CN104104629A

CN104104629A - Rapid signal detection method based on echo state network

Info

Publication number: CN104104629A
Application number: CN201410266891.5A
Authority: CN
Inventors: 阮秀凯; 施肖菁; 李昌; 张耀举; 唐震洲; 谈燕花; 蒋小洛
Original assignee: Wenzhou University
Current assignee: Wenzhou University
Priority date: 2014-05-27
Filing date: 2014-05-27
Publication date: 2014-10-15

Abstract

The invention relates to a rapid signal detection method based on an echo state network. Firstly construction of an echo state network structure suitable for a rapid signal detection problem is given, and then concrete forms of corresponding echo state network reading functions are designed according to constellation diagram characteristics of different transmitting signals; and then a reserve pool weight matrix form of the echo state network of the rapid signal detection problem is designed, the number of conditions of a weight matrix is reduced by adopting a method of cutting undersized singular values, and reading weight confirmation and updating criteria of the network are designed. With application of the technical schemes, the invention provides the rapid signal detection method based on the echo state network so that severe dependence of existing signal detection methods on data amount is overcome, and the situation that characteristics of being abrupt and short in data frames of signals of a modern communication system are not considered is also overcome, and thus detection is accurate.

Description

A Fast Signal Detection Method Based on Echo State Network

技术领域 technical field

本发明涉及无线通信的信号处理技术领域，特别是通信发射与接收机之间的信道具有深度衰落、接收端信号存在较为严重的符号间干扰、发送数据具有一定的突发性、接收端数据帧长度较短的情况，采用回声状态网络实现无线通信系统的短帧信号直接检测快速方法。 The present invention relates to the technical field of wireless communication signal processing, especially the channel between the communication transmitter and the receiver has deep fading, the signal at the receiving end has relatively serious inter-symbol interference, the transmitted data has a certain burstiness, and the data frame at the receiving end In the case of short length, the echo state network is used to realize the fast method of direct detection of short frame signal in wireless communication system. the

背景技术 Background technique

突发信号在现代通信中广泛应用，在非协作或对抗通信系统中，突发信号采取随机选择时间进行突发方式发送，持续时间点，在瞬间将信号传送完毕，而接收或截获方由于无法获得突发信号同步头与信号探测序列的先验知识，对于突发信号的处理需要增加检测环节，以确定当前是否有信号及其信号的起始与结束为止。突发信号的快速检测是后续信号处理的前提。由于信号长度过短，已往处理传统的盲信号处理方法常不适用，特别是基于统计量方法的肓处理方法都将不再适用，所以需要一种仅依赖小数据量快速收敛的快速检测方法。快速检测技术的实际应用对提高通信质量和保证信息的可靠性具有重要意义，其研究成果对带限的数字通信系统也起着重要作用，一方面，伴随着无线通信技术的日益快速发展，越来越多的通信场合需要考虑到电池节能、数据的短时突发性、收发双方的非完全协作性以及应急通信系统的需求。例如：无线传感网联合流星突发通信在水文、大气监测、火情监测和海上浮标海样采集系统中可发挥重要作用，该类网络因为特别注重能耗问题，数据长度短、信号突发和间隙性成为其固有特点，这些都使得传统检测方法的大数据依赖性无法得到满足。这就迫切需要一种减少数据量依赖并能实际应用的肓处理方法，它必须要求能快速检测正交相移键控(QPSK，Quadrature Phase Shift Key)和正交幅度调制(QAM，QuadratureAmplitude Modulation)信号的同时具有减少数据量依赖、还必须具有结构简单、软硬件代价小的的特点。 Burst signals are widely used in modern communications. In non-cooperative or confrontational communication systems, burst signals are sent in a burst mode at a randomly selected time. The duration of the signal is transmitted in an instant, and the receiving or intercepting party cannot To obtain the prior knowledge of the burst signal synchronization header and the signal detection sequence, the processing of the burst signal needs to add a detection link to determine whether there is a signal and the start and end of the signal. Rapid detection of burst signals is the premise of subsequent signal processing. Due to the short length of the signal, the traditional blind signal processing methods in the past are often not applicable, especially the blind processing methods based on statistical methods will no longer be applicable, so a fast detection method that only relies on a small amount of data to quickly converge is needed. The practical application of fast detection technology is of great significance to improve communication quality and ensure the reliability of information, and its research results also play an important role in band-limited digital communication systems. More and more communication occasions need to consider battery energy saving, short-term burst of data, incomplete coordination between the sending and receiving parties, and the needs of emergency communication systems. For example: wireless sensor network combined with meteor burst communication can play an important role in hydrology, atmospheric monitoring, fire monitoring and sea buoy sea sample collection system. Because this type of network pays special attention to energy consumption, the data length is short and the signal burst And interstitiality has become its inherent characteristics, which make the big data dependence of traditional detection methods unable to be satisfied. This is an urgent need for a blind processing method that reduces the dependence on the amount of data and can be used in practice. It must be able to quickly detect Quadrature Phase Shift Keying (QPSK, Quadrature Phase Shift Key) and Quadrature Amplitude Modulation (QAM, Quadrature Amplitude Modulation) At the same time, the signal has the characteristics of reducing data volume dependence, simple structure, and low software and hardware costs. the

回声状态网络(Echo State Network，ESN))以及相应的学习算法为递归神经网络的研究开辟了崭新的道路ESN跟植于非线性动力学的ESN方法因其具有模型精确、建模能力强、生物合理性以及可拓展性和节约性等诸多优点而引起了人们的兴趣。它引入一个称作储备池的内部网络，当外部的输入序列进入这个内部网络时，便在其中激发出复杂多样的非线性状态空间，然后再通过一个简单的读出网络来得到网络输出，与之前递归神经网络的最大不同之处是在训练过程中，储备池内部的连接权值是固定不变的，调整仅仅针对读出网络进行。由于大大降低了训练的计算量，又避免了大多数基于梯度下降的学习算法所难回避的局部极小现象，并同时能够取得很好的建模精；ESN方法中通过引入储备池，权值矩阵具有了稀疏性，仅部分输出权值需要进行更新。作为一种新的反馈神经网络范式，在继承了反馈神经网络的动态特性的同时克服了反馈神经网络的学习难度。 Echo State Network (ESN)) and the corresponding learning algorithm have opened up a new path for the research of recurrent neural network. ESN is based on the ESN method of nonlinear dynamics because of its accurate model, strong modeling ability, biological It has aroused people's interest because of its rationality and many advantages such as scalability and economy. It introduces an internal network called a reserve pool. When an external input sequence enters this internal network, a complex and diverse nonlinear state space is excited in it, and then a simple readout network is used to obtain the network output. The biggest difference of the previous recurrent neural network is that during the training process, the connection weight inside the reserve pool is fixed, and the adjustment is only for the readout network. Since the calculation amount of training is greatly reduced, the local minimum phenomenon that is difficult to avoid in most learning algorithms based on gradient descent is avoided, and at the same time, good modeling precision can be achieved; by introducing a reserve pool in the ESN method, the weight The matrix is sparse, and only some output weights need to be updated. As a new feedback neural network paradigm, it overcomes the learning difficulty of feedback neural network while inheriting the dynamic characteristics of feedback neural network. the

