CN108696468B - Parameter estimation method of two-phase coding signal based on undersampling - Google Patents

Parameter estimation method of two-phase coding signal based on undersampling Download PDF

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CN108696468B
CN108696468B CN201810380229.0A CN201810380229A CN108696468B CN 108696468 B CN108696468 B CN 108696468B CN 201810380229 A CN201810380229 A CN 201810380229A CN 108696468 B CN108696468 B CN 108696468B
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CN108696468A (en
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付宁
邓立宝
曹杰
黄国兴
乔立岩
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Harbin Institute of Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/18—Phase-modulated carrier systems, i.e. using phase-shift keying
    • H04L27/20—Modulator circuits; Transmitter circuits
    • H04L27/2032—Modulator circuits; Transmitter circuits for discrete phase modulation, e.g. in which the phase of the carrier is modulated in a nominally instantaneous manner
    • 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
    • H04L27/2626—Arrangements specific to the transmitter only
    • H04L27/2627—Modulators
    • H04L27/264—Pulse-shaped multi-carrier, i.e. not using rectangular window
    • 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

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Abstract

The invention discloses a parameter estimation method of a two-phase coding signal based on undersampling, and relates to a parameter estimation method of a two-phase coding signal. The invention aims to solve the problem of overhigh sampling rate in the prior art. The multichannel parallel sampling system provided by the invention can realize the undersampling of BPSK signals, and the lowest equivalent sampling rate is only
Figure DDA0001640762960000011
Accurate estimation of the signal parameters is possible. When the signal frequency is very high, the sampling method can complete sampling and parameter estimation at a rate far less than the Nyquist sampling frequency, and can greatly reduce the pressure of sampling equipment. For band-limited signals with bandwidth B, the sampling rate of the invention is that of the Nyquist sampling rate
Figure DDA0001640762960000012
And (4) doubling. Aiming at non-band-limited signals, Nyquist sampling can not realize sampling without information loss theoretically, and the sampling rate of the invention is
Figure DDA0001640762960000013
The invention is used in the field of communication signal processing.

Description

Parameter estimation method of two-phase coding signal based on undersampling
Technical Field
The invention relates to the field of communication signal processing, in particular to a parameter estimation method of a two-phase coding signal based on undersampling.
Background
Binary Phase Shift Keying (BPSK) belongs to Phase modulation, is a relatively important class in digital modulation, is widely applied to pulse compression radar, and can obtain a large time-bandwidth product. And the signal has wide application in digital communication systems. Estimation of BPSK signal parameters is a prerequisite and basis for decoding the signal. Therefore, the parameter estimation method for the BPSK signal has high research value.
There are many scholars who show great interest in the estimation of parameters of BPSK signals, and many methods for the estimation of parameters of BPSK signals have appeared. In 1983, Veter a J and Veterbi AM proposed methods for maximum likelihood estimation. A series of carrier frequency estimation methods based on this has emerged later. Gardner proposed the cycle spectrum theory in 1986, after which many cycle spectrum-based parameter estimation methods were proposed, which have been widely used in the field of communications. In 2000, Mounir Ghogho et al proposed a nonlinear frequency estimation method, which can convert the frequency estimation of BPSK signals into the frequency estimation of single-frequency-point signals, and has a good effect. Estimation of the symbol length for BPSK signals is done primarily using wavelet transforms. The above methods can all achieve estimation of BPSK signal parameters. But we know from nyquist's sampling theorem that in order to fully reconstruct an analog signal from sampled samples, the sampling rate must be greater than or equal to twice the signal bandwidth. If the sampling rate does not meet the Nyquist sampling theorem, the spectrum aliasing will be caused, and the signal parameters cannot be accurately distinguished. As the signal bandwidth increases, the pressure on the sampling equipment increases, and high-speed sampling also leads to increased pressure on back-end data storage and data processing. It is therefore necessary to study methods for undersampling parameter estimation of signals.
