CN109688076B - Blind detection method of noise chaotic neural network based on discrete multi-level hysteresis - Google Patents

Abstract

The invention discloses a blind detection method of a noise chaotic neural network based on discrete multi-level hysteresis, which comprises the following steps: constructing a received data matrix X _N ; performing singular value decomposition on the received data matrix X _{N ;} And construct the performance function; introduce the piecewise annealing function into the chaotic neural network, construct the discrete multilevel hysteresis chaotic neural network based on the piecewise annealing; construct the new improved model of the noise chaotic neural network based on the discrete multilevel hysteresis. Equation, iterative operation is performed on the dynamic equation of the improved new model, and then the result of each iteration is substituted into the energy function E(t) of the noise chaotic neural network based on discrete multilevel hysteresis, when the energy function E (t) reaches the minimum value, the discrete multi-level hysteresis chaotic neural network reaches equilibrium, and the iteration ends. The invention improves the activation function to construct a noise chaotic neural network model with discrete multi-level hysteresis, and better avoids the neural network from falling into the minimum value point.

Description

Blind detection method of noise chaotic neural network based on discrete multi-level hysteresis

Technical Field

The invention relates to a blind detection method of a noise chaotic neural network based on discrete multilevel hysteresis, belonging to the field of wireless communication signal processing, in particular to the technical field of Hopfield neural network blind detection.

Background

With the wide application of the Discrete Hopfield Neural network in image restoration, associative memory and the like, the Stability of the network is the basis of the applications, and the network is stabilized to an immobile point in the end, and the documents [ Gao h.s., Zhang j., Stability for Discrete Hopfield Neural Networks with Delay [ C ].2008 source International Conference on Natural Computation, Jinan, China, October 18-20,2008, 560-. The documents [ H.J.Liu, Y.Sun.Blanket level image restoration using Hopfield Neural Networks [ A ]. Proceedings of IEEE International Conference on Neural Networks [ C ], San Francisco, CA, USA, Mar.1993(3): 1656) -1661 ] are also restricted to real Neural Networks. Literature [ zhu, complex Hopfield neural network blind signal detection [ D ]. Nanjing: nanjing post and telecommunications university library, 2012:102-147 ], and a document [ Ruixikkai, Zhang aspiration ] QAM signal blind detection based on a continuous Hopfield type neural network [ J ] electronic and informatics, 2011 (7 in 2011): 1-6 ] respectively propose discrete multi-level complex and continuous multi-level complex Hopfield neural networks, but are easy to fall into local minimum points, and the required data volume length is large. In order to overcome the problems, the invention improves the annealing function after introducing the Chaotic Neural Network (Complex-valued transient Neural Network Real-imaging-type Hard-Multistate-activation-functional CTCNN-RIHM) to avoid falling into the local optimal solution, adopts the piecewise annealing function to accelerate the convergence speed of blind detection, introduces random noise to enable the Chaotic Neural Network to better avoid a local minimum point, and proposes to introduce hysteresis characteristics into the Chaotic Neural Network according to the response characteristics of the hysteresis in the Neural Network to change the activation function to construct the hysteresis activation function. Then, a signal blind detection method (Complex-valued Hysteresis noise Hopfield Neural Network Real-imaging-type Hard-Multistate-activation-function HNCTCNN _ RIHM) of the noise Chaotic Neural Network based on discrete multi-level Hysteresis is provided, a new activation function is constructed, and the search efficiency of the Chaotic Neural Network is improved.

Disclosure of Invention

In order to overcome the defects of the prior art and the performance problem of the chaotic neural network method, the invention provides a blind detection method of the noise chaotic neural network based on discrete multi-level hysteresis by utilizing the characteristics of random noise and hysteresis in the neural network, and further improves the performance of the blind detection method of the chaotic neural network.

