引自youtube上一个教授
beamforming为何具有方向性,可以理解为天线阵列中不同的天线的信号在某个方向的矢量叠加,由于不同相位上的消长,导致总的效果具有方向性,MIMO中很大一部分是通过控制不同天线延迟和幅度的叠加来合理控制beamforming来使信号更加集中
这是一个ULA的beamforming仿真
clc;
clear;
theta = [-90:90]/180*pi;
% Mobile RF
dBase = 0.06;
fBase = 2.5e9;
cBase = 3e8;
%Accoustic
%dBase = 0.2;
%fBase = 1e3;
%cBase = 343;
d=dBase;
f=fBase;
c=cBase;
lambda = c/f;
PhaseOffsetFraction = d*sin(theta) /lambda;
Frames=10;
N=3;
MultFactor=2;
SpaceFactor=2;
thetaOffset=90;
thetaOffsetStep=pi/2/Frames;
figure(1)
clf
hold off
MaxAbs = 1+MultFactor*N-1;
BeamsAntennas = ones(N,181);
for n = 1:N
K=MultFactor*n;
for k=1:(K-1)
BeamsAntennas(n,:) = BeamsAntennas(n,:) + exp(1i*k*d*sin(theta)/lambda*2*pi);
end
%beam(n, : ) = beam( n, : )/(1+K);
subplot(2,N,n)
semilogy(abs (BeamsAntennas(n, : )))
title( [num2str(K) , ' Antennas, ' ,num2str(d) , 'mSpacing'] , 'fontsize' ,16)
set(gca, 'XLim' ,[1 181])
set(gca, 'xtick' , [1:30:181])
set(gca, 'XTickLabel' ,{[-90:30:90] })
set(gca, 'YLim' , [1e-2 10^((1-rem( log10(MaxAbs),1))+log10(MaxAbs))])
end
pause
%%
thetaOffset=pi/2;
BeamsSpacing = ones(N, 181);
for n = 1:N
K=MultFactor*n;
for k=1: (K-1)
BeamsSpacing(n, : ) = BeamsSpacing(n, : ) + ...
exp(1i*k*SpaceFactor*d*sin(theta)/lambda*2*pi);
end
%beam(n, : ) = beam(n, : )/( 1+K);
subplot(2,N, n+N)
semilogy(abs (BeamsSpacing(n, : )))
title([num2str(K),' Ant, d=' ,num2str(SpaceFactor*d) , ' m,Phase=' , num2str(thetaOffset/pi*180) , ' deg'], 'fontsize',16)
set(gca, 'XLim' , [1 181])
set(gca, 'xtick' , [1:30:181])
set(gca, 'XTickLabel' ,{[-90: 30:90]})
set(gca, 'YLim' , [1e-2 10^((1-rem(log10(MaxAbs),1))+log10(MaxAbs))])
end
%天线越多,beamforming越强。
%%
%%
pause
SpaceFactor=0.5;
for Section=1:2
if Section==2
d=dBase;
SpaceFactor=1;
end
for movieupdate=1:Frames;
if Section==2
thetaOffset=thetaOffset+thetaOffsetStep;
end
BeamsSpacing = ones(N,181);
for n = 1:N
K=MultFactor*n;
for k=1: (K-1)
BeamsSpacing(n, : ) = BeamsSpacing(n, : ) +
exp(1i*k*SpaceFactor*d*sin((theta-thetaOffset) ) / lambda*2*pi);
end
%beam(n, : ) = beam( n, :)/( 1+K);
subplot(2,N, n+N)
semilogy( abs (BeamsSpacing( n, : )))
title([num2str(K), 'Ant,d=' , num2str(SpaceFactor*d) , 'm, ...
Phase=' , num2str(thetaOffset/pi*180), 'deg' ], 'fontsize',16)
set(gca, 'XLim' , [1 181])
set(gca , 'xtick' , [1:30:181])
set(gca, 'XTickLabel' ,{[-90:30:90]})
set(gca, 'YLim' ,[1e-2 10^((1-rem(log10(MaxAbs),1))+log10(MaxAbs))])
end
pause
if Section==1
SpaceFactor=SpaceFactor+4/Frames;
end
end
pause
end