BPSK signals can be characterized by a finite number of parameters, i.e., the frequency location and complex amplitude of a set of segmented sinusoidal signals, which can be expressed as follows:
Figure GDA0002611560730000011
whereinIs the amplitude of the signal, tau is the duration of the signal,
Figure GDA0002611560730000013
is the number of symbols, T (T ≦ τ/D) Is the symbol length of the signal. For BPSK, cdIs 0 or 1, and is randomly selected. The phase function of the signal may be defined by the following equation.
Figure GDA0002611560730000014
Wherein f iscIs the carrier frequency of the signal and,
Figure GDA0002611560730000021
is the initial phase of the signal and takes the value of [0,2 pi]And (4) internal random selection. The pi (t) function is defined as follows:
Figure GDA0002611560730000022
for ease of analysis, formula one is rewritten as:
Figure GDA0002611560730000023
wherein A, T and fcThe definition of (A) is as above.
Figure GDA0002611560730000024
Is the number of segments the signal is separated by phase jumps.
Figure GDA0002611560730000025
Is composed of an initial phase
Figure GDA0002611560730000026
And modulation phase ckFunction ξ of π compositionk(t) is defined as follows:
ξk(t)＝u(t-tk)-u(t-tk+1)，0≤t1＜…＜tK+1＜τ
where u (t) is a step function. From the above analysis of the BPSK signal form, we can see that the BPSK signal can be defined by a finite number of parameters A, fc、
Figure GDA0002611560730000027
To indicate.
Due to the parametrizable nature of BPSK signals, several sub-nyquist sampling schemes have been proposed for BPSK signals. The domestic electronic science and research team proposes to combine the compressive sensing theory with the cyclic spectrum of the signal, realize the undersampling of the signal and complete the estimation of the carrier frequency. In 2010, Jesse Berent provides an undersampling method based on a limited new information rate for a segmented sinusoidal signal, and can realize the estimation of carrier frequency, amplitude, phase and discontinuity position of the signal through a small number of frequency domain samples. However, the number of sampling points required by the existing under-sampling method is large, and the estimation effect is unstable in a noise environment. To date, there is no stable, few samples, easy to implement, under-sampling scheme for BPSK signals, and it is important to design a simple and effective under-sampling structure.
Disclosure of Invention
The invention aims to solve the problem of overhigh sampling rate in the prior art, and provides a parameter estimation method of a two-phase coding signal based on undersampling.
A parameter estimation method based on an undersampled two-phase coded signal comprises the following steps:
the method comprises the following steps: the signal x (t) enters the channel alpha and the channel beta simultaneously after passing through the power divider Y; dividing a signal x (t) in a channel alpha into two paths through a power divider Y1, and then obtaining a signal Y (t) through a multiplier after self-multiplication;
step two: the main channel and the delay channel are simultaneously at the sampling rate
Figure GDA0002611560730000028
Uniformly sampling y (t) to obtain a sampling value y [ n ] of the main channel]The sampling value of the delay path being ye[n]，TsFor a sampling time interval, the number of samples in the main channel and the delay channel is N and N, respectivelyeN is more than or equal to 1, NeNot less than 1; the delay channel is delayed by T compared with the main channeleSatisfy the following requirements
Figure GDA0002611560730000031
fcIs the signal carrier frequency;
step three: from the sampled values y [ n ]]And ye[n]Obtaining an estimate of the carrier frequency using a rotation subspace invariant algorithm
Figure GDA0002611560730000032
Estimation of sum amplitude
Figure GDA0002611560730000033
n is a discrete count value of the channel α;
step four, in the channel β, the signal x (t) passes through a low-pass filter with the bandwidth of B to obtain a signal z (t) with a sampling rate
Figure GDA0002611560730000034
The signal z (t) is sampled,
Figure GDA0002611560730000035
for a sampling interval, obtaining sampled values
Figure GDA0002611560730000036
Is a discrete count value for channel β;
step five: based on the value of the sample
Figure GDA0002611560730000037
Combining the Filter obtained in step three with a nulling Filter (Annihilating Filter)
Figure GDA0002611560730000038
Obtaining an estimate of a discontinuity
Figure GDA0002611560730000039
And phase estimation
Figure GDA00026115607300000310
The invention has the beneficial effects that:
the multichannel parallel sampling system provided by the invention can realize the under-sampling of BPSK signals, and the lowest equivalent sampling rate is only
Figure GDA00026115607300000311
And signal parameters can be accurately estimated. When the signal frequency is very high, the sampling method provided by the invention can complete sampling and parameter estimation at a rate far less than the Nyquist sampling frequency, and can greatly reduce the pressure of sampling equipment.
