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MATLAB code for MSK


 Copy the MATLAB Code from here

 

MATLAB Code 

clc;
clear;
close all;

% Define a bit sequence
bitSeq = [0, 1, 0, 0, 1, 1, 1, 0, 0, 1];

% Perform MSK modulation
[modSignal, timeVec] = modulateMSK(bitSeq, 10, 10, 10000);

% Plot the modulated signal
subplot(2,1,1);
samples = 1:numel(bitSeq);
stem(samples, bitSeq);
title('Original message signal');
xlabel('Time (s)');
ylabel('Amplitude');

% Plot the modulated signal
subplot(2,1,2);
samples = 1:10000;
plot(samples / 10000, modSignal(1:10000));
title('MSK modulated signal');
xlabel('Time (s)');
ylabel('Amplitude');

% Perform MSK demodulation
demodBits = demodMSK(modSignal, 10, 10, 10000);

% Function to perform MSK modulation
function [signal, timeVec] = modulateMSK(bits, carrierFreq, baudRate, sampleFreq)
% Converts a binary bit sequence into an MSK-modulated signal
% Inputs:
% bits - Binary input sequence
% carrierFreq - Carrier frequency
% baudRate - Symbol rate
% sampleFreq - Sampling frequency
% Outputs:
% signal - Modulated MSK signal
% timeVec - Corresponding time vector

% Convert bits to NRZ format (-1, 1)
diffEncBits = 2 * bits - 1;
diffEncBits = [-1, diffEncBits]; % Append initial value

% Define time parameters
numBits = length(bits);
symbDur = 1 / baudRate;
timeVec = 0:1/sampleFreq:numBits * symbDur - (1/sampleFreq);

% Compute phase shifts
phaseShift = zeros(1, numBits + 1);
for idx = 2:numBits+1
phaseShift(idx) = mod(phaseShift(idx-1) + ((pi * idx) / 2) * (diffEncBits(idx-1) - diffEncBits(idx)), 2 * pi);
end
phaseShift = phaseShift(2:end);
diffEncBits = diffEncBits(2:end);

% Generate MSK waveform
symbolIdx = floor(timeVec / symbDur) + 1;
signal = cos(2 * pi * (carrierFreq + diffEncBits(symbolIdx) / (4 * symbDur)) .* timeVec + phaseShift(symbolIdx));
end

% Function to perform MSK demodulation
function bitSeq = demodMSK(signal, carrierFreq, baudRate, sampleFreq)
% Recovers a binary bit sequence from an MSK-modulated signal
% Inputs:
% signal - MSK-modulated input signal
% carrierFreq - Carrier frequency
% baudRate - Symbol rate
% sampleFreq - Sampling frequency
% Outputs:
% bitSeq - Demodulated binary sequence

symbDur = 1 / baudRate;
samplesPerSymbol = round(symbDur * sampleFreq);
numSamples = length(signal);

% Generate reference MSK waveforms for bits 0 and 1
refWave1 = modulateMSK([1], carrierFreq, baudRate, sampleFreq);
refWave0 = modulateMSK([0], carrierFreq, baudRate, sampleFreq);

bitSeq = logical.empty;

% Demodulation using correlation
for startIdx = 1:samplesPerSymbol:numSamples
if startIdx + samplesPerSymbol > numSamples
break;
end
sampleSegment = signal(startIdx:startIdx+samplesPerSymbol-1);

% Compute cross-correlation with reference waveforms
corr1 = xcorr(sampleSegment, refWave1);
corr0 = xcorr(sampleSegment, refWave0);

% Compare correlation values to determine bit
if max(corr1) + abs(min(corr1)) > max(corr0) + abs(min(corr0))
bitSeq = [bitSeq, 1];
else
bitSeq = [bitSeq, 0];
end
end
end

Output


 




In Minimum Shift Keying (MSK), the two frequencies used for 0 and 1 depend on the carrier frequency \( f_c \) and the baud rate \( R_b \) (symbols per second).

Formula for MSK frequencies:

The two frequencies are given by:

\[ f_0 = f_c - \frac{1}{4T} \] \[ f_1 = f_c + \frac{1}{4T} \]

where \( T = \frac{1}{\text{baud rate}} \) is the symbol duration.

Given values:

  • Carrier frequency: \( f_c = 10 \) Hz
  • Baud rate: \( R_b = 10 \) symbols/sec
  • Symbol duration: \( T = \frac{1}{10} = 0.1 \) sec

Now, calculating the frequencies:

\[ f_0 = 10 - \frac{1}{4 \times 0.1} = 10 - \frac{1}{0.4} = 10 - 2.5 = 7.5 \text{ Hz} \] \[ f_1 = 10 + \frac{1}{4 \times 0.1} = 10 + 2.5 = 12.5 \text{ Hz} \]

 

Further Reading

  1. MATLAB code fro GMSK

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