CN116232824A - Parameter blind estimation method for measuring and controlling composite modulation signal - Google Patents
Parameter blind estimation method for measuring and controlling composite modulation signal Download PDFInfo
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Abstract
The invention discloses a parameter blind estimation method for measuring and controlling a composite modulation signal, and belongs to the field of signal processing. To realize modulation index K of composite modulation signal p The invention introduces the sum K for the first time p The related frequency domain characteristic index-power level ratio P is first generated by using the ideal complex modulation signal to generate a reference set (K p P), the construction method is described as: firstly, generating an ideal complex modulation signal set under a unified carrier system, wherein the modulation index K of the ideal complex modulation signal set p In [0.2,1.4 ]]The value of the inner non-equal interval is taken; generating a frequency spectrum by fast fourier transform; then the frequency domain spectral lines are rapidly sequenced to obtain spectral line components with maximum power level and second maximum power level, and the ratio of the spectral line components to the second maximum power level is calculated to obtain the power level ratio P to construct a mapping reference set (K p P). The actual modulation index estimation flow is as follows: the receiving end stores the reference set (K) p P), except that there is no a priori knowledge. Actual power level ratio
The calculation method of (2) is the same as the construction method of P; finally, three Hermite and cube-spline mixed interpolation methods are introduced to realize the debugging index K p And completes the demodulation flow.
Description
Technical Field
The invention belongs to the field of signal processing, in particular to parameter estimation, identification and demodulation flow design of a composite modulation signal.
Background
The composite modulation (Composite Modulation, CM) refers to a multi-layer modulation scheme that multi-user baseband data is modulated onto a unified carrier wave by adopting different modulation modes, and is a key technology for improving the transmission efficiency, the anti-interference capability and the safety of the aerospace measurement and control communication system. At present, the demand of space communication on cognitive radio is rapidly increased, and in order to realize the spectrum sharing, adaptive modulation and flexible transmission demands of a next generation measurement and control communication system, blind estimation on modulation parameters such as symbol rate, carrier frequency, modulation type and modulation index of a composite modulation signal is required. However, the composite modulation scheme introduces nonlinear coupling among multiple layers of modulation methods, and adds loss factors such as channel noise and large-scale frequency offset introduced by a space transmission channel, so that a receiving end accurately estimates the parameters and demodulates the parameters into baseband user information under the condition of no priori knowledge becomes a great challenge. Therefore, research on a new robust and efficient complex modulation signal parameter blind estimation method is widely focused.
The current blind parameter estimation method of the composite modulation signal is limited in research, and the blind parameter estimation method of the single modulation signal faces difficulties when being introduced into the composite modulation due to the complexity and nonlinearity of the composite modulation scheme. The traditional signal parameter estimation flow is 'post-demodulation estimation', in the process, demodulation depends on an accurate modulation index, and the estimation of the modulation index depends on a reliable demodulation signal, so that the dilemma causes the estimation of the modulation parameter to be in a dilemma without prior knowledge. Meanwhile, the theoretical optimal parameter Maximum Likelihood (ML) estimation algorithm under single modulation loses practicality due to the requirement of priori knowledge and huge calculation amount; the higher order accumulation (HOS) as a signal extractable feature performs well in parameter estimation of single modulation signals, but loses effectiveness when applied to complex modulation.
Modulation parameter K as an important component of the modulation parameter p The nonlinear modulation relation between all the residual modulation signals and the external main carrier wave is reflected, the frequency domain power distribution and the frequency spectrum characteristic of the residual modulation signals are directly influenced, but the estimation research of the parameters is more limited. In the estimation of the modulation index, the normalized Hilbert variation method directly estimates the modulation index by using the inverse solution of the time waveform of the received composite modulation signal, but the performance of the method is affected by phase synchronization, and the performance is obviously reduced due to the phase error under the low signal-to-noise ratio; in the modulation index estimation of the composite modulation signal aiming at the unified S-band (USB), the spectrum characteristic is extracted as a reliable signal characteristic, but the calculation amount of the whole estimation process is increased by solving the subsequent Bessel equation. How to eliminate the error influence caused by the phase noise as much as possible and reduce the calculation amount and complexity of the estimation process is an important technical problem focused and solved by the invention.
