注水算法.doc

1.1功率注水算法 注水算法是根据某种准则，并根据信道状况对发送功率进行自适应分配，通常是信道状况好的时刻，多分配功率，信道差的时候，少分配功率，从而最大化传输速率。实现功率的“注水”分配，发送端必须知道CSI。当接收端完全知道信道而发送端不知道信号时，发送天线阵列中的功率平均分配是合理的。当发送端知道信道，可以增加信道容量。 考虑一个维的零均值循环对称复高斯信号向量，r为发送信道的秩。向量在传送之前被乘以矩阵()。在接收端，接受到的信号向量y被乘以。这个系统的有效输入输出关系式由下式给出：其中是维的变换的接受信号向量，是协方差矩阵为的零均值循环对称复高斯变换噪声向量。向量必须满足已限制总的发送能量。可以看出，i=1,2,rMIMO信道的容量是单个平行SISO信道容量之和，由下式给出其中(i=1,2,r)反映了第i个子信道的发送能量，且满足。可以在子信道中分配可变的能量来最大化互信息。现在互信息最大化问题就变成了：最大化目标在变量中是凹的，用拉格朗日法最大化。最佳能量分配政策注水算法：Step1:迭代计数p=1,计算Step2:用计算，i=1,2,r-p+1Step3:若分配到最小增益的信道能量为负值,即设，p=p+1，转至Step1.若任意非负，即得到最佳注水功率分配策略。1.2 发送端知道信道时的信道容量% in this programe a highly scattered enviroment is considered. The% Capacity of a MIMO channel with nt transmit antenna and nr recieve% antenna is analyzed. The power in parallel channel (after% deposition) is distributed as water-filling algorithmclear allclose allclcnt_V = 1 2 3 2 4;nr_V = 1 2 2 3 4;N0 = 1e-4;B = 1;Iteration = 1e2; % must be grater than 1e2SNR_V_db = -10:3:20;SNR_V = 10.(SNR_V_db/10);color = b;r;g;k;m;notation = -o;-;-;-;-s;for(k = 1 : 5) nt = nt_V(k); nr = nr_V(k); for(i = 1 : length(SNR_V) Pt = N0 * SNR_V(i); for(j = 1 : Iteration) H = random(rayleigh,1,nr,nt); S V D = svd(H); landas(:,j) = diag(V); Capacity(i,j) PowerAllo = WaterFilling_alg(Pt,landas(:,j),B,N0); end end f1 = figure(1); hold on plot(SNR_V_db,mean(Capacity),notation(k,:),color,color(k,:) clear landasendf1 = figure(1)legend_str = ;for( i = 1 : length(nt_V) legend_str = legend_str ;. nt = ,num2str(nt_V(i), , nr = ,num2str(nr_V(i);endlegend(legend_str)grid onset(f1,color,1 1 1)xlabel(SNR in dB)ylabel(Capacity bits/s/Hz)注水算法子函数function Capacity PowerAllo = WaterFilling_alg(PtotA,ChA,B,N0);% WaterFilling in Optimising the Capacity%=% Initialization%=ChA = ChA + eps;NA = length(ChA); % the number of subchannels allocated toH = ChA.2/(B*N0); % the parameter relate to SNR in subchannels% assign the power to subchannelPowerAllo = (PtotA + sum(1./H)/NA - 1./H;while(length(find(PowerAllo 0) IndexN = find(PowerAllo 0); MP = length(IndexP); PowerAllo(IndexN) = 0; ChAT = ChA(IndexP); HT = ChAT.2/(B*N0); PowerAlloT = (PtotA + sum(1./HT)/MP - 1./HT; PowerAllo(IndexP) = PowerAlloT;endPowerAllo = PowerAllo.; Capacity = sum(log2(1+ PowerAllo. .* H);注意：是的奇异值，所以对H奇异值分解后要平方ChA.21.3 发送端不知道信道时的信道容量功率均等发送，信道容量的表达式为clear allclcnt_V = 1 2 3 2 4;nr_V = 1 2 2 3 4;N0 = 1e-4;B = 1;Iteration = 1e2; % must be grater than 1e2SNR_V_db = -10:3:20;SNR_V = 10.(SNR_V_db/10);color = b;r;g;k;m;notation = :o;:;:;:;:s;for(k = 1 : length(nt_V) nt = nt_V(k); nr = nr_V(k); for(i = 1 : length(SNR_V) Pt = N0 * SNR_V(i); for(j = 1 : Iteration) H = random(rayleigh,1,nr,nt); S V D = svd(H); landas(:,j) = diag(V); Capacity_uninf(i,j)=log2(det(eye(nr)+Pt/(nt*B*N0)* H*H); Capacity(i,j) PowerAllo = WaterFilling_alg(Pt,landas(:,j),B,N0); end end f1 = figure(1); hold onplot(SNR_V_db,mean(Capacity),notation(k,:),color,color(k,:)hold onplot(SNR_V_db,mean(Capacity_uninf),notation_uninf (k,:),color,color(k,:)clear landasendgrid onset(f1,color,1 1 1)xlabel(SNR in dB)ylabel(Capacity bits/s/Hz)f1 = figure(1)legend_str = ;for( i = 1 : length(nt_V) legend_str = legend_str ;. nt = ,num2str(nt_V(i), , nr = ,num2str(nr_V(i);endlegend(legend_str)grid onset(f1,color,1 1 1)xlabel(SNR in dB)ylabel(Capacity bits/s/Hz)由图形中可以看出：1. 在小信噪比时，相同信噪比下利用CSI的功率注水算法获得容量优于未知CSI的平均功率分配算法；相同容量下已知CSI信噪比比未知CSI时的信噪比小3dB.2. 当信噪比增大到一定程度时，功率注水算法所获得的信道容量将收敛到平均功率分配的信道容量。