if the output identification result is less than or equal to 1.8, the modulation mode of the identification result is pi/4-DQPSK. From fig. 5, it can be seen that the intensities of the largest 2 spectral lines of the higher-order spectrum of the pi/4-DQPSK signal are close, while the intensities of the largest 2 spectral lines of the higher-order spectrum of the QPSK signal are different greatly, so that η is set to 1.8. When QPSK has 1 weaker line that may not be detected, the discrimination can be improved by separating the QPSK signal from the case of 2 lines.

Fig. 6 shows the probability chart of the identification of different signals when the compression ratio is 4, and it can be seen from fig. 6 that, when the signal-to-noise ratio is 5dB, the identification rate of 100% is realized except for QPSK signals, and when the signal-to-noise ratio is 10dB, the identification probability of all signals reaches 100%, which means that only one fourth of the nyquist sampling frequency of the AD sampling rate is needed, the detection probability of 100% of signals in the signal set { QPSK, OQPSK, pi/4-DQPSK, 8PSK } can be realized, the amount of sampled data is one fourth of uniform sampling, and the storage pressure is also reduced.

Claims

1. a modulation identification method based on the same signal of the constellation diagram of compressed sensing, is characterized in that comprising the following steps:

Step 1: Non-uniform sampling of the signal;

Assuming that the required Nyquist sampling frequency of the signal is f _nyq , and the sampling frequency of the digital-to-analog converter is f _ADC , the sampling compression ratio obtained is

The relationship between the non-uniform sampling signal and the Nyquist sampling signal is expressed as y=Ψr, where y is the M×1-dimensional compressed sampling signal, r is the N×1-dimensional Nyquist sampling signal, and Ψ is the M×N-dimensional observation matrix, Ψ is expressed as

where k _j ∈[1,ω], ψ _ij ∈Ψ, get y[j]=r[ω(j-1)+k _j ];

Step 2: Since the QPSK signal, OQPSK signal and π/4-DQPSK are four-phase shift modulation, the non-uniform sampling signal is subjected to fourth-order nonlinear transformation to obtain y ₄ , y ₄ [j]=(y[j]) ⁴ , j=0,1,...,M-1;

Step 3: Perform coarse reconstruction on the fourth-order nonlinear transformation of the non-uniform sampling signal to obtain the quartic spectrum u, and the coarse reconstruction method is u=ΦΨ ^H y ₄ , where u is the fourth power of N×1-dimensional reconstruction spectrum, Φ is the N×N-dimensional Fourier transform basis, that is, the Fourier transform is performed on Ψ ^H y ₄ ; the fourth power spectrum of the signal is obtained by the Fourier transform of the fourth-order nonlinear transformed signal, that

in

represents the Fourier transform;

Step 4: Find the positions of the 3 peaks with the largest 4th power spectrum u of the signal, denoted as F _max ={f _m1 , f _m2 , f _m3 }, where |u(f _m1 )|≥|u(f _m2 )|≥|u(f _m3 )|;

Step 5: Divide y ₄ into two segments of M/2×1-dimensional vectors y _4,1 and y _4,2 equally, and construct a new N/2×N/2-dimensional discrete Fourier basis Φ _N/2 , At the same time, the M×N-dimensional observation matrix Ψ is divided into four parts of M/2×N/2 dimensions as follows:

Step 6: Obtain the quadratic spectrum of the two slices u ₁ and u ₂ as: u ₁ =Φ _N/2 Ψ ₁ ^H y _4,1 , u ₂ =Φ _N/2 Ψ ₄ ^H y _4,2 ;

Step 7: Find the positions F _max,1 ={f _m1,1 ,f _m2,1 ,f _m3,1 _} and F _max,2 ₌ {f _{m1, 2} ,f _m2,2 ,f _m3,2 }, where |u ₁ (f _m1,1 )|≥|u ₁ (f _m2,1 )|≥|u ₁ (f _m3,1 )|, |u ₂ (f _m1,2 )|≥|u ₂ (f _m2,2 )|≥|u ₂ (f _m3,2 )|;

Step 8: Find the union F _max,o =F _max,1 ∪F _max,2 ;

Step 9: Find the intersection F _max,a =F _max ∩F _max,o ;

Step 10: Obtain the number of elements N _r in F _max,a ;

If N _r is 0, the modulation mode of the output identification result is 8PSK; if N _r is 1, the modulation mode of the output identification result is OQPSK; if N _r is 3, the modulation mode of the output identification result is QPSK; if N _r is 2, go to step 11 ;

Step 11: If N _r is 2, judge

Whether it is greater than the threshold η, if it is greater than η, the modulation mode of the output recognition result is QPSK; if it is less than or equal to η, the modulation mode of the output recognition result is π/4-DQPSK, where η=1.8.