Disclosure of Invention
The invention aims to overcome the defects of the existing modulation index estimation method and construct a complete parameter estimation identification and demodulation flow aiming at the composite modulation signal of the aerospace measurement and control unified carrier system. The set of estimation flow has the advantages of effectively synchronizing phases, eliminating phase noise introduced by an aerospace link, along with less prior knowledge, and low calculation amount and complexity.
The invention provides a new extractable characteristic quantity based on the frequency domain spectral line characteristics of a composite modulation signal: power level ratio P, taking into account modulation index K p And the power level ratio P is an overrun function relationThe method introduces a mixed interpolation method combining segmented Hermite and Cubic-spline to approach the function relation, so as to give an estimated value of the modulation index and perform demodulation based on the estimated value.
The technical scheme of the invention is a parameter blind estimation method for measuring and controlling composite modulation signals, and the implementation process of the method comprises the following steps:
step 1: constructing an ideal complex modulation signal reference set (K p ,P)；
Step 1.1: generating an ideal complex modulation signal set;
the signal set contains five complex modulation signals under unified carrier system, namely PCM/BPSK/PM, PCM/QPSK/PM, PCM/BPSK1+BPSK2/PM, PCM/QPSK1+QPSK2/PM, PCM/BPSK+QPSK/PM, and the modulation index K of these signals p In [0.2,1.4 ]]The value of the internal non-equal interval is taken, the ideal composite modulation signal has no noise interference, and the phase noise and Doppler frequency shift are not considered; here a model of the transmitted signal s (t) of the ideal complex modulated signal is given:
wherein ,xB (t) is an equivalent low pass signal, f c Is the main carrier frequency phi 0 Is the initial phase of the primary carrier wave,
representing the real part->
x B (t) is:
wherein A represents the amplitude of the modulated signal, x I (t) represents the in-phase component, x, of the equivalent low-pass signal Q (t) represents the quadrature component of the equivalent low-pass signal; k (K) p Is the modulation index, s i (t) is an inner layer modulation signal, specifically divided into BPSK, QPSK and multi-user combination modes, wherein
The number of the inner layer modulation signals is represented, namely the number of users under a unified carrier system;
the signal model for the inner layer modulation is as follows:
s i (t)＝a i (t)cos(2πf i t+φ i,0 )-b i (t)sin(2πf i t+φ i,0 ) (5)
wherein ,
wherein ,ai(t) and bi (t) is two baseband signal code elements after pulse shaping, f i Is the carrier frequency of the inner layer residual carrier modulation, phi i,0 Is the initial phase of the inner layer residual carrier modulation, i refers to the number of inner layer modulated signals, i is taken
For baseband signal symbol a i(t) and bi (t), c i,k ，d i,k Are non-return-to-zero bipolar symbols g i (T) represents a rectangular pulse, T i Representing the duration of the ith shaped pulse, wherek represents the kth user information symbol;
step 1.2: transforming the ideal complex modulated signal to the frequency domain using a Fast Fourier Transform (FFT) method;
step 1.3: the spectral lines of the frequency domain are rapidly sequenced to obtain spectral line components with the maximum power level and the second largest power level, and the two spectral line components are respectively displayed on a main carrier omega=omega c ＝2πf c And the primary subcarrier frequency point; the primary subcarrier frequency points refer to:
ω＝ω c ±ω m ＝2π(f c ±f 1 ) (8)
omega when there is only one path of inner layer residual carrier modulation m ＝2πf 1 F of (f) 1 Refers to the subcarrier frequency; when the inner layer residual carrier modulation includes multipath, f 1 Refers to the subcarrier frequency with the smallest value, at this time omega m ＝2πf 1 ＝2πf m ；
Step 1.3: calculating the ratio of the two to obtain the power level ratio P, thus constructing a mapping reference set (K p ,P)；
Step 2: performing fast Fourier transform on one or more composite modulation signals actually received by a receiving end to generate a frequency spectrum of the composite modulation signals;
step 3: the spectral lines of the frequency domain are rapidly sequenced to obtain spectral line components with the maximum power level and the second largest power level, and the ratio of the maximum power level to the second largest power level is calculated to obtain the actual power level ratio
Step 4: in the stored reference set (K p Approximation of K using a hybrid interpolation method on the basis of P) p And P, and substitutes into
Obtaining modulation index estimated value->
Step 5: after obtaining the estimated value of the modulation index, demodulating the composite modulation signal to a baseband;
step 5.1: down-converting the received complex modulated signal;
step 5.2: phase synchronization of the main carrier is realized by using a phase-locked loop;
step 5.3: implementing the modulation index estimation flow to realize outer layer PM coherent demodulation;
step 5.4: branching of inner-layer multipath modulation signals is realized through a band-pass filter;
step 5.5: the inner layer modulation adopts a quadrature demodulation method for demodulation;
step 5.6: and outputting the demodulated multipath user information code elements, and calculating the error rate.
