深入分析：恒虚警率检测算法之Switch-CFAR

　　转发和使用请注明来源，以下为本人精心整理，还请尊重本人劳动成果与产权！由于本人现有知识和能力有限，如存在错误之处请指正！下面为正文内容：

　　1.S-CFAR检测算法（Switching，开关CFAR）

　　　S-CFAR检测算法是通过参考单元内数据确定筛选门限，将小于筛选门限的参考单元划分至S_0，将大于筛选门限的参考单元划分至S_1，当S₀的单元数目n₀大于抗干扰数目时，可用S₀来估计杂波背景功率水平。

　　实现的步骤具体可以分为三步：

　　（1）根据CA的思想求解出门限水平$T=\alpha Z$,其中$\alpha$为衰减系数（通过人为选择）。

　　（2）根据（1）中求解得到的门限水平T分别与参考窗内每个单元采样值$x_i$进行比较，如果$x_i>T$则将$x_i$放入$S_1$序列，否则将$x_i$放入$S_0$序列中。

　　（3）如果$S_0$序列中单元数目$n_0$超过整数门限$N_T$，那么采用$S_0$中的样本估计阈值，反之则利用全体参考单元的样本估计阈值。参考单元中是否存在目标的判决规则如下：

$x>\frac{\beta_0}{n_0}\Sigma_{x_i=S_0} x_i,n_0>N_T$ 

$x>\frac{\beta_1}{2N}\Sigma_{i=1}^{2N} x_i,n_0 <= N_T$

　　其中，S-CFAR检测算法的检测性能与$\alpha$、$\beta_0$、$\beta_1$和$N_T$有关。S-CFAR的设计流程中可以简化设计使$\beta_0=\beta_1=\beta$，其余参数的设计如下：（1）设计干扰目标数目（最大可容纳的干扰目标数量）为$N_i$,整数门限$N_T$满足关系$N_T=2N-N_i-1$.（2）在选定$N_T$以后，对每个区间的$\alpha$值，根据$P_{fa}$式可以计算出来门限系数$\beta$。

　　改进的SOS-CFAR算法中，更新了判决规则为如下，其中$k$为选择序号。

$x>\beta_0 x(k) x_i,n_0>N_T$  

$x>\frac{\beta_1}{2N}\Sigma_{i=1}^{2N} x_i,n_0 <= N_T$ 

　　比较S-CFAR与SOS-CFAR两种算法的区别主要在于更新了$n_0>N_T$时的判决规则（门限水平估计准则），这两种算法的框图可以如下图表示（图片绘制较粗糙，但可以反映原理）。

 

 

　　为什么会出现上述两种判决规则，如何理解$n_0$与整数门限$N_T$间的关系呢？我的理解是，如果背景杂波占据了$N_t/N$比例（这个比例比较大）的参考窗，那么可以用这部分的参考单元即$S _0$的采样值作为功率水平的估计（估计方式可以采用CA,OS等）；反之如果背景杂波占据的比例非常小，其强度可以忽略不计，则可以用参考窗内全体采样值的平均进行估计（准确地说此时参考窗内被强杂波占据）。　　

　　理解判决规则后自然需要推导出S-CFAR算法的虚警概率$P_{FA}$，经典版本S-CFAR的虚警概率具体形式如下：

$$P\left( N,N_T,\alpha ,\beta _0,\beta _1 \right) =\frac{1}{1+\sigma}\sum_{n_0=0}^{N_t}{\sum_{m=M_0}^{min\left( M,n_0 \right)}{\sum_{n=0}^{n_0-m}{\sum_{k=0}^m{\left( \begin{array}{c} M\\ m\\ \end{array} \right)}}}}\left( \begin{array}{c} 2N-M\\ n_0-m\\ \end{array} \right) \left( \begin{array}{c} n_0-m\\ n\\ \end{array} \right) \left( \begin{array}{c} m\\ k\\ \end{array} \right) \frac{\left( -1 \right) ^{k+n}V\left( k,n \right)}{\left( 1+\sigma _I \right) ^M}+\frac{1}{1+\sigma}\sum_{n_0=N_t+1}^{2N}{\sum_{m=M_0}^{min\left( M,n_0 \right)}{\sum_{n=0}^{n_0-m}{\sum_{k=0}^m{\left( \begin{array}{c} M\\ m\\ \end{array} \right)}}}}\left( \begin{array}{c} 2N-M\\ n_0-m\\ \end{array} \right) \left( \begin{array}{c} n_0-m\\ n\\ \end{array} \right) \left( \begin{array}{c} m\\ k\\ \end{array} \right) \frac{\left( -1 \right) ^{k+n}W\left( k,n \right)}{\left( 1+\sigma _I \right) ^m}$$

