CN111327549A

CN111327549A - Orthogonal analysis normal-mode signal recovery method

Info

Publication number: CN111327549A
Application number: CN202010138071.3A
Authority: CN
Inventors: 樊宽刚; 刘平川; 王文帅; 陈宇航; 杨杰; 杨斌
Original assignee: Buddhist Tzu Chi General Hospital
Current assignee: Jiangxi Permanent Magnet Maglev Technology Co ltd
Priority date: 2020-03-03
Filing date: 2020-03-03
Publication date: 2020-06-23
Anticipated expiration: 2040-03-03
Also published as: CN111327549B

Abstract

A method for recovering orthonormal mode signal includes optimizing and improving orthogonality of signal source; the method comprises the following specific steps: initializing and setting a signal source, and setting the signal source to be recovered as a normal mode signal which is orthogonal to each other; using an antenna array to receive signals, and after receiving a signal source S, transmitting a signal X AS an AS for the subsequent steps to carry out relevant processing; and signal modulus recovery is carried out by utilizing the orthogonality and the constant mode characteristic of a signal source. And according to the orthogonality of the signal source, a new limiting condition in signal recovery is given

Performing signal phase recovery by using a Gerchberg-Saxton iterative mode; carrying out signal recovery performance evaluation by using the average modulus error and the bit error rate; the signal recovery is complete and it is moved into blind equalization. The signal recovered by the method provided by the invention has higher accuracy, anti-interference capability and fewer limiting conditions.

Description

Orthogonal analysis normal-mode signal recovery method

Technical Field

The invention relates to the technical field of wireless communication, in particular to a method for recovering orthogonal analysis normal-mode signals.

Background

Blind equalization and blind estimation are important problems in the field of signal processing, and adaptive antenna matrices are commonly used to solve such problems. Blind estimation mainly focuses on estimation of the number of signal sources and estimation of the arrival angle of signals. Blind equalization focuses more on compensating for signal distortions in the channel and separates and recovers the original signal from the various signals received by the antennas through an antenna array. At present, instruments and equipment in various industries increasingly adopt a wireless communication mode to carry out communication between modules or systems, and a typical application scene of blind equalization and blind separation is signal processing in a wireless communication system. The blind equal-balance signal recovery technology ensures the accuracy of the wireless signal after multi-channel transmission, can recover useful parts in the original signal, and actually ensures the stability of a wireless communication system.

The Constant Modulus Algorithm (CMA) is a classic Algorithm for blind equalization and blind estimation, and has the characteristics of low computational complexity, easy implementation and good convergence. However, CMA also has problems of slow convergence rate, large steady-state error, and the like.

An Analytical Constant Modulus method (ACMA) is an improved Constant Modulus method, which uses the idea of mathematically extracting characteristic values to realize a blind equalization signal recovery method with faster convergence rate and wider limiting conditions. However, it is not considered that if the signal sources have the characteristic of mutual orthogonality, the method finds the limiting condition of the optimal weight vector and changes to a certain extent, so that the signal recovery accuracy still has a space to be improved, and particularly the signal recovery accuracy needs to be improved under the condition of strong noise interference. If the analysis normal mode method is used, the accuracy of signal recovery of the device using orthogonality between signals is not high enough, and communication is likely to be unstable in a severe communication environment.

Further optimization and improvement of the orthogonality of ACMA-based signal sources is therefore needed.

In the patent application of the invention, the meanings of technical words and formula parameters are as follows:

1. blind Equalization (Blind Equalization): an unknown input signal sequence is recovered through an output signal of an unknown channel. Are commonly used to compensate for channel, signal distortion in wireless communication systems.

2. Blind Estimation (Blind Estimation): on the basis of not knowing the initial signal information, the information related to the target signal, such as the number of signal sources, the angle at which the signal is transmitted to the antenna, etc., is estimated.

3. Constant Modulus Algorithm (CMA): a classic algorithm of blind equalization and blind estimation has the characteristics of low computational complexity, easiness in implementation and good convergence.

4. Analytical constant modulus method (ACMA): an improved constant modulus method can quickly recover original signals by using a linear algebra and matrix theory method.

