%------------------------------------------------------------------------
%NOTES:
%About entering matrix O:
%-- O is Tp*Nt matrix,as default 4*3 complex orthogonal is defined (rate 3/4).
%for [x1 -x2 -x3;x2* x1* 0;x3* 0 x1*;0 -x3* x2*] -----enter------> O=[1 -2 -3;2+j 1+j 0;3+j 0 1+j;0 -3+j 2+j];
%-- Alamouti Scheme: [x1 x2;-x2* x1*] -----enter------> O=[1 2;-2+j 1+j];
%-- A real orthogonal: [x1 x2;-x2 x1] -----enter------> O=[1 2;-2 1];
%-- For real orthogonal matrices define M_psk=2; as real signal constellation.
%-- O=[1]; is uncoded (no diversity).
%-- In this program entries of O cannot be like "a1*x1[*]+a2*x2[*]+...+an*xn[*]" only they can be like "x1 or -x1 or x1* or -x1*".
%------------------------------------------------------------------------
clear all
O=[1 -2 -3;2+j 1+j 0;3+j 0 1+j;0 -3+j 2+j]; %Complex or Real Orthogonal Matrix **define this**
Nt=size(O,2); %Number of Transmit antennas
co_time=size(O,1) %Block time length
Nr=1; %Number of Receive antennas **define this**
Nit=100; %Number of repeates for each snr **define this**
M_psk=4; %M-PSK constellation,M_psk=2^k **define this**
snr_min=3; %Min snr range for simulation **define this**
snr_max=15; %Max snr rande for simulation **define this**
graph_inf_bit=zeros(snr_max-snr_min+1,2); %Plot information
graph_inf_sym=zeros(snr_max-snr_min+1,2); %Plot information
num_X=1;
num_bit_per_sym=log2(M_psk);
for cc_ro=1:co_time
for cc_co=1:Nt
num_X=max(num_X,abs(real(O(cc_ro,cc_co))));
end
end
co_x=zeros(num_X,1);
for con_ro=1:co_time %Compute delta,epsilon,eta and conj matrices
for con_co=1:Nt
if abs(real(O(con_ro,con_co)))~=0
delta(con_ro,abs(real(O(con_ro,con_co))))=sign(real(O(con_ro,con_co)));
epsilon(con_ro,abs(real(O(con_ro,con_co))))=con_co;
co_x(abs(real(O(con_ro,con_co))),1)=co_x(abs(real(O(con_ro,con_co))),1)+1;
eta(abs(real(O(con_ro,con_co))),co_x(abs(real(O(con_ro,con_co))),1))=con_ro;
coj_mt(con_ro,abs(real(O(con_ro,con_co))))=imag(O(con_ro,con_co));
end
end
end
eta=eta.'; %Sort is not necessary
eta=sort(eta);
eta=eta.';
for SNR=snr_min:snr_max %Start simulation
clc
disp('Wait until SNR=');disp(snr_max);
SNR
n_err_sym=0;
n_err_bit=0;
graph_inf_sym(SNR-snr_min+1,1)=SNR;
graph_inf_bit(SNR-snr_min+1,1)=SNR;
for con_sym=1:Nit
bi_data=randint(num_X,num_bit_per_sym); %Random binary data
de_data=bi2de(bi_data); %Convert binary data to decimal for use in M-PSK mod.
% data=pskmod(de_data,M_psk,0,'gray');
data=pskmod(de_data,M_psk,0);
H=randn(Nt,Nr)+j*randn(Nt,Nr); %Path gains matrix
XX=zeros(co_time,Nt);
for con_r=1:co_time %Start space time coding
for con_c=1:Nt
if abs(real(O(con_r,con_c)))~=0
if imag(O(con_r,con_c))==0
XX(con_r,con_c)=data(abs(real(O(con_r,con_c))),1)*sign(real(O(con_r,con_c)));
else
XX(con_r,con_c)=conj(data(abs(real(O(con_r,con_c))),1))*sign(real(O(con_r,con_c)));
end
end
end
end %End space time coding
H=H.';
XX=XX.';
snr=10^(SNR/10);
Noise=(randn(Nr,co_time)+j*randn(Nr,co_time)); %Generate Noise
Y=(sqrt(snr/Nt)*H*XX+Noise).'; %Received signal
H=H.'; %Start decoding with perfect channel estimation
for co_ii=1:num_X
for co_tt=1:size(eta,2)
if eta(co_ii,co_tt)~=0
if coj_mt(eta(co_ii,co_tt),co_ii)==0
r_til(eta(co_ii,co_tt),:,co_ii)=Y(eta(co_ii,co_tt),:);
a_til(eta(co_ii,co_tt),:,co_ii)=conj(H(epsilon(eta(co_ii,co_tt),co_ii),:));
else
r_til(eta(co_ii,co_tt),:,co_ii)=conj(Y(eta(co_ii,co_tt),:));
a_til(eta(co_ii,co_tt),:,co_ii)=H(epsilon(eta(co_ii,co_tt),co_ii),:);
end
end
end
end
RR=zeros(num_X,1);
for ii=1:num_X %Generate decision statistics for the transmitted signal "xi"
for tt=1:size(eta,2)
for jj=1:Nr
if eta(ii,tt)~=0
RR(ii,1)=RR(ii,1)+r_til(eta(ii,tt),jj,ii)*a_til(eta(ii,tt),jj,ii)*delta(eta(ii,tt),ii);
end
end
end
end
% re_met_sym=pskdemod(RR,M_psk,0,'gray'); % = ML decision for M-PSK
re_met_sym=pskdemod(RR,M_psk,0);
re_met_bit=de2bi(re_met_sym);
re_met_bit(1,num_bit_per_sym+1)=0; %For correct demension of "re_met_bit"
for con_dec_ro=1:num_X
if re_met_sym(con_dec_ro,1)~=de_data(con_dec_ro,1)
n_err_sym=n_err_sym+1;
for con_dec_co=1:num_bit_per_sym
if re_met_bit(con_dec_ro,con_dec_co)~=bi_data(con_dec_ro,con_dec_co)
n_err_bit=n_err_bit+1;
end
end
end
end
end
Perr_sym=n_err_sym/(num_X*Nit); %Count number of error bits and symbols
graph_inf_sym(SNR-snr_min+1,2)=Perr_sym;
Perr_bit=n_err_bit/(num_X*Nit*num_bit_per_sym);
graph_inf_bit(SNR-snr_min+1,2)=Perr_bit;
end
x_sym=graph_inf_sym(:,1); %Generate plot
y_sym=graph_inf_sym(:,2);
subplot(2,1,1);
semilogy(x_sym,y_sym,'k-v');
xlabel('SNR, [dB]');
ylabel('Symbol Error Probability');
grid on
x_bit=graph_inf_bit(:,1);
y_bit=graph_inf_bit(:,2);
subplot(2,1,2);
semilogy(x_bit,y_bit,'k-v');
xlabel('SNR, [dB]');
ylabel('Bit Error Probability');
grid on
