5. 5
C?p bit v¨¤o dk st
00 1
01 J
11 -1
10 -j
2. D?ng t¨ªn hi?u v¨¤ ph? t¨ªn hi?u
2.1.Code m? ph?ng
%%Ng? Minh ??c- L12VT2- B12LDVT067
d=randint (1,1000);%chuoi nhi phan dau vao.
L=length(d);
SNR=15; %y so tin hieu tren tap am.
y=1;
N=5*10^6;%toc do du lieu.
Fc=10^7;%tan so song mang.
T=1/N;%thoi gian truyen bit.
t=0:T*L/(30*L-1):T*L;
%tao chuoi dk gom 1,-1,j va -j.
for x=1:2:L
if d(x)==0 && d(x+1)==0
dk((y-1)*60+1:y*60)=1;
y=y+1;
elseif d(x)==0 && d(x+1)==1
dk((y-1)*60+1:y*60)=j;
y=y+1;
elseif d(x)==1 && d(x+1)==1
dk((y-1)*60+1:y*60)=-1;
y=y+1;
elseif d(x)==1 &&d(x+1)==0
dk((y-1)*60+1:y*60)=-j;
y=y+1;
end
end
end
end
6. 6
end
%tao tin hieu phat st voi pha cua tin hieu phat la pi/4.
st=dk*exp(j*pi/4);
st_awgn=awgn(st,SNR,'measured');%tin hieu qua kenh
AWGN.
% Ve dang tin hieu ban dau
subplot(3,1,1)
stairs(d)
axis([0 100 -1.5 1.5])
title( 'Chuoi ban dau' )
subplot(3,1,2)
stairs(b)
axis([0 100 -0.5 1.5])
title( 'Chuoi phat' )
subplot(3,1,3)
plot(t,a)
title( 'Chuoi QPSK phat di' )
%Giai dieu che ban tin QPSK.
%tim pha cua tin hieu tai phia thu.
for x=1:60*L/2
if angle(st_awgn(x))<=pi/2 && angle(st_awgn(x))>0
phi(x)=pi/4;
elseif angle(st_awgn(x))<=pi && angle(st_awgn(x))>pi/2
phi(x)=3*pi/4;
elseif angle(st_awgn(x))<=0 && angle(st_awgn(x))>-pi/2
phi(x)= 7*pi/4;
elseif angle(st_awgn(x))<=-pi/2 && angle(st_awgn(x))>-pi
phi(x)=5*pi/4;
end
end
end
end
end
%tim lai vecto phat.
z=1;
for x=30:60:60*L/2
if phi(x)==pi/4
r((z-1)*30+1:z*30)=0;
r(z*30+1:z*30+30)=0;
z=z+2;
elseif phi(x)==3*pi/4
r((z-1)*30+1:z*30)=0;
r(z*30+1:z*30+30)=1;
z=z+2;
elseif phi(x)==5*pi/4
r((z-1)*30+1:z*30)=1;
r(z*30+1:z*30+30)=1;
z=z+2;
elseif phi(x)==7*pi/4
7. 7
r((z-1)*30+1:z*30)=1;
r(z*30+1:z*30+30)=0;
z=z+2;
end
end
end
end
end
%ve bieu do chom sao QPSK.
h=scatterplot(st_awgn,1,0,'xb');
hold on
scatterplot(st,1,0,'or',h)
title('bieu do chom sao tin hieu QPSK')
%ve dang song tin hieu.
for x=1:30*L
sdc(x)=cos(2*pi*Fc*t(x)+ angle(st(x)));
sdc_awgn(x)=cos(2*pi*Fc*t(x)+angle(st_awgn(x)));
end
figure(2)
plot(t,sdc)
title('dang song tin hieu tai dau ra bo dieu che')
figure(3)
plot(t,sdc_awgn);
title('dang song tin hieu khi qua kenh awgn')
figure(4)
plot(t,r)
title('dang song tin hieu sau khi duoc khoi phuc')
%ve mat(chua lam duoc).
%% Mau mat cua tin hieu tai cac diem tren he thong
%ve pho cua tin hieu.
%pho tin hieu dieu che.
f=(-30*L/2:30*L/2-1)/(30*L*(t(2)-t(1)));
pho_dc=fft(sdc,30*L);
pho_dc=fftshift(pho_dc);
figure(5)
plot(f,abs(pho_dc).^2/(30*L))
title('pho tin hieu sau dieu che')
%pho tin hieu khi qua kenh awgn.
pho_awgn=fft(sdc_awgn,30*L);
pho_awgn=fftshift(pho_awgn);
figure(6)
plot(f,abs(pho_awgn).^2/(30*L))
title('pho tin hieu qua kenh awgn')
%pho tin hieu khi khoi phuc tai phia thu.
pho_r=fft(r,30*L);
pho_r=fftshift(pho_r);
8. 8
figure(7)
plot(f,abs(pho_r).^2/(30*L))
title('pho tin hieu khi duoc khoi phuc')
%ve duong cong xac xuat loi.