发明内容 Contents of the invention

本发明的目的在于克服现有信号检测方法对于数据量的严重依赖，且未考虑现代通信系统的信号具有突发性和短数据帧的特征，本发明提供了一种基于回声状态网络的信号快速检测方法。 The purpose of the present invention is to overcome the heavy dependence of the existing signal detection method on the amount of data, and does not consider the characteristics of bursty and short data frames of the signal of the modern communication system. The present invention provides a fast signal detection method based on the echo state network. Detection method. the

本发明的技术方案：一种基于回声状态网络的信号快速检测方法，其特征在于，包括有以下步骤： Technical scheme of the present invention: a kind of signal fast detection method based on echo state network, it is characterized in that, comprises the following steps:

第一步：假设源信号发送序列{s_n}是独立同分布的，不失一般性，不考虑噪声影响，无任何训练序列参与，单输入多输出无线通信系统接收方程、信号检测方程可表述如下 Step 1: Assuming that the source signal transmission sequence {s _n } is independent and identically distributed, without loss of generality, without considering the influence of noise, without any training sequence participation, the receiving equation and signal detection equation of the single-input multiple-output wireless communication system can be expressed as follows

${((x x ((t t))))}_{q q \times \times 11} = = {Σ Σ}_{j j = = 00}^{L L} {(({H h}_{i i}))}_{q q \times \times 11} s the s ((t t - - i i)) = = {[[{H h}_{00},, . . . . . .,, {H h}_{L L}_{h h}]]}_{q q \times \times ((L L + + 11))} {((s the s ((t t))))}_{((L L + + 11)) \times \times 11}$

X_N＝SΓ^H X _N = SΓ ^H

其中：上标H表示共轭转置，q为过采样因子/接收天线个数，Γ＝Γ_L(H_i)是(H_i，i＝0，1，…，L)构成的平滑矩阵，是通信信道的冲激响应，L_h为信道阶数，L为均衡器长度，(X_N)_N×(L+1)q＝[x_L(t)，…，x_L(t+N-1)]^T是接收数据阵，而发送信号阵为S(t)＝[s_N(t)，s_N(t-1)，…，s_N(t-M-L)]_N×(L+M+1)； Where: superscript H represents conjugate transpose, q is oversampling factor/number of receiving antennas, Γ=Γ _L (H _i ) is a smooth matrix composed of (H _i , i=0, 1, ..., L), is the impulse response of the communication channel, L _h is the channel order, L is the equalizer length, (X _N ) _N×(L+1)q ＝[x _L (t),…, x _L (t+N- 1)] ^T is the receiving data array, and the sending signal array is S(t)=[s _N (t), s _N (t-1),..., s _N (tML)] _{N×(L+M+1 )} ;

第二步：首先随机产生一组随机初始序列作为初始输入进入储备池W阵，经过储备池W阵作用之后输出一组新的串行序列，该串行序列通过串并变换之后产生出输出信号阵s(t-1)；该输出信号阵与ESN网络的权值矩阵W_out进行相乘之后获得序列v(t-1)，进而分别通过|·|和Arg(·)运算提取出新序列的幅度和相位，然后分别进入幅度读出函数算子f(|·|)和相位读出函数算子g(·)进行非线性映射，然后将映射后的幅度和相位重新组合成极坐标表现形式，组成新的输出序列s(t)，该输出序列经过时间延时单元z^-1作用之后作为储备池的新输入反馈给网络，该网络周而复始地运行，直到算法收敛为止； Step 2: First randomly generate a set of random initial sequences as the initial input into the reserve pool W array, and output a new set of serial sequences after the reserve pool W array acts, and the serial sequence generates an output signal after serial-to-parallel conversion array s(t-1); the output signal array is multiplied by the weight matrix W _out of the ESN network to obtain the sequence v(t-1), and then the new sequence is extracted through |·| and Arg(·) operations respectively Then enter the amplitude readout function operator f(|·|) and phase readout function operator g(·) for nonlinear mapping, and then recombine the mapped amplitude and phase into a polar coordinate representation Form, form a new output sequence s(t), the output sequence is fed back to the network as a new input of the reserve pool after the time delay unit z ^-1 acts, and the network runs repeatedly until the algorithm converges;

第三步：根据待检测信号的特征设计读出函数 Step 3: Design the readout function according to the characteristics of the signal to be detected

记单个读出函数为 Denote a single readout function as

其中A表示信号点振幅，表示信号点相位，f(A)表示读出函数的振幅映射，表示读出函数的相位映射，j表示虚数单位，exp(·)是指数函数， where A represents the signal point amplitude, Represents the signal point phase, f(A) represents the amplitude mapping of the readout function, Represents the phase map of the readout function, j represents the imaginary unit, exp(·) is the exponential function,

(1)当原发送信号为PSK信号时 (1) When the original sent signal is a PSK signal

首先设计ESN读出函数的振幅映射部分： First design the amplitude mapping part of the ESN readout function:

f(A)＝tanh(A) f(A)＝tanh(A)

这里tanh(·)表示双曲正切函数， Here tanh(·) represents the hyperbolic tangent function,

若调制为π/4-四相相移键控(π/4-QPSK)方式，则M＝4，θ为相角，则ESN读出函数的相位映射为： If the modulation is π/4-quaternary phase shift keying (π/4-QPSK) mode, then M=4, θ is the phase angle, then the phase mapping of the ESN readout function is:

$g g ((θ θ,, M m)) = = \underset{p p = = &PlusMinus; &PlusMinus; 2,0 2,0}{Σ Σ} ((\frac{\frac{π π}{22}}{{11 + + e e}^{((- - a a ((θ θ + + p p \cdot \cdot \frac{π π}{M m}))))}} - - \frac{π π}{M m}))$

若调制为其它类型的相移键控方式，则ESN读出函数的相位映射为： If the modulation is other types of phase shift keying, the phase mapping of the ESN readout function is:

$g g ((θ θ,, M m)) = = \underset{p p = = &PlusMinus; &PlusMinus; 11,, &PlusMinus; &PlusMinus; 33,, \cdot \cdot \cdot \cdot \cdot \cdot,, &PlusMinus; &PlusMinus; ((M m - - 11))}{Σ Σ} ((\frac{\frac{22 π π}{M m}}{{11 + + e e}^{((- - a a ((θ θ + + p p \cdot &Center Dot; \frac{π π}{M m}))))}} - - \frac{π π}{M m})),, θ θ &Element; &Element; ((- - π π,, π π]],, M m = = 4,8,16 4,8,16,, \cdot &Center Dot; \cdot \cdot \cdot \cdot$

