Method, system, device and medium for identifying MIMO-OFDM space-time coding mode under non-Gaussian noise

Abstract

The invention discloses a method, system, device and medium for identifying MIMO-OFDM space-time coding mode under non-Gaussian noise. The method comprises: extracting correlation features applicable to MIMO-OFDM signals under non-Gaussian noise environment, and constructing a feature space for feature optimization selection; constructing a feature optimization selection model based on an extreme gradient boosting sequence floating backward selection algorithm, and determining a feature set for final classification according to feature importance; constructing a classifier model based on tree-enhanced naive Bayes, and classifying and identifying space-time coding modes according to features selected by feature optimization; the system, device and medium perform space-time coding mode identification based on the method for identifying MIMO-OFDM space-time coding mode under non-Gaussian noise; the invention extracts time-lag correlation peak features applicable to MIMO-OFDM signals under non-Gaussian noise environment, constructs a feature selection model and performs feature optimization selection to determine a feature set for final classification, thereby realizing the identification of MIMO-OFDM space-time coding mode under non-Gaussian noise, and having good identification performance under the condition of low generalized signal-to-noise ratio.

Description

Technical Field

[0001] The present invention belongs to the technical field of communication signal demodulation, and in particular relates to a method, system, device and medium for identifying a MIMO-OFDM space-time coding mode under non-Gaussian noise. Background Art

[0002] Identification of MIMO-OFDM space-time coding schemes under non-Gaussian noise is one of the important contents of deep sensing technology for non-cooperative MIMO systems. Space-time block coding (STBC) is a relatively common space-time coding scheme. Its combination with MIMO-OFDM can greatly improve the effectiveness and reliability of wireless communications. Based on the analysis of the current status of research on classification and identification of space-time coded signals, in actual communications, some natural and artificial factors, such as atmospheric noise caused by lightning, multi-user interference, and various artificial noises, make the communication environment noise extremely complex. This type of noise is usually described by non-Gaussian distribution. When the noise environment is non-Gaussian noise, the existing methods will face failure, and the accuracy, real-time and robustness of signal classification effects are facing severe challenges. Therefore, research on identification of MIMO-OFDM space-time coding schemes under non-Gaussian noise is of great significance.

[0003] In recent years, many scholars have conducted research related to the recognition of space-time block coding (STBC). Regarding the recognition of space-time block codes (STBC): Shi et al. used the second-order cyclostationarity of dual receiving antennas to distinguish between spatial multiplexing (SM) codes and Alamouti (AL) codes (Shi M, Barness Y, Su W. STC and BLAST MIMO Modulation Recognition [C] / / IEEE. IEEE, 2007.). Based on the prior conclusion that the discrete Fourier transform of the fourth-order moment and the fourth-order lag product can be used for blind signal classification, Deyoung et al. proposed four methods suitable for solving the blind recognition problem of SM (Spatial Multiplexing) signals and AL (Alamouti) signals, including a likelihood ratio detection decision algorithm based on the fourth-order moment and three Fourier transform algorithms based on the fourth-order lag product (Deyoung MR, Heath RW, Evans BL. Using Higher Order Cyclostationarity to Identify Space-Time Block Codes [C] / / Global Telecommunications Conference, 2008.). Choqueuse et al. proposed the maximum likelihood method for blind recognition of STBC (Choqueuse V, Marazin M, Collin L, et al. Blind Recognition of Linear Space–Time Block Codes: A Likelihood-Based Approach [J]. IEEE Transactions on Signal Processing, 2010, 58 (3): 1290-1299.). Eldemerdash et al. proposed a series of methods based on fourth-order moments to distinguish SM codes and AL codes under Nakagami fading (Eldemerdash M, Yahia A, Marey M, et al. Fourth-Order Statistics for Blind Classification of Spatial Multiplexing and Alamouti Space-Time Block Code Signals [J]. IEEE Transactions on Communications, 2013, 61 (6): 2420-2431.).These algorithms have relatively ideal recognition accuracy under low signal-to-noise ratio and limited number of receiving antennas, but they rely on prior information such as data rate, carrier phase and frequency offset, phase noise and propagation channel parameters. Some methods have high computational costs and the types of space-time codes that can be classified are also relatively limited.

[0004] In addition, Choqueuse et al. used the Frobenius norm of the spatiotemporal correlation function to distinguish several STBCs (Choqueuse V, Yao K, Collin L, et al. Hierarchical Space-Time Block Code Recognition Using Correlation Matrices [J]. IEEE Transactions on Wireless Communications, 2008, 7 (9): 3526-3534.). Marey et al. developed and analyzed the application of second-order cyclostationarity in identifying STBCs using two receiving antennas under different transmission impairment conditions (Marey M, Dobre OA, Inkol R. Classification of Space-Time Block Codes Based on Second-Order Cyclostationarity with Transmission Impairments [J]. IEEE Transactions on Wireless Communications, 2012, 11 (7): 2574-2584.). Marey et al. used space-time redundancy and could use the cross-correlation of signals received from different antennas as identification features to perform STBC identification (Marey M, Dobre OA, Inkol R. Blind STBC Identification for Multiple-Antenna OFDM Systems [J]. IEEE Transactions on Communications, 2014, 62 (5): 1554-1567.). Yan et al. used the characteristics of high-order cumulants to avoid the influence of Gaussian noise, and mined some features for distinguishing STBC signals based on the fourth-order cumulants, and then used an interval detector for STBC detection and identification (Yan W, Zhang L, Ling Q. An algorithm for space–time block code classification using higher-order statistics (HOS) [J]. Springer Plus, 2016, 5 (1): 1-13.). Chung et al. mentioned that STBC signals are correlated in the time domain, and they have a special cyclic frequency in the high-order cyclic cumulants, while VBLAST transmitted from different antennas are uncorrelated. Based on this characteristic, the authors used the fourth-order cyclic cumulant algorithm to blindly identify STBC and VBLAST signals.(Chung B, Zhang T. Blind recognition of space time block code in MIMO systems [J]. Digital Signal Processing, 2018, 83: 1-8.). Zhang et al. proposed a residual network (RN) based model for identifying 6 STBC signals with a single receiving antenna, including coding matrices of the same length (Zhang L, Zhang Y, Yan W, et al. Blind identification of space–time block codes based on deep learning [J]. Chinese Journal of Aeronautics, 2022, 35 (1): 10.). Zhang et al. proposed a CNN-based multi-delay feature fusion automatic STBC recognition method. The proposed scheme uses dilated convolution with different dilation rates to realize automatic multi-delay feature extraction, combines the extracted different delay features, and realizes STBC recognition based on the two proposed multi-delay feature fusion methods (Zhang Y, Yan W, Zhang L, et al. Automatic Space-Time Block Code Recognition Using Convolutional Neural Network With Multi-DelayFeatures Fusion[J]. IEEE Access, 2021, PP(99):1-1.). However, the above algorithms are mostly focused on Gaussian noise frequency selective channel environments. Under the interference of non-Gaussian noise, the recognition algorithm under the Gaussian distribution noise assumption may face performance degradation or even failure.

