matlab_project.m

contains Pulse Position Modulation (PPM)

% This MATLAB code is a basic simulator for a digital communication system
% It contains Pulse Position Modulation (PPM) and the students are required
% to include On-Off Keying (OOK), and Binary Phase Shift Keying (BPSK)

% The only thing the students are required to do (for the first part) is 
% to fill under the statements ending with !!!!!!!!!!!!!!!!!!!! 
% Then you should obtain the figures as described in the handouts and
% submit the project update and final report...

% Written by Ismail Guvenc for EEL4512: Introduction to Communication
% Systems, Spring 2006

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Initialize the variables first
clear all; close all;
no_of_bits  = 10000;
delta       = 0.8e-9;                       % This is the delay between two possible positions in PPM (in seconds)
Tm          = 0.277e-9;                     % This parameter effects our pulse shape
fs          = 5e10;                         % Sampling frequency (in Herz)
EbNo_vals   = 5:12;                         % The SNR range (in dB) that we are going to investigate the Bit error rates (BERs)
total_error = zeros(1,length(EbNo_vals));   % Total number of bits received in error. Initialize it first to zero for all SNR
modul_type  = 1;                            % 1: PPM, 2: BPSK, 3: OOK
% You need to change the modul_type to have different modulations. PPM simulation already works good. 
% For BPSK and OOK, you should complete the required places indicated with exclamation marks

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Generate the pulse to be transmitted
t_pulse     = -0.4e-9:1/fs:0.4e-9;              % This is the time support of the pulse
y           = (1-4*pi*(t_pulse/Tm).^2).*exp(-2*pi*(t_pulse/Tm).^2);     % Generate the pulse using a certain expression
% The above pulse is a second derivative of a Gaussian pulse, and was
% a commonly pronounced pulse shape for Ultrawideband Systems until the announcement of the FCC spectral mask
y           = y/sqrt(sum(y.^2));                % Normalize the pulse energy to 1
% If you remember, the energy of a signal is the sum of squares of all the
% samples of the signal (you may check that the energy of the above pulse 'y' is unitary)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Generates (no_of_bits) bits, which are equally likely to be 0 or 1
bits        = randn(1,no_of_bits)>0;
% We are going to transmit these bits over an AWGN channel, and observe the
% bit error rates at different signal to noise ratios (SNRs)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for bit_no=1:no_of_bits

    bit = bits(bit_no);

    % Transmitter ------------------------------------------
    % Switch to the modulation type initialized above, and map the bits onto the pulse using that modulation type
    if modul_type == 1
        % There are "41 samples" in my pulse, so I transmit the pulse within
        % the first 41 samples for bit 0, and at the second 41 samples for bit 1
        PPM_pulse_delay  = 41*bit;                 % Pulse may be 1/0 delta away from the nominal position
        sig              = zeros(1,2*length(y));
        sig((PPM_pulse_delay+1):(PPM_pulse_delay+41)) = y;  % Note that here I use bit information to change the pulse position
        % This was where we are "mapping" the information to the pulse. I
        % can also change the polarity or amplitude of the pulse as should be done below...
    elseif modul_type == 2
        % FILL IN HERE TO IMPLEMENT TRANSMITTER FOR BPSK!!!!!!!!!!!!!!!!!
    elseif modul_type == 3
        % FILL IN HERE TO IMPLEMENT TRANSMITTER FOR OOK!!!!!!!!!!!!!!!!!!
    end
    % Note that for OOK and BPSK, as opposed to PPM, I send the pulse
    % always at the first position, i.e. at the first 41 samples.
    % Modulation for these two schemes occurs by multiplying the right handside of the above
    % equation (e.g. bit * y or things like that ... ) as opposed to PPM's time-shift