(1) For band-limited signals with bandwidth B, the sampling rate of the invention is that of the Nyquist sampling rate
Figure GDA00026115607300000312
And (4) doubling.
(2) Aiming at non-band-limited signals, Nyquist sampling can not realize sampling without information loss theoretically, and the sampling rate of the invention is
Figure GDA00026115607300000313
Embodiments of the present invention may illustrate that the sampling rate of the present invention is 0.19 percent of the nyquist sampling.
Drawings
FIG. 1 is a block diagram of a multi-channel parallel sampling system;
FIG. 2 shows carrier frequency f of each method under different SNRcEstimating an effect graph;
FIG. 3 shows the discontinuity point position t of each method under different SNRkEstimating an effect graph;
FIG. 4 shows the phase of each method under different SNR
Figure GDA00026115607300000314
And estimating an effect map.
In the figure, Nyquist is a Nyquist sampling method, EXP is a sampling method based on an exponential kernel, Parallel is a sampling method based on multichannel Parallel, the abscissa Input SNR of the figure is an Input signal-to-noise ratio, and the ordinate NMSE is a normalized mean square error.
Detailed Description
The first embodiment is as follows: a parameter estimation method based on an undersampled two-phase coded signal comprises the following steps:
aiming at the problem of parameter estimation of BPSK signals, the invention provides an under-sampling method based on a multi-channel parallel structure. The sampling structure provided by the method of the invention has two parts, namely a channel alpha and a channel beta, and the estimation of different parameters of the signal is respectively realized. The signal is subjected to signal self-multiplication in a channel alpha to remove modulation information, then the low-speed sampling is carried out by a two-channel time delay sampling structure, and the estimation of the signal amplitude and the carrier frequency is realized by utilizing an ESPRIT algorithm. The signal is sampled at low speed after being filtered by a low-pass Filter in a channel beta, and the position and the phase of the discontinuity point of the signal can be estimated from a sampling value by utilizing an nulling Filter (Annihilating Filter) in combination with carrier frequency information estimated by the channel alpha. The specific structural block diagram is shown in fig. 1.
The method comprises the following steps: the signal x (t) enters the channel alpha and the channel beta simultaneously after passing through the power divider Y; dividing a signal x (t) in a channel alpha into two paths through a power divider Y1, and then obtaining a signal Y (t) through a multiplier after self-multiplication;
step two: the main channel and the delay channel are simultaneously at the sampling rate
Figure GDA0002611560730000041
Uniformly sampling y (t) to obtain a sampling value y [ n ] of the main channel]The sampling value of the delay path being ye[n]，TsFor a sampling time interval, the number of samples in the main channel and the delay channel is N and N, respectivelyeN is more than or equal to 1, NeNot less than 1; the delay channel is delayed by T compared with the main channeleSatisfy the following requirements
Figure GDA0002611560730000042
fcIs the signal carrier frequency;
step three: from the sampled values y [ n ]]And ye[n]Obtaining an estimate of the carrier frequency using a rotation subspace invariant algorithm
Figure GDA0002611560730000043
Estimation of sum amplitude
Figure GDA0002611560730000044
n is a discrete count value of the channel α;
step four, in the channel β, the signal x (t) passes through a low-pass filter with the bandwidth of B to obtain a signal z (t) with a sampling rate
Figure GDA0002611560730000045
The signal z (t) is sampled,
Figure GDA0002611560730000046
for a sampling interval, obtaining sampled values
Figure GDA0002611560730000047
Is a discrete count value for channel β;
step five: based on the value of the sample
Figure GDA0002611560730000048
Obtained by combining the zeroing filter with the third step
Figure GDA0002611560730000049
Obtaining an estimate of a discontinuity
Figure GDA0002611560730000051
And phase estimation
Figure GDA0002611560730000052
The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: the expression of the signal y (t) in the first step is as follows:
Figure GDA0002611560730000053
where A is the amplitude of the signal x (t), t is the time, τ is the duration of the signal, j is the imaginary unit,
Figure GDA0002611560730000054
for the initial phase of the signal, K is the number of segments of the signal x (t) separated by phase jumps ξk(t) is an intermediate variable, ξk(t)＝u(t-tk)-u(t-tk+1)，0≤t1＜…＜tK+1< τ, u (t) is a step function, tkIs the position of a discontinuity caused by a phase jump;
for bi-phase coded signals, ckTake a value of 0 or 1, and thus
Figure GDA0002611560730000055
y (t) is written as:
wherein the intermediate variable
Figure GDA0002611560730000057
It can be seen that the modulation information of the signal x (t) is removed from the multiplication, and y (t) can be regarded as a piece of complex exponential signal.