The invention adopts the following technical scheme: the blind detection method of the noise chaotic neural network based on discrete multi-level hysteresis is characterized by comprising the following steps of:

step SS 1: constructing a received data matrix X_N；

Step SS 2: for the received data matrix X_NPerforming singular value decomposition;

step SS 3: setting a weight matrix W_RIConstructing a performance function;

step SS 4: introducing a piecewise annealing function into the chaotic neural network, and constructing a discrete multi-level chaotic neural network based on piecewise annealing;

step SS 5: introducing random noise on the basis of the discrete multilevel chaotic neural network subjected to segmented annealing in the step SS4, constructing a discrete multilevel noise-based chaotic neural network, improving a traditional activation function, introducing a hysteresis activation function to improve the error code performance of a blind detection method, constructing a dynamic equation of an improved new model of the discrete multilevel hysteresis-based chaotic neural network, performing iterative operation on the dynamic equation of the improved new model, substituting the result of each iteration into an energy function E (t) of the discrete multilevel hysteresis-based chaotic neural network, and when the energy function E (t) reaches the minimum value, balancing the discrete multilevel hysteresis chaotic neural network and finishing the iteration.

As a preferred embodiment, the constructing of step SS1 receives a data matrix X_NThe method specifically comprises the following steps: the receiving end receives a signal sent by a single user, and a receiving equation of a discrete time channel is obtained through sampling:

X_N＝SΓ^T

in the formula, X_NIs a matrix of received data, S is a matrix of transmitted signals, and Γ is a matrix of channel impulse responses h_jjA constructed block Toeplitz matrix; (.)^TRepresenting the transpose of the matrix.

As a preferred embodiment, the transmission signal matrix S in step SS1 is:

S＝[s_L+M(k),L,s_L+M(k+N-1)]^T＝[s_N(k),L,s_N(k-M-L)]_N×(L+M+1)；

wherein, M is the channel order, L is the equalizer order, and N is the required data length; s_L+M(k)＝[s(k),L,s(k-L-M)]^T(ii) a The time k is a natural number;

the channel impulse response h in the step SS1_jjComprises the following steps: h is_jj＝[h₀,L,h_M]_q×(M+1)Jj ═ 0,1, L, M; q is an oversampling factor, and takes the value of a positive integer;

the received data matrix in step SS1 is: x_N＝[x_L(k),L,x_L(k+N-1)]^TIs N × (L +1)_qReceiving a data matrix, wherein x_L(k)＝Γ·s_L+M(k)。

As a preferred embodiment, step SS2 specifically includes:

for the received data matrix X_NSingular value decomposition is carried out, namely:

in the formula (DEG)^HIs the Hermitian transpose;

u is a nx (L + M +1) unitary matrix in singular value decomposition;

0 is an (N- (L + M +1)) × (L +1) q zero matrix;

v is (L +1) qx (L +1) q unitary matrix;

U_cis N × (N- (L + M +1)) unitary matrix;

d is a (L + M +1) × (L +1) q singular value matrix.

As a preferred embodiment, step SS3 specifically includes: setting a weight matrix W_RI＝[A-Q_RI]Where A is an NxN dimensional identity matrix,

Q_Ris the real part of the complementary projection operator Q, Q_IRepresenting the imaginary part of the complementary projection operator Q,

the performance function is constructed accordingly as follows:

wherein s is an N-dimensional complex vector whose elements have a real part of s_RIts imaginary part is s_IThe real part and the imaginary part belong to the set B, B { + -1, + -3, L, + -g_n|g_n＝1+2(n-1)}，g₁＝1，Δg＝g_ii+1-g_ii＝2，ii∈[1，n-1]And 2n is the number of levels of the transmission signal set; k is a discrete time;

represents the optimized estimate of the signal, argmin () represents the variable value at which the objective function takes a minimum value, d is the delay factor, d is 0, L, M + L.

As a preferred embodiment, the dynamic equation of the improved model of the discrete multi-level chaotic neural network based on piecewise annealing in step SS4 is:

s_i(t)＝σ(x_i(t))；

wherein s is_i(t)，x_i(t) is S and X, respectively_NState of the ith component at time t, ω_ijIs from the jth component s_jTo the ith component s_iA weight value between, and w_ii＝w_ji(ii) a t is the running time in the iteration process of the discrete multilevel chaotic neural network based on the segmented annealing, and the continuous time t and the discrete time k in the discrete multilevel chaotic neural network based on the segmented annealing realize the conversion through an Euler formula;

alpha is a disturbance coefficient, and epsilon is a coupling factor; lambda is an attenuation factor, and lambda is more than or equal to 0 and less than or equal to 1;

