CN104363078B - The real orthogonal space time packet blind-identification method of under determined system based on robust Competition Clustering - Google Patents

Abstract

The invention relates to a blind recognition method of a real orthogonal space-time block code of an underdetermined system based on robust competitive clustering, and belongs to the technical field of signal processing. In this method, firstly, the received signal model related to the virtual channel matrix is obtained by modeling. Since the virtual channel matrix contains space-time code information, it can be used for space-time code identification; secondly, the robust competitive clustering algorithm is used to blindly estimate the Virtual channel matrix; again, according to the characteristics of the real orthogonal space-time block code, extract the sparsity of the correlation matrix of the virtual channel matrix and the identification characteristic parameter of the energy ratio of the energy ratio of the non-main diagonal element energy and the main diagonal element energy; Finally, the orthogonal space-time block code identification is carried out according to this parameter. The algorithm adopted in the present invention can effectively blindly identify the real orthogonal space-time block code signal with less complexity, and can work well under the condition of lower input signal-to-noise ratio, thereby improving system performance; and using robust Competitive clustering algorithm can also blindly estimate the number of source signals, which has broad application prospects.

Description

Blind Identification Method of Real Orthogonal Space-Time Block Codes for Underdetermined Systems Based on Robust Competitive Clustering

technical field

The invention belongs to the technical field of signal processing, and relates to a blind recognition method of a real orthogonal space-time block code of an underdetermined system based on robust competitive clustering.

Background technique

The disadvantage of receiving diversity is that the calculation load at the receiving end is very high, which may lead to a large power consumption of the mobile station in the downlink. Diversity gains can also be obtained by using space-time coding at the transmitter, and only simple linear processing is required for decoding at the receiver. Space-time codes organically combine antenna transmit diversity technology, channel coding and modulation technology, which can effectively improve the transmission performance of fading channels. Communication signal recognition is of great significance in civil and military communications. Pass-through communication signal identification mainly includes modulation identification and channel coding identification. In non-cooperative communication reconnaissance, in order to intercept signal information, it is necessary to know the modulation method, channel coding method and coding parameters. The space-time code is a kind of code for the transmitted symbols in the MIMO system. The identification of the space-time code is one of the important contents of the non-cooperative MIMO system. To decode the received signal, it is necessary to know its coding method. There is no public report on this Therefore, it is necessary to further identify the types of space-time block codes.

Sparse Component Analysis (SCA) uses the sparse properties of signals in the time domain or its transform domain instead of independent properties to achieve blind signal separation. The basic assumption of SCA is that the source signal is assumed to be sparse. A sparse signal means that the value of the signal is equal to zero or close to zero at most of the sampling moments, and only a few sampling moments are obviously not zero. The probability distribution of a typical sparse signal is Laplace distribution.

Contents of the invention

In view of this, the purpose of the present invention is to provide a method for blind identification of real orthogonal space-time block codes for underdetermined systems based on robust competitive clustering. This method aims at the problem of space-time block code type identification for underdetermined systems, introducing Sparse signal analysis for blind recognition of orthogonal space-time block codes.

To achieve the above object, the present invention provides the following technical solutions:

A method for blind identification of real orthogonal space-time block codes for underdetermined systems based on robust competitive clustering. In this method, firstly, the received signal model related to the virtual channel matrix is obtained by modeling. Since the virtual channel matrix contains space-time code information, so it can be used for space-time code identification; secondly, use the robust competitive clustering algorithm to blindly estimate the virtual channel matrix; thirdly, according to the characteristics of real orthogonal space-time block codes, extract the sparsity of the correlation matrix of the virtual channel matrix and the identification feature parameter of the energy ratio of the energy ratio of the non-main diagonal element energy to the main diagonal element energy ratio; finally, the orthogonal space-time block code identification is carried out according to this parameter.

