不要在不使用cvx优化的场合使用log_det，应改为log(det(..))，否者可能会出现奇怪的错误

跑代码的时候遇到的问题
matlab 复制代码
%% 分解为功率和单位模，交替优化功率分量和单位模

clc;clear;
Nt = 8;  % 发射天线数目  8
Nr = 4;  % 接收天线数目  4
Ne = 6;  % Eve天线数目   6
noisePower = 1;
SNRTotaldB = -5:5:35; %%%%最大发射功率单位dB
SNRTotal = 10.^(SNRTotaldB./10);  %%%% 最大发射功率约束，单位dB
channelNum = 2000; %%% 生成10次信道

%tilde_f = sqrt(1/2) * ( randn(Nt,1) + j*randn(Nt,1) );
% tilde_f = tilde_f / norm(tilde_f);
[hBsUserSet] = channelGenerate(Nr,Nt,channelNum);%生成100次信道HBsUe，H维度NrxNt
[hBsEveSet] = channelGenerate(Ne,Nt,channelNum);%生成100次信道HBsEve，H维度NexNt

rateSet = zeros(channelNum,length(SNRTotal));%生成最终速率数组
rateSetCmp = zeros(channelNum,length(SNRTotal));%生成最终速率数组

cvx_begin
cvx_end
for indexh = 1:channelNum
    hBsUser = hBsUserSet(:,:,indexh); %具体单次信道hBsUser实现
    hBsEve = hBsEveSet(:,:,indexh); %具体单次信道hBsEve实现
    objBeamformingCollect = [];
    objCmpUnit = [];
    for indexp = 1:length(SNRTotaldB)
        %Q维度为NtxNt，qCmpUnit是对比方案，代表在各个天线上分配相同发射功率
        QCmpUnit = diag(SNRTotal(indexp)/Nt*ones(1,Nt));
        %%%% 计算基于协方差矩阵QCmpUnit的安全可达造率
        rateCmpUnit = 1/log(2)*log_det(eye(Nr)+hBsUser*QCmpUnit*hBsUser')... % matlab 换行指令。。
            - 1/log(2)*log_det(eye(Ne)+hBsEve*QCmpUnit*hBsEve') ;
        objCmpUnit =  [objCmpUnit, max(real(rateCmpUnit),0)];
 
        %% 采用交替优化方法，表达式为  tilde_f 和 tilde_p
        %%  log(1+tilde_p * norm(hBsUser*tilde_f)^2) - log(1+tilde_p * norm(hBsEve*tilde_f)^2)
        objBefore =10;
        objAfter = 10 * objBefore;
        count = 0;
        objAfterSet = [];
        tilde_f = sqrt(1/2) * ( randn(Nt,1) + j*randn(Nt,1) );
        while(abs((objAfter-objBefore)/objBefore)>= 5e-4 && count~=50)
            fprintf('第%g个信道实现，SNR为%g时的,第%g次内部迭代\n',indexh, SNRTotaldB(indexp), count);
            objBefore = objAfter;
            %%%%%%% 
            % tilde_p
            
            if( norm(hBsUser*tilde_f) >= norm(hBsEve*tilde_f) )
                 tilde_p = SNRTotal(indexp);
            else
                 tilde_p = 0;
            end
%             tilde_p = SNRTotal(indexp);
            fprintf('\n\n');
            fprintf('tilde_p的值为%g\n', tilde_p); 
            % tilde_f
            A = eye(Nt) + tilde_p * (hBsUser'*hBsUser);
            B = eye(Nt) + tilde_p * (hBsEve'*hBsEve);
            [V,D] = eig(A,B);
            % [V,D] = eig(A,B) 返回广义特征值的对角矩阵 D 和满矩阵 V，其列是对应的右特征向量，使得 A*V = B*V*D。
            Max_Eigen_value= max(max(D)); %%最大广义特征值
            d = diag(D);%%% D是对角矩阵，提取对角元素
            [pos1] = find(d == Max_Eigen_value);
            tilde_f = V(:,pos1)/norm(V(:,pos1)); %最大广义特征值对应的归一化广义特征向量
            %%%%%
            objAfter = 1/log(2)*log(1+tilde_p * norm(hBsUser*tilde_f)^2)...
              - 1/log(2)*log(1+tilde_p * norm(hBsEve*tilde_f)^2); 
            objAfter2 = 1/log(2)*log_det(eye(Nr)+tilde_p * hBsUser* (tilde_f*tilde_f') *hBsUser')... % matlab 换行指令。。
            - 1/log(2)*log_det(eye(Ne)+tilde_p*hBsEve* (tilde_f*tilde_f') *hBsEve')  ;
            fprintf('obj2 - obj1 = %g\n', objAfter2 - objAfter );
            if(abs(objAfter2 - objAfter) > 1)
                fprintf('1/log(2)*log(1+tilde_p * norm(hBsUser*tilde_f)^2) is %g \n', 1/log(2)*log(1+tilde_p * norm(hBsUser*tilde_f)^2) );
                fprintf('1/log(2)*log_det(eye(Nr)+tilde_p * hBsUser* (tilde_f*tilde_f) *hBsUser is %g \n', 1/log(2)*log_det(eye(Nr)+tilde_p * hBsUser* (tilde_f*tilde_f') *hBsUser') );
                fprintf('- 1/log(2)*log(1+tilde_p * norm(hBsEve*tilde_f)^2) is %g \n', - 1/log(2)*log(1+tilde_p * norm(hBsEve*tilde_f)^2) );
                fprintf('- 1/log(2)*log_det(eye(Ne)+tilde_p*hBsEve* (tilde_f*tilde_f) *hBsEve) is %g \n', real(- 1/log(2)*log_det(eye(Ne)+tilde_p*hBsEve* (tilde_f*tilde_f') *hBsEve')) );
                fprintf('内部 is %g\n', det(eye(Ne)+tilde_p*hBsEve* (tilde_f*tilde_f') *hBsEve'));
                fprintf('用log_det了 is %g\n', log_det(eye(Ne)+tilde_p*hBsEve* (tilde_f*tilde_f') *hBsEve'));
                fprintf('用log(det(了 is %g\n', log(det(eye(Ne)+tilde_p*hBsEve* (tilde_f*tilde_f') *hBsEve')));
            end
            count = count + 1;
            objAfterSet=[objAfterSet, objAfter];
        end
        objIter = max(real(objAfter),0);
        objBeamformingCollect = [objBeamformingCollect, objIter];
    end
    rateSet(indexh, :) = objBeamformingCollect;
    rateSetCmp(indexh, :) = objCmpUnit;
    fprintf('The %gth channel realization is over \n', indexh);
end






average_rateSet = mean(rateSet);
average_rateSetCmp = mean(rateSetCmp);

%% 画图
hold off;
plot(SNRTotaldB, average_rateSet,'color',[0.22 0.37 0.06],'linestyle','-','marker','^','LineWidth',1.5); % 
hold on;
plot(SNRTotaldB, average_rateSetCmp,'m->','LineWidth',1.5);
% axis tight;
xlabel('最大发射功率(dB)','fontsize',11);
ylabel('可达安全速率(bps/Hz)','fontsize',11);
legend('波束赋形优化方案','等功率发送对比方案','Location','northwest','fontsize',11);
grid on;







%%%%%%

% A = rand(2,9)
% 
% A * A'
% 
% norm(A)^2
% 
% 
%
其中时不时会出现这种情况：也就是当我不是在用cvx来优化问题，只是想用log_det函数去代替log(det())函数的功能时，log_det有时候会跳出这样的问题。
cvx forum上没有查到相关的解释