How to generate a MSK signal?

It turned out to form a FSK signal, but how to ensure phase continuity is not clear? The first picture shows the problem...

Answer 1

[Yukthi S]

Hi @Red,

I assume that you aim to achieve phase continuity to transform the generated FSK signal into an MSK signal.To do so, I made some changes to the code to ensure phase continuity in the generated signal.

1. Frequencies are set to "br" and "br/2" where br is the bit rate. This modification makes sure that the frequency deviation is "br/2" which is a characteristic of MSK modulation.
2. A “phase” variable is introduced and updated after each bit to maintain phase continuity.
3. Cosine functions are dynamically updated with frequencies and phase to achieve MSK.

The modified code is given below to help you get started:

clc;
clear all;
close all;

% M-sequence generator setup
n = 4;  % Degree of the polynomial (can be adjusted)
c = [1 0 0 1 1];  % Feedback polynomial coefficients (example for n=4)
c = c(2:end); 
M = 2^n - 1;  % Length of the M-sequence

% Initialize the shift register with a non-zero state
shift_register = [1 zeros(1, n-1)];
a = zeros(1, M);

% Generate M-sequence
for j = 1:M
    feedback_bit = mod(sum(shift_register .* c), 2);
    a(j) = shift_register(end);
    shift_register = [feedback_bit, shift_register(1:end-1)];
end

bp = 0.001;  % Bit period
disp('Binary information at Transmitter:');

Binary information at Transmitter:

disp(a);

     0     0     0     1     0     0     1     1     0     1     0     1     1     1     1

% Representation of transmitting binary information as digital signal
bit = [];
for n = 1:length(a)
    if a(n) == 1
        se = ones(1, 100);
    else
        se = zeros(1, 100);
    end
    bit = [bit se];
end
t1 = bp/100:bp/100:100*length(a)*(bp/100);

% MSK Modulation
A = 1;  % Amplitude of carrier signal
br = 1/bp;  % Bit rate
f1 = br;  % Frequency for binary '1'
f2 = br/2;  % Frequency for binary '0'(ensuring frequency deviation iss br/2)
t2 = bp/99:bp/99:bp;
ss = length(t2);
m = [];
phase = 0;  % Initial phase to maintain phase continuity

for i = 1:length(a)
    if a(i) == 1
        freq = f1;
    else
        freq = f2;
    end
    y = A * cos(2 * pi * freq * t2 + phase);
    m = [m y];
    % Update phase for continuity
    phase = phase + 2 * pi * freq * bp;
end

t3 = bp/99:bp/99:bp*length(a);
figure;
hold on;
plot(t1, bit, 'LineWidth', 2, 'DisplayName', 'Digital Signal');% Plot digital signal
grid on;
% Plot MSK modulated signal
plot(t3, m, 'DisplayName', 'MSK Modulated Signal');
xlabel('Time (sec)');
ylabel('Amplitude (volt)');
title('Digital Signal and MSK Modulated Signal');
legend show;
axis([0 bp*length(a) -1.5 1.5]);

Hope you will find this helpful!