　　其中，$W(k,n)$的具体形式如下：

$$\boldsymbol{W}\left( \boldsymbol{k},\boldsymbol{n} \right) =\frac{\boldsymbol{\xi }_{\boldsymbol{k},\boldsymbol{n}}^{\boldsymbol{n}_0}\left[ 1-\frac{\boldsymbol{\xi }_{k,\boldsymbol{N}}\boldsymbol{\sigma }_{\boldsymbol{I}}}{\left( 1+\sigma _I \right) \left( \boldsymbol{\xi }_{k,\boldsymbol{n}}+\boldsymbol{\rho }_{k,\boldsymbol{n}}+\left( 1+\sigma \right) ^{-1} \right)} \right] ^{-\boldsymbol{m}}}{\left( \boldsymbol{\rho }_{k,\boldsymbol{n}}+\left( 1+\sigma \right) ^{-1} \right) \left( \boldsymbol{\xi }_{k,\boldsymbol{n}}+\boldsymbol{\rho }_{k,\boldsymbol{n}}+\left( 1+\sigma \right) ^{-1} \right) ^{\boldsymbol{n}_0}} \\ \boldsymbol{\xi }_{k,\boldsymbol{n}}=\boldsymbol{n}_0\beta _0^{-1}-\left( \boldsymbol{k}+\boldsymbol{n} \right) \alpha \geqslant 0 \\ \boldsymbol{\rho }_{k,\boldsymbol{n}}=\alpha \left[ \frac{\boldsymbol{M}-\boldsymbol{m}+\boldsymbol{k}}{1+\sigma _I}+2\boldsymbol{N}-\boldsymbol{M}-\boldsymbol{n}_0+\boldsymbol{m}+\boldsymbol{n} \right]$$

 　　其中，$V(k,n)$的具体形式如下：

$$\boldsymbol{V}\left( \boldsymbol{k},\boldsymbol{n} \right) =\frac{\boldsymbol{\xi }_{\boldsymbol{k},\boldsymbol{n}}^{2\boldsymbol{N}}\left[ 1-\frac{\boldsymbol{\xi }_{k,\boldsymbol{N}}\boldsymbol{\sigma }_{\boldsymbol{I}}}{\left( 1+\sigma _I \right) \left( \boldsymbol{\xi }_{k,\boldsymbol{n}}+\boldsymbol{\rho }_{k,\boldsymbol{n}}+\left( 1+\sigma \right) ^{-1} \right)} \right] ^{-\boldsymbol{M}}}{\left( \boldsymbol{\rho }_{k,\boldsymbol{n}}+\left( 1+\sigma \right) ^{-1} \right) \left( \boldsymbol{\xi }_{k,\boldsymbol{n}}+\boldsymbol{\rho }_{k,\boldsymbol{n}}+\left( 1+\sigma \right) ^{-1} \right) ^{2\boldsymbol{N}}} \\ \boldsymbol{\xi }_{k,\boldsymbol{n}}=2\boldsymbol{N}\beta _{1}^{-1}-\left( 2\boldsymbol{N}-\boldsymbol{n}_0+\boldsymbol{k}+\boldsymbol{n}+\alpha \right) \geqslant 0 \\ \boldsymbol{\rho }_{k,\boldsymbol{n}}=\alpha \left[ \frac{\boldsymbol{M}-\boldsymbol{m}+\boldsymbol{k}}{1+\sigma _I}+2\boldsymbol{N}-\boldsymbol{M}-\boldsymbol{n}_0+\boldsymbol{m}+\boldsymbol{n} \right]$$

　　上述虚警概率和相关公式主要参考了“Constant false-alarm rate algorithm based on test cell information”等论文（可在谷歌学术上搜索得到），具体公式推导由于篇幅问题不再展开。从虚警概率公式可见，该公式与先前的恒虚警率检测算法的虚警概率公式（多为关于门限系数$\alpha$的闭合函数形式）不同，由多个变量（包含衰减系数$\alpha$，整数门限$N_t$，门限系数$\beta$，功率系数$\sigma$）共同作用，因此采用二分法求解门限系数显得困难，故多篇论文中采用了交叉验证的方式来求解合适的门限系数$\beta$。