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the present embodiment differs from the first or second embodiment in that: in the second step, y [ n ]]And ye[n]The expression of (a) is:
Figure GDA0002611560730000058
Figure GDA0002611560730000059
other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the difference between this embodiment mode and one of the first to third embodiment modes is: in the third step, the sampling value y [ n ] is used as the basis]And ye[n]Obtaining an estimate of the carrier frequency using a rotation subspace invariant algorithm
Figure GDA00026115607300000510
Estimation of sum amplitude
Figure GDA00026115607300000511
The specific process of n being the discrete count value of the channel α is as follows:
step A: the sampling values of the main channel and the delay channel are expressed in a matrix form: y ═ Y [ 0%],y[1],…y[N-1]]，Ye＝[ye[0],ye[1],…ye[Ne-1]]And Y ═ YeD, wherein the expression of the intermediate matrix D is as follows:
Figure GDA0002611560730000061
and B: calculating an intermediate matrix phi according to a rotation subspace invariant algorithm by the following formula, wherein the matrix phi and the intermediate matrix D have the same characteristic value;
Φ＝(Y*Y)-1Y*Ye(6)
when in use
Figure GDA0002611560730000062
Then, the carrier frequency is determined by the characteristic value of the intermediate matrix phi;
Figure GDA0002611560730000063
wherein, the angle is taken, and the eig is taken as a characteristic value;
and C: carrier frequency to be estimated
Figure GDA0002611560730000064
Substituting into equation (3) to estimate amplitude
Figure GDA0002611560730000065
A′＝YV-1(8)
Wherein the intermediate variable
Figure GDA0002611560730000066
Amplitude A of the signal is passed
Figure GDA0002611560730000067
And (6) estimating.
Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the difference between this embodiment and one of the first to fourth embodiments is: sampling value in the fourth step
Figure GDA0002611560730000068
The expression of (a) is:
Figure GDA0002611560730000069
wherein
Figure GDA00026115607300000610
Is the number of sample samples for channel β,
Figure GDA00026115607300000611
other steps and parameters are the same as in one of the first to fourth embodiments.
The sixth specific implementation mode: the difference between this embodiment and one of the first to fifth embodiments is: in the fifth step, according to the sampling value
Figure GDA00026115607300000612
Obtained by combining the zeroing filter with the third step
Figure GDA00026115607300000613
Obtaining an estimate of a discontinuity
Figure GDA00026115607300000614
And phase estimation
Figure GDA00026115607300000615
The specific process comprises the following steps:
step five, first: by sampling values
Figure GDA00026115607300000616
Computing signal FourierCoefficient of the number Z [ m ] of the leaf stage]Assuming the low pass filter in path β is an ideal filter, the sampled values can be passed
Figure GDA00026115607300000617
Fourier coefficient Z [ m ] of signal Z (t) is calculated],|m|≤M。
Figure GDA0002611560730000071
Wherein m is a discrete count value of the frequency spectrum;
step five two: obtaining Fourier series coefficient Z [ m ]]And a discontinuity tkAnd phase
Figure GDA0002611560730000072
The relationship of (1);
Figure GDA0002611560730000073
wherein
Figure GDA0002611560730000074
Let the intermediate variable
Figure GDA0002611560730000075
If it is
Figure GDA0002611560730000076
Then:
Figure GDA0002611560730000077
wherein the intermediate variable
Figure GDA0002611560730000078
And A is0＝0,Ak+1＝0；
Step five and step three: calculating filter coefficients for nullizable Q (m) zm;
Figure GDA0002611560730000079
Figure GDA00026115607300000710
where H (z) is a nulling filter and z is a count variable of the z transform domain;
2M +1 is 2(K +1) +1 continuous Fourier series coefficients Z [ M ], and the coefficients h [ K ] of the zero filter are obtained by calculation according to a formula (13);
step five and four: estimating parameters from nulling filter coefficients
Figure GDA00026115607300000711
And
Figure GDA00026115607300000712
filter coefficient h [ k ]]Substituting into formula (12) to obtain the root of the filter, and estimating
Figure GDA00026115607300000713
Will be provided with
Figure GDA0002611560730000081
And
Figure GDA0002611560730000082
substituting into formula (11), calculating to obtain the estimate of intermediate variable
Figure GDA0002611560730000083
According to the formula
Figure GDA0002611560730000084
Calculate out
Figure GDA0002611560730000085
Phase passing
Figure GDA0002611560730000086
And (4) calculating.