    % Additive White Gaussian Noise (AWGN) Channel ---------
    noisy_sig       = [];
    % The noisy_sig will be a matrix, which contains the replicas of the noisy signal with different noise levels
    % at different SNR values. First, we define a noise vector below. Then,
    % depending on the SNR, we scale its amplitude in the FOR loop, and add
    % to the transmitted signal. Note again that the transmitted signal
    % energy is normalied to 1, so we calculate the corresponding noise
    % variance according to the Eb/No by setting Eb to 1
    noise           = randn(1,length(sig));                             % Power of the noise will be adjusted inside the loop
    for EbNo = EbNo_vals                                                % Investigate a certain EbNo range to evaluate the BER
        % Note that for double-sided noise spectrum, Noise variance \sigma^2  = No/2
        noise_var   = 0.5 * 10^(-EbNo/10);                              % Calculate the noise power corresponding to a certain EbNo
        Chan_Noise  = noise * sqrt(noise_var);                          % Scale the noise amplitude according to the noise variance calculated
        noisy_sig   = [noisy_sig ; sig + Chan_Noise];                   % Add noise to the signal (at a new row of the matrix)
    end

    % RECEIVER ----------------------------------------------
    % At the receiver, we analyze different SNRs in a for loop, and
    % see if the bit is received in error or not. If so, we increment the
    % total error for the corresponding SNR.
    for EbNo_ind = 0:(length(EbNo_vals)-1)
        signal = noisy_sig((EbNo_ind+1),:);

        if modul_type == 1                                    % PPM: Look at correlations at two different pulse positions
            corr0  = sum(signal(1:41).*y);                    % Correlate the received signal at 0-position
            corr1  = sum(signal((1:41)+41).*(y));             % Correlate the received signal at 1-position
        elseif modul_type == 2                                % BPSK
            % FILL IN HERE TO IMPLEMENT THE RECEIVER FOR BPSK!!!!!!!!!!!!!!!!!
            % corr0  = ...                                    % Correlate the received signal at 0-position
            % corr1  = 0;                                     % Threshold...
        elseif modul_type == 3                                % OOK
            % FILL IN HERE TO IMPLEMENT THE RECEIVER FOR OOK!!!!!!!!!!!!!!!!!!
            % corr0  = ...                                    % Correlate the received signal at 0-position
            % corr1  = ...                                    % Threshold...
        end
        % For OOK and BPSK, corr0 value should be the correlation at the first pulse position,
        % and corr1 value should be the threshold that I should use (e.g., it is 0 for BPSK)
        % To test a particular modulation, comment out all the rest, but
        % the one that you would like to test at the transmitter and the receiver

        % Compare the correlations at two different hypothesis (position, polarity etc.)
        % Choose the bit (as the estimated received bit) corresponding to the one that has larger correlation
        if corr0 > corr1
            received_bits(EbNo_ind+1) = 0;
        else
            received_bits(EbNo_ind+1) = 1;
        end
    end

    % Compare the received bits at different SNRs with the transmitted bit
    % Increment the total_error for each SNR if the received bit is different than the transmitted bit
    total_error = total_error + abs(received_bits-bit);

    % Display the bit number at multiples of 100 on the screen (for simulation tracking purposes)
    if mod(bit_no,100)== 0;  bit_no, end
end

% Divide the number of bits received in error with the total number of bits transmitted
% This will be our bit error rate (BER)
sim_error = total_error/bit_no                   

% Now obtain the theoretical BERs using the Q-function
EbNo_non_dB = 10.^(EbNo_vals/10);               % First convert the EbNo from dB to actual values
if modul_type == 1
    theo_error  = Q_fn (sqrt(EbNo_non_dB));       % Now calculate the BER (for PPM) using the Q-function
elseif modul_type == 2
    % theo_error  = Q_fn (???);     % MUST BE MODIFIED ACCORDING TO BPSK BER!!!!!!!!!!!!!!!!!
elseif modul_type == 3
    % theo_error  = Q_fn (???);     % MUST BE MODIFIED ACCORDING TO OOK BER!!!!!!!!!!!!!!!!!
end

% Plot and appropriately label the BER with respect to EbNo
semilogy(EbNo_vals,sim_error), grid on, hold on,
semilogy(EbNo_vals,theo_error,'o')
xlabel('E_b/N_0 (dB)'), ylabel('BER'), legend('PPM (simulation)','PPM (theory)')