σ(x_i(t)) is an activation function of a neuron;

receiving signal s (t) ═ s₁(t)，s₂(t)，L，s_N(t)]^TThe complex signal is: { s_j(t)＝s_Ri(t)+i·s_ij(t)，s_Rj(t)∈B，s_Ij(t) belongs to B | j ═ 1,2, L, N }, and when the discrete multi-level chaotic neural network based on the piecewise annealing reaches the final balance, s of each neuron is confirmed to be s_i(t)＝x_i(t)，s_i(t) is the sending signal; modeling the annealing function z in segments_i(t) introducing the adjustment of the self-feedback connection coefficient as the self-feedback connection weight, γ, of the ith neuron₁，γ₂Is a variable z_iControl parameter of (t), γ₁，γ₂∈(0，1)，z_i(0) And (4) randomly generating.

As a preferred embodiment, the dynamic equation of the improved new model of the noise chaotic neural network based on discrete multilevel hysteresis in step SS5 is:

s_i(t)＝σ(x_i(t))；

wherein s is_i(t)，x_i(t) is S and X, respectively_NState of the ith component at time t, ω_ijIs from the jth component s_jTo the ith component s_iA weight value between, and w_ij＝w_ji(ii) a t is the running time in the iterative process of the noise chaotic neural network based on discrete multi-level hysteresis, and the continuous time t and the discrete time k in the noise chaotic neural network based on the discrete multi-level hysteresis realize conversion through an Euler formula;

alpha is a disturbance coefficient, and epsilon is a coupling factor; lambda is an attenuation factor, and lambda is more than or equal to 0 and less than or equal to 1;

σ(x_i(t)) is an activation function of a neuron;

receiving signal s (t) ═ s₁(t)，s₂(t)，L，s_N(t)]^TThe complex signal is: { s_j(t)＝s_Rj(t)+i·s_Ij(t)，s_Rj(t)∈B，s_Ij(t) is formed by B | j ═ 1,2, L, N }, and when the noise chaotic neural network based on the discrete multilevel hysteresis reaches the final balance, s of each neuron is confirmed to be s_i(t)＝x_i(t)，s_i(t) is the sending signal;

modeling the annealing function z in segments_i(t) introducing the adjustment of the self-feedback connection coefficient as the self-feedback connection weight, γ, of the ith neuron₁，γ₂Is a variable z_iControl parameter of (t), γ₁，γ₂∈(0，1)，z_i(0) Randomly generating;

η_i(t) represents a random noise function, in order to further avoid the chaotic neural network from entering a local minimum point, wherein: eta_i(t)＝η_i(t)/ln(e+γ₁(1-η_i(t)))。

As a preferred embodiment, the steps are as followsThe hysteresis activation function in SS5 is σ (x), which is specifically expressed as follows: σ (x) ═ σ_R(x)+i·σ_I(x) And σ_R(x)＝σ_I(x)：

m represents R or I, and m represents R or I,

representing rounding down, | t | representing taking the absolute value, t being the function argument, mod (·, N) representing taking the remainder of N, a being a constant, a ∈ (0, 1).

As a preferred embodiment, the energy function e (t) of the discrete multi-level hysteresis noise chaotic neural network is:

in the synchronous update mode:

in the asynchronous update mode:

wherein:

n represents the number of the neurons of the discrete multi-level hysteresis noise chaotic neural network;

e (k) is an energy function of the discrete multi-level hysteresis noise chaotic neural network;

to receive the signal, b ═ (Δ g)²，

s_Rj(k)，s_Ij(k) Are respectively the signal s_RIj(k) The real and imaginary components of (a).

The invention achieves the following beneficial effects: the invention applies the piecewise annealing function and the random noise to the MQAM constellation signal of the discrete multi-level chaotic neural network, improves the activation function to construct a discrete multi-level hysteresis noise chaotic neural network model, and better avoids the neural network from falling into a minimum value point. Meanwhile, the novel model method can reduce the length of data volume, improve the noise resistance of multi-level blind detection, and comprehensively improve the performance of multi-level blind detection in various aspects. MATLAB simulation verification proves that compared with the traditional discrete multilevel neural network blind detection method, the method avoids trapping in minimum value points, reduces the data size length, improves the anti-noise capability of blind detection, and has better convergence performance compared with a segmented annealed multilevel discrete chaotic neural network and a segmented annealed multilevel noise chaotic neural network.

Drawings

FIG. 1 is a noise chaotic neural network model based on discrete multi-level hysteresis according to the present invention.