The multichannel parallel sampling system provided by the invention needs N to be more than or equal to 1 continuous samplingSample values y [ n ]]And NeMore than or equal to 1 continuous sampling value ye[n]And
Figure GDA0002611560730000087
a continuous sampling value
Figure GDA0002611560730000088
Duration of the signal is tau, sampling rate f of the main channelsNeed to satisfy fsIs more than or equal to 1/tau. The sampling rate of the parallel channels needs to be satisfied
Figure GDA0002611560730000089
The invention passes through the equivalent sampling rate fsysTo evaluate the system, the equivalent sampling rate is defined as the total number of samples taken over time τ. The equivalent sampling rate of the present invention can be calculated by the following formula:
Figure GDA00026115607300000810
the minimum equivalent sampling rate is
Figure GDA00026115607300000811
Other steps and parameters are the same as those in one of the first to fifth embodiments.
The first embodiment is as follows:
in order to verify the performance of the method, the sampling system provided by the invention is compared with the existing Nyquist sampling system and the index regeneration nuclear sampling system for analysis.
The system performance of the following three sampling methods is first compared by table one. For carrier frequency of fcThe BPSK signal of (1), signal duration τ, contains K segments. The Nyquist sampling system requires that the sampling rate is not less than 2 times of the signal bandwidth, and the BPSK signal is a non-band-limited signal, so the Nyquist sampling method can not sample the BPSK signal without information loss theoreticallys＝20fc. Exponential regeneration nuclear sampling system proposed by Jesse Berent et alThe total sampling rate needs to satisfy
Figure GDA00026115607300000812
The sampling rate of the invention needs to meet
Figure GDA00026115607300000813
The specific parameter settings are shown in table one:
table-simulation parameter set-up
Figure GDA00026115607300000814
Figure GDA0002611560730000091
As can be seen from table one, the sampling rate of the nyquist sampling method is related to the carrier frequency, and a higher sampling rate is required when the carrier frequency is larger. The sampling rate of the method and the method of the index kernel is only related to the segment number and the duration of the signal, so the method has great advantages when processing high-frequency signals.
For quantitative description of the accuracy of parameter estimation, comparison is facilitated. Normalized Mean Square Error (NMSE) was introduced as an evaluation index.
Figure GDA0002611560730000092
Figure GDA0002611560730000093
Figure GDA0002611560730000094
Wherein f isk、tkAnd
Figure GDA0002611560730000095
is a parameter that is true to the user,
Figure GDA0002611560730000096
and
Figure GDA0002611560730000097
is an estimated value.
Consider the case of no noise. BPSK signal modulated by 11-bit Barker code, i.e. the number of signal segments K equals 7, the carrier frequency f of the signalc250MHz, signal duration is set to τ -1 e-6sec, symbol period set to Tb＝8e-8sec, the signal start time is set to 0.1 τ. Initial phase of signal
Figure GDA0002611560730000098
At [0,2 π]And (4) internal random selection. The sampling rate in the Nyquist sampling scheme is set to 10GHz, the system sampling rate of the multichannel parallel sampling structure provided by the invention is 19MHz, and the sampling rate of the exponential regeneration kernel sampling is set to 25 MHz. The recovered parameter and original parameter pairs are shown in graph two. It can be seen from table two that the three methods are accurate in estimating the carrier frequency and the discontinuity point position. The exponential regeneration kernel has a certain error in estimating the phase.