　　设置功率系数$\sigma_1$和$\sigma$为0，参考窗长度$2N=64$即$N=32$,设置整数门限$N_t=32$,设置衰减系数$\alpha$为[0.1,1]并且步进为0.1，设置门限系数$\beta$和$\beta_1$为[10:50]并且步进为0.1，代入上述的虚警概率公式中求解并取对数形式，可以得到虚警概率关于不同门限系数和衰减系数的曲线如下图所示.可以看到当衰减系数从1降低至0.1时，S-CFAR的虚警概率曲线逐渐偏离CA-CFAR的虚警概率曲线，这意味着要实现相同的检测性能时S-CFAR需要花销比CA-CFAR更大的门限系数代价，同时在均匀背景下为实现相同的性能S-CFAR需要有更多的CFAR损失；而衰减系数更大时其逼近CA,这不利于多目标背景下的目标检测。因此在衰减系数的选择上需要进行折中选择，这里可以选择门限系数$\alpha=0.3$.

 

 

 

　　选择完合适的衰减系数后需要进一步确定整数门限$N_t$，整数门限的选择影响着最大可容纳干扰数目（$N_i=nN-N_t-1$）。从图中可见，随着整数门限的下降，虚警概率$P_{fa}$关于门限系数$\beta$的曲线会逐渐偏离$N_t=32$时的曲线。整数门限越大，意味着参考窗内可容纳干扰数目越小，对多目标背景下目标检测越不利。因此，选择合适的整数门限，对多目标背景检测是有意义的。这里可以选择整数门限$N_t=17$。

 

 　　综上分析，这里可以选择的参数为：虚警概率$p_{fa}=10^{-5}$,衰减系数$\alpha=0.3$,整数门限$N_t=17$,门限系数$\beta=15.03$.

　　以上程序的代码如下所示。

 