[0005] Through the above analysis, the problems and defects of the prior art are as follows:

[0006] (1) Most existing space-time block coding scheme identification methods require prior information such as channel parameters, modulation scheme, and noise distribution, and the number of space-time block coding schemes that can be classified is also relatively limited;

[0007] (2) Existing research on space-time block coding recognition methods mainly focuses on Gaussian noise frequency selective channel environments. However, under the interference of non-Gaussian noise, the existing recognition algorithms under the Gaussian distribution assumption face performance degradation or even failure;

[0008] (3) Most of the existing space-time block coding recognition algorithms are traditional, with relatively simple features, and do not consider the complementarity between different features and the optimal selection of features. Summary of the invention

[0009] In order to overcome the problems existing in the above-mentioned prior art, the present invention provides a method, system, device and medium for identifying MIMO-OFDM space-time coding mode under non-Gaussian noise. By extracting the time-delay correlation peak features suitable for MIMO-OFDM signals in a non-Gaussian noise environment, a feature selection model is constructed and feature optimization selection is performed to determine the feature set for final classification; the method for identifying MIMO-OFDM space-time coding mode under non-Gaussian noise can be effectively implemented, and good classification accuracy is still achieved under the condition of a small generalized signal-to-noise ratio.

[0010] In order to achieve the above object, the technical solution adopted by the present invention is:

[0011] A method for identifying a MIMO-OFDM space-time coding mode under non-Gaussian noise comprises the following steps:

[0012] Step 1: extract the time-delay correlation peak features applicable to MIMO-OFDM signals in non-Gaussian noise environments, and construct a feature space for feature optimization selection;

[0013] Step 2: construct a feature optimization selection model based on the extreme gradient boosting sequence floating backward selection algorithm, and determine the feature set for final classification according to feature importance;

[0014] Step three, construct a classifier model based on tree-enhanced naive Bayes, and classify and identify the space-time coding method according to the selected features.

[0015] Further, the specific process of step one is:

[0016] First, the nth sample of the signal received from the i-th receiving antenna under non-Gaussian noise can be expressed as:

[0017]

[0018] Among them, h fi represents the channel between the fth transmitting antenna and the ith receiving antenna, L h represents the number of channels in all transmit-receive antenna pairs, where i = 0, 1, N r ,s (f) (n) is the sequence s sent from antenna f (f) The nth element of (i) (n) is with s (f) (n) noises that are independent of each other and follow an α-stable distribution;

[0019] Calculate the time-delay correlation of the received signal under different receiving antennas, and its expression is:

[0020]

[0021] Among them, λ represents the space-time coding category, L (λ) is the block length of the space-time coding method, τ represents different time delays, y (·) Represents the received signals of different receiving antennas; the time-delay correlation of the received signal is calculated by using different correlation characteristic functions, and the time-delay correlation peaks at time delays τ = 1, 2, and 4 are extracted respectively:

[0022] F (λ) (τ)=max(A (λ) (n,τ)), where τ=1,2,4

[0023] The multiple peak features extracted under different related feature functions are used as the feature space for feature optimization selection; the related feature functions used are as follows:

[0024] (1) Correlation function 1 features, its expression is:

[0025] R BNC-1 (X,Y)=E(g 1 (X)g 2 (Y)), where g(x) = (2 / π)arctan(πx / 2);

[0026] (2) Correlation function 2 features, its expression is:

[0027] R BNC-2 (X,Y)=E(g 1 (X)g 2 (Y)), where g(x) = x / (1 + |x|);

[0028] (3) Fractional low-order correlation (FLOC) feature, whose expression is:

[0029]

[0030] Among them, z ＝|z|p-1z*,z∈C；

[0031] (4)相位分数低阶相关(PFLOC)特征，其表达式为：

[0032]

[0033] 其中，z-<q>< / q>＝(z*)<q>< / q>＝(z<q>< / q>)*＝(||z||q-1z*)*＝||z||q-1z,z∈C；

[0034] (5)基于广义高斯核函数的相关熵的相关特征，其表达式为：

[0035]

[0036] 其中，广义高斯核函数表达式为：

[0037]

[0038]

[0039]

[0040] 其中，β∈R+表示广义高斯分布函数的特征指数，μ∈R表示位置参数；

[0041] (6)基于高斯核函数的相关熵的相关特征，其表达式为：

[0042]

[0043] 其中，高斯核函数：σ是核函数核长参数。

[0044] 进一步，所述步骤二的具体过程为：

[0045] 基于极端梯度提升算法，建立空时编码方式和相关特征空间的映射数据集为:

[0046] D＝{(xi,yi)∣i＝1～n,xi∈Rm,yi∈R}

[0047] 数据集有m个特征，n个训练样本，每个样本对应一个标签y；其中m为特征空间中提取的特征点个数，yi为第i个样本对应的空时编码方式；而且每个决策树的输出yi的定义如下:

[0048]

