quantization_threshold.m

source Matlab traites the UWB

%
%
clear all;
%
% Necessary path
addpath ../
addpath ../rng;


% Some parameters
FS_CONT = 20e9;
PACKET_LENGTH = 4;
TC = 2e-9;
Eb = 1;
snr_dB = 10;
% Receiver
T_INT = 1e-9;
N_INT = 1;
% From SNR in dB to the variance of the noise
snr = 10.^(snr_dB/10);
s2 = Eb ./ (snr);
% Simulation
L = 1000;

samples_per_chip = TC * FS_CONT;

% Get a pulse
chip_span = 0.5;
[monopulse,t] = get_monopulse(1,chip_span,1e-9,TC,samples_per_chip);

% Normalize
monopulse = Eb*monopulse./norm(monopulse);
% $$$ % Better?
% $$$ dt = 1/FS_CONT;
% $$$ monopulse = Eb*monopulse/sqrt(dt*sum(monopulse.^2));


% Create the signal to be transmitted
tx_signal = conv(monopulse,upsample(ones(1,PACKET_LENGTH),2*samples_per_chip));
tx_signal = tx_signal(1:2*PACKET_LENGTH*samples_per_chip);

% Indices for the energy receiver
signal_start_0 = cumsum(ones(1,PACKET_LENGTH)*(2*samples_per_chip))-(2* ...
						  samples_per_chip);

n = samples_per_chip-rem(samples_per_chip,T_INT*FS_CONT);
signal_idx_0 = repmat(signal_start_0,n,1)+repmat((0:n-1)',1,PACKET_LENGTH) + 1;
signal_idx_1 = signal_idx_0 + samples_per_chip;

% Values for the quantizer
max_thresh = norm(monopulse);
thresh = [linspace(0,max_thresh,10)];
%thresh = 0.5;
%thresh = 0;

for l = 1:length(thresh)
  for k = 1:L
    % Add the noise
    noise = sqrt(s2/samples_per_chip)*randn(1,PACKET_LENGTH*2*samples_per_chip);
    rx_signal = tx_signal + noise;

    % Energy receiver
    [rx_down_0,samples_per_tint] = ...
        ed_receiver(rx_signal(reshape(signal_idx_0,1, PACKET_LENGTH*n)),T_INT, ...
                    FS_CONT,N_INT,thresh(l));
    [rx_down_1,samples_per_tint] = ...
        ed_receiver(rx_signal(reshape(signal_idx_1,1, PACKET_LENGTH*n)),T_INT, ...
                    FS_CONT,N_INT,thresh(l));

    % Decision rule and detection
    rx_down = sum(reshape((rx_down_0 - rx_down_1),n/(T_INT*FS_CONT), ...
                          PACKET_LENGTH),1);

    idx_dec0 = find(rx_down>0);
    idx_dec1 = find(rx_down<0);
    idx_unknown = find(rx_down==0);

    decoded = [];
    decoded(idx_dec0) = 0;
    decoded(idx_dec1) = 1;
    decoded(idx_unknown) = round(rand(1,length(idx_unknown)));

    % Compute the BER
    [num_err,ber_sim(l,k)] = symerr(decoded,zeros(1,PACKET_LENGTH));
    end
end

semilogy(thresh,mean(ber_sim,2),'.',0,mean(ber_sim(1,:),2),'r*');
fprintf('SNR [dB] = %d\n',snr_dB);
fprintf('min BER  = %.7f\n',min(mean(ber_sim,2)));