Table two parameter recovery comparison
Figure GDA0002611560730000099
Figure GDA0002611560730000101
Example two:
the experiment is used for analyzing the performance of the method provided by the invention under the noise condition, Gaussian white noise is superposed on a signal, and the input signal-to-noise ratio is defined by the following formula:
Figure GDA0002611560730000102
in this experiment, the signal duration was set to τ -1 e-7sec, multichannel parallel sampling systems and exponential regenerative nuclear sampling systemsThe effective sampling rate is set to be 1GHz, the sampling rate of the Nyquist sampling system is set to be 10GHz, and the other parameters are the same as the first experiment. The input signal-to-noise ratio was varied from-20 dB to 100dB, and 100 times of experiments were performed, and the average recovery results were obtained as shown in fig. 2 to 4.
As can be seen from fig. 2 to fig. 4, the sampling structure provided by the present invention still has higher noise robustness under the condition of fewer sampling samples, and can more accurately estimate the carrier frequency, the position of the discontinuity point, and the phase parameter.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.

Claims (6)

1. A method for estimating parameters of an under-sampled two-phase encoded signal, comprising: the parameter estimation method based on the two-phase coding signal of undersampling comprises the following steps:
the method comprises the following steps: the signal x (t) enters the channel alpha and the channel beta simultaneously after passing through the power divider Y; dividing a signal x (t) in a channel alpha into two paths through a power divider Y1, and then obtaining a signal Y (t) through a multiplier after self-multiplication;
step two: the main channel and the delay channel are simultaneously at the sampling rate
Figure FDA0002611560720000011
Uniformly sampling y (t) to obtain a sampling value y [ n ] of the main channel]The sampling value of the delay path being ye[n]，TsFor a sampling time interval, the number of samples in the main channel and the delay channel is N and N, respectivelyeN is more than or equal to 1, NeNot less than 1; the delay channel is delayed by T compared with the main channeleSatisfy the following requirements
Figure FDA0002611560720000012
fcIs the signal carrier frequency;
step three: from the sampled values y [ n ]]And ye[n]Obtaining an estimate of the carrier frequency using a rotation subspace invariant algorithm
Figure FDA0002611560720000013
Estimation of sum amplitude
Figure FDA0002611560720000014
n is a discrete count value of the channel α;
step four, in the channel β, the signal x (t) passes through a low-pass filter with the bandwidth of B to obtain a signal z (t) with a sampling rate
Figure FDA0002611560720000015
The signal z (t) is sampled,
Figure FDA0002611560720000016
for a sampling interval, obtaining sampled values
Figure FDA0002611560720000017
Figure FDA0002611560720000018
Is a discrete count value for channel β;
step five: based on the value of the sample
Figure FDA0002611560720000019
Obtained by combining the zeroing filter with the third step
Figure FDA00026115607200000110
Obtaining an estimate of a discontinuity
Figure FDA00026115607200000111
And phase estimation
Figure FDA00026115607200000112
2. The method of claim 1, wherein the method comprises: the expression of the signal y (t) in the first step is as follows:
Figure FDA00026115607200000113
where A is the amplitude of the signal x (t), t is the time, τ is the duration of the signal, j is the imaginary unit,
Figure FDA00026115607200000114
for the initial phase of the signal, K is the number of segments of the signal x (t) separated by phase jumps ξk(t) is an intermediate variable, ξk(t)＝u(t-tk)-u(t-tk+1)，0≤t1＜…＜tK+1< τ, u (t) is a step function, tkIs the position of a discontinuity caused by a phase jump;
for bi-phase coded signals, ckTake a value of 0 or 1, and thus
Figure FDA0002611560720000021
y (t) is written as:
Figure FDA0002611560720000022
wherein the intermediate variable
Figure FDA0002611560720000023