Further, the method specifically includes the following steps:

Step 1: Modeling to obtain the received signal model related to the virtual channel matrix:

Wherein, S(k)=[S ₁ (k), S ₂ (k),...,S _N (k)] ^Τ is the kth group of data composed of N symbols specially transmitted, and each symbol independent distribution A=Ω ^Τ is an n _R L×N dimensional virtual channel matrix, which is an independent vector composed of statistical independent information sources, V(k) is a n _R ×L dimensional noise matrix, and its elements are zero-mean variance Gaussian random variable of , v _m (k) is an L-dimensional row vector;

Step 2: Blindly estimate the virtual channel matrix using the robust competitive clustering algorithm

The mixture model for underdetermined blind separation can be expressed as:

Y(k)=AS(k)+V(k)

In the formula, S(k) is the source signal vector, A is the mixing matrix, and V(k) is Gaussian white noise; comparing with the formula in step 1, it can be seen that the two models are actually consistent, so the method of estimating the mixing matrix A To estimate the virtual channel matrix; the mixed signal has the characteristics of surface clustering, using this characteristic under the condition that the number of source signals is unknown, use the competitive clustering learning algorithm to estimate

out of the clustering plane, and then use the potential function method to estimate the intersection line of the clustering plane, thus obtaining the estimation of the mixing matrix;

Suppose the normal vector of the estimated clustering plane is M is the estimated number of clustering planes, which is not necessarily equal to the actual number of clustering planes random selection vector matrix Generally take Q≥M, and regularize: p _i =p _i /||p _i || ₂ i=1,...,Q; constitute the objective function:

Estimate local maxima: p _i =p _i /||p _i ||; if ξ _i =g(p _i )/max(g(P))≥ε, then p _i is the column vector of the mixing matrix;

Step 3: Estimate the virtual channel correlation matrix R=A ^Τ A=ΩΩ ^Τ

(m=1,2,...,n _R ) is an n _T -dimensional row vector, and I _N is an identity matrix;

Step 4: Estimate the number of symbols N:

Among them, K is the time of observation, that is, the number of transmitted data groups; λ _i is the ith feature of the decomposed autocorrelation matrix R _y arranged in descending order, P=2n _R L;

Step 5: According to the characteristics of the real orthogonal space-time block code, extract the variance characteristic parameters of the non-main diagonal elements of the correlation matrix of the virtual channel matrix, and predict the pattern:

Where F is the number of main diagonal elements, when D>D _th , take γ=γ ₂ , when D≤D _th , take γ=γ ₁ ;

Step 6: According to the characteristics of the real orthogonal space-time block code, extract the sparsity characteristic parameter of the correlation matrix of the virtual channel matrix:

Due to the orthogonal space-time block code It is a diagonal matrix of N×N dimensions, and the sparsity should be θ=N, instead of the sparseness θ>N of the R matrix of the orthogonal space-time block code, the characteristic parameter θ=N is taken;

Step 7: Make a comparison and judgment, that is, if θ=N, it means that the OSTBC signal is used; otherwise, the NOSTBC signal is used.

The beneficial effect of the present invention is that: the method of the present invention carries out blind recognition of orthogonal space-time block codes by introducing sparse signal analysis, and proposes the sparsity of the correlation matrix of the virtual channel matrix and the energy of non-main diagonal elements and the energy of main diagonal elements The identification characteristic parameters of the energy ratio of the ratio can improve the identification effect and further reduce the influence of noise. The algorithm adopted by the invention can effectively blindly identify real orthogonal space-time block code signals with less complexity, and can work well under the condition of lower input signal-to-noise ratio, thereby improving system performance. Moreover, the number of source signals can be blindly estimated by using the robust competitive clustering algorithm, which has wide application prospects.

Description of drawings

In order to make the purpose, technical scheme and beneficial effect of the present invention clearer, the present invention provides the following drawings for illustration:

Figure 1 is a model diagram of the OSTBC MIMO system;

Figure 2 is a diagram of the OSTBC system identification model;

Fig. 3 is the flowchart of DS-RCA algorithm;

Fig. 4 is insufficient sparse mixed signal component figure;

Figure 5 is a mixed signal and source number estimation diagram;

Fig. 6 is an estimated performance diagram of N;

Fig. 7 is the transformation figure of feature parameter θ, D;

Figure 8 is a graph of algorithm recognition performance.

