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1、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r x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V）。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:其中维的变换的接受信号向量，r-ij是协方差矩阵为 的零均值循环对称复高斯 变换噪声向量。
2、向量 必须满足 已限制总的发送能量。可以看出,i=l,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=l,2,r)反映了第i个子信道的发送能量，且满足扎=f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。最佳能量分配政策訥注水算法：St epl:迭代计数p=1,计算St ep2 :用口计算,i=1,2,，rp+1St ep3:若分配到最小增益的信道能量为负值，即设Z,-,.+： = 0,p=p+1，转至 St epl.若任意 非负，即得到最佳注水功率分配策略。l.2 发送端知道信道时的信道容
3、量% in this programe a highly seattered 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% decomposition) is distributed as water-filling algorithm clear all close allclcnt_V = 1 2 3 2 4;nr_V =
4、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 二-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 = s
5、vd(H);landas(:,j) = diag(V);Capacity(i,j) PowerAllo = WaterFilling_alg(Pt,landas(:,j),B,N0); endendf1 = figure(1);hold onplot(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), ,
6、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 subcha
7、nnels 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);PowerAll
8、oT = (PtotA + sum(1./HT)/MP - 1./HT;PowerAllo(IndexP) = PowerAlloT;endPowerAllo = PowerAllo.;Capacity = sum(log2(1+ PowerAllo. .* H);审u61015XIEtf! fri lE15Is-注意：HHU 的奇异值，所以对H奇异值分解后要平方ChA.V1.3 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;1;Iteration = 1e2; % m
9、ust be grater than 1e2SNR_V_db = -10:3:20;SNR_V10.(SNR_V_db/10);1 ， 1 ， ， ， ， ， ， 1 ， ， ：color = b;r;g;k;mnotationfor(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);Capacity(i,j)=log2(det(eye(nr)+Pt/(nt*B*N
10、0)* H*H); end end hold on plot(SNR_V_db,mean(Capacity),notation(k,:),color,color(k,:) clear landasendf2= figure(2)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(f2,color,1 1 1)xlabel(SNR in dB) ylabel(C
11、apacity bits/s/Hz)2fiiE1nS3S a J 血T:4;劭：；-.:2. :.:ii iE1.4 已知信道和未知信道容量比较 clear all close allclcnt_V= 1 232 4;nr_V= 1 223 4;N0 =1e-4;B= 1;Iteration =1e2;% must be greater than 1e2SNR_V_db = -10:3:20;color =，1 ，1 ， Jb;r;g;k;m;notation 二，_o，;，_，;，_，;，_“，；，_s，;notation_uninf二，:o，;，:，;，:，；，：，；，：$，;for(k
12、= 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);
13、endend 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)己一WF-flljfl !li=N=llUKCSI ff=?rM P Wff-alg HFnl-2 P-UNrai Ert=2 fl Wnafcg i*ii=2/t?3T UHCSI i=2”R3 ri WF-sig -U