[0049] 其中，k是决策树的数量，ft(·)为回归树，F是所有可能的回归树集合；为了避免过拟合，极端梯度提升算法使用树的复杂度函数作为目标损失函数的常数项；极端梯度提升算法的目标函数的详细公式如下：

[0050]

[0051]

[0052]

[0053] 其中，C是常数，xi是输入向量，Tt表示树中的叶子数，w是第k棵树的叶节点权重值；yi和分别表示类别的实际值和预测值；γ是叶节点的系数，λ是叶权重惩罚的标准项，γ和λ用来限制模型过拟合的可能性；l(·)是平方损失函数，ft(·)为回归树，Ω(·)是回归函数模型；同时，极端梯度提升算法对目标函数执行二阶泰勒展开；根据泰勒公式，目标函数G(t)近似表示如下：

[0054]

[0055] 其中，gi和分别是泰勒展开式中第一项和二次项的系数；

[0056] 利用特征空间中的所有特征，基于极端梯度提升算法生成模型过程中的信息，通过使目标函数G(t)一阶导数为0来求解最佳权重，以此来确定分割样本的特征，选用被用作分割样本的特征的次数weight作为特征的重要性度量分数；

[0057] weight＝|X|

[0058] 其中，X是所求特征分类到叶子节点的集合；得到特征的重要性度量分数并按降序排序；

[0059] 之后再结合改进的序列后向搜索策略，即从特征空间的原始候选集合开始，每轮减少一个无关特征，依次从当前完整特征集中剔除该轮迭代中特征重要性度量得分最低即排序最靠后的特征，再根据评价算法计算待剔除特征与其他剩余特征的皮尔逊相关系数：

[0060]

[0061] 其中，cov(X,Y)是两个特征属性变量X,Y之间的协方差，δX，δY分别是X,Y的样本标准差；之后并行地选出与度量分数排序末尾特征相关的靠后的特征，并剔除该特征，重新进行新一轮的预测和排序，记录每轮迭代过程中保留特征集下的预测分类准确率，用于确定预测分类准确率最高的保留特征子集，遍历所有子集的分类预测准确率情况，选择分类准确度最高且特征数量最少的特征子集作为最优特征子集，即为最终特征优化选择的结果。

[0062] 进一步，所述步骤三的具体过程为：

[0063] 树增强朴素贝叶斯中，加入类变量属性，属性之间的关联性的前提是要在某一分类属性确定下进行重新计算，不同的类属性值会有不同的属性关联性，利用条件互信息描述在给定类变量Z时，特征属性变量X,Y之间的依赖强度如下所示：

[0064]

[0065] 其中，z为类别属性时，x,y为特征属性，P(x|z)表示在z发生的条件下，出现x情况的概率；

[0066] 计算完特征选择之后的各个属性对的互信息值后，进行贝叶斯网络的构建，

[0067] 每一个节点的条件概率表用以下公式表示：

[0068]

[0069] 其中，xi代表子特征，πi代表子特征依赖的所有父特征的集合，θ代表子特征的条件概率表，所有特征的条件概率表的集合用Θ表示，再加上贝叶斯网络的结构G，用以下公式表示整个贝叶斯网络：

[0070] B＝＜G,Θ＞

[0071] 从而估计类条件概率，得到新样本的类别；通过训练集D计算P(C),P(x1|C),,P(xn|C)的估计值,根据最大似然原理,当给定一个未知类别的测试数据(x1,xn),能够使得最大的类别C即是(x1,xn)所属的类别：

[0072]

[0073] 其中，P(C)为类概率估计，表示属于类别C的概率，P(Xi|C)为条件概率估计。

[0074] 本发明的另一目的在于提供一种非高斯噪声下MIMO-OFDM空时编码方式识别系统，其特征在于，所述非高斯噪声下MIMO-OFDM空时编码方式识别系统包括：

[0075] 特征空间构建模块，用于提取适用于非高斯噪声环境下MIMO-OFDM信号的时滞相关峰值特征，构建用于特征优化选择的特征空间；

[0076] 特征优化选择模块，用于构建基于极端梯度提升序列浮动后向选择算法的特征优化选择模型，根据特征重要性确定用于最终分类的特征集合；

[0077] 空时编码方式识别模块，用于构建基于树增强朴素贝叶斯的分类器模型，根据优选出的特征对空时编码方式进行分类识别。

[0078] 进一步的，一种非高斯噪声下MIMO-OFDM空时编码方式识别设备，包括：

[0079] 存储器，用于存储计算机程序；

[0080] 处理器，用于执行所述计算机程序时实现权利要求1至4任一项所述非高斯噪声下MIMO-OFDM空时编码方式识别方法。

[0081] 进一步的，一种计算机可读存储介质，所述计算机可读存储介质存储有计算机程序，所述计算机程序被处理器执行时能够基于非高斯噪声下MIMO-OFDM空时编码方式识别方法进行非高斯噪声下MIMO-OFDM空时编码方式识别。

[0082] 本发明有益效果如下：

[0083] 1、本发明利用适应于非高斯下进行分类识别的信号处理，包括非线性变换，分数低阶化和基于相关熵的处理，克服了在非高斯噪声的干扰下，现有的高斯分布假设下识别算法面临性能退化甚至失效的问题。

[0084] 2、本发明使用了适用于非高斯噪声下多种相关特征函数来对峰值特征进行提取，克服了传统识别方法中特征单一，没有考虑不同特征之间的互补性的问题。

[0085] 3、本发明使用了极端梯度提升序列浮动后向选择算法来实现对特征的优化选择，提高了特征选择的速度和识别精度。

[0086] 4、本发明使用了基于树增强朴素贝叶斯的分类器模型，解决了条件间的部分属性依赖的问题，既满足了计算复杂度简单的要求，又能提高分类准确率。

[0087] 综上，本发明通过提取适用于非高斯噪声环境下MIMO-OFDM信号的时滞相关峰值特征，构建特征选择模型并进行特征优化选择以确定最终分类的特征集合；能够有效实现非高斯噪声下MIMO-OFDM空时编码方式识别方法，且在较小广义信噪比的条件下仍然具有较好的分类精度。附图说明