5. Kernel function: a function that maps data to a high dimension.

Househodler transformation: transforming a vector into a mirror image reflected by a hyperplane

QZ decomposition: a matrix decomposition method can extract eigenvalues of a matrix.

QR decomposition: a matrix decomposition method decomposes a matrix into a normal orthogonal matrix and an upper triangular matrix.

The meaning of the parameters of each formula is:

w^Trepresents transposition;

represents conjugation;

w^*represents a conjugate transpose;

represents a column vector;

represents a row vector;

representing vector i (when i occurs in this form, identifying the different vectors);

represents the inner product;

pinv () represents the generalized inverse;

row () represents the row space of the matrix;

()_ifor a matrix, the ith row of a matrix is represented, and for a vector, the ith element is represented;

()ⁱrepresents the ith column of the matrix;

()_ijelements representing the ith row and the jth column;

SVD (X) is a singular value decomposition of the X matrix.

Technical scheme

The invention aims to disclose a method for recovering an orthogonal analytic normal mode signal, which optimizes and improves the orthogonality of a signal source on the basis of ACMA. The invention distinguishes the target normal mode signal from other abnormal mode signals, compensates the interference caused by noise or other signals and can recover the target signal.

In order to achieve the technical object of the present invention, a method for recovering an orthonormal mode signal includes the steps of:

the method comprises the following steps: and initializing and setting a signal source, and setting the signal source to be recovered as a normal mode signal which is orthogonal to each other.

Step two: signals are received using an antenna array. After the antenna receives the signal source S, the transmission signal X is AS for the subsequent steps to perform related processing.

Step three: and signal modulus recovery is carried out by utilizing the orthogonality and the constant mode characteristic of a signal source. And according to the orthogonality of the signal source, a new limiting condition in signal recovery is given

Step four: the signal phase recovery is performed using a Gerchberg-Saxton iterative approach.

Step five: and evaluating the signal recovery performance by using the average modulus error and the bit error rate.

Step six: the signal recovery is complete and it is moved into blind equalization.

Further, the step two of establishing a data model of the signal received through the antenna specifically includes:

X＝AS (1)

wherein X represents the output signal of each antenna and A represents the response matrix of the antenna; s represents the signal source matrix, for a total of d rows,

respectively corresponding to d different signals; having delta normal-mode signals in the signal source matrix, using

To represent the portion of the normal mode signal in the signal source matrix; in reality, the received signal may be represented as noise interference

N represents a noise matrix; the weight matrix is denoted W, W ═ pinv (a);

representing each row weight vector corresponding to each signal sequence; the formula (1) can be expressed as a formula (2) after conversion;

without loss of generality, the modulus values of all normal-mode signals can be converted to 1 by linear transformation.

Further, the third step of performing signal modulus recovery by using the signal source orthogonality and the normal mode characteristic specifically comprises:

for a known matrix X: m × n dimension with rank d, if a suitable W: δ × m can be found to satisfy the condition

We can recover the normal mode signal in S, where

Is a normal mode signal sequence;

according to the normal mode characteristic and the orthogonal characteristic of the signal source, through vector inner product representation, Householder transformation, addition of new orthogonal limiting conditions and expansion of a QZ iteration method, the conditions required to be met by the signal can be transformed, parameter vectors corresponding to different weight limits are calculated, proper weight vectors are taken out through the parameter vectors, and the proper weight vectors are obtained through the parameter vectors

The modulus of the signal is restored. Calculated weight vector

Is subjected to linear transformation to make its modulus n^1/2Thereby meeting the requirement that the modulus of the recovered normal-mode signal is 1.

Further, the phase recovery problem is solved by using Gerchberg-Saxton iteration in the fourth step, specifically:

to solve the phase recovery problem, the pair

Performing Gerchberg-Saxton (GS) iterations

Due to interference from noise and other factors, via

The calculated and recovered signals also have a certain phase difference, and the problem of the phase difference caused by noise and interference can be effectively recovered after GS iteration is adopted.