这里a为衰减因子，a＞0； Here a is the attenuation factor, a>0;

(2)当原发送信号为QAM信号时 (2) When the original sent signal is a QAM signal

设计8QAM振幅函数如下 Design the 8QAM amplitude function as follows

$f f ((x x)) = = \frac{22 \sqrt{22}}{11 + + exp exp ((- - ax ax))} - - \sqrt{22} + + \frac{\sqrt{1010} - - \sqrt{22}}{11 + + exp exp ((- - a a ((x x - - \frac{\sqrt{1010} + + \sqrt{22}}{22}))))}$

其中a为衰减因子， where a is the attenuation factor,

设计8QAM信号相位激励函数形式如下 Design the 8QAM signal phase excitation function in the following form

$\begin{matrix} g g ((x x)) = = - - ((π π - - arctan arctan \frac{11}{33})) + + 22 arctan arctan \frac{11}{33} \cdot \cdot {((11 + + exp exp ((- - ax ax))))}^{- - 11} + + \frac{π π}{22} \cdot \cdot {((11 + + exp exp ((- - a a ((x x &PlusMinus; &PlusMinus; \frac{π π}{22}))))))}^{- - 11} \\ + + ((\frac{π π}{44} - - arctan arctan \frac{11}{33})) \cdot \cdot {((((11 + + exp exp ((- - a a ((x x &PlusMinus; &PlusMinus; \frac{\frac{π π}{44} + + arctan arctan \frac{11}{33}}{22}))))))}^{- - 11} + + ((11 + + exp exp {((- - a a ((x x + + \frac{\frac{77 π π}{44} - - arctan arctan \frac{11}{33}}{22}))))))}^{- - 11})) \end{matrix}$

其中a为衰减因子， where a is the attenuation factor,

同法设计获得16QAM信号的振幅与相位函数形式； The amplitude and phase function form of the 16QAM signal is obtained by the same method design;

16QAM振幅函数形式如下 The form of the 16QAM amplitude function is as follows

$f f ((x x)) = = \frac{22 \sqrt{22}}{11 + + exp exp ((- - ax ax))} + + \frac{\sqrt{1010} - - \sqrt{22}}{11 + + exp exp ((- - a a ((x x - - \frac{\sqrt{1010} + + \sqrt{22}}{22}))))} + + \frac{\sqrt{1818} - - \sqrt{1010}}{11 + + exp exp ((- - a a ((x x - - \frac{\sqrt{1818} + + \sqrt{1010}}{22}))))} - - \sqrt{22}$

16QAM信号，相位函数形式如下： 16QAM signal, the phase function form is as follows:

其中当i＝1时，当i＝2时，当i＝3时，当i＝4时， in When i=1, When i=2, When i=3, When i=4,

第四步：设计ESN网络储备池权值并保证其连接稀疏性 Step 4: Design the ESN network reserve pool weight and ensure its connection sparsity

根据第一步的信号模型，首先构造储备池W阵，将接收信号矩阵X_N作如下转化其中上标*表示共轭，则存在如下QR分解形式： $X_{N}^{T} = [Q, Q_{c}] \cdot [\begin{matrix} R \\ 0 \end{matrix}] = QR$ 其中，为一正交矩阵，为一非零上三角矩阵，进而构造ESN储备池W矩阵：W＝QQ^H， According to the signal model in the first step, first construct the reserve pool W matrix, and convert the received signal matrix X _N as follows Where the superscript * represents conjugation, then there is the following QR decomposition form: $x_{N}^{T} = [Q, Q_{c}] \cdot [\begin{matrix} R \\ 0 \end{matrix}] = QR$ in, is an orthogonal matrix, is a non-zero upper triangular matrix, and then constructs the ESN reserve pool W matrix: W=QQ ^H ,

为保证储备池矩阵的稀疏性，设计如下方法： In order to ensure the sparsity of the reserve pool matrix, the following method is designed:

如果则将W(a，b)的值赋值为0，否则W(a，b)保持不变，ρ∈[0，1]为一个常数，a和b分别表示W矩阵元素的行列位置； if Then assign the value of W(a, b) to 0, otherwise W(a, b) remains unchanged, ρ∈[0,1] is a constant, and a and b represent the row and column positions of W matrix elements respectively;

第五步：设计读出权值矩阵更新法则 Step 5: Design the readout weight matrix update rule

构造如下优化问题 The following optimization problem is constructed

${\overset{^^}{W W}}_{out out} = = arg arg min min {{\frac{11}{22} {| | | | {W W}_{out out} | | | |}_{22}^{22} + + \frac{C C}{N N} \cdot &Center Dot; L L ((R R,, {u u}_{i i}^{T T} {W W}_{out out}))}}$

对于信号检测问题，采用常数模准则，即其中： For the signal detection problem, the constant modulus criterion is adopted, namely in:

R＝E{Re(s)⁴}/E{Re(s)²}，u_i＝[u_i，u_i-1，…，u_i-L+1]^T，i＝L-1，L，…，N-1，Re(·)表示取实部运算，E(·)为求数学期望运算， R=E{Re(s) ⁴ }/E{Re(s) ² }, u _i =[u _i , u _i-1 ,..., u _i-L+1 ] ^T , i=L-1, L ,..., N-1, Re(·) represents the operation of taking the real part, E(·) is the operation of seeking the mathematical expectation,

为不敏感损失函数，采用线性不敏感函数，进而获得 As an insensitive loss function, a linear insensitive function is used to obtain

${\overset{^^}{W W}}_{out out} = = {((\frac{C C}{N N} {U u}^{H h} U u + + I I))}^{- - 11}$

其中上标-1表示矩阵求逆运算，然后设计读出权值更新法则如下： The superscript -1 represents the matrix inversion operation, and then the design readout weight update rule is as follows:

${\overset{^^}{W W}}_{out out} ((t t)) = = ((11 - - η η)) {\overset{^^}{W W}}_{out out} ((t t - - 11)) + + η η {\overset{^^}{W W}}_{out out} ((00))$

这里η∈(0，1)，为输出权值初始值，中心抽头为0.05+j0.05，其余抽头值均为0。 Here η ∈ (0, 1), is the initial value of the output weight, the center tap is 0.05+j0.05, and the other tap values are all 0.