Further, the specific method in the step 4 is as follows:
step 4.1: from using the Hermit interpolation method 3 times
Mapping to +.>
The Hermit interpolation method is the function value y at a known node i ＝f(x i ) First derivative value y of corresponding node i ′＝f′(x i ) Solving an interpolation polynomial with equal function and derivative values; let the functional relationship be f (x), where x 0 ,x 1 The function value at is y 0 ,y 1 The first derivative has a value y' 0 ,y 1 ' 3 rd order Hermit polynomials as interpolation functions satisfy the following conditions:
obtaining 3-degree Hermit interpolation function representation of two nodes by using a basis function construction method:
H 3 (x)＝y 0 α 0 (x)+y 1 α 1 (x)+y 0 β 0 (x)+y 1 β 1 (x) (10)
in the formula ,α0 (x)，α 1 (x)，β 0 (x)，β 1 (x) Is an interpolation basis function, given its definition:
in the above, l 0 (x)＝x-x 1 /x 0 -x 1 ，l 1 (x)＝x-x 0 /x 1 -x 0 Combining equation (11), we get the expression of the 3 rd order Hermit interpolation function:
the estimated value expression of the modulation index under the 3-time Hermit interpolation method is deduced:
wherein, l=1, 2, m;
step 4.2: from using the cube-spline interpolation method
Mapping to +.>
Spline interpolation does not fit a single higher order polynomial to all data points at a time, but rather a geomagnetic polynomial to a small subset of data points; setting a modulation index K p And the power level ratio P is defined as f (x), and the power level ratio P is calculated in a stored reference set (K p M distinct nodes P (0), P (2), P (m-1) are taken from the P interval of P), and the corresponding modulation index value is K p (i) =f (P (i)), if the piecewise function S (x) satisfies the condition:
(1) S (x) is a polynomial of degree 3 or less over each subinterval [ P (i), P (i+1) ];
(2) S (x) has a second continuous derivative on P (i), i=0, 2, on each node;
(3) S (x) also satisfies the condition S (P) on node P (i), i=1, 2,..m i )＝K p (i),i＝0,1,2,...,m-1；
S (x) is used as a cubic spline interpolation function. In the cube-spline interpolation estimation flow, natural boundary conditions are selected to solve coefficients of an interpolation function, namely, primary derivative values of a Cubic spline interpolation function at nodes are equal to primary derivative values of an original function at the nodes;
S′(P i )＝f′(P i ),S′(P i+1 )＝f′(P i+1 ) (14)
then the estimate under the Cubic-spline interpolation is given by:
wherein the function gamma l (·)，β l (. Cndot.) is defined by the formula:
wherein, l=1, 2,..m-1;
the first derivative value of the interpolation function involved in the formula is determined as follows:
first, a mutually different boundary point P (i), i=1, 2, is set, and the interval length divided by m is d l ,l＝0,1,2,...,m-1
wherein wl Defined as follows:
in practical application, the invention embeds the two interpolation functions into callable functions, and directly calls the callable functions in the later estimation flow;
step 4.3: taking the average value of the two estimated values as the final estimated value to output
Compared with other complex modulation signal modulation index estimation methods, the method has the advantages of less prior knowledge, small final estimation error, high estimation precision of the modulation index, low final demodulation error rate, effective reduction of calculation complexity, avoidance of solving problems of an overrun equation in the modulation index estimation process, and excellent performance.