[0088] 图1是本发明实施例提供的非高斯噪声下MIMO-OFDM空时编码方式识别方法流程图。

[0089] 图2是本发明实施例提供的非高斯噪声下MIMO-OFDM空时编码方式识别系统结构示意图。

[0090] 图3是本发明实施例提供的极端梯度提升序列浮动后向选择算法流程图。

[0091] 图4是本发明实施例提供的非高斯噪声下MIMO-OFDM空时编码方式识别系统的仿真实验结果示意图；其中，图(4)a为不同广义信噪比下空时编码四种码型的分类精度；图4(b)为非高斯α稳定噪声在不同的特征指数α条件下本发明所提方法的分类识别性能。具体实施方式

[0092] 为了使本发明的目的、技术方案及优点更加清楚明白，以下结合实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。

[0093] 针对现有技术存在的问题，本发明提供了一种非高斯噪声下MIMO-OFDM空时编码方式识别方法及系统，下面结合附图对本发明作详细的描述。

[0094] 本发明提供的非高斯噪声下MIMO-OFDM空时编码方式识别方法业内的普通技术人员还可以采用其他的步骤实施，图1的本发明提供的非高斯噪声下MIMO-OFDM空时编码方式识别方法仅仅是一个具体实施例而已。

[0095] 如图1所示，本发明实施例提供的非高斯噪声下MIMO-OFDM空时编码方式识别方法包括：

[0096] S101：提取适用于非高斯噪声环境下MIMO-OFDM信号的时滞相关峰值特征，构建用于特征优化选择的特征空间；本发明中的特征空间直接决定提取的原始特征集对于不同空时编码方式是否可以有效分类；

[0097] S102：构建基于极端梯度提升序列浮动后向选择算法的特征优化选择模型，根据特征重要性确定用于最终分类的特征集合；本发明中的特征选择直接决定了用于最终分类的特征集合，在原始特征空间里根据重要性度量分数标准优化选择具有代表性，预测分类准确度最高的特征子集；

[0098] S103：构建基于树增强朴素贝叶斯的分类器模型，根据优选出的特征对空时编码方式进行分类识别。

[0099] 本发明实施例提供的S101中，提取适用于非高斯噪声环境下MIMO-OFDM信号的时滞相关峰值特征，构建用于特征优化选择的特征空间，具体过程为：

[0100] 在非高斯α稳定分布噪声下，我们考虑采用MIMO-OFDM系统以及Nt个发射天线和Nr个接收天线,在该系统中，数据符号在调制后进行空时编码，之后通过MIMO信道发送到发射天线，并由接收天线接收。分别将数据符号流解析成数据块，每个数据块dw＝[dw(0),dw(1),…,dw(N-1)]由N个数据符号组成，第m个OFDM块经过STBC编码器将每Ns个数据映射成一个大小为Nt×LN的空时码矩阵在从Nt个天线发送，Ns为每个编码矩阵的传递的符号数，L为编码矩阵的长度。MIMO-OFDM信号选用的四种典型的空时编码方式的编码矩阵分别表示为:

[0101] (1)SM(空间复用)

[0102] 发射天线数Nt＝2，码率rate＝2，编码矩阵长度为L＝1，编码矩阵的具体表示为：

[0103]

[0104] (2)Alamouti(阿拉穆帝)

[0105] 发射天线数Nt＝2，码率rate＝1，编码矩阵长度为L＝2，每组STBC码可传输的符号数Ns＝2，编码矩阵的具体表示为：

[0106]

[0107] (3)STBC3(OSTBC-3 / 4)

[0108] 发射天线数Nt＝3，码率编码矩阵长度为L＝4，每组STBC码可传输的符号数Ns＝3，编码矩阵的具体表示为：

[0109]

[0110] (4)STBC4(OSTBC-1 / 2)

[0111] 发射天线数Nt＝3，码率编码矩阵长度为L＝8，则每组STBC码可传输的符号数Ns＝4，编码矩阵的具体表示为：

[0112]

[0113] 非高斯噪声下从第i个接收天线接收到的信号的第n个样本可以表示为：

[0114]

[0115] 这里hfi和Lh表示第f个发射天线和第i个接收天线之间的信道，以及所有发射-接收天线对中信道数量，其中i＝0，1，，Nr,s(f)(n)是从天线f上发送的序列s(f)的第n个元素。w(i)(n)是与s(f)(n)彼此独立的服从α稳定分布的噪声，α稳定分布随机变量的概率密度函数没有闭合形式，因而用特征函数表示，其表达式为:

[0116]

[0117] 其中其中，α为特征指数，特征指数α的取值范围1≤α≤2，特征指数α越小，拖尾越长，噪声的冲击性越强，特别地，当α＝2时，上面的特征函数与方差为2γ的高斯分布的特征函数相同，因此高斯分布是α稳定分布的一种特例。这里采用的是标准SαS分布，即对称参数β＝0，位置参数δ＝0，并且分散系数γ＝1。

[0118] 计算不同接收天线下的时滞相关，其表达式为：

[0119]

[0120] 其中，λ表示空时编码类别，L(λ)是λ空时编码方式的块长度，τ代表不同时滞,y(·)表示不同接收天线的接收信号。通过使用不同相关特征函数来计算接收信号的时滞相关，分别提取在时滞τ＝1,2,4的时滞相关峰值：

[0121] F(λ)(τ)＝max(A(λ)(n,τ)),其中，τ＝1,2,4

[0122] 将提取到的不同相关特征函数下的多个峰值特征作为特征优化选择的特征空间。所用的相关特征函数如下：

[0123] (1)相关函数1特征，其表达式为：

[0124] RBNC-1(X,Y)＝E(g1(X)g2(Y))，其中，g(x)＝(2 / π)arctan(πx / 2)；

[0125] (2)相关函数2特征，其表达式为：

[0126] RBNC-2(X,Y)＝E(g1(X)g2(Y))，其中，g(x)＝x / (1+|x|)；

[0127] (3)分数低阶相关(FLOC)特征，其表达式为：

[0128]