detailed description

The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

Consider a conventional real orthogonal space-time block code system with n _T transmit antennas and n _R receive antennas. The signals are grouped before transmission, and N symbols are transmitted through L time slots, let S(k)=[S ₁ (k), S ₂ (k),...,S _N (k)] ^Τ as special The transmitted k-th group of data consists of N symbols, and each symbol is distributed independently. S(k) is mapped to an n _T × L dimensional space-time coding matrix C(k) with L time slots through space-time modulation. C(k) can be expressed in the following form:

Among them, X _i is the n _T ×L dimensional coding matrix of the i-th symbol s _i (k), and has the following properties:

in, is an n _T ×n _T identity matrix.

The received data signal Y(k) of the kth group can be expressed as

Y(k)=GC(k)+V(k) (3)

in,

G is a channel response matrix of n _R × n _T dimensions, (m=1,2,...,n _R ) is an n _T -dimensional row vector; Y(k) is an n _R ×L-dimensional matrix, and y _m (k) is an L-dimensional row vector, expressed as The kth group of signals received by the mth antenna. V(k) is a noise matrix of n _R × L dimensions, and its elements are zero-mean variance Gaussian random variable of , v _m (k) is an L-dimensional row vector.

Substituting formula (1) into formula (3), we can get

in, Ω _m is an N×L dimensional matrix.

Transpose (4) to get

Formula (6) can be expressed as

in, A= ^ΩΤ is an n _R L×N dimensional virtual channel matrix, which is an independent vector composed of statistically independent information sources.

Analyze the correlation matrix of the virtual channel matrix, so that R=A ^Τ A=ΩΩ ^Τ can be obtained

For orthogonal space-time block codes, the (i, i)th element of R is

Using formula (2) to get

The (i, j)th element of R is

Since R _ij is a scalar, then Using formula (2) can get:

Therefore, when i≠j, R _ij =0. According to formula (2) and formula (10), it can be seen that

So the R of the orthogonal space-time block code is a diagonal matrix of N×N dimensions. When n _R =1, If it is not an orthogonal space-time block code, the formula (2) is not valid, so R is not a diagonal matrix, that is, the formula (11) is not valid.

According to this characteristic of the matrix R, the characteristic parameter θ of the sparsity of the matrix R is proposed, namely:

θ represents the number of nonzeros in R.

Due to the orthogonal space-time block code It is a diagonal matrix of N×N dimensions, and the sparsity should be θ=N; the sparsity of the R matrix of the non-orthogonal space-time block code is θ>N; the characteristic parameter θ=N is taken.

Due to the existence of noise and algorithm estimation error, the estimated orthogonal space-time block code The matrix is not strictly diagonal, so for After taking the absolute value, the The γ bits smaller than the maximum value of the diagonal elements are all set to zero to reduce the influence of noise, and let γ be the elimination parameter.

Because the selection of the bath parameter γ directly affects the value of the characteristic parameter θ. If it is an orthogonal space-time block code, a larger cancellation parameter γ=γ ₁ should be selected to make θ=N and have a higher recognition rate; if it is a non-orthogonal space-time block code, a smaller cancellation parameter should be taken The bath parameter γ=γ ₂ will make θ>N and have a higher recognition rate.

Divide the elements in the matrix R into two parts: main diagonal elements and non-main diagonal elements. According to the characteristics of the matrix R, the energy ratio characteristic parameter D of the ratio of the energy of the off-diagonal elements of the matrix R to the energy of the main diagonal elements is proposed. Since D is small, it can be set as:

where F is the number of main diagonal elements.

Since the R of the orthogonal space-time block code is a diagonal matrix of N×N dimensions, theoretically there should be non-diagonal element variance D=0, but in practice, due to the estimation error of the R matrix, D will not be strictly zero. In order to solve the selection problem of the elimination parameter γ, the orthogonal space-time block code and the non-orthogonal space-time block code are used The non-diagonal elements of the matrix have the characteristics of different degrees of dispersion. In this paper, the matrix The ratio D of the energy of the off-main diagonal elements and the energy of the main diagonal elements is used as another characteristic parameter to predict the code pattern, determine the parameter γ value, and set the threshold as D _th .