%tao chuoi bit ngau nhien QPSK.
Dk=randint(1,5*10^5,[0 3]);
Phi=2*pi*Dk/4 + pi/4;
sk=exp(j*Phi);
SNRdB=0:15;%dB
for k=1:length(SNRdB)
st=awgn(sk,SNRdB(k),'measured');
for c=1:length(Dk)
if angle(st(c))<=pi/2 && angle(st(c))>0
phi(c)=pi/4;
elseif angle(st(c))<=pi && angle(st(c))>pi/2
phi(c)=3*pi/4;
elseif angle(st(c))<=3*pi/2 && angle(st(c))>pi
phi(c)= 5*pi/4;
elseif angle(st(c))<=2*pi && angle(st(c))>3*pi/2
phi(c)=7*pi/4;
end
end
end
end
end
error=phi-phi;
%tim so symbol sai.
so_loi=length(find(error~=0));
BER(k)=so_loi/(5*10^5);
end
% BER theo ly thuyet truyen dan QPSK la:
BER_lt=erfc(sqrt(10.^(SNRdB./10)));
%ve do thi.
figure(8)
semilogy(SNRdB,BER,'*',SNRdB,BER_lt);
xlabel('SNR')
ylabel('BER')
legend('theo mo phong','theo ly thuyet')
title('duong cong bit loi QPSK')
grid
9. 9
2.2. K?t qu? m? ph?ng
a) D?ng s¨®ng t¨ªn hi?u t?i ??u ra b? ?i?u ch?
b) D?ng s¨®ng t¨ªn hi?u khi ?i qua k¨ºnh AWGN
10. 10
c) D?ng s¨®ng t¨ªn hi?u sau khi ???c kh?i ph?c
d) Bi?u ?? ch¨°m sao t¨ªn hi?u QPSK
11. 11
e) Ph? t¨ªn hi?u sau ?i?u ch?
f) Ph? t¨ªn hi?u qua k¨ºnh AWGN
12. 12
g) Ph? t¨ªn hi?u sau khi kh?i ph?c
h) ???ng cong bit l?i QPSK
13. 13
2.3.M? ph?ng Monte-Carlo
clear
N = 5*10^7; % number of symbols
Es_N0_dB = [ -3:14]; % multiple Eb/N0 values
ipHat = zeros(1,N);
for ii = 1:length(Es_N0_dB)
ip = (2*(randi(1,N)>0.5) -1) + j*(2*(rand(1,N)>0.5) -1); %
s = (1/sqrt(2))*ip; % normalization of energy to 1
n = 1/sqrt(2)*[randi(1,N) + j*N)]; % white guassian noise, 0dB
variance
y = s + 10^( -Es_N0_dB(ii)/20)*n; % additive white gaussian
noise
% demodulation
y_re = real(y); % real
y_im = imag(y); % imaginary
ipHat(find(y_re < 0 & im 0)) = -1 + -1*j;
ipHat(find(y_re >= 0 & im > 0)) = 1 + 1*j;
ipHat(find(y_re < 0 & im >= 0)) = -1 + 1*j;
ipHat(find(y_re >= 0 & im < 0)) = 1 - 1*j;
nErr(ii) = size(find([ip - ipHat]),2); % couting the number of
errors
end
simSer_QPSK = nErr/N;
theorySer_QPSK = erfc(sqrt(0.5*(10.^(Es_N0_dB/10)))) -
(1/4)*(erfc(sqrt(0.5*(10.^(Es_N0_dB/10)) ))).^2;
close all
figure
semilogy(Es_N0_dB,theorySer_QPSK, 'b. -');
hold on
semilogy(Es_N0_dB,simSer_QPSK, 'mx -');
axis([ -3 15 10^ -5 1])
grid on
legend( 'theory -QPSK' , 'simulation -QPSK' );
![6
end
%tao tin hieu phat st voi pha cua tin hieu phat la pi/4.
st=dk*exp(j*pi/4);
st_awgn=awgn(st,SNR,'measured');%tin hieu qua kenh
AWGN.
% Ve dang tin hieu ban dau
subplot(3,1,1)
stairs(d)
axis([0 100 -1.5 1.5])
title( 'Chuoi ban dau' )
subplot(3,1,2)
stairs(b)
axis([0 100 -0.5 1.5])
title( 'Chuoi phat' )
subplot(3,1,3)
plot(t,a)
title( 'Chuoi QPSK phat di' )
%Giai dieu che ban tin QPSK.