Further, the fifth step uses the average modulus error and the bit error rate to perform signal recovery performance evaluation, specifically:

after the phase difference is compensated, a recovered normal-mode signal can be obtained; using mean modulus error

And bit error rate

To judge the signal recovery effect.

Further, step six completes signal recovery, and applies OCMA to blind equalization, specifically:

after an original signal s passes through a linear time invariant LTI channel and is selected, under the condition of interference, a blind equalizer is regulated and controlled by adopting an OCMA method, so that the signal is recovered; because the signal source continuously sends signals circularly, if the factor is considered in the method, a limit condition is added; based on the cyclic transmission signal characteristics and linear transformation of the signal source, new constraints can be obtained

Adding it to the original constraints, and then using the same method, the normal mode signal can be successfully recovered.

Compared with the existing analytic Constant Modulus method (ACMA), the orthogonal analytic Constant Modulus signal recovery method has the following beneficial effects:

1. compared with ACMA, the signal recovered by the method provided by the invention has higher accuracy;

2. the method has higher robustness, and has better anti-interference capability than ACMA under the condition that the communication environment is noisy;

3. fewer constraints are required compared to other improved CMA methods;

4. the CMA converges faster than other improvements;

5. wide application range, and can be used for all devices using signal source orthogonality to transmit signals

The invention is further illustrated by the following specific embodiments in conjunction with the accompanying drawings.

Drawings

FIG. 1 is a diagram illustrating a typical application scenario of OCMA;

FIG. 2 is a diagram of a process of blind equalization using OCMA;

FIG. 3 is a flow block diagram of the present invention;

fig. 4a is a graph of the average modulus error of channel 1 at SNR of 20 dB;

fig. 4b is a graph of the average modulus error for channel 2 at SNR of 20 dB;

fig. 4c is a plot of the mean modulus error of channel 3 for SNR 20 dB;

fig. 4d is a graph of the mean modulus error of channel 4 at SNR of 20 dB;

fig. 5a is a recovering constellation diagram of OCMA signal of S1 channel under SNR of 20 dB;

fig. 5b is the recovery constellation diagram of OCMA signal of S2 channel under SNR of 20 dB;

fig. 5c is the recovery constellation diagram of OCMA signal of S3 channel under SNR of 20 dB;

fig. 5d is the recovery constellation diagram of OCMA signal of S4 channel under SNR of 20 dB;

fig. 5e is the ACMA signal recovery constellation of S1 channel at SNR of 20 dB;

fig. 5f is the ACMA signal recovery constellation of S2 channel at SNR of 20 dB;

fig. 5g is the ACMA signal recovery constellation of S3 channel at SNR of 20 dB;

fig. 5h is the ACMA signal recovery constellation of S4 channel at SNR of 20 dB;

FIG. 6aa is a comparison of the error rates of S1 for four channels;

fig. 6ab is a comparison graph of the bit error rate of S2 for four channels;

FIG. 6ac is a comparison graph of the bit error rate of S3 for four channels;

FIG. 6 illustrates a comparison of the bit error rate of S4 for four channels;

FIG. 6ba is a comparison graph of the error rate of S2 for three channels;

fig. 6bb is a comparison graph of the bit error rate of S3 for three channels;

FIG. 6bc is a comparison graph of the error rate of S4 for three channels;

FIG. 6ca is a comparison graph of the bit error rate of S3 for two channels;

FIG. 6cb is a comparison of the bit error rate of S4 for two channels;

fig. 7aa is a visual diagram of OCMA signal recovery when SNR is 10 dB;

fig. 7ab is a visual diagram of ACMA signal recovery when SNR is 10 dB;

FIG. 7ac is a graph comparing the mean modulus error of the two algorithms at SNR of 10 dB;

FIG. 7ba is a diagram showing the recovery of OCMA signal when SNR is 20 dB;

fig. 7bb is a visual diagram of ACMA signal recovery when SNR is 20 dB;

FIG. 7bc is a comparison graph of the mean modulus error of the two algorithms when SNR is 20 dB;

FIG. 7ca is a visual diagram of the recovery of the OCMA signal when the SNR is 30 dB;

fig. 7cb is a visual diagram of ACMA signal recovery when SNR is 30 dB;

fig. 7cc is a comparison graph of the mean modulus error of the two algorithms at SNR of 30 dB.

