BPSK modulation in LFM signal using Kasami Code

Hello,

Could you help me to modulate the phase of a LFM signal using Kasami sequence?

clear all;

close all;

waveform = phased.LinearFMWaveform('PulseWidth',100e-6,...

'SweepBandwidth',200e3,'PRF',4e3);

plot(waveform);

kasamiseq = comm.KasamiSequence('Polynomial',[6 1 0], ...

'InitialConditions',[0 0 0 0 0 0 0 1],'SamplesPerFrame',512);

I used this code to generate LFM signal and Kasami sequence.

I am trying to bulid a PC-FMCW Radar by using phase coded LFM signal like in the figure attached.

Answer 1

[Naren]

Hello Hussein,

I understand you are trying to modulate the phase of LFM signal using Kasami sequence for PC-FMCW radar.

To modulate the phase of a LFM signal using kasami sequence, you can use the following steps:

1. Generate a Kasami sequence using the "comm.KasamiSequence" function, as you have already done in the code you provided.
2. Create a vector to store the modulated LFM signal and generate an LFM signal using "phased.LinearFMWaveform" function.
3. For each bit in the Kasami sequence, if the bit is 1, add a random phase shift to the LFM signal's phase. If the bit is 0, do not apply a phase shift.
4. Store the modulated LFM signal in the vector created in step 2. Repeat steps 5-6 for each bit in the Kasami sequence until the end of the sequence. Plot the modulated LFM signal to visualize the phase modulation.

Here is a sample code for better understanding,

% Generate a Kasami sequence
waveform = phased.LinearFMWaveform('PulseWidth',100e-6,...
    'SweepBandwidth',200e3,'PRF',4e3);
kasamiSeq = comm.KasamiSequence('Polynomial',[6 1 0], 'InitialConditions',[0 0 0 0 0 0 0 1],'SamplesPerFrame',512);

% Create a vector to store the modulated signal
modLFM = zeros(length(waveform()),1);

% Generate an LFM signal
LFM = waveform();

% Set the phase of the LFM signal to 0
LFM_phase = zeros(length(LFM),1);

% Iterate over each bit in the Kasami sequence
for i = 1:length(kasamiSeq)
    % If the bit is 1, add a random phase shift to the LFM signal's phase
    if  kasamiSeq.InitialConditions(i) == 0
        phase_shift = rand*2*pi; % Generate a random phase shift between 0 and 2*pi
        LFM_phase = LFM_phase + phase_shift; % Add the phase shift to the LFM signal's phase
    end
    
    % Combine the new phase with the original LFM signal's magnitude
    modLFM = modLFM + LFM.*exp(1j*LFM_phase);
end

For further information, kindly refer the following documentation:

• Generate Kasami sequence - MATLAB (mathworks.com)
• Linear Frequency Modulated Pulse Waveforms - MATLAB & Simulink (mathworks.com)