Fig. 2 is a graph comparing the convergence time of the blind detection algorithm for CTCNN _ RIHM and piecewise annealed CTCNN _ RIHM at the same signal-to-noise ratio.

FIG. 3 is a comparison graph of the bit error rate of CTCNN _ RIHM and the annealing by segment CTCNN _ RIHM, the annealing by segment NCTCNN _ RIHM, and the annealing by segment CHNTCNN _ RIHM at a data size length of 300. In the figure, a CTCNN _ RIHM (Complex-valued discrete-guided Chaotic direct-effective Chaotic-type Neural Network Real-type Hard-Multistate-activation-function) method is a signal blind detection method of a discrete multi-level Chaotic Neural Network, a segmented annealing CTCNN _ RIHM is a signal blind detection method based on a discrete multi-level segmented simulated annealing Chaotic Neural Network, a segmented annealing CNTN _ RIHM (Complex-valued non-valued discrete-guided Chaotic Neural Network Real-type Hard-type-effective-activation-function) is a signal blind detection method based on a discrete multi-level noise segmented simulated annealing Chaotic Neural Network, and a segmented annealing CHNTN _ RIHM (Complex-valued nonlinear transformed Chaotic-type Chaotic-effective Chaotic-function) is a signal blind detection method based on a discrete multi-level noise segmented simulated annealing Chaotic Neural Network.

Fig. 4 is a constellation convergence diagram of the piecewise annealing CHNTCNN _ RIHM method of the present invention when the data size length is 300 and the signal-to-noise ratio is 30 dB.

Detailed Description

The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.

The invention provides a signal blind detection method of a noise chaotic neural network based on discrete multi-level hysteresis, which comprises the following specific implementation processes:

the receiving equation for discrete time channels when ignoring noise is defined as follows

X_N＝SΓ^T (1)

In the formula, X_NIs a received data array, S is a transmitted signal array, and Γ is a channel impulse response h_jjA constructed block Toeplitz matrix; (.)^TRepresenting a matrix transposition;

wherein the transmission signal matrix is:

S＝[s_L+M(k),L,s_L+M(k+N-1)]^T＝[s_N(k),L,s_N(k-M-L)]_N×(L+M+1)m is the channel order, L is the equalizer order, and N is the required data length; s_L+M(K)＝[s(k)，L，s(k-L-M)](ii) a The time k is a natural number; h is_jj＝[h₀，L，h_M]_q×(M+1)Jj ═ 0,1, L, M; q is an oversampling factor, and takes the value of a positive integer; x_N＝[x_L(k)，L，x_L(k+N-1)]^TIs an N x (L +1) q received data array, where x_L(k)＝Г·s_L+M(k)；

For formula (1), when the f is full of columns, there must be

Satisfy Qs_N(k-d)＝0；U_cIs an N × (N- (L + M +1)) unitary matrix, decomposed by singular values

Obtaining the compound;

wherein:

(·)^His the Hermitian transpose;

u is a nx (L + M +1) unitary matrix in singular value decomposition;

0 is an (N- (L + M +1)) × (L +1) q zero matrix;

v is (L +1) qx (L +1) q unitary matrix;

U_cis N × (N- (L + M +1)) unitary matrix;

d is a (L + M +1) × (L +1) q singular value matrix;

setting a weight matrix W_RI＝[A-Q_RI]Where A is an NxN dimensional identity matrix,

Q_Ris the real part of the complementary projection operator Q, Q_IRepresenting the imaginary part of the complementary projection operator Q,

the performance function is constructed and the optimization process is as follows:

wherein s is an N-dimensional complex vector whose elements have a real part of s_RIts imaginary part is s_IThe real part and the imaginary part belong to the set B, B { + -1, + -3, L, + -g_n|g_n＝1+2(n-1)}，g₁＝1，Δg＝g_ii+1-g_ii＝2，ii∈[1，n-1]And 2n is the number of levels of the transmission signal set.

Representing the estimated value of the signal, argmin () representing the value of the variable at which the target function takes a minimum value, d being the delay factor, d being 0, L, M + L. Thus, the blind detection problem becomes a global optimal solution problem of the optimization problem of the formula (3).