Detailed Description

The core idea of the Orthogonal analysis normal mode signal recovery method (OCMA) of the invention is as follows: the problem of separation, decomposition and recovery of the normal mode signals which are mutually orthogonal is converted into a characteristic value problem. First, all the normal mode signals are orthogonal and independent to each other, and the mode value is set to be 1. It is assumed that there are several signal sources with the same frequency at different positions in space, and signals are sent out at the same time. FIG. 1 shows typical applications of OCMAWith a schematic view, as shown in fig. 1, a signal from a signal source is received by an antenna array. In a typical application scenario of this signal recovery, the signal S in space₁…S_dTypically, the signal source is transmitted to an antenna X in an arbitrary direction, and the X transmits the received signal to a beamformer for beamforming. Then giving a proportional weight w, and then obtaining a recovered signal S after recovery₁…S_d。

Fig. 3 is a flow chart of the present invention, and as shown in fig. 3, a specific embodiment of a method for recovering an orthogonal analytic normal mode signal of the present invention is:

step one A1: and initializing and setting a signal source to be recovered into normal-mode signals which are orthogonal to each other.

Step two A2: signals are received using an antenna array.

Modeling data of signals received via an antenna as

X＝AS (1)

Where X represents the output signal of each antenna and a represents the response matrix of the antenna. S represents the signal source matrix, for a total of d rows,

corresponding to d different signals, respectively. Having delta normal-mode signals in the signal source matrix, using

To represent the portion of the signal source matrix that is normally mode. In reality, the received signal may be represented as noise interference

N represents a noise matrix. The weight matrix is denoted by W, which is pinv (a).

Is a weight vector for each row corresponding to each signal sequence. The formula (1) can be expressed as formula (2) by conversion.

Without loss of generality, the modulus values of all normal-mode signals can be converted to 1 by linear transformation. In the operation process, due to the existence of noise, certain influence can be generated on the independence of the normal-mode signals by some transformations, but the influence is small and can be ignored. The number of sampling points is represented by n, and the response matrix A and the normal mode signal matrix

With full rank and sufficient phase richness, the influence of these transformations on the independence is smaller as n is increased. The invention aims to recover a normal-mode signal matrix

X in the real world represents the signal we receive through the antenna and is therefore known in practice. We then find the appropriate W to recover the signal source.

Step three A3: and signal modulus recovery is carried out by utilizing the orthogonality and the constant mode characteristic of a signal source.

We can recover the normal mode signal in S, where

Is a sequence of normal mode signals. Defining a cost function

Where row (X) represents the line space of X, we want the cost function

As small as possible. The recovered normal-mode signal should satisfy

The first term in formula (4) may be represented by [ U, ∑, V ]]Svd (x). If there are d signal sources, then the rank of X is d, there will be d non-zero singular values. We select the vectors corresponding to the non-zero singular values in V to form a new matrix

Then

May constitute a set of bases of row (x), the first condition in equation (4) may be rewritten as

In the formula (5), the reaction mixture is,

representing the weight vector acting on row (x) orthonormal basis, we need to estimate W: δ × m to be reduced from m-dimension to d-dimension,

now a vector of dimension 1 × d

To represent

Column i. Then

The second constraint of the formula (4) can be rewritten as

Definition of

Because of the fact that

Is known, then P_kIs known, then the problem to be solved translates to find a linearly independent weight vector

Can satisfy

For convenient calculation, the vector is calculated according to the matrix Y: d × d

Define the following two transformation modes

Can be handled by a formula (7)

Conversion to inner product form

The condition that needs to be satisfied

Can be converted into

Then all the

Grouped into a matrix P n × d²In (1).