[0129] 其中，z＝|z|p-1z*,z∈C；

[0130] (4)相位分数低阶相关(PFLOC)特征，其表达式为：

[0131]

[0132] 其中，z-<q>< / q>＝(z*)<q>< / q>＝(z<q>< / q>)*＝(|z|q-1z*)*＝|z|q-1z,z∈C；

[0133] (5)基于广义高斯核函数的相关熵的相关特征，其表达式为：

[0134]

[0135] 其中，广义高斯核函数表达式为：

[0136]

[0137]

[0138]

[0139] 其中，β∈R+表示广义高斯分布函数的特征指数，μ∈R表示位置参数；

[0140] (6)基于高斯核函数的相关熵的相关特征，其表达式为：

[0141]

[0142] 其中，高斯核函数：σ是核函数核长参数。

[0143] 本发明实施例提供的S102中，构建基于极端梯度提升序列浮动后向选择算法的特征优化选择模型，根据特征重要性确定用于最终分类的特征集合的具体过程为：

[0144] 基于极端梯度提升算法，建立空时编码方式和相关特征的映射。给定数据集为:

[0145] D＝{(xi,yi)∣i＝1～n,xi∈Rm,yi∈R}

[0146] 数据集有m个特征，n个训练样本，每个样本对应一个标签y。其中m为特征空间中提取的特征点个数，yi为第i个样本对应的空时编码方式。而且每个决策树的输出yi的定义如下:

[0147]

[0148] 其中，k是决策树的数量，ft(·)为回归树，F是所有可能的回归树集合。为了避免过拟合，极端梯度提升算法使用树的复杂度函数作为目标损失函数的常数项。极端梯度提升算法的目标函数的详细公式如下：

[0149]

[0150]

[0151]

[0152] 其中，C是常数，xi是输入向量，Tt表示树中的叶子数，w是第k棵树的叶节点权重值。yi和分别表示类别的实际值和预测值。γ是叶节点的系数，λ是叶权重惩罚的标准项，γ和λ用来限制模型过拟合的可能性。l(·)是平方损失函数，ft(·)为回归树，Ω(·)是回归函数模型。同时，极端梯度提升算法对目标函数执行二阶泰勒展开。根据泰勒公式，目标函数G(t)近似表示如下：

[0153]

[0154] 其中，gi和分别是泰勒展开式中第一项和二次项的系数。

[0155] 极端梯度提升算法在训练过程中为了提高生成新树的效率，会在每轮迭代中给出各个特征的重要度评分，从而表明每个特征对模型训练的重要性，为下一次迭代建立梯度方向的新树提供依据。通过每个属性分割点改进性能度量的量来计算单个决策树的重要性，并由节点负责的观察数量加权。最后，在模型中的所有决策树中对要素重要性进行平均。本发明利用特征空间中的所有特征，基于极端梯度提升算法生成模型过程中的信息，通过使目标函数G(t)一阶导数为0来求解最佳权重，以此来确定分割样本的特征，选用在树中被用作分割样本的特征的次数weight作为特征的重要性度量分数。

[0156] weight＝|X|

[0157] 其中，X是所求特征分类到叶子节点的集合。得到特征的重要性度量分数并按降序排序。

[0158] 之后再结合改进的序列后向搜索策略：从特征空间的原始候选集合开始，每轮减少一个无关特征。依次从当前完整特征集中剔除该轮迭代中特征重要性度量得分最低(即排序最靠后)的特征，再根据评价算法计算待剔除特征与其他剩余特征的皮尔逊相关系数：

[0159]

[0160] 其中，cov(X,Y)是两个特征属性变量X,Y之间的协方差，δX，δY分别是X,Y的样本标准差。之后并行地选出与度量分数排序末尾特征相关的靠后的特征，并剔除该特征，重新进行新一轮的预测和排序，记录每轮迭代过程中保留特征集下的预测分类准确率，用于确定预测分类准确率最高的保留特征子集。

[0161] 为保证模型训练的可靠性和稳定性，每轮迭代中对训练集随机抽取。每次选取特征数据集的70％作为训练集及特征集重要性排序，并保证每次抽取出的样本类别比例与整个数据集中样本类别的比例相同，数据集的30％作为测试集用于求出预测分类精度。遍历所有子集的分类预测准确率情况，选择分类准确度最高同时特征数量最少的特征子集作为最优特征子集，即为最终特征优化选择的结果。

[0162] 本发明实施例提供的S103，具体过程为：

[0163] 树增强朴素贝叶斯中，加入了类变量属性，因为属性之间的关联性的前提是要在某一分类属性确定下进行重新计算，不同的类属性值会有不同的属性关联性，利用条件互信息描述在给定类变量Z时，特征属性变量X,Y之间的依赖强度如下所示：

[0164]

[0165] 其中，z为类别属性时，x,y为特征属性，P(x|z)表示在z发生的条件下，出现x情况的概率。

[0166] 计算完各个属性对的互信息值后，进行贝叶斯网络的构建，构造一个无向完全图，以描述属性为结点，以条件互信息为边的权重；构造上述无向完全图的最大生成树；在上述最大生成树中选择一个描述属性结点为根结点，将所有边的方向设置成由根结点指向外，把无向图转换成有向树(不能含有回路)；在上述有向树中添加结点和结点到各个描述属性结点的有向边，得到贝叶斯网。

[0167] 每一个节点的条件概率表用以下公式表示：

[0168]

[0169] 其中，xi代表子特征，πi代表子特征依赖的所有父特征的集合，θ代表子特征的条件概率表，所有特征的条件概率表的集合用Θ表示，再加上贝叶斯网络的结构G，用以下公式表示整个贝叶斯网络：

[0170] B＝＜G,Θ＞

[0171] 从而估计类条件概率，得到新样本的类别。通过训练集D计算P(C),P(x1|C),,P(xn|C)的估计值,根据最大似然原理,当给定一个未知类别的测试数据(x1,xn),能够使得最大的类别C即是(x1,xn)所属的类别：

