Week 10 || MAP and ML Rule for AWGN || NPTEL || Simulation of Communication Systems Using MATLAB

[@shivanidhok3831]

Hi everyone. Due to some technical glitch, the MATLAB screen was not recorded. Following are the MATLAB codes for last three questions.
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Q8. MPAM (Simulation)
clc;clear;close all;
% Plot Symbol error probability/Probability of error for M-ary pulse
% amplitude modulation (PAM).
%% Setup simulation parameters
N = 1e+6; % Number of realizations of noise and symbols
M = 2; % Number of constellation points
No = 1; % Noise variance
E_avg = linspace(0,10,21); % Average energy
%% Get Constellation points (Not normalized by E_avg)
A = -(M-1):2:(M-1);
%% Get the simulation for all the values of average energy
for ii = 1:length(E_avg)
% Get normalized constellation points
dmin = sqrt(12.*E_avg(ii)./(M.^2-1));
A_const = A.*0.5.*dmin;
% Get N random constellation points for transmission
idx = randi(M,[N,1]); % N random indices between 1 to M
sm = transpose(A_const(idx)); % Get random symbols to be transmitted
% Add noise to the transmitted symbol
n = sqrt(No).*randn(N,1); % AWGN noise with 0 mean and variance No
y = sm+n; % Recieved signal

% ML decoding, min-distance decoding
d_all = abs(y-A_const);
[val idx_dec] = min(transpose(d_all));
sm_dec = transpose(A_const(idx_dec));
% Get probability of error = Number of errors/N
num_errors = sum(idx~=idx_dec');
Pe(ii) = num_errors./N;
end
%% Plot the Probability of error
semilogy(E_avg,Pe);
xlabel('Average energy');
ylabel('Probability of error');
grid on;
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Q9. Binary PAM (Analysis+Simulation)
clc;clear;close all;
% Plot Symbol error probability/Probability of error for binary pulse
% amplitude modulation (PAM) and match with analytical expression
%% Setup simulation parameters
N = 1e+6; % Number of realizations of noise and symbols
M = 2; % Number of constellation points
No = 1; % Noise variance
E_avg = linspace(0,10,21); % Average energy
%% Get Constellation points (Not normalized by E_avg)
A = -(M-1):2:(M-1);
%% Get the simulation for all the values of average energy
for ii = 1:length(E_avg)
% Get normalized constellation points
dmin = sqrt(12.*E_avg(ii)./(M.^2-1));
A_const = A.*0.5.*dmin;
% Get N random constellation points for transmission
idx = randi(M,[N,1]); % N random indices between 1 to M
sm = transpose(A_const(idx)); % Get random symbols to be transmitted
% Add noise to the transmitted symbol
n = sqrt(No).*randn(N,1); % AWGN noise with 0 mean and variance No
y = sm+n; % Recieved signal

% ML decoding, min-distance decoding
d_all = abs(y-A_const);
[val idx_dec] = min(transpose(d_all));
sm_dec = transpose(A_const(idx_dec));
% Get probability of error = Number of errors/N
num_errors = sum(idx~=idx_dec');
Pe(ii) = num_errors./N;
Pe_ana(ii) = qfunc(sqrt(E_avg(ii)./No));
end
%% Plot the Probability of error
semilogy(E_avg,Pe_ana,'LineWidth',2);
hold on;
semilogy(E_avg,Pe,'o','LineWidth',2);
hold off;
xlabel('Average energy');
ylabel('Probability of error');
grid on;
legend('Analytical','Simulation');
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Q10. MPSK (Simulation)
clc;clear;close all;
% Plot Symbol error probability/Probability of error for M-ary phase
% shift keying.
%% Setup simulation parameters
N = 1e+6; % Number of realizations of noise and symbols
M = 4; % Number of constellation points
No = 1; % Noise variance
E_avg = linspace(0,10,21); % Average energy
%% Get Constellation points (Not normalized by E_avg)
A = exp(-j.*2.*pi.*(0:M-1)./M);
%% Get the simulation for all the values of average energy
for ii = 1:length(E_avg)
% Get normalized constellation points
A_const = A.*sqrt(E_avg(ii));
% Get N random constellation points for transmission
idx = randi(M,[N,1]); % N random indices between 1 to M
sm = transpose(A_const(idx)); % Get random symbols to be transmitted
% Add noise to the transmitted symbol
n = sqrt(No./2).*(randn(N,1)+1i.*randn(N,1)); % AWGN noise with 0 mean and variance No
y = sm+n; % Recieved signal

% ML decoding, min-distance decoding
d_all = abs(y-A_const);
[val idx_dec] = min(transpose(d_all));
sm_dec = transpose(A_const(idx_dec));
% Get probability of error = Number of errors/N
num_errors = sum(idx~=idx_dec');
Pe(ii) = num_errors./N;
end
%% Plot the Probability of error
semilogy(E_avg,Pe);
xlabel('Average energy');
ylabel('Probability of error');
grid on;

[@lokeshraybarman7007]

Highly helpful session ❤❤❤

[@Ankitvermacp3]

Mam I think the MATLAB simulation part didn’t get shared in the Google Meet. Could you provide the code snippet for it?