Drawings
FIG. 1 is a diagram of a novel composite modulation receiver architecture incorporating the modulation index blind estimation method of the present invention;
FIG. 2 is a graph showing the performance of NMSE in comparison with the blind estimation of the modulation index based on time-frequency analysis (TF) according to the blind estimation method of the modulation index of the present invention;
FIG. 3 is a graph showing the performance of NMSE for blind estimation of modulation index based on Spectral Analysis (SA) and the blind estimation of modulation index according to the present invention;
FIG. 4 is a graph of the interpolated reference set (K) constructed under non-equidistant sampling and uniform sampling methods p P) a graph comparing the effect of the estimated NMSE;
fig. 5 is a demodulation error rate diagram of PCM/BPSK/PM, PCM/QPSK/PM, where (a) is a demodulation error rate diagram of PCM/BPSK/PM, and (b) is a demodulation error rate diagram of PCM/QPSK/PM;
FIG. 6 is a diagram of the demodulation error rate of demodulation under a single subcarrier compared with the TF and SA methods;
FIG. 7 is a diagram of the demodulation error rate of PCM/BPSK1+BPSK2/PM, PCM/QPSK1+QPSK2/PM, and PCM/BPSK+QPSK/PM, wherein (a) is a diagram of the demodulation error rate of PCM/BPSK1+BPSK2/PM, (b) is a diagram of the demodulation error rate of PCM/QPSK1+QPSK2/PM, and (c) is a diagram of the demodulation error rate of PCM/BPSK+QPSK/PM;
fig. 8 is a diagram of demodulation error rate compared with TF and SA methods in demodulation under two-way subcarrier.
Detailed Description
According to the complex modulation signal modulation index estimation flow indicated by the present invention, the specific implementation of the present invention is divided into 3 parts: error performance analysis of modulation index, influence of reference set interval sampling method and final error rate performance analysis
1. Error performance analysis of modulation index
The invention provides an index for measuring the precision of a modulation index estimation scheme:
wherein W represents the total number of simulation tests,
represents the modulation index estimate for the ω -th trial, ω=1, 2,..>
Representing the true value of the modulation index for the omega trial.
In the present invention, 1000 experiments were performed in total, i.e. w=1000 for each signal to noise ratio (denoted by η). In each test at a given signal-to-noise ratio, the actual modulation index of 5 CM signals
From [0.2,1.4 ]]The range was randomly generated and other experimental parameters are shown in table (1). According to the modulation index estimation steps (2) - (4), an estimated value of the modulation index is obtained
Substituting formula (20) to calculateRoot mean square error. Meanwhile, the blind estimation method provided by the invention is also compared with the error performance of the two prior art methods in the background technology, as shown in a figure (2). It is seen that, for the above 5 CM signals, the modulation index blind estimation method of the present invention and all NMSEs generated by the existing time-frequency analysis technique decrease with the increase of the received signal-to-noise ratio. The NMSE produced by the method of the present invention (denoted by "-productive" in the figure) is always smaller (better) than the NMSE produced by the Existing time-frequency based analysis technique (denoted by "-extracting" in the figure), especially at low signal-to-noise ratio. In addition, for PCM/QPSK/PM signals with η=12 dB, the modulation index estimation method proposed by the present invention and the prior art can both obtain the result nmse≡0.0056. I.e. eta is not more than 12dB, the NMSE performance difference of the two methods is more obvious, and the superior performance of the method under the condition of low signal-to-noise ratio is shown.
Meanwhile, the method of the invention is also compared with the existing estimation method based on Spectrum Analysis (SA), as shown in a figure (3). Existing SA-based estimators employ two spectral line selection strategies, single Frequency (SF) and Double Frequency (DF), to estimate K p . According to fig. 3, the NMSE generated by the technique of the present invention is always smaller than the existing generated NMSE for any one of the complex modulated signals in the signal set.
From the analysis, the blind estimation method of the modulation index disclosed by the invention is used for estimating the modulation index K p The estimation of (2) is more accurate, and particularly shows better performance in a low signal-to-noise ratio scene.