下面结合附图进一步详细说明： Further describe in detail below in conjunction with accompanying drawing:

附图说明 Description of drawings

图1是本发明适用于快速检测信号回声状态网络的示意图； Fig. 1 is the schematic diagram that the present invention is applicable to fast detection signal echo state network;

图2是本发明所涉及的信号分割示意图； Fig. 2 is a schematic diagram of signal segmentation involved in the present invention;

图3是本发明回声状态网络读出函数衰减因子a＝10，QPSK，8PSK，16PSK的读出函数图形； Fig. 3 is the echo state network readout function attenuation factor a=10 of the present invention, QPSK, 8PSK, the readout function figure of 16PSK;

图4是本发明当回声状态网络读出函数衰减因子a＝25时，8QAM相位读出函数图形； Fig. 4 is when the echo state network readout function attenuation factor a=25 of the present invention, 8QAM phase readout function figure;

图5是本发明不同范数指数p的取值时，代价函数凹凸性示意图； Figure 5 is a schematic diagram of the concavo-convexity of the cost function when different norm exponents p are taken in the present invention;

图6是本发明不同待检测信号时，回声状态网络信号检测性能比较图； Fig. 6 is when different signals to be detected of the present invention, the network signal detection performance comparative figure of echo state;

图7是本发明不同待检测信号时，回声状态网络信号检测方法的收敛曲线图； Fig. 7 is the convergence curve diagram of the echo state network signal detection method when the present invention has different signals to be detected;

图8是本发明QPSK信号时，数据量为1000，信噪声比为20dB，ESN算法单次实验运行轨迹图； When Fig. 8 is the QPSK signal of the present invention, the amount of data is 1000, the signal-to-noise ratio is 20dB, and the ESN algorithm single-time experiment running locus diagram;

图9是本发明8PSK信号时，数据量为1000，信噪声比为20dB，ESN算法单次实验运行轨迹图； Fig. 9 is when 8PSK signal of the present invention, data size is 1000, and signal-to-noise ratio is 20dB, ESN algorithm single experiment running locus figure;

图10是本发明8QAM信号时，数据量为1000，信噪声比为20dB，ESN算法单次验运行轨迹图； Fig. 10 is when 8QAM signal of the present invention, data amount is 1000, and signal-to-noise ratio is 20dB, ESN algorithm single-time test operation locus diagram;

图11是本发明16QAM信号时，数据量为1000，信噪声比为20dB，ESN算法单次实验运行轨迹图。 Fig. 11 is a running track diagram of a single experiment of the ESN algorithm when the data volume is 1000 and the signal-to-noise ratio is 20dB when the 16QAM signal of the present invention is used. the

具体实施方式 Detailed ways

基于回声状态网络的突发短帧信号快速检测方法，包括如下几个步骤： The rapid detection method of burst short frame signal based on echo state network, including the following steps:

第一步假设源信号发送序列{s_n}是独立同分布的；不失一般性，不考虑噪声影响，无任何训练序列参与，单输入多输出(SIMO)无线通信系统接收方程、快速检测方程可表述如下 The first step assumes that the source signal transmission sequence {s _n } is independent and identically distributed; without loss of generality, the influence of noise is not considered, and no training sequence is involved. The receiving equation and fast detection equation of single-input multiple-output (SIMO) wireless communication system can be expressed as follows

${((x x ((t t))))}_{q q \times \times l l} = = {Σ Σ}_{j j = = 00}^{L L} {(({H h}_{i i}))}_{q q \times \times l l} s the s ((t t - - i i)) = = {[[{H h}_{00},, . . . . . .,, {H h}_{L L}_{h h}]]}_{q q \times \times ((L L + + 11))} {((s the s ((t t))))}_{((L L + + 11)) \times \times 11}$

X_N＝SΓ^H X _N = SΓ ^H

其中：上标H表示共轭转置，q为过采样因子/接收天线个数，Γ＝Γ_L(H_i)是(H_i，i＝0，1，…，L)构成的平滑矩阵，是通信信道的冲激响应，L_h为信道阶数，L为均衡器长度，(X_N)_N×(L+1)q＝[x_L(t)，…，x_L(t+N-1)]^T是接收数据阵，而发送信号阵为S(t)＝[s_N(t)，s_N(t-1)，…，s_N(t-M-L)]_N(L+M+1)； Where: superscript H represents conjugate transpose, q is oversampling factor/number of receiving antennas, Γ=Γ _L (H _i ) is a smooth matrix composed of (H _i , i=0, 1, ..., L), is the impulse response of the communication channel, L _h is the channel order, L is the equalizer length, (X _N ) _N×(L+1)q ＝[x _L (t),…, x _L (t+N- 1)] ^T is the receiving data array, and the sending signal array is S(t)=[s _N (t), s _N (t-1),..., s _N (tML)] _N(L+M+1) ;

第二步：(如图1所示)构造适用于信号快速检测的回声状态网络，图中，|·|为取信号点幅度(模值)运算，f(|·|)表示幅度读出函数算子；Arg(·)为取信号点相位运算，g(·)表示相位读出函数算子，∠表示所获得的相位，s(t-1)，s(t)分别表示回声状态网络输入和输出信号输出，z^-1表示延迟，S/P表示信号帧的串/并变换，S(t-1)表示储备池权值矩阵输出信号序列进行串并变换后的矩阵，V(t-1)表示S(t-1)与ESN读出权值相乘后的输出序列，e表示自然数，j表示虚数单位，f_readout(·)表示读出函数，箭头方向表示信号的流向。 The second step: (as shown in Figure 1) Construct an echo state network suitable for fast signal detection, in the figure, |·| is the operation of taking the signal point amplitude (modulus value), and f(|·|) represents the amplitude readout function Operator; Arg(·) is the phase operation of the signal point, g(·) represents the phase readout function operator, ∠ represents the obtained phase, s(t-1), s(t) represent the echo state network input respectively and output signal output, z ^-1 represents the delay, S/P represents the serial/parallel conversion of the signal frame, S(t-1) represents the matrix after the serial-parallel conversion of the output signal sequence of the reserve pool weight matrix, V(t- 1) represents the output sequence after multiplying S(t-1) and ESN readout weight, e represents a natural number, j represents an imaginary number unit, f _readout ( ) represents a readout function, and the direction of the arrow represents the flow direction of the signal.