FIG. 1 is a signal blind detection model of a noise chaotic neural network based on discrete multilevel hysteresis, which is constructed by the invention and comprises a weight matrix, an activation function, an attenuation factor, a coupling factor and a self-feedback term. The dynamic equation of the system is as follows:

s_i(t)＝σ(x_i(t)) (5)；

performing iterative operation on the equation, substituting the result of each iteration into an energy function E (t) of the improved discrete multi-level chaotic neural network, and when the energy function E (t) reaches the minimum value, namely s_i(t)＝s_i(t-1), balancing the discrete multi-level chaotic neural network, and finishing iteration;

wherein s is_i(t)，x_i(t) is S and X, respectively_NState of the ith component at time t, ω_ijIs from the jth component s_jTo the ith component s_iA weight value between, and w_ij＝w_ji(ii) a t is the running time in the network iteration process, and the continuous time t and the discrete time k in the network are converted by an Euler formula;

η_i(t) represents a random noise function to further avoid the chaotic neural network from entering a local minimumAnd (4) point. Wherein: eta_i(t)＝η_i(t)/ln(e+γ₁(1-η_i(t)))；

Alpha is a disturbance coefficient, and epsilon is a coupling factor of the network; lambda is an attenuation factor, and lambda is more than or equal to 0 and less than or equal to 1;

σ (g) is the activation function of the neuron;

receiving signal s (t) ═ s₁(t),s₂(t),L,s_N(t)]^TComplex signal s_j(t)＝s_Rj(t)+i·s_Ij(t),s_Rj(t)∈B,s_Ij(t) ∈ B | j ═ 1,2, L, N }, and when the network reaches final equilibrium, s for each neuron can be approximated as_i(t)＝x_i(t)，s_i(t) is the desired transmit signal;

step annealing function z_i(t) introducing the adjustment of the self-feedback connection coefficient as the self-feedback connection weight, γ, of the ith neuron₁,γ₂Is a variable z_iControl parameter of (t), γ₁,γ₂∈(0,1)，z_i(0) Randomly generating;

σ (g) is the activation function of the neuron, σ (g) ═ σ_R(g)+i·σ_I(g) And σ_R(g)＝σ_I(g)：

Wherein m represents R or I,

representing rounding down, | g | representing taking the absolute value, t being the argument of the function, mod (·, N) representing taking the remainder of N, a being a constant, a ∈ (0, 1).

b.) energy function

In the synchronous update mode:

in the asynchronous update mode:

wherein:

n represents the number of the neurons of the chaotic neural network;

e (k) is an energy function of the chaotic neural network;

to receive the signal, b ═ (Δ g)²，

s_Rj(k)，s_Ij(k) Are respectively the signal s_RIj(k) The real and imaginary components of (a);

in order to realize signal blind detection by using the improved discrete multi-level chaotic neural network, the signal blind detection problems of the equations (2) and (3) are solved, so that the minimum point of the energy function corresponds to the minimum point of the performance function. Interconversion is carried out between the continuous time t and the discrete time k through an Euler formula, and when the neural network is stable, x (t) is recorded as an estimated value of s (t); the signal at the solution point of the minimum value of the energy function e (k) is the transmission signal to be detected.

In conclusion, the improved signal blind detection method based on the discrete multi-level chaotic neural network ensures that the network can avoid local minimum points, reduces the length of required data volume, improves the anti-noise capability and finally reaches the balance of the network.

Fig. 2 is a comparison graph of the convergence time of the blind detection algorithm of the CTCNN _ RIHM and the piecewise annealing CTCNN _ RIHM under the same signal-to-noise ratio, and it can be known from the comparison graph that the convergence speed of the blind detection using the piecewise annealing function is faster.

Fig. 3 is a comparative simulation experiment chart of the step annealing CHNTCNN _ RIHM method, the CTCNN _ RIHM method, and the step annealing CTCNN _ RIHM method of the present invention, and the step annealing cntnrihm method, where the simulation result is a comparison chart of the error rate of the step annealing cntnrihm method when the data size length is 300, in which 100 Monte clauo experiments are performed under the same conditions. Fig. 4 is a constellation convergence diagram of the piecewise annealing CHNTCNN _ RIHM method of the present invention.