The problem we need to solve translates into finding all linearly independent vectors

Can satisfy

For each one

We can calculate its corresponding normal mode signal

When i ≠ j, use

And

representing different signal sequences, since we set the normal-mode signals to be orthogonal to each other, we can obtain

Further obtain

Defining a matrix

G d × d, can be obtained

Order to

Then can obtain

Take a constant

We can define one

The solution space of equation (11) can be expressed as

Wherein

Is a particular solution of the formula (11),

is the basis of a P-kernel function, c₁,…,c_nFor ease of computation, we find a unitary matrix M of (n +1) × (n +1) dimensions that satisfies

M may be a Householder transformation matrix

Applying M to K can result in

By these definitions, we can convert the satisfaction of conditional expression (11) into

Through the above transformation, the problem to be solved becomes to find all linear independent solutions

Satisfy the requirement of

As

A basis for the kernel function, any solution of equation (16)

Can all be expressed as

In this expression, let us say

Is a parameter vector. Then order

The solution of equation (16) can be expressed as

Each linear independent solution

All correspond to linearly independent solutions

And each non-zero parameter vector

As

The basis of the kernel function is then determined,

can pass through the pair

Singular value vectors corresponding to singular values of 0 are obtained by singular value decomposition. When in use

After being solved by singular value decomposition, the problem we need to solve finally turns into for a given matrix X and calculated Y₁…Y_δWe need to find all linear non-zero parameter vectors

So that it satisfies

For the case of two matrices, the iterative computation can be performed using the QZ iterative method, but not for multiple matrices. We need to solve Y using an extended QZ iteration method₁…Y_δWhile diagonalizing, delta > 2. The expanded QZ iterative method can enable us to find two matrixes Q and Z, and the two matrixes are connected with Y₁…Y_δBy multiplication, we can obtain a rough upper triangular matrix R₁…R_δWherein R is_k＝QY_kZ, k is 1, …, δ, which corresponds to the extraction of the eigenvalues of the matrix. Q and Z are obtained by iteration method, and initial values are set as Q⁽⁰⁾＝I，Z⁽⁰⁾I. Assuming that the iteration stops by the end of the k-th step, k is 1,2, …. We need to find a Q^(k)So that

Minimum; find a Z^(k)Make it

And minimum. | | non-woven hair_LFRepresenting the Frobenius norm of the lower triangular matrix.

In the k-th iteration step, we assume the matrix R₁＝Q^(k-1)Y₁Z^(k-1),…,R_δ＝Q^(k-1)Y₁Z^(k-1)Instead of approximating the triangular matrix, we need to find a unitary matrix Q that can transform R₁…R_δThe norm of the lower triangular matrix of (a) is minimized. For a single matrix R₁In other words, Q may be regarded as the Householder transformation matrix H₁,…,H_d-1The product of (c) is obtained by QR decomposition. H_iCan make the matrix R₁…R_δThe ith column of the lower triangular array is close to 0, H_iThe column corresponding to the self-influence will not influence other columns. H_iCan pass through

And (5) resolving. Q can be represented as

After finding the appropriate Q, the next step is to find the appropriate Z. Z is calculated similarly to Q, except that Z is represented by T_iComposition of T_iAnd H_iSimilarly, by

And (6) calculating.

Q, Z are obtained and then multiplied to Y in left and right directions respectively₁…Y_δIn this way, R of an approximate upper triangular matrix can be obtained₁…R_δElement on diagonal line thereofThe elements may be approximated as eigenvalues. Then R is₁…R_δAll eigenvalues of (a) are put into a matrix R.

Let A be R^-1，

Given by the row of a. Now has worked out

Then need to be satisfied

Is/are as follows

It can also be calculated that,

that is, after each Y is subjected to singular value decomposition, the singular value vector corresponding to the largest singular value. Calculated

Step four A4: the phase recovery problem is solved using a Gerchberg-Saxton iteration.

To solve the phase recovery problem, the pair

Performing Gerchberg-Saxton (GS) iterations

Due to interference from noise and other factors, via

The signal recovered by calculation also has a certain phase difference. r is₁/r₂(cos(θ₁-θ₂)+i sin(θ₁-θ₂) Can be used to explain the phenomenon that produces constellation rotation in a constellation diagram, where r represents the modulus of the signal and θ represents the phase angle of the signal.