下面结合图1给出该网络的工作流程：首先随机产生一组随机初始序列作为初始输入进入储备池W阵，经过储备池W阵作用之后输出一组新的串行序列，该串行序列通过串并变换之后产生出输出信号阵s(t-1)；该输出信号阵与ESN网络的权值矩阵W_out进行相乘之后获得序列v(t-1)，进而分别通过|·|和Arg(·)运算提取出新序列的幅度和相位，然后分别进入幅度读出函数算子f(|·|)和相位读出函数算子g(·)进行非线性映射，然后将映射后的幅度和相位重新组合成极坐标表现形式，组成新的输出序列s(t)，该输出序列经过时间延时单元z^-1作用之后作为储备池的新输入反馈给网络。该网络周而复始地运行，直到算法收敛为止； The workflow of the network is given below in combination with Figure 1: First, a set of random initial sequences are randomly generated as the initial input into the reserve pool W array, and a new set of serial sequences are output after the reserve pool W array is processed, and the serial sequence is passed through The output signal array s(t-1) is generated after the serial-to-parallel conversion; the output signal array is multiplied with the weight matrix W _out of the ESN network to obtain the sequence v(t-1), and then passed through |·| and Arg The (·) operation extracts the amplitude and phase of the new sequence, and then enters the amplitude readout function operator f(|·|) and the phase readout function operator g(·) respectively for nonlinear mapping, and then the mapped amplitude and the phase are recombined into a polar coordinate form to form a new output sequence s(t), which is fed back to the network as a new input of the reserve pool after the action of the time delay unit z ^-1 . The network runs repeatedly until the algorithm converges;

本发明适用于现代无线通信系统中常用的PSK和QAM数字调制方式；接下来将根据该两类调制方式的信号特征进行读出函数f_readout(·)的设计，该两类信号的特征见附图2。记单个读出函数为 The present invention is applicable to PSK and QAM digital modulation mode commonly used in the modern wireless communication system; Next will carry out the design of readout function f _readout ( ) according to the signal characteristic of these two types of modulation modes, the characteristic of these two types of signals is shown in the appendix figure 2. Denote a single readout function as

其中A表示信号点振幅，表示信号点相位，f(A)表示读出函数的振幅映射，表示读出函数的相位映射，j表示虚数单位，exp(·)是指数函数。 where A represents the signal point amplitude, Represents the signal point phase, f(A) represents the amplitude mapping of the readout function, denotes the phase map of the readout function, j denotes the imaginary unit, and exp(·) is the exponential function.

f(A)＝tanh(A) f(A)＝tanh(A)

那么，PSK相位约束条件为 Then, the PSK phase constraints are

s∈T＝{exp(j2π(m-1)/M)，m＝1，2，…，M} s∈T={exp(j2π(m-1)/M), m=1, 2,..., M}

这里，exp(·)是指数函数，j是虚数单位，M表示PSK的星座点个数，π是圆周率， Here, exp(·) is an exponential function, j is an imaginary number unit, M represents the number of constellation points of PSK, π is a circle ratio,

$g g ((θ θ,, M m)) = = \underset{p p = = &PlusMinus; &PlusMinus; 2,0 2,0}{Σ Σ} ((\frac{\frac{π π}{22}}{11 + + {e e}^{((- - a a ((θ θ + + p p \cdot &Center Dot; \frac{π π}{M m}))))}} - - \frac{π π}{M m}))$

$g g ((θ θ,, M m)) = = \underset{p p = = &PlusMinus; &PlusMinus; 11,, &PlusMinus; &PlusMinus; 33,, . . . . . .,, &PlusMinus; &PlusMinus; ((M m - - 11))}{Σ Σ} ((\frac{\frac{22 π π}{M m}}{11 + + {e e}^{((- - a a ((θ θ + + p p \cdot &Center Dot; \frac{π π}{M m}))))}} - - \frac{π π}{M m})),, θ θ &Element; &Element; ((- - π π,, π π]],, M m = = 4,8,16 4,8,16,, . . . . . .$

这里a为衰减因子，a＞0，其取值不但控制着函数的陡峭程度而且影响函数的拐点数目；值得注意，π/4-QPSK和8PSK信号相位函数同属单节S型函数复合拼接而成，形式上较为类似，都呈现“多阶梯”曲线现象。其不同点在于除阶梯数目和位置的不同以外，对于π/4-QPSK信号，相位函数在{±π/4，±3π/4}位置出现平台，而在原点位置并不出现平台；而对于8PSK信号而言平台位置(见附图3)除出现在{±π/4，±π/2，±3π/4，0，π}位置上以外，原点位置也必须具有平台；这和星座图本身是密切相关的(参见附图2)； Here a is the attenuation factor, a > 0, its value not only controls the steepness of the function but also affects the number of inflection points of the function; it is worth noting that the phase functions of π/4-QPSK and 8PSK signals belong to the compound splicing of single-section S-shaped functions , which are relatively similar in form, showing the phenomenon of "multi-step" curves. The difference is that except for the difference in the number of steps and positions, for π/4-QPSK signals, the phase function has a platform at {±π/4, ±3π/4}, but no platform at the origin; and for For 8PSK signals, the platform position (see accompanying drawing 3) except appearing on {±π/4, ±π/2, ±3π/4, 0, π} positions, the origin position must also have a platform; this and the constellation diagram itself is closely related (see Figure 2);

与MPSK信号情况不同，QAM信号同时具有多种振幅和相位。将QAM信号表述为极坐标形式，那么有其中A表示信号点模值，表示信号点对应的相位，exp(·)是指数函数，j是虚数单位， Unlike the case of MPSK signals, QAM signals have multiple amplitudes and phases at the same time. Expressing the QAM signal as a polar coordinate form, then we have Where A represents the modulus value of the signal point, Indicates the phase corresponding to the signal point, exp(·) is an exponential function, j is an imaginary unit,

如对于方形16QAM而言，其极坐标形式的模值为相位为这里arctan(·)为反正切函数，π是圆周率， For example, for square 16QAM, the modulus of its polar coordinate form is Phase is Here arctan( ) is arc tangent function, π is pi,

设计8QAM振幅函数如下 Design the 8QAM amplitude function as follows

其中a为衰减因子，它控制着函数图形的陡峭程度，衰减因子a取值过小，则无法达到“多阈值”的效果，而a取值趋于无穷大时，此时则出现类似于阶梯函数所特有的“阶跃”阶梯，则说明离散振幅函数被包含在该函数形式之中，仅是它的一种特例而已。幅度阈值出现在和的相应位置上，两个阈值差分别为和 Among them, a is the attenuation factor, which controls the steepness of the function graph. If the value of the attenuation factor a is too small, the effect of "multi-threshold" cannot be achieved. When the value of a tends to infinity, it will appear similar to a step function. The unique "step" ladder shows that the discrete amplitude function is included in the function form, and it is only a special case of it. Amplitude threshold occurs at and At the corresponding position of , the difference between the two thresholds is and

接下来设计设计8QAM信号，相位函数；因为8QAM星座点本身关于坐标轴具有对称性质，则使得所有第二、第三和第四象限的星座点相位均可由第一象限的相位简单计算而来。但是由于相位分布呈现非均匀变化，使得8QAM相位函数的设计变得略显复杂。 Next, design the 8QAM signal and phase function; because the 8QAM constellation point itself has a symmetric property about the coordinate axis, the phases of all the constellation points in the second , third and fourth quadrants can be simply calculated from the phases in the first quadrant. However, due to the non-uniform change of the phase distribution, the design of the 8QAM phase function becomes slightly complicated.