%tim pha cua tin hieu tai phia thu.
for x=1:60*L/2
if angle(st_awgn(x))<=pi/2 && angle(st_awgn(x))>0
phi(x)=pi/4;
elseif angle(st_awgn(x))<=pi && angle(st_awgn(x))>pi/2
phi(x)=3*pi/4;
elseif angle(st_awgn(x))<=0 && angle(st_awgn(x))>-pi/2
phi(x)= 7*pi/4;
elseif angle(st_awgn(x))<=-pi/2 && angle(st_awgn(x))>-pi
phi(x)=5*pi/4;
end
end
end
end
end
%tim lai vecto phat.
z=1;
for x=30:60:60*L/2
if phi(x)==pi/4
r((z-1)*30+1:z*30)=0;
r(z*30+1:z*30+30)=0;
z=z+2;
elseif phi(x)==3*pi/4
r((z-1)*30+1:z*30)=0;
r(z*30+1:z*30+30)=1;
z=z+2;
elseif phi(x)==5*pi/4
r((z-1)*30+1:z*30)=1;
r(z*30+1:z*30+30)=1;
z=z+2;
elseif phi(x)==7*pi/4](https://image.slidesharecdn.com/bitpln-130701014846-phpapp01/85/Bai-t-p-l-n-6-320.jpg)
![8
figure(7)
plot(f,abs(pho_r).^2/(30*L))
title('pho tin hieu khi duoc khoi phuc')
%ve duong cong xac xuat loi.
%tao chuoi bit ngau nhien QPSK.
Dk=randint(1,5*10^5,[0 3]);
Phi=2*pi*Dk/4 + pi/4;
sk=exp(j*Phi);
SNRdB=0:15;%dB
for k=1:length(SNRdB)
st=awgn(sk,SNRdB(k),'measured');
for c=1:length(Dk)
if angle(st(c))<=pi/2 && angle(st(c))>0
phi(c)=pi/4;
elseif angle(st(c))<=pi && angle(st(c))>pi/2
phi(c)=3*pi/4;
elseif angle(st(c))<=3*pi/2 && angle(st(c))>pi
phi(c)= 5*pi/4;
elseif angle(st(c))<=2*pi && angle(st(c))>3*pi/2
phi(c)=7*pi/4;
end
end
end
end
end
error=phi-phi;
%tim so symbol sai.
so_loi=length(find(error~=0));
BER(k)=so_loi/(5*10^5);
end
% BER theo ly thuyet truyen dan QPSK la:
BER_lt=erfc(sqrt(10.^(SNRdB./10)));
%ve do thi.
figure(8)
semilogy(SNRdB,BER,'*',SNRdB,BER_lt);
xlabel('SNR')
ylabel('BER')
legend('theo mo phong','theo ly thuyet')
title('duong cong bit loi QPSK')
grid](https://image.slidesharecdn.com/bitpln-130701014846-phpapp01/85/Bai-t-p-l-n-8-320.jpg)
![13
2.3.M? ph?ng Monte-Carlo
clear
N = 5*10^7; % number of symbols
Es_N0_dB = [ -3:14]; % multiple Eb/N0 values
ipHat = zeros(1,N);
for ii = 1:length(Es_N0_dB)
ip = (2*(randi(1,N)>0.5) -1) + j*(2*(rand(1,N)>0.5) -1); %
s = (1/sqrt(2))*ip; % normalization of energy to 1
n = 1/sqrt(2)*[randi(1,N) + j*N)]; % white guassian noise, 0dB
variance
y = s + 10^( -Es_N0_dB(ii)/20)*n; % additive white gaussian
noise
% demodulation
y_re = real(y); % real
y_im = imag(y); % imaginary
ipHat(find(y_re < 0 & im 0)) = -1 + -1*j;
ipHat(find(y_re >= 0 & im > 0)) = 1 + 1*j;
ipHat(find(y_re < 0 & im >= 0)) = -1 + 1*j;
ipHat(find(y_re >= 0 & im < 0)) = 1 - 1*j;
nErr(ii) = size(find([ip - ipHat]),2); % couting the number of
errors
end
simSer_QPSK = nErr/N;
theorySer_QPSK = erfc(sqrt(0.5*(10.^(Es_N0_dB/10)))) -
(1/4)*(erfc(sqrt(0.5*(10.^(Es_N0_dB/10)) ))).^2;
close all
figure
semilogy(Es_N0_dB,theorySer_QPSK, 'b. -');
hold on
semilogy(Es_N0_dB,simSer_QPSK, 'mx -');
axis([ -3 15 10^ -5 1])
grid on
legend( 'theory -QPSK' , 'simulation -QPSK' );](https://image.slidesharecdn.com/bitpln-130701014846-phpapp01/85/Bai-t-p-l-n-13-320.jpg)