Depend on After the autocorrelation matrix R _y is obtained, first decompose its characteristics, and then use the MDL criterion to estimate the signal subspace dimension of R _y as The diagonal matrix E composed of the eigenvector matrix U _S of the signal subspace and its corresponding eigenvalues can be obtained. It can be seen From this, the number N of symbols can be estimated.

The MDL criterion based on signal theory is widely used in rank estimation, and the MDL calculation is as follows:

Where K is the observation time, that is, the number of transmitted data sets; λ _i is the ith feature of the decomposed autocorrelation matrix R _y arranged in descending order, P=2n _R L . The dimension of the signal subspace is

Since the restriction condition of the MDL rule is: the dimension of the signal subspace is smaller than the space dimension of the received signal, that is, 2N<P=2n _R L, then when the code rate r=N/L<n _R , the MDL rule estimation is applicable.

On the basis of the above-mentioned theory and mathematical model, the real orthogonal space-time block code blind recognition algorithm of Robust Competitive Clustering (RCA) is realized, and the recognition system model is established first:

Since R=A ^Τ A=ΩΩ ^Τ , the key is to get A. It can be seen from formula (7), is an instantaneous mixed-signal model, giving After that, the robust competitive clustering algorithm can be used to estimate Then it can be estimated

Since the whole algorithm uses the RCA algorithm to estimate the virtual channel correlation matrix during the simulation, this section will briefly introduce the steps of the RCA algorithm to estimate the virtual channel correlation matrix.

The mixed model of underdetermined blind separation can be expressed as

Y(k)=AS(k)+V(k) (17)

Where S(k) is the source signal vector, A is the mixing matrix, and V(k) is Gaussian white noise. Comparing with formula (7), it can be seen that the two models are actually consistent, so the method of estimating the mixing matrix A is used to estimate the virtual channel matrix.

The RCA algorithm combines the advantages of hierarchical clustering and segmentation clustering algorithms. In order to overcome the problem of comparison of noise and outliers in general clustering algorithms, the RCA algorithm introduces the concept of robust statistics, and adjusts clustering through competitive clustering learning. The center parameter vector and its potential. The potential of the cluster center can be regarded as the probability that the sampled data belongs to the cluster center. The larger the potential, the more sampled data the cluster center contains. When the algorithm converges, by comparing the size of the cluster center potential, the cluster center with relatively large potential is taken as the vector in the straight line direction, and their number is also the number of source signals.

Regarding the insufficient sparse mixed signal of the underdetermined system, the mixed signal has the characteristic of surface clustering. Using this characteristic, under the condition that the number of source signals is unknown, the clustering plane is estimated by using the competitive clustering learning algorithm, and then the potential function method is used to Estimates the intersection of the cluster planes, from which an estimate of the number of sources and the mixing matrix is obtained. The RCA algorithm for estimating the virtual channel correlation matrix is summarized as follows:

(1) set is the input signal data vector matrix, t is the sampling time, and N is the length of the sampling data. Utilization formula: t=1,...,N, project the sampling data onto the unit hemisphere, and also remove the sampling data of ||y(t)||<0.01(t=1,...,N) during projection .

(2) set is the plane normal vector matrix, β _i is the ith plane normal vector, using the formula: β _i =sign(β _i1 )β _i /||β _i ||,i=1,...,C to convert the plane The normal vector is projected onto the same unit hemisphere as the input signal data vector, and C is the maximum possible number C _max of the hypothetical clustering plane, generally taken as a is the number of active source signals at each moment, take d=0, and make the initial value of w _it 1 for any i, t.

(3) Formula: calculate calculate are the median of the th cluster and the median of the deviation, respectively.

(4) Update w _it :

Update α(d):

(5) Update U: s=1,...,C; j=1,...,N

(6) d=d+1, update B: β _i = β _i /||β _i ||

(7) if Delete repeated cluster centers, calculate and compare the relative size of each cluster center potential, that is, the size of ξ _s , take ξ _s ≥ ε cluster center parameter β _s as the normal vector a _s of the cluster plane, ξ _s The number of cluster centers ≥ε is also the number of cluster planes, otherwise return to step (3).