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%% S-CFAR的虚警概率计算 clc;clear;close all;   %% 参数设置 sigma = 0; sigmaI = 0; alpha_array = 0.1:0.1:1.0; %衰减系数 beta_array = 10:0.1:50; M = 0; N = 32; Nt = 17; Pfa = zeros(length(alpha_array),length(beta_array));   %% 计算虚警概率 for index = 1:length(alpha_array)     alpha = alpha_array(index);     for index1 = 1:length(beta_array)         beta0 = beta_array(index1);         Qn0 = 0;         for n0 = 0:Nt             M0 = max(0,n0 - 2 * N + M);             for m = M0:min(n0,M)                 for n = 0:(n0-m)                     for k = 0:m                         rou = alpha * ((M - m + k) / (1 + sigmaI) + 2 * N - M - n0 + m + n);                         phy =  2 * N / beta0  - (2 * N - n0 + k + n) * alpha;                         if(phy < 0)                             break;                         else                            V = phy^(2*N) * (1-(phy*sigmaI/(1+sigmaI)/(phy+rou+(1+sigma)^(-1)))^(-M)) / (rou+(1+sigma)^(-1)) / (phy+rou+(1+sigma)^(-1))^(2*N);                            Qn0 = Qn0 + 1 / (1+sigma) * nchoosek(M,m) * nchoosek(2*N-M,n0-m) * nchoosek(n0-m,n) * nchoosek(m,k) * (-1)^(k+n) / (1+sigmaI)^M * V;                         end                     end                 end             end         end           Pn0 = 0;         for n0 = Nt+1:2*N             M0 = max(0,n0 - 2 * N + M);             for m = M0:min(M,n0)                 for n = 0:n0-m                     for k = 0:m                         phy = n0 / beta0 - (k + n) * alpha;                         rou = alpha * ((M - m + k) / (1 + sigmaI) + 2* N - M - n0 + m + n);                         if phy < 0                             break;                         else                            W = phy^n0 * (1 - (phy*sigmaI/(1+sigmaI))/(phy+rou+(1+sigma)^(-1)))^(-m)/(rou +(1+sigma)^(-1))/(phy + rou + (1+sigma)^(-1))^n0;                            Pn0 = Pn0 + 1 / (1+sigma) * nchoosek(M,m) * nchoosek(2*N-M,n0-m) * nchoosek(n0-m,n) * nchoosek(m,k) * (-1)^(k+n) * W / (1+sigmaI)^m;                         end                     end                 end             end         end         Pfa(index,index1) = Pn0 + Qn0;     end end Pfa_ca = (1+beta_array/2/N).^(-2*N); %% 绘制曲线 plot(beta_array,log10(Pfa_ca),'Color','#FFD700','LineWidth',2,'Marker','<','MarkerIndices',2:4:length(beta_array));hold on; plot(beta_array,log10(Pfa(1,:)),'Color','#DC143C','LineWidth',2,'Marker','+','MarkerIndices',4:4:length(beta_array));hold on; plot(beta_array,log10(Pfa(2,:)),'Color','#FF1493','LineWidth',2,'Marker','*','MarkerIndices',6:4:length(beta_array));hold on; plot(beta_array,log10(Pfa(3,:)),'Color','#8B008B','LineWidth',2,'Marker','v','MarkerIndices',8:4:length(beta_array));hold on; plot(beta_array,log10(Pfa(4,:)),'Color','#483D8B','LineWidth',2,'Marker','^','MarkerIndices',10:4:length(beta_array));hold on; plot(beta_array,log10(Pfa(5,:)),'Color','#0000FF','LineWidth',2,'Marker','o','MarkerIndices',12:4:length(beta_array));hold on; plot(beta_array,log10(Pfa(6,:)),'Color','#6495ED','LineWidth',2,'Marker','d','MarkerIndices',14:4:length(beta_array));hold on; plot(beta_array,log10(Pfa(7,:)),'Color','#00BFFF','LineWidth',2,'Marker','p','MarkerIndices',16:4:length(beta_array));hold on; plot(beta_array,log10(Pfa(8,:)),'Color','#00CED1','LineWidth',2,'Marker','s','MarkerIndices',18:4:length(beta_array));hold on; plot(beta_array,log10(Pfa(9,:)),'Color','#00FA9A','LineWidth',2,'Marker','x','MarkerIndices',20:4:length(beta_array));hold on; plot(beta_array,log10(Pfa(10,:)),'Color','#DAA520','LineWidth',2,'Marker','>','MarkerIndices',22:4:length(beta_array));hold on; h = legend('CA','\alpha=0.1','\alpha=0.2','\alpha=0.3','\alpha=0.4','\alpha=0.5','\alpha=0.6','\alpha=0.7','\alpha=0.8','\alpha=0.9','\alpha=1.0','NumColumns',2); set(h,'edgecolor','none'); xlabel('\beta'); ylabel('log_{10}Pfa'); grid minor;

 

　

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%% S-CFAR的虚警概率计算 clc;clear;close all;   %% 参数设置 sigma = 0; sigmaI = 0; alpha = 0.3; %衰减系数 beta_array = 5:0.1:50; M = 0; N = 32; Nt_array = 12:5:32; Pfa = zeros(length(Nt_array),length(beta_array));   %% 计算虚警概率 for index = 1:length(Nt_array)     Nt = Nt_array(index);     for index1 = 1:length(beta_array)         beta0 = beta_array(index1);         Qn0 = 0;         for n0 = 0:Nt             M0 = max(0,n0 - 2 * N + M);             for m = M0:min(n0,M)                 for n = 0:(n0-m)                     for k = 0:m                         rou = alpha * ((M - m + k) / (1 + sigmaI) + 2 * N - M - n0 + m + n);                         phy =  2 * N / beta0  - (2 * N - n0 + k + n) * alpha;                         if(phy < 0)                             break;                         else                            V = phy^(2*N) * (1-(phy*sigmaI/(1+sigmaI)/(phy+rou+(1+sigma)^(-1)))^(-M)) / (rou+(1+sigma)^(-1)) / (phy+rou+(1+sigma)^(-1))^(2*N);                            Qn0 = Qn0 + 1 / (1+sigma) * nchoosek(M,m) * nchoosek(2*N-M,n0-m) * nchoosek(n0-m,n) * nchoosek(m,k) * (-1)^(k+n) / (1+sigmaI)^M * V;                         end                     end                 end             end         end           Pn0 = 0;         for n0 = Nt+1:2*N             M0 = max(0,n0 - 2 * N + M);             for m = M0:min(M,n0)                 for n = 0:n0-m                     for k = 0:m                         phy = n0 / beta0 - (k + n) * alpha;                         rou = alpha * ((M - m + k) / (1 + sigmaI) + 2* N - M - n0 + m + n);                         if phy < 0                             break;                         else                            W = phy^n0 * (1 - (phy*sigmaI/(1+sigmaI))/(phy+rou+(1+sigma)^(-1)))^(-m)/(rou +(1+sigma)^(-1))/(phy + rou + (1+sigma)^(-1))^n0;                            Pn0 = Pn0 + 1 / (1+sigma) * nchoosek(M,m) * nchoosek(2*N-M,n0-m) * nchoosek(n0-m,n) * nchoosek(m,k) * (-1)^(k+n) * W / (1+sigmaI)^m;                         end                     end                 end             end         end         Pfa(index,index1) = Pn0 + Qn0;     end end   %% 绘制曲线 plot(beta_array,log10(Pfa(1,:)),'Color','#DC143C','LineWidth',2,'Marker','+','MarkerIndices',2:4:length(beta_array));hold on; plot(beta_array,log10(Pfa(2,:)),'Color','#FF1493','LineWidth',2,'Marker','*','MarkerIndices',4:4:length(beta_array));hold on; plot(beta_array,log10(Pfa(3,:)),'Color','#8B008B','LineWidth',2,'Marker','v','MarkerIndices',6:4:length(beta_array));hold on; plot(beta_array,log10(Pfa(4,:)),'Color','#483D8B','LineWidth',2,'Marker','^','MarkerIndices',8:4:length(beta_array));hold on; plot(beta_array,log10(Pfa(5,:)),'Color','#0000FF','LineWidth',2,'Marker','o','MarkerIndices',10:4:length(beta_array));hold on; h = legend('Nt=12','Nt=17','Nt=22','Nt=27','Nt=32','NumColumns',1); set(h,'edgecolor','none'); xlabel('\beta'); ylabel('log_{10}Pfa'); grid minor;