2. Influence of reference set sampling interval
In step 1 of the present invention, 5 kinds of noiseless CM signals are used to construct corresponding reference data set pairs (K p P) is used as the basis for the hybrid interpolation scheme. In order to minimize the deviation caused by the "Dragon phenomenon" generated by the mixed interpolation, the invention proposes to apply the method to K p The elements in (a) are non-uniformly sampled, i.e. non-equally spaced. From Table (1), a predetermined interval Kp ε [0.2,1.4 ]]Divided into [0.2,0.6 ], [0.6, 1.0) and [1.0,1.4 ]]Three subintervals, the subintervals are 0.05, 0.1 and 0.05 in length, respectively. At the same time, and with the use of uniformly sampled reference dataThe modulation index estimation method of the set compares the performance of the average NMSE index, where the length of each subinterval divided uniformly is 0.06, and the other parameters remain consistent with table (1). The results are shown in FIG. 4
As seen from fig. 4, when the signal-to-noise ratio is lower than-5 dB, the NMSE performance under the two construction methods is similar; and at
Under the condition of high signal-to-noise ratio, the reference set constructed under the unequal interval sampling method is used as interpolation basis to be much smaller than the NMSE of uniform sampling, so the method of unequal interval sampling is adopted to construct the interpolation reference set in the invention.
3. Error rate performance analysis
In the module, the demodulation flow described in the step 5 is used to demodulate 5 signals in the signal set, and the error rate is used as an index for analysis.
3.1 CM signal demodulation of Single-channel subcarriers
First using different modulation indices (K p = 0.2,0.4,0.6,0.8..1.4) generating PCM/BPSK/PM signals and PCM/QPSK/PM signals, each signal having a sampling point number of 2 x 10 6 The number of experiments is 500, and then the error rate is demodulated and calculated at the receiving end through AWGN channel transmission, as shown in figure (5). And secondly, the invention is still compared with the prior TF and SA methods, and the average error rate is shown in a figure (6).
FIG. 5 shows the implementation of the blind estimation method of the modulation index proposed by the present invention for K p Causing the bit error rate to drop rapidly with increasing signal to noise ratio; compared with other existing methods and technologies, the modulation index blind estimation method provided by the invention always obtains better error rate performance, and for PCM/QPSK/PM signals, when eta is more than or equal to 9.14dB, the error rate of the receiver is lower than 10 -3 To achieve the same bit error rate performance, the other methods require a minimum of 10.63dB for η. Compared with the two technologies, the method has small calculation complexity.
3.2 CM demodulation of two-way subcarrier
Then using different modulation indexes (K p = 0.2,0.4,0.6,0.8, 1.4) PCM/bpsk1+bpsk2/PM, PCM/QPSK1+qpsk2/PM, PCM/BPSK+QPSK/PM signals, the number of sampling points of each signal is 2 x 10 6 The number of experiments is 500, and then the data is transmitted through an AWGN channel to be demodulated at a receiving end and the error rate is calculated. Fig. 7 shows the demodulation error rate performance of 3 signals, and fig. 8 shows the comparison with TF and SA methods.
FIG. 7 shows the implementation of the blind estimation method of the modulation index proposed by the present invention on K of two-way subcarriers p Causing the bit error rate to drop rapidly with increasing signal to noise ratio; compared with other existing methods and technologies, the modulation index blind estimation method provided by the invention always obtains better error rate performance; but when the received signal-to-noise ratio is [0dB,8dB]In the range, BER appears slightly higher than in the existing method, but the loss of bit error rate is tolerable compared to the reduction of computational complexity.
Table 1 below shows the interpolation reference data set (K p P). The specific use flow is as follows: the receiving end stores only the reference data set (K p P) and does not store other a priori knowledge. After receiving the actual complex modulated signal, the receiving end performs Fast Fourier Transform (FFT) according to the implementation process steps; quick sequencing of frequency domain spectral lines; calculating the ratio of the maximum spectral line to the next maximum spectral line to obtain the power level ratio of the actual received signal
Using the interpolation reference set (K) stored in table 1 p P) give the fall-on [0.2,1.4 ] using the hybrid interpolation method in the implementation step]Modulation index estimation in interval +.>
Table 1: the receiving end stores the interpolation reference set (K) p ,P)
Table 2 below is the simulation parameter settings during the implementation. The parameter settings of the table are given in accordance with a unified standard established by the spatial data systems Consultation Committee (CCSDS). For generating a complex modulated signal under a unified carrier regime.