Step five A5: and evaluating the signal recovery performance by using the average modulus error and the bit error rate.

And bit error rate

To judge the signal recovery effect.

Step six a 6: signal recovery is done and OCMA is applied to blind equalization.

Fig. 2 shows a flow chart of a process of blind equalization using OCMA, in which an original signal s is subjected to signal selection via a linear time invariant LTI channel, and then a blind equalizer is adjusted and controlled by using an OCMA method under the condition of interference, so as to recover the signal, as shown in fig. 2. Since the signal source continuously sends signals circularly, if the factor is considered in the method of the present invention, a restriction condition is added. This limitation is caused by

To obtain wherein

And

representing the behavior of the weight vector of the same channel at different time instants, in an ideal situationBoth are equal. Thus B is equal to 0, equivalent to BB ^*0, available

Order to

In the formula:

in fact, by linear transformation, the redundant part in the equations (23) and (24) can be eliminated. Order to

A new constraint is derived

Adding it to OCMA K to obtain

The normal mode signal can be successfully recovered by using the same method.

In simulation, ACMA and OCMA are used for simultaneously recovering the same group of signal sources, and the recovery effect is observed. Normal mode part in signal source

The QPSK signal is adopted, the number of the antennas is m to 4, the antenna spacing is set to be lambda/2, wherein lambda represents the wavelength of the carrier signal of the signal source. Suppose that there are 4 signal sources and all signal sources emit normal mode signals, and the angle of arrival θ is 0 °,30 °,60 °, 20 °]And all normal mode signals have a modulus value of 1. In order to make the recovered signal accurate, n > d must be satisfied²Sample n is taken as 200, and SNR is 20 dB. After the signals are recovered, the average modulus error of the signals recovered by the ACMA algorithm and the OCMA algorithm is calculated, and the results are shown in fig. 4a, b, c, and d. Fig. 4a, b, c and d are the average modulus error contrast of the signal recovery of 4 channels under the SNR of 20dB, respectively, and these four graphs represent four different channels, respectively, and are used to compare the signals recovered by the OCMA method and the ACMA method, and the difference in modulus from the original signal, where a value is about small, indicates that the effect is better, and it can be seen from these four graphs that the OCMA method is more accurate than the signal recovered by the ACMA, where the SNR is 20 dB. The GS iteration is the Gerchberg-Saxton iteration, which can reduce the mean modulus error of the signal by increasing the number of iterations, but looks like two straight lines because the convergence rates of ACMA and OCMA are extremely fast, because the GS iteration is performed up to 2 steps before it converges more or less.

Fig. 5a, b, c and d are the recovering constellations of S1, 2, 3 and 4 channel OCMA signals respectively under SNR 20dB, fig. 5e, f, g and h are the recovering constellations of S1, 2, 3 and 4 channel ACMA signals respectively under SNR 20dB, which is the recovering effect of the constellation diagram observing two algorithms, as shown in fig. 5a, b, c, d, e, f, g and h, these 8 constellations are used for relatively intuitive observation, whether the recovered signals are recovered in place in phase, it can be seen that both ACMA and OCMA can recover phase, and the effect is not much.

Fig. 6aa, ab, ac and ad are time error code rate comparison diagrams of the channels S1, S2, S3 and S4, respectively, as shown in fig. 6aa, ab, ac and ad, when the signal recovery of each channel is compared in 4 channels, the error rate gradually decreases with the increase of the signal-to-noise ratio. It can be seen that the signal recovered by OCMA generally has a lower error rate under the same signal-to-noise ratio. Defining that if a signal is recovered, the average modulus error is above 0.35, and then the signal is determined as a recovery error, and the error rate is

s _ error represents the number of signals recovering the error, and compares the error of ACMA with that of OCMA in the case of multiple channelsAnd (4) rate.

Fig. 6ba, bc and bd are time error rate comparison graphs of channels S2, S3 and S4, respectively, and it can be seen that under the condition of the same signal-to-noise ratio, the signal recovered by OCMA generally has a lower error rate.