The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (8)

1. The blind detection method of the noise chaotic neural network based on discrete multi-level hysteresis is characterized by comprising the following steps of:

step SS 1: constructing a received data matrix X_N；

Step SS 2: for the received data matrix X_NPerforming singular value decomposition;

step SS 3: setting a weight matrix W_RIConstructing a performance function;

step SS 4: introducing a piecewise annealing function into the chaotic neural network, and constructing a discrete multi-level chaotic neural network based on piecewise annealing;

step SS 5: introducing random noise on the basis of the discrete multilevel chaotic neural network subjected to segmented annealing in the step SS4, constructing a discrete multilevel noise-based chaotic neural network, improving a traditional activation function, introducing a hysteresis activation function to improve the error code performance of a blind detection method, constructing a dynamic equation of an improved new model of the discrete multilevel hysteresis-based chaotic neural network, performing iterative operation on the dynamic equation of the improved new model, substituting the result of each iteration into an energy function E (t) of the discrete multilevel hysteresis-based chaotic neural network, and finishing the iteration when the energy function E (t) reaches the minimum value, wherein the discrete multilevel hysteresis chaotic neural network reaches the balance;

the dynamic equation of the improved model of the discrete multilevel chaotic neural network based on the segmented annealing in the step SS4 is as follows:

s_i(t)＝σ(x_i(t))

wherein s is_i(t)，x_i(t) is S and X, respectively_NState of the ith component at time t, ω_ijIs from the jth component s_jTo the ith component s_iA weight value between, and w_ij＝w_ji(ii) a t is the running time in the iteration process of the discrete multilevel chaotic neural network based on the segmented annealing, and the continuous time t and the discrete time k in the discrete multilevel chaotic neural network based on the segmented annealing realize the conversion through an Euler formula;

alpha is a disturbance coefficient, and epsilon is a coupling factor; lambda is an attenuation factor, and lambda is more than or equal to 0 and less than or equal to 1;

σ(x_i(t)) is an activation function of a neuron;

receiving signal s (t) ═ s₁(t),s₂(t),…,s_N(t)]^TThe complex signal is: { s_j(t)＝s_Rj(t)+i·s_Ij(t)，s_Rj(t)∈B，s_Ij(t) is equal to 1,2, …, N ∈ B | j, and when the discrete multi-level chaotic neural network based on the piecewise annealing reaches the final balance, s of each neuron is confirmed_i(t)＝x_i(t)，s_i(t) is the sending signal; modeling the annealing function z in segments_i(t) introducing an adjustment of the self-feedback connection coefficientAs the self-feedback connection weight, γ, of the ith neuron₁,γ₂Is a variable z_iControl parameter of (t), γ₁,γ₂∈(0,1)，z_i(0) And (4) randomly generating.

2. The blind detection method for the noise chaotic neural network based on the discrete multilevel hysteresis (DGS) of claim 1, wherein the step SS1 is implemented by constructing a received data matrix X_NThe method specifically comprises the following steps: the receiving end receives a signal sent by a single user, and a receiving equation of a discrete time channel is obtained through sampling:

X_N＝SΓ^T

in the formula, X_NIs a matrix of received data, S is a matrix of transmitted signals, and Γ is a matrix of channel impulse responses h_jjA constructed block Toeplitz matrix; (.)^TRepresenting the transpose of the matrix.

3. The blind detection method of the discrete multilevel hysteresis-based noise chaotic neural network according to claim 2, wherein the transmission signal matrix S in the step SS1 is:

S＝[s_L+M(k),…,s_L+M(k+N-1)]^T＝[s_N(k),…,s_N(k-M-L)]_N×(L+M+1)；

wherein, M is the channel order, L is the equalizer order, and N is the required data length; s_L+M(k)＝[s(k),…,s(k-L-M)]^T(ii) a The time k is a natural number;

the channel impulse response h in the step SS1_jjComprises the following steps: h is_jj＝[h₀，…，h_M]_q×(M+1)Jj ═ 0,1, …, M; q is an oversampling factor, and takes the value of a positive integer;

the received data matrix in step SS1 is: x_N＝[x_L(k),…,x_L(k+N-1)]^TIs N x (L +1) q received data matrix, where x_L(k)＝Γ·s_L+M(k)。

4. The blind detection method of the discrete multi-level hysteresis-based noise chaotic neural network according to claim 1, wherein the step SS2 specifically comprises:

for the received data matrix X_NSingular value decomposition is carried out, namely:

in the formula (DEG)^HIs the Hermitian transpose;

u is a nx (L + M +1) unitary matrix in singular value decomposition;

0 is an (N- (L + M +1)) × (L +1) q zero matrix;

v is (L +1) qx (L +1) q unitary matrix;

U_cis N × (N- (L + M +1)) unitary matrix;

d is a (L + M +1) × (L +1) q singular value matrix.