Table 2: simulation parameter setting
| Parameters (parameters) | Numerical value |
| Radio Frequency (RF) frequency | 8GHz |
| Intermediate frequency of | |
| Subcarrier | |
| 1 | 8KHz |
| Subcarrier | |
| 2 frequency | 16KHz |
| Symbol rate | 4KSps |
| Sampling rate | 200MHz |
| Roll-off factor | 0.35 |
| Primary carrier initial phase | 0rad |
| Initial phase of subcarrier | 0rad |
| Transmission channel setup | AWGN |
| Signal to noise ratio (SNR, eta) | [-12dB,12dB] |
Claims (2)
1. A parameter blind estimation method for measuring and controlling composite modulation signals includes the following steps:
step 1: constructing an ideal complex modulation signal reference set (K p ,P)；
Step 1.1: generating an ideal complex modulation signal set;
the signal set contains five complex modulation signals under unified carrier system, namely PCM/BPSK/PM, PCM/QPSK/PM, PCM/BPSK1+BPSK2/PM, PCM/QPSK1+QPSK2/PM, PCM/BPSK+QPSK/PM, and the modulation index K of these signals p In [0.2,1.4 ]]The value of the internal non-equal interval is taken, the ideal composite modulation signal has no noise interference, and the phase noise and Doppler frequency shift are not considered; here a model of the transmitted signal s (t) of the ideal complex modulated signal is given:
wherein ,xB (t) is an equivalent low pass signal, f c Is the main carrier frequency phi 0 Is the initial phase of the primary carrier wave,
representing the real part->
x B (t) is:
wherein A represents the amplitude of the modulated signal, x I (t) represents the in-phase component, x, of the equivalent low-pass signal Q (t) represents the quadrature component of the equivalent low-pass signal; k (K) p Is the modulation index, s i (t) is an inner layer modulated signal, wherein
The number of the inner layer modulation signals is represented, namely the number of users under a unified carrier system;
the signal model for the inner layer modulation is as follows:
s i (t)＝a i (t)cos(2πf i t+φ i,0 )-b i (t)sin(2πf i t+φ i,0 ) (5)
wherein ,
wherein ,ai(t) and bi (t) is two baseband signal code elements after pulse shaping, f i Is the carrier frequency of the inner layer residual carrier modulation, phi i,0 Is the initial phase of the inner layer residual carrier modulation, i refers to the number of inner layer modulated signals, i is taken
For baseband signal symbol a i(t) and bi (t), c i,k ，d i,k Are non-return-to-zero bipolar symbols g i (T) represents a rectangular pulse, T i Representing the duration of the ith shaped pulse, where k represents the kth user information symbol;
step 1.2: transforming the ideal complex modulated signal to the frequency domain using a Fast Fourier Transform (FFT) method;
step 1.3: the spectral lines of the frequency domain are rapidly sequenced to obtain spectral line components with the maximum power level and the second largest power level, and the two spectral line components are respectively displayed on a main carrier omega=omega c ＝2πf c And the primary subcarrier frequency point; the primary subcarrier frequency points refer to:
ω＝ω c ±ω m ＝2π(f c ±f 1 ) (8)
omega when there is only one path of inner layer residual carrier modulation m ＝2πf 1 F of (f) 1 Refers to the subcarrier frequency; when the inner layer residual carrier modulation includes multipath, f 1 Refers to the subcarrier frequency with the smallest value, at this time omega m ＝2πf 1 ＝2πf m ；
Step 1.3: calculating the ratio of the two to obtain the power level ratio P, thus constructing a mapping reference set (K p ,P)；
Step 2: performing fast Fourier transform on one or more composite modulation signals actually received by a receiving end to generate a frequency spectrum of the composite modulation signals;
step 3: the spectral lines of the frequency domain are rapidly sequenced to obtain spectral line components with the maximum power level and the second largest power level, and the ratio of the maximum power level to the second largest power level is calculated to obtain the actual power level ratio
Step 4: in the stored reference set (K p Approximation of K using a hybrid interpolation method on the basis of P) p And P, and substitutes into
Obtaining modulation index estimated value->
Step 5: after obtaining the estimated value of the modulation index, demodulating the composite modulation signal to a baseband;
step 5.1: down-converting the received complex modulated signal;
step 5.2: phase synchronization of the main carrier is realized by using a phase-locked loop;
step 5.3: implementing the modulation index estimation flow to realize outer layer PM coherent demodulation;
step 5.4: branching of inner-layer multipath modulation signals is realized through a band-pass filter;
step 5.5: the inner layer modulation adopts a quadrature demodulation method for demodulation;
step 5.6: and outputting the demodulated multipath user information code elements, and calculating the error rate.