$\begin{matrix} g g ((x x)) = = - - ((π π - - arctan arctan \frac{11}{33})) + + 22 arctan arctan \frac{11}{33} \cdot \cdot {((11 + + exp exp ((- - ax ax))))}^{- - 11} + + \frac{π π}{22} \cdot &Center Dot; {((11 + + exp exp ((- - a a ((x x &PlusMinus; &PlusMinus; \frac{π π}{22}))))))}^{- - 11} \\ + + ((\frac{π π}{44} - - arctan arctan \frac{11}{33})) \cdot &Center Dot; {((((11 + + exp exp ((- - a a ((x x &PlusMinus; &PlusMinus; \frac{\frac{π π}{44} + + arctan arctan \frac{11}{33}}{22}))))))}^{- - 11} + + ((11 + + exp exp {((- - a a ((x x &PlusMinus; &PlusMinus; \frac{\frac{77 π π}{44} - - arctan arctan \frac{11}{33}}{22}))))))}^{-1 -1})) \end{matrix}$

附图4给出了当回声状态网络读出函数衰减因子a＝25时，8QAM相位读出函数图形。 Figure 4 shows the graph of the 8QAM phase readout function when the echo state network readout function attenuation factor a=25. the

同法可设计获得16QAM信号的振幅与相位函数形式。 The same method can be designed to obtain the amplitude and phase function form of 16QAM signal. the

当然，同样方法也可得到32QAM和64QAM信号读出函数的振幅和相位函数表达形式，不再列出； Of course, the same method can also be used to obtain the amplitude and phase function expressions of the 32QAM and 64QAM signal readout functions, which will not be listed anymore;

根据第一步的信号模型，首先构造储备池W阵，将接收信号矩阵X_N作如下转化 $X_{N}^{T} = {(S Γ^{H})}^{T} = Γ^{*} S^{T},$ 其中上标*表示共轭。则存在如下QR分解形式： $X_{N}^{T} = [{Q, Q}_{c}] \cdot [\begin{matrix} R \\ 0 \end{matrix}] = QR$ 其中，为一正交矩阵，为一非零上三角矩阵。进而构造ESN 储备池W矩阵：W＝QQ^H。 According to the signal model in the first step, first construct the reserve pool W matrix, and convert the received signal matrix X _N as follows $x_{N}^{T} = {(S Γ^{h})}^{T} = Γ^{*} S^{T},$ where the superscript * indicates conjugation. Then there is the following QR decomposition form: $x_{N}^{T} = [{Q, Q}_{c}] \cdot [\begin{matrix} R \\ 0 \end{matrix}] = QR$ in, is an orthogonal matrix, is a non-zero upper triangular matrix. Then construct ESN reserve pool W matrix: W=QQ ^H .

根据条件数知识，条件数事实上表示了矩阵计算对于误差的敏感性。对于线性方程组Bx＝b，如果B的条件数大，b的微小改变就能引起解x较大的改变，数值稳定性差。反之，如果B的条件数小，b有微小的改变，x的改变也很微小，数值稳定性好。它也可以表示b不变，而B有微小改变时，x的变化情况。那么通过如上由接收信号矩阵的QR分解酉基阵方法构建ESN储备池权值矩阵时，存在该矩阵W病态的可能，病态权值矩阵将可能导致算法性能受损甚至失效；本发明引入截断过小奇异值的方法来降低权值矩阵的条件数。 According to the knowledge of the condition number, the condition number actually expresses the sensitivity of the matrix calculation to the error. For the linear equation system Bx=b, if the condition number of B is large, a small change of b can cause a large change of the solution x, and the numerical stability is poor. Conversely, if the condition number of B is small, b changes slightly, and x changes very little, and the numerical stability is good. It can also represent the change of x when b is unchanged and B changes slightly. Then when the ESN reserve pool weight matrix is constructed by the QR decomposition unitary matrix method of the received signal matrix as above, there is a possibility that the matrix W will be ill-conditioned, and the ill-conditioned weight matrix may cause the algorithm performance to be damaged or even invalidated; the present invention introduces a truncation process The small singular value method is used to reduce the condition number of the weight matrix. the

如果则将W(a，b)的值赋值为0，否则W(a，b)保持不变。ρ∈[0，1]为一个常数，比如取ρ＝0.5，a和b分别表示W矩阵元素的行列位置。记cond(·)为求矩阵条件数运算，下面观察W条件数的变化(见表1)，从表1中可以发现采用该方法可使得W条件数大幅降低。 if Then assign the value of W(a, b) to 0, otherwise W(a, b) remains unchanged. ρ∈[0,1] is a constant, for example, ρ=0.5, a and b represent the row and column positions of W matrix elements respectively. Note that cond( ) is an operation to find the condition number of a matrix. Next, observe the change of the condition number of W (see Table 1). From Table 1, it can be found that using this method can greatly reduce the condition number of W.

表1 8PSK，数据长度500，SIMO采用因子q＝4，30dB条件数与ρ的变化关系(未稀疏W前条件数为：1.1411×10²⁰) Table 1 8PSK, data length 500, SIMO adopts factor q=4, 30dB condition number and ρ change relationship (condition number before W is not sparse: 1.1411×10 ²⁰ )

ρ ρ 0.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 1 1 cond(W) cond(W) 1.4785×10⁶ 1.4785×10 ⁶ 4.0351×10⁵ 4.0351×10 ⁵ 2.4782×10⁵ 2.4782×10 ⁵ 5.6897×10⁴ 5.6897×10 ⁴ 5.5779×10⁴ 5.5779×10 ⁴

由向量范数的几何意义(如附图5所示)可知 It can be seen from the geometric meaning of the vector norm (as shown in Figure 5) that

${(({| | {x x}_{11} | |}^{p p} + + {| | {x x}_{22} | |}^{p p}))}^{\frac{11}{p p}} = = 11 &DoubleLeftRightArrow; &DoubleLeftRightArrow; {| | {x x}_{11} | |}^{p p} + + {| | {x x}_{11} | |}^{p p} = = 11 &DoubleLeftRightArrow; &DoubleLeftRightArrow; \{\begin{matrix} | | {x x}_{11} | | = = {sin sin}^{22 / / p p} ((t t)) \\ | | {x x}_{11} | | = = {cos cos}^{22 / / p p} ((t t)) \end{matrix}$

当p＞1，p范数为凸函数，p≤1，p范数不为凸函数。二范数的凸性对求解优化问题至关重要。那么本发明采用p＝2情况的范数，构造如下优化问题 When p>1, the p-norm is a convex function, and p≤1, the p-norm is not a convex function. The convexity of the bi-norm is crucial for solving optimization problems. Then the present invention adopts the norm of p=2 situation, constructs following optimization problem

R＝E{Re(s)⁴}/E{Re(s)²}，u_i＝[u_i，u_i-1，…，u_i-L+1]^T，i＝L-1，L，…，N-1，Re(·)表示取实部运算，E(·)为求数学期望运算。 R=E{Re(s) ⁴ }/E{Re(s) ² }, u _i =[u _i , u _i-1 ,..., u _i-L+1 ] ^T , i=L-1, L ,..., N-1, Re(·) represents the operation of taking the real part, and E(·) is the operation of finding the mathematical expectation.