[0172]

[0173] 其中，P(C)为类概率估计，表示属于类别C的概率，P(Xi|C)为条件概率估计。

[0174] 如图2所示，本发明实施例提供的非高斯噪声下MIMO-OFDM空时编码方式识别系统包括：

[0175] 特征空间构建模块1，用于提取适用于非高斯噪声环境下MIMO-OFDM信号的时滞相关峰值特征，构建用于特征优化选择的特征空间；

[0176] 特征优化选择模块2，用于构建基于极端梯度提升序列浮动后向选择算法的特征优化选择模型，根据特征重要性确定用于最终分类的特征集合；

[0177] 空时编码方式识别模块3，用于构建基于树增强朴素贝叶斯的分类器模型，根据优选出的特征对空时编码方式进行分类识别。

[0178] 本发明提供的分类识别方法除可用于非高斯噪声下MIMO-OFDM空时编码方式识别外，还可用于高斯噪声下MIMO-OFDM空时编码方式识别。

[0179] 下面结合仿真实验对本发明的技术效果作详细的描述。

[0180] 为了评估本发明的性能，进行仿真验证。在仿真实验中，考虑非高斯噪声下MIMO-OFDM空时编码方式识别系统，待识别的空时编码方式包括4种：SM、AL、STBC3(OSTBC-3 / 4)、STBC4(OSTBC-1 / 2)。考虑了具有N＝64个子载波、循环前缀长度v＝5和正交相移键控(QPSK)的MIMO-OFDM系统，接收天线个数Nr＝2，信道选择为未知的频率选择性无线信道，非高斯噪声选择标准α稳定分布噪声，研究广义信噪比对分类性能影响时的仿真参数设置如下：非高斯α稳定分布噪声特征指数α＝1.5，广义信噪比分别选用在区间[-4,16]内且间隔为2dB的值，每个信噪比下产生4000个样本，样本中70％用于训练分类模型，剩余的30％用于求取当前的分类精度，仿真实验采取对8000个OFDM块进行平均的统计仿真，验证性能。研究特征指数α对分类性能影响时的仿真参数设置如下：特征指数α分别选用在区间[1.0,2.0]内且间隔为0.1的值。本发明所提的方法在不同条件下进行了识别精度的对比分析，其仿真结果如图4所示。图4的(a)给出了不同广义信噪比下空时编码四种码型的分类精度，由图4的(a)可以看出，随着广义信噪比的增加，本发明所提方法的分类识别性能逐渐提升，且低信噪比下也有较高的识别精度。图4的(b)给出了非高斯α稳定噪声在不同的特征指数α条件下本发明所提方法的分类识别性能，由图4的(b)可以看出，对于不同的特征指数α，在不同的噪声冲击下，本发明所提方法的在高斯与非高斯环境下均具有良好的识别精度。因此，与现有算法比较，本发明方法具有明显的分类识别性能优势。

[0181] 应当注意，本发明的实施方式可以通过硬件、软件或者软件和硬件的结合来实现。硬件部分可以利用专用逻辑来实现；软件部分可以存储在存储器中，由适当的指令执行系统，例如微处理器或者专用设计硬件来执行。本领域的普通技术人员可以理解上述的设备和方法可以使用计算机可执行指令和 / 或包含在处理器控制代码中来实现，例如在诸如磁盘、CD或DVD-ROM的载体介质、诸如只读存储器(固件)的可编程的存储器或者诸如光学或电子信号载体的数据载体上提供了这样的代码。本发明的设备及其模块可以由诸如超大规模集成电路或门阵列、诸如逻辑芯片、晶体管等的半导体、或者诸如现场可编程门阵列、可编程逻辑设备等的可编程硬件设备的硬件电路实现，也可以用由各种类型的处理器执行的软件实现，也可以由上述硬件电路和软件的结合例如固件来实现。

[0182] 以上所述，仅为本发明的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，都应涵盖在本发明的保护范围之内。