5. The blind detection method of the discrete multi-level hysteresis-based noise chaotic neural network according to claim 1, wherein the step SS3 specifically comprises: setting a weight matrix W_RI＝[A-Q_RI]Where A is an NxN dimensional identity matrix,

Q_Ris the real part of the complementary projection operator Q, Q_IRepresenting the imaginary part of the complementary projection operator Q,

the performance function is constructed accordingly as follows:

wherein s is an N-dimensional complex vector whose elements have a real part of s_RIts imaginary part is s_IThe real part and the imaginary part belong to the set B, B { + -1, + -3, …, + -g_n|g_n＝1+2(n-1)}，g₁＝1，Δg＝g_ii+1-g_ii＝2，ii∈[1，n-1]And 2n is the number of levels of the transmission signal set; k is a discrete time;

representing the optimal estimate of the signal, argmin () representing the value of the variable at which the objective function takes its minimum value, d being the delay factor, d being 0, …, M + L.

6. The blind detection method for the discrete multi-level hysteresis based noise chaotic neural network according to claim 1, wherein the dynamic equation of the improved new model of the discrete multi-level hysteresis based noise chaotic neural network in the step SS5 is as follows:

s_i(t)＝σ(x_i(t))

wherein s is_i(t)，x_i(t) is S and X, respectively_NState of the ith component at time t, ω_ijIs from the jth component s_jTo the ith component s_iA weight value between, and w_ij＝w_ji(ii) a t is the running time in the iterative process of the noise chaotic neural network based on discrete multi-level hysteresis, and the continuous time t and the discrete time k in the noise chaotic neural network based on the discrete multi-level hysteresis realize conversion through an Euler formula;

alpha is a disturbance coefficient, and epsilon is a coupling factor; lambda is an attenuation factor, and lambda is more than or equal to 0 and less than or equal to 1;

σ(x_i(t)) is an activation function of a neuron;

receiving signal s (t) ═ s₁(t),s₂(t),…,s_N(t)]^TThe complex signal is: { s_j(t)＝s_Rj(t)+i·s_Ij(t)，s_Rj(t)∈B，s_Ij(t) is equal to 1,2, …, N ∈ B | j, and when the noise chaotic neural network based on the discrete multilevel hysteresis reaches the final balance, s of each neuron is confirmed_i(t)＝x_i(t)，s_i(t) is the sending signal;

modeling the annealing function z in segments_i(t) introducing the adjustment of the self-feedback connection coefficient as the self-feedback connection weight, γ, of the ith neuron₁,γ₂Is a variable z_iControl parameter of (t), γ₁,γ₂∈(0,1)，z_i(0) Randomly generating;

η_i(t) represents a random noise function, in order to further avoid the chaotic neural network from entering a local minimum point, wherein: eta_i(t)＝η_i(t)/ln(e+γ₁(1-η_i(t)))。

7. The blind detection method of the discrete multilevel hysteresis-based noise chaotic neural network according to claim 1, wherein the hysteresis activation function in the step SS5 is σ (x), and is specifically expressed as follows: σ (x) ═ σ_R(x)+i·σ_I(x) And σ_R(x)＝σ_I(x)：

m represents R or I, and m represents R or I,

representing rounding down, | t | representing taking the absolute value, t being the function argument, mod (·, N) representing taking the remainder of N, a being a constant, a ∈ (0, 1).

8. The blind detection method of the discrete multi-level hysteresis based noise chaotic neural network according to claim 1, wherein an energy function e (t) of the discrete multi-level hysteresis based noise chaotic neural network is: in the synchronous update mode:

in the asynchronous update mode:

wherein:

n represents the number of the neurons of the discrete multi-level hysteresis noise chaotic neural network;

e (k) is an energy function of the discrete multi-level hysteresis noise chaotic neural network;

to receive the signal, b ═ (Δ g)²，

s_Rj(k)，s_Ij(k) Are respectively the signal s_RIj(k) The real and imaginary components of (a).

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