　　

 

　　将S-CFAR在邻近单目标背景下进行仿真,随机产生在200个距离单元内产生信杂比分别为15dB、20dB的邻近目标，经典均值类ML-CFAR和有序统计类OS-CFAR以及S-CFAR的检测结果如下图所示，OS-CFAR和S-CFAR成功检测除了邻近目标，具有较好的多目标检测性能。

 

 　　具体代码如下所示。

 

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clc;clear;close all; %% 均匀背景 % % lambda = 1; %指数分布参数 % % dB = 20; %背景杂波功率 % % SCR = 15; %信杂比 % % num = [1,1024]; %距离单元设置 % % [x,target] = uniform_background(lambda,dB,SCR,num); %产生均匀背景   %% 多目标背景 lambda = 1; %指数分布参数 dB = 20; %背景杂波功率 SCR1 = 15; %信杂比 SCR2 = 20; %信杂比 num = [1,200]; %距离单元设置 localRule = [20,3,10]; %距离规则 [x,target] = multi_background(lambda,dB,SCR1,SCR2,num,localRule); %产生邻近单目标背景   %% CFAR参数 Pfa = 1e-6; %虚警概率 NSlide = 32;%滑动单元大小 Pro_cell = 4; %保护单元大小   %% 绘图参数 len = num(2); plotNum = 2; markersize = 5; LineWidth = 1.5; figure(1); plot(target(:,1),form_Power_P2DB(target(:,2)),'s','Color',[1 0 1],'MarkerSize',markersize+2,'LineWidth',LineWidth),hold on; plot(form_Power_P2DB(x),'Color','[0.5 0.5 1]','LineWidth',LineWidth),hold on;   %% 恒虚警率检测算法测试 Nt = 17;beta = 15.03; rate = 0.75; %选择序号 alpha(1,1) = ca_threhold(Pfa,NSlide); %CA-CFAR标称因子计算 alpha(2,1) = go_threhold(Pfa,NSlide); %GO-CFAR标称因子计算 alpha(3,1) = so_threhold(Pfa,NSlide); %SO-CFAR标称因子计算 alpha(4,1) = os_threhold(Pfa,NSlide,rate); %OS-CFAR标称因子计算   [result_S] = func_cfar_s(x,beta,NSlide,Nt,Pro_cell); %求解S-CFAR门限 [result_CA] = func_cfar_ca(x,alpha(1,1),NSlide,Pro_cell); %求解CA-CFAR门限 [result_GO] = func_cfar_go(x,alpha(2,1),NSlide,Pro_cell); %求解GO-CFAR门限 [result_SO] = func_cfar_so(x,alpha(3,1),NSlide,Pro_cell); %求解SO-CFAR门限 [result_OS] = func_cfar_os(x,alpha(4,1),NSlide,Pro_cell,rate); %求解OS-CFAR门限 %% 绘制检测曲线 [T_opt] = T_opt_solve(Pfa,lambda,dB,num); %求解理想门限 plot(form_Power_P2DB(T_opt),'Color','#3CB371','Marker','+','MarkerIndices',2:plotNum:len,'LineWidth',LineWidth); hold on; plot(form_Power_P2DB(result_CA{1,2}),'Color','#DC143C','Marker','*','MarkerIndices',4:plotNum:len,'LineWidth',LineWidth); hold on; plot(form_Power_P2DB(result_GO{1,2}),'Color','#ADFF2F','Marker','v','MarkerIndices',6:plotNum:len,'markersize',markersize,'LineWidth',LineWidth); hold on; plot(form_Power_P2DB(result_SO{1,2}),'Color','#8A2BE2','Marker','^','MarkerIndices',8:plotNum:len,'markersize',markersize,'LineWidth',LineWidth); hold on; plot(form_Power_P2DB(result_OS{1,2}),'Color','#0000CD','Marker','o','MarkerIndices',10:plotNum:len,'markersize',markersize,'LineWidth',LineWidth); hold on; plot(form_Power_P2DB(result_S{1,2}),'Color','#7CFC00','Marker','p','MarkerIndices',12:plotNum:len,'markersize',markersize,'LineWidth',LineWidth); hold on grid minor; xlabel('\fontname{宋体}距离单元'); ylabel('\fontname{宋体}功率值\fontname{Times New Roman}(dB)'); ylim([0 50]); h = legend('TARGET','CLUTTER','OPT','CA-CFAR','GO-CFAR','SO-CFAR','OS-CFAR','S-CFAR','Location','SouthEast','NumColumns',1); set(h,'edgecolor','none')