为不敏感损失函数，本发明采用线性不敏感函数，则有 is an insensitive loss function, and the present invention adopts a linear insensitive function, then there is

$\begin{matrix} {&dtri; &dtri;}_{{W W}_{out out}} J J (({W W}_{out out})) = = {W W}_{out out} + + \frac{C C}{N N} \cdot \cdot {Σ Σ}_{i i = = L L - - 11}^{N N} ((\frac{&PartialD; &PartialD; (({f f}_{ϵ ϵ} (({| | {u u}_{i i}^{T T} {W W}_{out out} | |}^{22} - - R R))))}{{&PartialD; &PartialD; W W}_{out out}})) = = {w w}_{out out} + + \frac{C C}{N N} \cdot &Center Dot; {Σ Σ}_{i i = = L L - - 11}^{N N} {{\frac{&PartialD; &PartialD; (({u u}_{i i}^{T T} {W W}_{out out} {W W}_{out out}^{H h} {u u}_{i i}^{* *} - - R R))}{{&PartialD; &PartialD; W W}_{out out}}}} \\ = = {W W}_{out out} + + \frac{C C}{N N} \cdot &Center Dot; {Σ Σ}_{i i = = L L - - 11}^{N N} [[{u u}_{i i}^{T T} {W W}_{out out} {u u}_{i i}^{* *}]] = = {W W}_{out out} + + \frac{C C}{N N} \cdot &Center Dot; {U u}^{H h} {UW UW}_{out out} = = ((\frac{C C}{N N} \cdot &Center Dot; {U u}^{H h} U u + + I I)) {W W}_{out out} \end{matrix}$

其中I为单位阵。 in I is the unit matrix.

进而获得 and then get

其中上标-1表示矩阵求逆运算。然后设计读出权值更新法则如下： where the superscript -1 represents the matrix inversion operation. Then design the readout weight update rule as follows:

仿真实例 Simulation example

采用未作特殊说明，以下仿真结果，均采用滚降因子为0.1的滚降升余弦函数P(t)，2径多径信道c(t)＝δ(t)-0.7δ(t-T/3)，T为采样周期；进而获得过采样信道脉冲响应 $h (t) = c (t) &CircleTimes; P (t) = P (t) - 0.7 P (t - T / 3),$ 为卷积运算符；设置过采样因子q＝3。在SNR＝20dB，Monte Carlo实验次数为200，采用线性损失函数，ε＝1。N＝1000，读出权值阶数L＝9情况下获得。图6是本发明不同待检测信号时，回声状态网络信号检测性能比较图。 Without special instructions, the following simulation results all use the roll-off raised cosine function P(t) with a roll-off factor of 0.1, and the 2-path multipath channel c(t)=δ(t)-0.7δ(tT/3) , T is the sampling period; then obtain the oversampled channel impulse response $h (t) = c (t) &CircleTimes; P (t) = P (t) - 0.7 P (t - T / 3),$ is the convolution operator; set the oversampling factor q=3. At SNR=20dB, the number of Monte Carlo experiments is 200, and a linear loss function is used, ε=1. N=1000, obtained under the condition of readout weight order L=9. Fig. 6 is a comparison diagram of network signal detection performance in echo state when different signals to be detected are used in the present invention.

图7是本发明不同待检测信号时，回声状态网络信号检测方法的收敛曲线图。图8是本发明QPSK信号时，数据量为1000，信噪声比为20dB，ESN算法单次实验运行轨迹图。图9是本发明8PSK信号时，数据量为1000，信噪声比为20dB，ESN算法单次实验运行轨迹图。 Fig. 7 is a graph of convergence curves of the echo state network signal detection method of the present invention when different signals to be detected are used. Fig. 8 is a trajectory diagram of a single experiment run of the ESN algorithm when the QPSK signal of the present invention has a data volume of 1000 and a signal-to-noise ratio of 20dB. Fig. 9 is a running track diagram of a single experiment of the ESN algorithm when the data volume is 1000 and the signal-to-noise ratio is 20dB when the 8PSK signal of the present invention is used. the

图10是本发明8QAM信号时，数据量为1000，信噪声比为20dB，ESN算法单次实验运行轨迹图。图11是本发明16QAM信号时，数据量为1000，信噪声比为20dB，ESN算法单次实验运行轨迹图。 Fig. 10 is a running track diagram of a single experiment of the ESN algorithm when the data volume is 1000 and the signal-to-noise ratio is 20dB when the 8QAM signal of the present invention is used. Fig. 11 is a running track diagram of a single experiment of the ESN algorithm when the data volume is 1000 and the signal-to-noise ratio is 20dB when the 16QAM signal of the present invention is used. the

Claims

1. a kind of signal fast detection method based on echo state network, is characterized in that, comprises the steps:

Step 1: Assuming that the source signal transmission sequence {s _n } is independent and identically distributed, without loss of generality, without considering the influence of noise, without any training sequence participation, the receiving equation and fast detection equation of the single-input multiple-output wireless communication system can be expressed as follows

{((x x ((t t))))}_{q q \times \times 11} = = {Σ Σ}_{j j = = 00}^{L L} {(({H h}_{i i}))}_{q q \times \times 11} s the s ((t t - - i i)) = = {[[{H h}_{00},, \cdot \cdot \cdot \cdot \cdot &Center Dot;,, {H h}_{{L L}_{h h}}]]}_{q q \times \times ((L L + + 11))} {((s the s ((t t))))}_{((L L + + 11)) \times \times 11}

X _N = SΓ ^H

Where: superscript H represents conjugate transpose, q is oversampling factor/number of receiving antennas, Γ=Γ _L (H _i ) is a smooth matrix composed of (H _i , i=0, 1, ..., L), is the impulse response of the communication channel, L _h is the channel order, L is the equalizer length, Be the reception data matrix, and the transmission signal matrix is S (t)=[s _N (t), s _N (t-1), ..., s _N (tML)] _{N * (L+M+1)} ;