(8) Suppose the normal vector of the estimated clustering plane is M is the estimated number of clustering planes, which is not necessarily equal to the actual number of clustering planes random selection vector matrix Generally, Q≥M is taken and regularized: p _i =p _i /||p _i || ₂ i=1,...,Q.

(9) Form the objective function: Estimate local maxima: p _i =p _i /||p _i ||. If ξ _i =g(p _i )/max(g(P))≥ε, then p _i is the column vector of the mixing matrix, otherwise return to step (9).

The received signal model related to the virtual channel matrix is obtained by modeling. Since the virtual channel matrix contains space-time code information, it can be used for space-time code identification, and then the virtual channel matrix is estimated blindly by using the robust competitive clustering algorithm. Then, according to Based on the characteristics of real OFBCs, the identification characteristic parameters of the correlation matrix sparsity of the virtual channel matrix and the variance of non-main diagonal elements are proposed, and finally the OFBCs are identified using these parameters.

The steps of the blind recognition method (abbreviated as DS-RCA) of the RCA-based real orthogonal space-time block code using variance and sparsity of off-diagonal elements proposed by the present invention are shown in FIG. 3 .

The parameters selected in the simulation are as follows: the transmitted signal S _i (k) is a constellation symbol modulated by 16QAM, the transmitted data is 2000 groups, L=N=5, and the channel is a quasi-static stable channel. During the performance simulation, when the signal-to-noise ratio SNR=[-20:5]dB, the same is analyzed through 100 Monte Carlo experiments.

Embodiment 1: RCA estimation virtual channel analysis

Consider an underdetermined system with insufficiently sparse signals, ie n _T >n _R and multiple source signals k≥2 at each sampling instant. In the simulation, the number of transmitting antennas n _T =5, the number of receiving antennas n _R =3, and k=2. SNR=5dB. Perform RCA estimation virtual channel analysis.

Figure 4-c shows that the mixed signal is projected onto the upper hemisphere, with C _max =50, when estimating the clustering plane and mixing matrix, ε=0.5, ε ₁ =0.0005. From Figure 5-b, it can be seen that there are 10 clustering plane potentials whose relative size exceeds 0.5, which is equivalent to 10 clustering planes, that is, the number of actual clustering planes.

Using the estimated clustering planes, the source number and mixing matrix can be estimated. The estimated relative sizes of the mixed vectors and their potentials are shown in Fig. 5-a, there are 5 mixed vectors whose relative sizes exceed 0.5, so the estimated number of sources is 5:

Estimates of the orthogonal space-time block codes and non-orthogonal space-time block codes The matrices are shown in Table 1 respectively.

Table 1. estimate

It can be seen from Table 1 that due to the influence of errors in the estimation process, the The matrix is not diagonal. If combined with non-orthogonal space-time block codes Compared to a matrix, its off-diagonal elements are much smaller than those on the diagonal. As long as an appropriate threshold is designed, both can be identified.

Example 2: Estimation performance analysis of N

In the simulation, if you want to design the sparsity threshold, you must first know the number N of symbols in each group. The root mean square error RMSE of the estimated value of N is shown in Figure 6 for different numbers of transmitting antennas n _T and receiving antennas n _R , namely (n _T , n _R ).

It can be seen from the figure that when SNR≥-6dB, the MDL algorithm can be used to estimate N more accurately; under the same (n _T , n _R ), the symbol estimation performance of the orthogonal space-time block code is better than that of the non-orthogonal Space-time block code; when the transmitting antenna is constant, the performance of symbol estimation is improved with the increase of the number of receiving antennas; when the receiving antenna is constant, the performance of symbol estimation is also improved with the increase of the number of transmitting antennas.

Embodiment 3: the impact of noise on characteristic parameters

Given that N=5, the influence of the signal-to-noise ratio on the characteristic parameters of the orthogonal space-time block code and the non-orthogonal space-time block code is shown in FIG. 7 .