Claims

1. A method for identifying MIMO-OFDM space-time coding mode under non-Gaussian noise, characterized in that: The specific steps include: Step 1: extract the time-delay correlation peak features applicable to MIMO-OFDM signals in non-Gaussian noise environments, and construct a feature space for feature optimization selection; The specific process is: First, the nth sample of the signal received from the i-th receiving antenna under non-Gaussian noise can be expressed as: Among them, h fi represents the channel between the fth transmitting antenna and the ith receiving antenna, L h represents the number of channels in all transmit-receive antenna pairs, where i = 0, 1, ..., N r ,s (f) (n) is the sequence s sent from antenna f (f) The nth element of (i) (n) is with s (f) (n) noises that are independent of each other and follow an α-stable distribution; Calculate the time-delay correlation of the received signal under different receiving antennas, and its expression is: Among them, λ represents the space-time coding category, L (λ) is the block length of the space-time coding method, τ represents different time delays, y (·) Represents the received signals of different receiving antennas; the time-delay correlation of the received signal is calculated by using different correlation characteristic functions, and the time-delay correlation peaks at time delays τ = 1, 2, and 4 are extracted respectively: F (λ) (τ)=max(A (λ) (n,τ)), where τ=1,2,4 The multiple peak features extracted under different related feature functions are used as the feature space for feature optimization selection; the related feature functions used are as follows: (1) Correlation function 1 features, its expression is: R BNC-1 (X,Y)=E(g1(X)g2(Y)),including,g(x)=(2 / π)arctan(πx / 2)= (2) Correlation function 2 features, its expression is: R BNC-2 (X,Y) = E(g1(X)g2(Y)), where g(x) = x / (1 + |x|); (3) Fractional low-order correlation (FLOC) feature, whose expression is: Among them, z ＝|z|p-1z*,z∈C； (4) Phase fractional low-order correlation (PFLOC) feature, which is expressed as: where z -<q>< / q> =(z * ) <q>< / q> =(z <q>< / q> ) * =(|z| q-1 z * ) * =|z| q-1 z, z ∈ C; (5) The related features of the correlation entropy based on the generalized Gaussian kernel function are expressed as follows: Among them, the generalized Gaussian kernel function expression is: Among them, β∈R+ represents the characteristic index of the generalized Gaussian distribution function, μ∈R represents the location parameter; (6) The related features of the correlation entropy based on the Gaussian kernel function are expressed as follows: Among them, the Gaussian kernel function: σ is the kernel length parameter of the kernel function; Step 2: Build a feature optimization selection model based on the extreme gradient boosting sequence floating backward selection algorithm, and determine the feature set for final classification according to feature importance; the specific process is as follows: Based on the extreme gradient boosting algorithm, the mapping data set of space-time coding mode and related feature space is established as follows: D={(x i ,y i )∣i=1~n,x i ∈R m ,y i ∈R} The dataset has m features and n training samples, each of which corresponds to a label y; m is the number of feature points extracted in the feature space, and y is i is the space-time coding method corresponding to the i-th sample; and the output y of each decision tree i is defined as follows: Where k is the number of decision trees, f t (·) is a regression tree, and F is the set of all possible regression trees. In order to avoid overfitting, the extreme gradient boosting algorithm uses the complexity function of the tree as the constant term of the objective loss function. The detailed formula of the objective function of the extreme gradient boosting algorithm is as follows: Where C is a constant, x i is the input vector, T t represents the number of leaves in the tree, w is the leaf node weight value of the kth tree; y i and denote the actual value and predicted value of the category respectively; γ is the coefficient of the leaf node, λ is the standard term of the leaf weight penalty, γ and λ are used to limit the possibility of overfitting of the model; l(·) is the square loss function, f t (·) is a regression tree, Ω(·) is a regression function model; at the same time, the extreme gradient boosting algorithm performs a second-order Taylor expansion on the objective function; according to the Taylor formula, the objective function G(t) is approximately expressed as follows: Among them, g i and are the coefficients of the first and second terms in Taylor expansion respectively; Using all the features in the feature space, based on the information generated in the model process of the extreme gradient boosting algorithm, the optimal weight is solved by making the first-order derivative of the objective function G(t) equal to 0, so as to determine the features of the segmented samples, and the number of times the feature is used to segment the sample is selected as the feature importance measurement score; weight=|X| Where X is the set of leaf nodes of the desired feature classification; get the importance metric score of the feature and sort it in descending order; Then, combined with the improved sequential backward search strategy, starting from the original candidate set in the feature space, one irrelevant feature is reduced in each round, and the features with the lowest feature importance metric score in this round of iteration, that is, the features with the lowest ranking, are removed from the current complete feature set in turn. Then, the Pearson correlation coefficient between the features to be removed and other remaining features is calculated according to the evaluation algorithm: Among them, cov(X,Y) is the covariance between two feature attribute variables X and Y, δ X , δ Y are the sample standard deviations of X and Y respectively; then, the features at the end of the feature at the end of the metric score sorting are selected in parallel, and the features are removed, and a new round of prediction and sorting is performed again. The prediction classification accuracy under the retained feature set is recorded in each round of iteration to determine the retained feature subset with the highest prediction classification accuracy. The classification prediction accuracy of all subsets is traversed, and the feature subset with the highest classification accuracy and the least number of features is selected as the optimal feature subset, which is the result of the final feature optimization selection; Step 3: Construct a classifier model based on tree-enhanced naive Bayes to classify and identify the space-time coding method according to the features selected by feature optimization; the specific process is as follows: In tree-enhanced naive Bayes, class variable attributes are added. The premise of the correlation between attributes is to recalculate under a certain classification attribute. Different class attribute values ​​will have different attribute correlations. The conditional mutual information is used to describe the dependency strength between feature attribute variables X and Y when a given class variable Z is given as follows: Among them, when z is the category attribute, x and y are feature attributes, P(x|z) represents the probability of x occurring under the condition that z occurs; After calculating the mutual information values ​​of each attribute pair after feature selection, the Bayesian network is constructed. The conditional probability table of each node is expressed by the following formula: Among them, x i represents the sub-feature, π i Represents the set of all parent features that the child feature depends on, θ represents the conditional probability table of the child feature, and the set of conditional probability tables of all features is represented by Θ. Together with the structure G of the Bayesian network, the entire Bayesian network is represented by the following formula: B=<G,Θ> Thus, the class conditional probability is estimated and the category of the new sample is obtained; P(C), P(x1|C),…, P(x n |C), according to the maximum likelihood principle, when given a test data of unknown category (x1,…x n ), which can make The largest category C is (x1,…x n ) belongs to the category: Among them, P(C) is the class probability estimate, which represents the probability of belonging to category C, and P(X i |C) is the conditional probability estimate.