Step 2: First randomly generate a set of random initial sequences as the initial input into the reserve pool W array, and output a new set of serial sequences after the reserve pool W array acts, and the serial sequence generates an output signal after serial-to-parallel conversion array s(t-1); the output signal array is multiplied by the weight matrix W _out of the ESN network to obtain the sequence v(t-1), and then the new sequence is extracted through |·| and Arg(·) operations respectively Then, enter the amplitude readout function operator f(|·|) and phase readout function operator g(·) for nonlinear mapping, and then recombine the mapped amplitude and phase into polar coordinates The form of expression is to form a new output sequence s(t), which is fed back to the network as a new input of the reserve pool after the action of the time delay unit z ^-1 , and the network runs repeatedly until the algorithm converges;

Step 3: Design the readout function according to the characteristics of the signal to be detected

Denote a single readout function as

where A represents the signal point amplitude, Represents the signal point phase, f(A) represents the amplitude mapping of the readout function, Represents the phase map of the readout function, j represents the imaginary unit, exp(·) is the exponential function,

(1) When the original sent signal is a PSK signal

First design the amplitude mapping part of the ESN readout function:

f(A)=tanh(A)

Here tanh(·) represents the hyperbolic tangent function,

If the modulation is π/4-quaternary phase shift keying (π/4-QPSK) mode, then M=4, θ is the phase angle, then the phase mapping of the ESN readout function is:

g g ((θ θ,, M m)) = = \underset{p p = = &PlusMinus; &PlusMinus; 2,0 2,0}{Σ Σ} ((\frac{\frac{π π}{22}}{{11 + + e e}^{((- - a a ((θ θ + + p p \cdot \cdot \frac{π π}{M m}))))}} - - \frac{π π}{M m}))

If the modulation is other types of phase shift keying, the phase mapping of the ESN readout function is:

g g ((θ θ,, M m)) = = \underset{p p = = &PlusMinus; &PlusMinus; 11,, &PlusMinus; &PlusMinus; 33,, . . . . . .,, &PlusMinus; &PlusMinus; ((M m - - 11))}{Σ Σ} ((\frac{\frac{22 π π}{M m}}{11 + + {e e}^{((- - a a ((θ θ + + p p \cdot &Center Dot; \frac{π π}{M m}))))}} - - \frac{π π}{M m})),, θ θ &Element; &Element; ((- - π π,, π π]],, M m = = 4,8,16 4,8,16,, . . . . . .

Here a is the attenuation factor, a>0;

(2) When the original transmitted signal is a QAM signal

Design the 8QAM amplitude function as follows

f f ((x x)) = = \frac{22 \sqrt{22}}{11 + + exp exp ((- - ax ax))} - - \sqrt{22} + + \frac{\sqrt{1010} - - \sqrt{22}}{11 + + exp exp ((- - a a ((x x - - \frac{\sqrt{1010} + + \sqrt{22}}{22}))))}

where a is the attenuation factor,

Design the 8QAM signal phase excitation function in the following form

\begin{matrix} g g ((x x)) = = - - ((π π - - arctan arctan \frac{11}{33})) + + 22 arctan arctan \frac{11}{33} \cdot \cdot {((11 + + exp exp ((- - ax ax))))}^{- - 11} + + \frac{π π}{22} \cdot \cdot {((11 + + exp exp ((- - a a ((x x &PlusMinus; &PlusMinus; \frac{π π}{22}))))))}^{- - 11} \\ + + ((\frac{π π}{44} - - arctan arctan \frac{11}{33})) \cdot &Center Dot; {((((11 + + exp exp ((- - a a ((x x &PlusMinus; &PlusMinus; \frac{\frac{π π}{44} + + arctan arctan \frac{11}{33}}{22}))))))}^{- - 11} + + ((11 + + exp exp {((- - a a ((x x &PlusMinus; &PlusMinus; \frac{\frac{77 π π}{44} - - arctan arctan \frac{11}{33}}{22}))))))}^{- - 11})) \end{matrix}

where a is the attenuation factor,

The amplitude and phase function forms of the 16QAM signal are obtained by the same method,

The form of the 16QAM amplitude function is as follows

f f ((x x)) = = \frac{22 \sqrt{22}}{11 + + exp exp ((- - ax ax))} + + \frac{\sqrt{1010} - - \sqrt{22}}{11 + + exp exp ((- - a a ((x x - - \frac{\sqrt{1010} + + \sqrt{22}}{22}))))} + + \frac{\sqrt{1818} - - \sqrt{1010}}{11 + + exp exp ((- - a a ((x x - - \frac{\sqrt{1818} + + \sqrt{1010}}{22}))))} - - \sqrt{22}

16QAM signal, the phase function form is as follows:

in When i=1, When i=2, When i=3, When i=4,

Step 4: Design the ESN network reserve pool weight and ensure its connection sparsity

According to the signal model in the first step, first construct the reserve pool W matrix, and convert the received signal matrix X _N as follows Where the superscript * represents conjugation, then there is the following QR decomposition form:

x_{N}^{T} = [Q, Q_{c}] &Center Dot; [\begin{matrix} R \\ 0 \end{matrix}] = QR

in, is an orthogonal matrix, is a non-zero upper triangular matrix, and then constructs the ESN reserve pool W matrix: W=QQ ^H ,

In order to ensure the sparsity of the reserve pool matrix, the following method is designed:

if Then assign the value of W(a, b) to 0, otherwise W(a, b) remains unchanged, ρ∈[0,1] is a constant, and a and b represent the row and column positions of W matrix elements respectively;

Step 5: Design the readout weight matrix update rule

Construct the following optimization problem

{\overset{^^}{W W}}_{out out} = = arg arg min min {{\frac{11}{22} {| | | | {W W}_{out out} | | | |}_{22}^{22} + + \frac{C C}{N N} \cdot \cdot L L ((R R,, {u u}_{i i}^{T T} {W W}_{out out}))}}

For the signal detection problem, the constant modulus criterion is adopted, namely in:

R=E{Re(s) ⁴ }/E{Re(s) ² }, u _i =[u _i , u _i-1 ,..., u _i-L+1 ] ^T , i=L-1, L ,..., N-1, Re(·) represents the operation of taking the real part, E(·) is the operation of seeking the mathematical expectation,

As an insensitive loss function, a linear insensitive function is used to obtain

{\overset{^^}{W W}}_{out out} = = {((\frac{C C}{N N} {U u}^{H h} U u + + I I))}^{- - 11}

The superscript -1 represents the matrix inversion operation, and then the design readout weight update rule is as follows:

{\overset{^^}{W W}}_{out out} ((t t)) = = ((11 - - η η)) {\overset{^^}{W W}}_{out out} ((t t - - 11)) + + η η {\overset{^^}{W W}}_{out out} ((00))

Here η ∈ (0, 1), is the initial value of the output weight, the center tap is 0.05+j0.05, and the other tap values are all 0.