In the figure, the D and θ values of the non-orthogonal space-time block codes are greater than the D and θ values of the orthogonal space-time block codes, and the two basically do not overlap; with the SNR transformation, the D and θ values of the orthogonal space-time block codes The θ value is basically unchanged, while the D and θ values of the non-orthogonal space-time block code are changed; when the receiving antenna is unchanged and the transmitting antenna is increased, the D and θ values of the non-orthogonal space-time block code also increase. big. in addition,

In Figure 7-b, for the same signal and the same (n _T , n _R ), as the signal-to-noise ratio increases, the θ value of the non-orthogonal space-time block code also increases. These small conclusions show that the signal-to-noise ratio has a certain influence on the feature parameter extraction.

Embodiment 4: Algorithm recognition rate analysis

According to the simulation results of the appeal, D _th =1 is taken. When D>D _th , take When D≤D _th , take The sparsity feature parameter threshold θ _th =N=5. The recognition rate of DS-RCA algorithm is shown in Figure 8.

It can be seen from the figure that under the same conditions, the recognition rate of the orthogonal space-time block code is far superior to that of the orthogonal space-time block code, especially at low signal-to-noise such as SNR<-10dB; When the noise ratio SNR≥-5dB, the recognition rate of the orthogonal space-time block code reaches about 99%, while the recognition rate of the non-orthogonal space-time block code reaches 100% when the SNR≥-1dB; When the transmitting antenna increases, the recognition rate also increases; when the transmitting antenna remains unchanged, the recognition rate increases as the receiving antenna increases; during the simulation process, (n _T , n _R )=( 4,3) for best results.

Fig. 8-c compares the performance of the two algorithms, DS-RCA and DS-ICA, which utilize RCA and Independent Component Analysis (ICA) for virtual channel estimation, respectively. In the figure: the performance of DS-RCA algorithm is far superior to that of DS-ICA algorithm, especially in the case of low signal-to-noise ratio; when SNR≥-5dB, the recognition rate of DS-ICA algorithm can only reach about 60%. When SNR≤-10dB, the DS-ICA algorithm can basically not identify the two, the main reason is that in the stage of estimating the virtual channel, the effect of using the ICA algorithm to estimate the mixing matrix for the underdetermined system is poor; in addition, using DS-ICA The computational complexity of the algorithm is high, that is, for The computational complexity of doing the singular value decomposition is The computational complexity of pre-whitening is

The computational complexity of this algorithm mainly includes: the computational complexity of the RCA algorithm is Calculate the correlation matrix of A The computational complexity of is The computational complexity of computing the feature parameter θ is The computational complexity of calculating the characteristic parameter D is

Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that it can be described in terms of form and Various changes may be made in the details without departing from the scope of the invention defined by the claims.

Claims (1)

1. A underdetermined system real orthogonal space-time block code blind identification method based on robust competitive clustering is characterized in that: in the method, firstly, a received signal model related to a virtual channel matrix is obtained through modeling, and the virtual channel matrix contains space-time code information, so that the method can be used for space-time code identification; secondly, a virtual channel matrix is estimated blindly by using a robust competitive clustering algorithm; thirdly, extracting identification characteristic parameters of sparsity of a correlation matrix of the virtual channel matrix and an energy ratio of a ratio of non-main diagonal element energy to main diagonal element energy according to the characteristics of the real orthogonal space-time block code; finally, according to the parameter, orthogonal space-time block code identification is carried out;

the method specifically comprises the following steps:

the method comprises the following steps: modeling to obtain a received signal model related to the virtual channel matrix:

$\tilde{Y}\left(k\right)={\mathrm{\&Omega;}}^{T}S\left(k\right)+\tilde{V}\left(k\right)=AS\left(k\right)+\tilde{V}\left(k\right);$

wherein S (k) ═ S₁(k),S₂(k),...,S_N(k)]^ΤA kth group of data consisting of N symbols for transmission, and wherein each symbol is distributed independentlyA＝Ω^ΤIs n_RL × N dimension virtual channel matrix, which is an independent vector composed of statistical independent information sources, and V (k) is N_R× L-dimensional noise matrix whose elements are zero mean variance ofOf a Gaussian random variable, v_m(k) Is an L-dimensional row vector;

step two: blind estimation of virtual channel matrix by using robust competitive clustering algorithm