Fig. 7aa is a visual diagram of OCMA signal recovery when SNR is 10 dB; fig. 7ab is a visual diagram of ACMA signal recovery when SNR is 10 dB; FIG. 7ac shows the average modulus error comparison for the two algorithms at SNR of 10 dB; fig. 7ba is a diagram of an OCMA signal recovery diagram when the SNR is 20dB, fig. 7bb is a diagram of an ACMA signal recovery diagram when the SNR is 20dB, and fig. 7bc is a diagram of a comparison of average modulus errors when the SNR is 20 dB; FIG. 7ca is a visual diagram of the recovery of the OCMA signal when the SNR is 30 dB; fig. 7cb is a visual diagram of ACMA signal recovery when SNR is 30 dB; FIG. 7cc is a comparison of modulus error at SNR of 30 dB;

as shown in the figure, it is shown that under the condition of different signal-to-noise ratios, the signal recovery can be observed to determine whether the signal recovery is good or bad, all of the figures take the channel S1 as an example, and the two methods are respectively used for comparing the signal recovery, the original signal waveform is represented by a straight line, and the recovered signal is represented by a star line.

To aid in further understanding the invention, but will be understood by those skilled in the art: various substitutions and modifications are possible without departing from the spirit and scope of the invention and appended claims. Therefore, the invention should not be limited to the embodiments disclosed, but the scope of the invention is defined by the appended claims.

Claims

1. A method for recovering an orthogonal analytic normal mode signal comprises the following steps:

the method comprises the following steps: initializing and setting a signal source, and setting the signal source to be recovered as a normal mode signal which is orthogonal to each other;

step two: using an antenna array to receive signals, and after receiving a signal source S, transmitting a signal X AS an AS for the subsequent steps to carry out relevant processing;

step three: signal modulus recovery is carried out by utilizing the orthogonality and the normal mode characteristics of a signal source; and according to the orthogonality of the signal source, a new limiting condition in signal recovery is given

Step four: performing signal phase recovery by using a Gerchberg-Saxton iterative mode;

step five: carrying out signal recovery performance evaluation by using the average modulus error and the bit error rate;

2. The method according to claim 1, wherein the method further comprises: establishing a data model of the signals received by the antenna in the second step specifically comprises the following steps:

X＝AS (1)

N represents a noise matrix; the weight matrix is denoted W, W ═ pinv (a);

represents each row weight vector corresponding to each signal sequence; the formula (1) can be expressed as a formula (2) after conversion;

3. The method according to claim 1, wherein the method further comprises: and step three, signal modulus recovery is carried out by utilizing the signal source orthogonality and the constant modulus characteristic, and the method specifically comprises the following steps:

We can recover the normal mode signal in S, where

Is a normal mode signal sequence;

according to the normal mode characteristic and the orthogonal characteristic of the signal source, the conditions required to be met by the signal can be converted through the inner product representation of vectors, Householder transformation, addition of new orthogonal limiting conditions and expansion of a QZ iteration method, the appropriate weight vector is taken out through the parameter vector by calculating the parameter vector corresponding to different weight limits, and the appropriate weight vector is taken out through the parameter vector

The modulus of the signal is restored. Calculated weight vector

4. The method according to claim 1, wherein the method further comprises: and step four, solving the phase recovery problem by using Gerchberg-Saxton iteration, specifically:

to solve the phase recovery problem, the pair

Performing Gerchberg-Saxton (GS) iterations

Due to interference from noise and other factors, via

5. The method according to claim 1, wherein the method further comprises: and step five, evaluating the signal recovery performance by using the average modulus error and the bit error rate, specifically:

And

to judge the signal recovery effect.

6. The method according to claim 1, wherein the method further comprises: step six, completing signal recovery, and applying OCMA to blind equalization, specifically:

the original signal s, after signal selection through linear time invariant LTI channel, is interferedUnder the condition, an OCMA method is adopted to regulate and control the blind equalizer so as to recover the signal; because the signal source continuously sends signals circularly, if the factor is considered in the method, a limit condition is added; based on the cyclic transmission signal characteristics and linear transformation of the signal source, new constraints can be obtained

Adding it to the original constraints, and then using the same method, successfully recovering the normal mode signal.