Robust Signal Detection with Prefix and Postfix in MATLAB

MATLAB Code

clc;
clear;
close all;

% Parameters
fs = 1000; % Sampling frequency
msgLength = 100; % Length of the message
pnLength = 50; % Length of PN sequence
silenceLength = 20; % Length of silence before and after
lagAmount = 50; % Amount of lag (can be negative for lead)
threshold = 0.5; % Threshold for correlation peak detection

% Generate Unique PN Sequences
pnPrefix = 2 * (randi([0, 1], 1, pnLength) - 0.5);
pnPostfix = 2 * (randi([0, 1], 1, pnLength) - 0.5);

% Generate Message
originalMessage = (randi([0, 1], 1, msgLength));
message = 2*originalMessage - 1;

% Construct Dataframe
dataframe = [pnPrefix, message, pnPostfix];

% Introduce Lag or Lead
if lagAmount > 0
%laggedFrame = [zeros(1, lagAmount), dataframe(1:end - lagAmount)];
laggedFrame = [zeros(1, lagAmount), dataframe];
else
laggedFrame = [dataframe(-lagAmount + 1:end), zeros(1, -lagAmount)];
end

% Correlation with PN Sequences
corrPrefix = xcorr(laggedFrame, pnPrefix);
corrPostfix = xcorr(laggedFrame, pnPostfix);

% Normalize Correlation
corrPrefix = corrPrefix / max(corrPrefix);
corrPostfix = corrPostfix / max(corrPostfix);

% Adjust indices to align with laggedFrame
corrLen = length(laggedFrame);
prefixIndices = (1:length(corrPrefix)) - corrLen;
postfixIndices = (1:length(corrPostfix)) - corrLen;

% Detect Peaks in Correlation (Apply Threshold)
prefixPeaks = prefixIndices(corrPrefix > threshold);
postfixPeaks = postfixIndices(corrPostfix > threshold);

% Estimate Start and End of Message
if ~isempty(prefixPeaks)
startMessage = max(1, prefixPeaks(1) + length(pnPrefix));
else
startMessage = -1; % Detection failed
end

if ~isempty(postfixPeaks)
endMessage = min(length(laggedFrame), postfixPeaks(end) - length(pnPostfix) - 1);
else
endMessage = -1; % Detection failed
end

% Retrieve Original Message
if startMessage > 0 && endMessage > 0 && endMessage > startMessage
retrievedMessage = laggedFrame(startMessage+1:endMessage+pnLength+1)>0;
else
retrievedMessage = [];
end

% Display Original Message
disp('Original Message:'), disp(originalMessage);

% Display Results
disp('Retrieved Message:'), disp(retrievedMessage);

% Plot Results
figure;
subplot(3, 1, 1); plot(dataframe); title('Original Dataframe');
subplot(3, 1, 2); plot(laggedFrame); title('Lagged/Lead Dataframe');
subplot(3, 1, 3); plot(corrPrefix, 'b'); hold on; plot(corrPostfix, 'r');
title('Correlation with PN Sequences');
legend('Prefix Correlation', 'Postfix Correlation');

Output

Original Message:

1 0 0 0 1 1 0 1 1 0 0 0 0 1 0 0 1 1 0 1 1 ......

Retrieved Message:

1 0 0 0 1 1 0 1 1 0 0 0 0 1 0 0 1 1 0 1 1 ......

Copy the aforementioned MATLAB Code from here

% The code is developed by SalimWireless.com clc; clear; close all; % Parameters fs = 1000; % Sampling frequency msgLength = 100; % Length of the message pnLength = 50; % Length of PN sequence silenceLength = 20; % Length of silence before and after lagAmount = 50; % Amount of lag (can be negative for lead) threshold = 0.5; % Threshold for correlation peak detection % Generate Unique PN Sequences pnPrefix = 2 * (randi([0, 1], 1, pnLength) - 0.5); pnPostfix = 2 * (randi([0, 1], 1, pnLength) - 0.5); % Generate Message originalMessage = (randi([0, 1], 1, msgLength)); message = 2*originalMessage - 1; % Construct Dataframe dataframe = [pnPrefix, message, pnPostfix]; % Introduce Lag or Lead if lagAmount > 0 %laggedFrame = [zeros(1, lagAmount), dataframe(1:end - lagAmount)]; laggedFrame = [zeros(1, lagAmount), dataframe]; else laggedFrame = [dataframe(-lagAmount + 1:end), zeros(1, -lagAmount)]; end % Correlation with PN Sequences corrPrefix = xcorr(laggedFrame, pnPrefix); corrPostfix = xcorr(laggedFrame, pnPostfix); % Normalize Correlation corrPrefix = corrPrefix / max(corrPrefix); corrPostfix = corrPostfix / max(corrPostfix); % Adjust indices to align with laggedFrame corrLen = length(laggedFrame); prefixIndices = (1:length(corrPrefix)) - corrLen; postfixIndices = (1:length(corrPostfix)) - corrLen; % Detect Peaks in Correlation (Apply Threshold) prefixPeaks = prefixIndices(corrPrefix > threshold); postfixPeaks = postfixIndices(corrPostfix > threshold); % Estimate Start and End of Message if ~isempty(prefixPeaks) startMessage = max(1, prefixPeaks(1) + length(pnPrefix)); else startMessage = -1; % Detection failed end if ~isempty(postfixPeaks) endMessage = min(length(laggedFrame), postfixPeaks(end) - length(pnPostfix) - 1); else endMessage = -1; % Detection failed end % Retrieve Original Message if startMessage > 0 && endMessage > 0 && endMessage > startMessage retrievedMessage = laggedFrame(startMessage+1:endMessage+pnLength+1)>0; else retrievedMessage = []; end % Display Original Message disp('Original Message:'), disp(originalMessage); % Display Results disp('Retrieved Message:'), disp(retrievedMessage); % Plot Results figure; subplot(3, 1, 1); plot(dataframe); title('Original Dataframe'); subplot(3, 1, 2); plot(laggedFrame); title('Lagged/Lead Dataframe'); subplot(3, 1, 3); plot(corrPrefix, 'b'); hold on; plot(corrPostfix, 'r'); title('Correlation with PN Sequences'); legend('Prefix Correlation', 'Postfix Correlation'); web('https://www.salimwireless.com/search?q=prefix%20postfix', '-browser');

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