The hybrid model of underdetermined blind separation can be expressed as:

Y(k)＝AS(k)+V(k)

wherein S (k) is a source signal vector, A is a mixing matrix, and V (k) is Gaussian white noise; comparing with the formula in the step one to know that the two models are actually consistent, so that the method for estimating the mixing matrix A is used for estimating the virtual channel matrix; the mixed signal has the characteristic of surface clustering, under the condition that the number of source signals is unknown, a clustering plane is estimated by utilizing a competitive clustering learning algorithm by utilizing the characteristic, and then an intersecting line of the clustering plane is estimated by utilizing a potential function method, so that the estimation of a mixed matrix is obtained;

assume that the estimated normal vector of the clustering plane isM is the estimated number of clustering planes, which is not necessarily equal to the actual number of clustering planesRandomly selecting a vector matrixGenerally, Q is more than or equal to M and is regularized: p is a radical of_i＝p_i/||p_i||₂1, ·, Q; and (3) forming an objective function:

$\mathrm{\&phi;}\left(p\right)=\underset{i=1}{\overset{Q}{\&Sigma;}}\underset{j=1}{\overset{M}{\&Sigma;}}\exp (-\frac{<p_i,{\mathrm{\&beta;}}_j>}{{\mathrm{\&sigma;}}^2}),$

estimating a local maximum:p_i＝p_i/||p_iif ξ |)_i＝g(p_i) (g (P) ≥ p_iIs the column vector of the mixing matrix;

step three: estimating a virtual channel correlation matrix R ═ A^ΤA＝ΩΩ^Τ

$R=(b_1{b}_1^T+b_2{b}_2^T+...+b_{n_R}{b}_{n_R}^T)I_N=\left(\underset{m=1}{\overset{n_R}{\mathrm{\&Sigma;}}}\right|\left|b_m\right|{|}^2)I_N;$

Is n_TDimension row vector, I_NIs an identity matrix;

step four: estimating the number of symbols N:

$\hat{M}=2N,\hat{M}=\arg \underset{m=0,1,...,P-1}{min}MDL\left(m\right)$

$MDL\left(a\right)=-\log {\left(\frac{{\mathrm{\&Pi;}}_{i=a+1}^P{\mathrm{\&lambda;}}_i^{1/(P-a)}}{{\mathrm{\&Sigma;}}_{i=a+1}^P{\mathrm{\&lambda;}}_i/(P-a)}\right)}^{K(P-a)}+\frac{a(2P-a)}{2}\log K,(a=1,2,\mathrm{...},P)$

wherein K is the observation time, namely the number of the transmitted data groups; lambda [ alpha ]_iFor decomposing an autocorrelation matrix R_yI-th feature in descending order, P ═ 2n_RL；

Step five: extracting non-main diagonal element variance characteristic parameters of a correlation matrix of a virtual channel matrix according to the characteristics of real orthogonal space-time block codes, and pre-judging code types:

$D=\frac{\underset{i\&NotEqual;j}{\&Sigma;}{r}_{ij}}{\frac{1}{F}\underset{k}{\&Sigma;}{r}_{kk}^2}$

wherein F is the number of main diagonal elements, when D > D_thWhen, get γ ═ γ₂When D is less than or equal to D_thWhen, get γ ═ γ₁；

Step six: extracting sparsity characteristic parameters of a correlation matrix of a virtual channel matrix according to the characteristics of the real orthogonal space-time block code:

$\mathrm{\&theta;}=\left|\right|R|{|}^0=\underset{i,j}{\&Sigma;}|R_{ij}{|}^0$

due to orthogonal space-time block codesThe method is an N × N-dimensional diagonal matrix, the sparsity is theta-N, while the sparsity theta of an R matrix of the non-orthogonal space-time block code is more than N, and a characteristic parameter theta is taken as N;

step seven: making a comparison decision, namely if theta is equal to N, indicating that the OSTBC signal is adopted; otherwise, the NOSTBC signal is used.