2. The blind estimation method for measuring and controlling parameters of composite modulation signals according to claim 1, wherein the specific method in step 4 is as follows:
step 4.1: from using the Hermit interpolation method 3 times
Mapping to +.>
The Hermit interpolation method is the function value y at a known node i ＝f(x i ) First derivative value y of corresponding node i ′＝f′(x i ) Solving an interpolation polynomial with equal function and derivative values; let the functional relationship be f (x), where x 0 ,x 1 The function value at is y 0 ,y 1 The first derivative has a value y' 0 ,y′ 1 3 times Hermit polynomialAs an interpolation function, the following condition is satisfied:
obtaining 3-degree Hermit interpolation function representation of two nodes by using a basis function construction method:
H 3 (x)＝y 0 α 0 (x)+y 1 α 1 (x)+y 0 β 0 (x)+y 1 β 1 (x) (10)
in the formula ,α0 (x)，α 1 (x)，β 0 (x)，β 1 (x) Is an interpolation basis function, given its definition:
in the above, l 0 (x)＝x-x 1 /x 0 -x 1 ，l 1 (x)＝x-x 0 /x 1 -x 0 Combining equation (11), we get the expression of the 3 rd order Hermit interpolation function:
the estimated value expression of the modulation index under the 3-time Hermit interpolation method is deduced:
wherein, l=1, 2, m;
step 4.2: from using the cube-spline interpolation method
Mapping to +.>
Spline interpolation does not fit a single higher order polynomial to all data points at a time, but rather a geomagnetic polynomial to a small subset of data points; setting a modulation index K p And the power level ratio P is defined as f (x), and the power level ratio P is calculated in a stored reference set (K p M distinct nodes P (0), P (2), P (m-1) are taken from the P interval of P), and the corresponding modulation index value is K p (i) =f (P (i)), if the piecewise function S (x) satisfies the condition:
(1) S (x) is a polynomial of degree 3 or less over each subinterval [ P (i), P (i+1) ];
(2) S (x) has a second continuous derivative on P (i), i=0, 2, on each node;
(3) S (x) also satisfies the condition S (P) on node P (i), i=1, 2,..m i )＝K p (i),i＝0,1,2,...,m-1；
S (x) is used as a cubic spline interpolation function. In the cube-spline interpolation estimation flow, natural boundary conditions are selected to solve coefficients of an interpolation function, namely, primary derivative values of a Cubic spline interpolation function at nodes are equal to primary derivative values of an original function at the nodes;
S′(P i )＝f′(P i ),S′(P i+1 )＝f′(P i+1 ) (14)
then the estimate under the Cubic-spline interpolation is given by:
wherein the function gamma l (·),β l (. Cndot.) is defined by the formula:
wherein, l=1, 2,..m-1;
the first derivative value of the interpolation function involved in the formula is determined as follows:
first, a mutually different boundary point P (i), i=1, 2, is set, and the interval length divided by m is d l ,l＝0,1,2,...,m-1
wherein wl Defined as follows:
in practical application, the invention embeds the two interpolation functions into callable functions, and directly calls the callable functions in the later estimation flow;
step 4.3: taking the average value of the two estimated values as the final estimated value to output
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| CN113014523A (en) * | 2021-02-25 | 2021-06-22 | 电子科技大学 | Composite modulation signal blind identification method based on fusion characteristics |
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| CN110764067A (en) * | 2019-10-15 | 2020-02-07 | 哈尔滨工程大学 | Fourier transform LFM-BPSK composite modulation radar signal parameter estimation method |
| CN113014523A (en) * | 2021-02-25 | 2021-06-22 | 电子科技大学 | Composite modulation signal blind identification method based on fusion characteristics |
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