ser_13_final.m

Analyze the performance of wireless channels in different scenarios over Rayleigh fading channels wi

%% THis prog is working 

N = 10000;	% nb. of symbols for AWGN simulation
E_s=1;
N_0=10.^(0:-.2:-5);
rho_v = E_s./N_0;
N_d = 1000;	% number of data symbols sent over each channel
N_ch = 1000;	% number of channel simulations
E_s = 1;	% symbol energy

d_min = sqrt(2);	% min distance for dominant error event


rho_v = E_s./N_0;		% average SISO SNR
N_e_av=2;

%*********** theoretical BER over AWGN channel*****************************


SER_AWGN = 0.5*erfc(sqrt(rho_v*d_min^2/2)/sqrt(2));
semilogy(10*log10(rho_v),SER_AWGN)
axis([0 15 1e-20 1])

xlabel 'E_s/N_0 [dB]'
ylabel 'symbol error rate (SER)'
hold on


%%%%%%%%%%%%%%% simulation of BER over AWGN channel

s = sqrt(E_s/2) * (sign(randn(1,N)) );

% loop over SNR
SER_AWGN_sim = [];
for sig_n2 = N_0	% vector of noise powers

	rho = E_s/sig_n2;

	% noise vector at variance sig_n2
	n = sqrt(sig_n2/2)*(randn(1,N) + j*randn(1,N));
	
	% received signal
	r = s + n;
	
	% determine SER
	SER = 1- mean((sign(real(r)) == sign(real(s))));
	BER=mean((sign(real(r)) -sign(real(s))))	
	SER_AWGN_sim = [SER_AWGN_sim SER];
	
end
semilogy(10*log10(rho_v),SER_AWGN_sim,'o')
drawnow;
disp 'simulated SER for AWGN channel'
hold on;

pause



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% for SISO Rayleigh channel
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%% theoretical SER over Rayleigh channel

% exact equation for BER (see Proakis, (14-3-7))
BER_Rayl = 0.5*(1-sqrt(rho_v./(1+rho_v)));

% convert to approx. eqn. for SER
SER_Rayl = 0.5*(1-sqrt(rho_v*d_min^2/4./(1+rho_v*d_min^2/4)));

semilogy(10*log10(rho_v),SER_Rayl,'r-')
axis([0 30 1e-5 1])

disp 'analytical SER for Rayleigh channel'

hold on;




%%%%%%%%%%%%%%% simulation of SER over Rayleigh channel

% transmitted BPSK symbols 
s = sqrt(E_s/2) * (sign(randn(1,N_d))); 

% loop over SNR
SER_Rayl_sim = [];
for sig_n2 = N_0

	rho = E_s/sig_n2;		% average SISO SNR
	
	% noise vector at variance sig_n2
	n = sqrt(sig_n2/2)*(randn(1,N_d) + j*randn(1,N_d));

	%loop over channel realizations
	SER = 0;
	for i=1:N_ch;

		% channel transfer coefficient (complex Gaussian)
		h = sqrt(1/2)*(randn(1) + j*randn(1));

		% received signal
		y = h*s + n;
		
		% channel "equalization": 
		z = y/h;
	
		% determine SER
		S_err = ((sign(real(z)) ~= sign(real(s))));
		SER = SER + mean(S_err);
		
		

	end
		
	SER_Rayl_sim = [SER_Rayl_sim SER/N_ch];
	
	
end

semilogy(10*log10(rho_v),SER_Rayl_sim,'ro');
axis([0 30 1e-5 1]);
hold on;
disp 'simulated SER for Rayleigh channel'


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% for SIMO Rayleigh channel; M = 2 diversity branches
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%% analytical SER over M = 2 diversity branches Rayleigh channel

M = 2;	% number of diversity branches

% Chernoff bound
%SER_M2_cb = N_e_av*(rho_v*d_min^2/4/M).^(-M);

%semilogy(10*log10(rho_v),SER_M2_cb,'g--')

disp 'upper bound on SER computed by Chernoff-bound for Rayleigh channel; M = 2 diversity branches'

% convert to approx. eqn. for SER
SER_Ray2 = 0.25*(1-sqrt(rho_v*d_min^2/8./(1+rho_v*d_min^2/8)));

semilogy(10*log10(rho_v),SER_Ray2,'g--')


%%%%%%%%%%%%%%% simulation of SER over M = 2 diversity branches Rayleigh channel

% transmitted QPSK symbols 
s = sqrt(E_s/2) * (sign(randn(1,N_d))); 

% loop over SNR
SER_M2_sim = [];
for sig_n2 = N_0

	rho = E_s/sig_n2;		% average SISO SNR
	
	% noise vector at variance sig_n2
	n = sqrt(sig_n2/2)*(randn(M,N_d) + j*randn(M,N_d));

	%loop over channel realizations
	SER = 0;
	for i=1:N_ch;

		% channel transfer coefficient (complex Gaussian)
		h = sqrt(1/2)*(randn(M,1) + j*randn(M,1));

		% received signal
		y = h*s + n;
		
		% maximum ratio combining 
		z = h'*y;
	
		% determine SER
		S_err = ((sign(real(z)) ~= sign(real(s))));

		SER = SER + mean(S_err);
		
			
	end
		
	SER_M2_sim = [SER_M2_sim SER/N_ch];
	
	
end

semilogy(10*log10(rho_v),SER_M2_sim,'go')
axis([0 30 1e-5 1])

disp 'simulated SER for Rayleigh channel with diversity; M = 2'
pause