3. A method for parameter estimation based on an undersampled bi-phase encoded signal according to claim 1 or 2, characterized by: in the second step, y [ n ]]And ye[n]The expression of (a) is:
Figure FDA0002611560720000024
Figure FDA0002611560720000025
4. a method for parameter estimation based on an undersampled bi-phase encoded signal according to claim 3, characterized in that: in the third step, the sampling value y [ n ] is used as the basis]And ye[n]Obtaining an estimate of the carrier frequency using a rotation subspace invariant algorithm
Figure FDA0002611560720000026
Estimation of sum amplitude
Figure FDA0002611560720000027
The specific process of n being the discrete count value of the channel α is as follows:
step A: the sampling values of the main channel and the delay channel are expressed in a matrix form: y ═ Y [ 0%],y[1],…y[N-1]]，Ye＝[ye[0],ye[1],…ye[Ne-1]]And Y ═ YeD, wherein the expression of the intermediate matrix D is as follows:
Figure FDA0002611560720000028
and B: calculating an intermediate matrix phi according to a rotation subspace invariant algorithm by the following formula, wherein the matrix phi and the intermediate matrix D have the same characteristic value;
Φ＝(Y*Y)-1Y*Ye(6)
when in use
Figure FDA0002611560720000029
Then, the carrier frequency is determined by the characteristic value of the intermediate matrix phi;
Figure FDA00026115607200000210
wherein, the angle is taken, and the eig is taken as a characteristic value;
and C: carrier frequency to be estimated
Figure FDA0002611560720000031
Substituting into equation (3) to estimate amplitude
Figure FDA0002611560720000032
A′＝YV-1(8)
Wherein the intermediate variable
Figure FDA0002611560720000033
Amplitude A of the signal is passed
Figure FDA0002611560720000034
And (6) estimating.
5. The method of claim 4, wherein the method comprises: sampling value in the fourth step
Figure FDA0002611560720000035
The expression of (a) is:
Figure FDA0002611560720000036
wherein
Figure FDA0002611560720000037
Is the number of sample samples for channel β,
Figure DEST_PATH_FDA0001640762930000038
6. the method of claim 5, wherein the method comprises: in the fifth step, according to the sampling value
Figure FDA0002611560720000039
Using zero filtersCombining the results obtained in step three
Figure FDA00026115607200000310
Obtaining an estimate of a discontinuity
Figure FDA00026115607200000311
And phase estimation
Figure FDA00026115607200000312
The specific process comprises the following steps:
step five, first: by sampling values
Figure FDA00026115607200000313
Calculating Fourier series coefficient Z m of signal]；
Figure FDA00026115607200000314
Wherein m is a discrete count value of the frequency spectrum;
step five two: obtaining Fourier series coefficient Z [ m ]]And a discontinuity tkAnd phase
Figure FDA00026115607200000319
The relationship of (1);
Figure FDA00026115607200000315
wherein
Figure FDA00026115607200000316
Let the intermediate variable
Figure FDA00026115607200000317
If it is
Figure FDA00026115607200000318
Then:
Figure FDA0002611560720000041
wherein the intermediate variable
Figure FDA0002611560720000042
And A is0＝0,Ak+1＝0；
Step five and step three: calculating filter coefficients for nullizable Q (m) zm;
Figure FDA0002611560720000043
Figure FDA0002611560720000044
where H (z) is a nulling filter and z is a count variable of the z transform domain;
2M +1 is 2(K +1) +1 continuous Fourier series coefficients Z [ M ], and the coefficients h [ K ] of the zero filter are obtained by calculation according to a formula (13);
step five and four: estimating parameters from nulling filter coefficients
Figure FDA0002611560720000045
And
Figure FDA0002611560720000046
filter coefficient h [ k ]]Substituting into formula (12) to obtain the root of the filter, and estimating
Figure FDA0002611560720000047
Will be provided with
Figure FDA0002611560720000048
And
Figure FDA0002611560720000049
substituting into formula (11), calculating to obtain the estimate of intermediate variable
Figure FDA00026115607200000410
According to the formula
Figure FDA00026115607200000411
Calculate out
Figure FDA00026115607200000412
Phase passing
Figure FDA00026115607200000413
And (4) calculating.
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