 

　

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%% 本程序主要实现S-CFAR恒虚警率检测算法的函数形式 function result = func_cfar_s(x,beta,NSlide,Nt,Pro_cell)     %x:原始杂波数据     %alpha：标称因子     %Nslide：滑动窗大小     %Pro_cell:保护单元大小     %Nt:整数门限       persistent left;     persistent right;     persistent Half_Slide;     persistent Half_Pro_cell;     persistent len;           if isempty(left)         left = 1 + Half_Pro_cell + Half_Slide; %设置左边界         right = length(x) - Half_Pro_cell - Half_Slide; %设置右边界         Half_Slide = NSlide / 2; %半滑动窗         Half_Pro_cell = Pro_cell / 2; %一侧保护单元长度         len = length(x); %杂波单元     end             T = zeros(1,len); %CMLD检测阈值     target = java.util.LinkedList; %利用Java链表来实现目标的存储       for i = 1:left - 1 %左边界         cell_right = x(1,i + Half_Pro_cell + 1 : i + Half_Slide * 2 + Half_Pro_cell);         S0 = cell_right(cell_right <= mean(cell_right));         S1 = cell_right(cell_right > mean(cell_right));         if length(S0) > Nt             T(1,i) = mean(S0) * beta;         else             T(1,i) = mean(cell_right) * beta;         end         if T(1,i) < x(i)             target.add(i); %加入目标         end     end           for i = left:right %中间区域         cell_left = x(1,i - Half_Pro_cell - Half_Slide : i - Half_Pro_cell - 1);         cell_right = x(1,i + Half_Pro_cell + 1 : i + Half_Pro_cell + Half_Slide);         cell = [cell_left,cell_right];         S0 = cell(cell <= mean(cell));         S1 = cell(cell > mean(cell));         if length(S0) > Nt             T(1,i) = mean(S0) * beta;         else             T(1,i) = mean(cell) * beta;         end         if T(1,i) < x(i)             target.add(i); %加入目标         end     end           for i = right + 1 : len         cell_left = x(1,i - Half_Pro_cell - Half_Slide * 2 : i - Half_Pro_cell - 1);         S0 = cell_left(cell_left <= mean(cell_left));         S1 = cell_left(cell_left > mean(cell_left));         if length(S0) > Nt             T(1,i) = mean(S0) * beta;         else             T(1,i) = mean(cell_left) * beta;         end         if T(1,i) < x(i)             target.add(i);         end     end           result = {'CFAR_S',T,target}; %采用字典类型 end