2. A system for identifying MIMO-OFDM space-time coding mode under non-Gaussian noise according to claim 1, characterized in that: The MIMO-OFDM space-time coding mode identification system under non-Gaussian noise includes: The feature space construction module is used to extract the time-delay correlation peak features applicable to MIMO-OFDM signals in non-Gaussian noise environments and construct a feature space for feature optimization selection. First, the nth sample of the signal received from the i-th receiving antenna under non-Gaussian noise can be expressed as: Among them, h fi represents the channel between the fth transmitting antenna and the ith receiving antenna, L h represents the number of channels in all transmit-receive antenna pairs, where i = 0, 1, ..., N r ,s (f) (n) is the sequence s sent from antenna f (f) The nth element of (i) (n) is with s (f) (n) noises that are independent of each other and follow an α-stable distribution; Calculate the time-delay correlation of the received signal under different receiving antennas, and its expression is: Among them, λ represents the space-time coding category, L (λ) is the block length of the space-time coding method, τ represents different time delays, y (·) Represents the received signals of different receiving antennas; the time-delay correlation of the received signal is calculated by using different correlation characteristic functions, and the time-delay correlation peaks at time delays τ = 1, 2, and 4 are extracted respectively: F (λ) (τ)=max(A (λ) (n,τ)), where τ=1,2,4 The multiple peak features extracted under different related feature functions are used as the feature space for feature optimization selection; the related feature functions used are as follows: (1) Correlation function 1 features, its expression is: R BNC-1 (X,Y)=E(g1(X)g2(Y)),including,g(x)=(2 / π)arctan(πx / 2)= (2) Correlation function 2 features, its expression is: R BNC-2 (X,Y) = E(g1(X)g2(Y)), where g(x) = x / (1 + |x|); (3) Fractional low-order correlation (FLOC) feature, whose expression is: Among them, z ＝|z|p-1z*,z∈C； (4) Phase fractional low-order correlation (PFLOC) feature, which is expressed as: where z -q >= (z * ) q >= (z q ) * = (|z| q-1 z * ) * = |z| q-1 z, z ∈ C; (5) The related features of the correlation entropy based on the generalized Gaussian kernel function are expressed as follows: Among them, the generalized Gaussian kernel function expression is: Among them, β∈R+ represents the characteristic index of the generalized Gaussian distribution function, μ∈R represents the location parameter; (6) The related features of the correlation entropy based on the Gaussian kernel function are expressed as follows: Among them, the Gaussian kernel function: σ is the kernel length parameter of the kernel function; The feature optimization selection module is used to build a feature optimization selection model based on the extreme gradient boosting sequence floating backward selection algorithm, and determine the feature set for final classification according to the feature importance: Based on the extreme gradient boosting algorithm, the mapping data set of the space-time coding method and the related feature space is established as follows: D={(x i ,y i )∣i=1~n,x i ∈R m ,y i ∈R} The dataset has m features and n training samples, each of which corresponds to a label y; m is the number of feature points extracted in the feature space, and y is i is the space-time coding method corresponding to the i-th sample; and the output y of each decision tree i is defined as follows: Where k is the number of decision trees, f t (·) is a regression tree, and F is the set of all possible regression trees. In order to avoid overfitting, the extreme gradient boosting algorithm uses the complexity function of the tree as the constant term of the objective loss function. The detailed formula of the objective function of the extreme gradient boosting algorithm is as follows: Where C is a constant, x i is the input vector, T t represents the number of leaves in the tree, w is the leaf node weight value of the kth tree; y i and denote the actual value and predicted value of the category respectively; γ is the coefficient of the leaf node, λ is the standard term of the leaf weight penalty, γ and λ are used to limit the possibility of overfitting of the model; l(·) is the square loss function, f t (·) is a regression tree, Ω(·) is a regression function model; at the same time, the extreme gradient boosting algorithm performs a second-order Taylor expansion on the objective function; according to the Taylor formula, the objective function G(t) is approximately expressed as follows: Among them, g i and are the coefficients of the first and second terms in Taylor expansion respectively; Using all the features in the feature space, based on the information generated in the model process of the extreme gradient boosting algorithm, the optimal weight is solved by making the first-order derivative of the objective function G(t) equal to 0, so as to determine the features of the segmented samples, and the number of times the feature is used to segment the sample is selected as the feature importance measurement score; weight=|X| Where X is the set of leaf nodes of the desired feature classification; get the importance metric score of the feature and sort it in descending order; Then, combined with the improved sequential backward search strategy, starting from the original candidate set in the feature space, one irrelevant feature is reduced in each round, and the features with the lowest feature importance metric score in this round of iteration, that is, the features with the lowest ranking, are removed from the current complete feature set in turn. Then, the Pearson correlation coefficient between the features to be removed and other remaining features is calculated according to the evaluation algorithm: Among them, cov(X,Y) is the covariance between two feature attribute variables X and Y, δ X , δ Y are the sample standard deviations of X and Y respectively; then, the features at the end of the feature at the end of the metric score sorting are selected in parallel, and the features are removed, and a new round of prediction and sorting is performed again. The prediction classification accuracy under the retained feature set is recorded in each round of iteration to determine the retained feature subset with the highest prediction classification accuracy. The classification prediction accuracy of all subsets is traversed, and the feature subset with the highest classification accuracy and the least number of features is selected as the optimal feature subset, which is the result of the final feature optimization selection; The space-time coding mode recognition module is used to build a classifier model based on tree-enhanced naive Bayes to classify and identify the space-time coding mode according to the selected features: In tree-enhanced naive Bayes, class variable attributes are added. The premise of the correlation between attributes is to recalculate under a certain classification attribute. Different class attribute values ​​will have different attribute correlations. The conditional mutual information is used to describe the dependency strength between feature attribute variables X and Y when a given class variable Z is given as follows: Among them, when z is the category attribute, x and y are feature attributes, P(x|z) represents the probability of x occurring under the condition that z occurs; After calculating the mutual information values ​​of each attribute pair after feature selection, the Bayesian network is constructed. The conditional probability table of each node is expressed by the following formula: Among them, x i represents the sub-feature, π i Represents the set of all parent features that the child feature depends on, θ represents the conditional probability table of the child feature, and the set of conditional probability tables of all features is represented by Θ. Together with the structure G of the Bayesian network, the entire Bayesian network is represented by the following formula: B=<G,Θ> Thus, the class conditional probability is estimated and the category of the new sample is obtained; P(C), P(x1|C),…, P(x n |C), according to the maximum likelihood principle, when given a test data of unknown category (x1,…x n ), which can make The largest category C is (x1,…x n ) belongs to the category: Among them, P(C) is the class probability estimate, which represents the probability of belonging to category C, and P(X i |C) is the conditional probability estimate.

3. A device for identifying MIMO-OFDM space-time coding mode under non-Gaussian noise, characterized in that: include: Memory for storing computer programs; A processor, used for implementing the method for identifying the MIMO-OFDM space-time coding mode under non-Gaussian noise as described in any one of claims 1 to 2 when executing the computer program.

4. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it can identify the MIMO-OFDM space-time coding mode under non-Gaussian noise based on the MIMO-OFDM space-time coding mode identification method under non-Gaussian noise.

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