MATLAB code for MSK

• 📘 Overview
• 🧮 MATLAB Codes
• 🧮 Theory
• 🧮 Simulator for MSK
• 🧮 Differences Between MSK and FSK
• 📚 Further Reading

 Copy the MATLAB Code from here

% The code is developed by SalimWireless.com 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 web('https://www.salimwireless.com/search?q=minimum%20shift%20keying%20msk', '-browser');

 

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:

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

 

Minimum Shift Keying (MSK) Simulator

Bitstream (comma separated):

Carrier Frequency (Hz):

Baud Rate (symbols/sec):

Sampling Rate (Hz):

Differences Between MSK and FSK

 In FSK, if bits change from 0 to 1, and f₀ ≠ f₁, the carrier switches frequency — but phase continuity is not maintained unless explicitly enforced. This causes a sudden jump in phase at the bit boundary. In MSK, the phase is not static or abruptly switching. It evolves linearly over time based on the bit value, ensuring continuity. For bit duration Tb, the frequency deviation is: 

Δf = ±(1 / 4Tb)

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Further Reading

1.  Minimum Shift Keying (MSK)
2. Gaussian Minimum Shift Keying (GMSK)
   
3. MATLAB code for GMSK
4. Difference Between MSK and GMSK