# How to simulate two channel estimates within coherence time

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Joshua Green el 7 de Oct. de 2022
Respondida: Muskan el 8 de Sept. de 2023
Hello all,
So I am having trouble in simulating my research.
I need to estimate a wireless channel (rayleigh fading) at both the Tx and Rx within coherence time to obtain similar channnel estimates but not completely the same, rather, somewhat similar.
I tried code out there already, however, when I simulate it twice, it ends up producing uncorrelated channels.
I need a lot of help on this. Thank you!
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### Respuestas (1)

Muskan el 8 de Sept. de 2023
Hi Joshua,
I understand that you want to estimate a Rayleigh Fading at both the Tx and Rx within coherence time to obtain similar channel estimates.
As per my understanding of the question, you can try the following:
coherence_time = 1; % Coherence time in seconds
sampling_rate = 1000; % Sampling rate in Hz
doppler_frequency = 10; % Doppler frequency in Hz
num_samples = coherence_time * sampling_rate;
% Generate channel estimate at the Tx
channel_tx = (randn(num_samples, 1) + 1i * randn(num_samples, 1)) / sqrt(2);
% Apply Doppler shift to the channel at the Tx
t = (0:num_samples-1) / sampling_rate;
doppler_shift_tx = exp(1i * 2 * pi * doppler_frequency * t.');
channel_tx = channel_tx .* doppler_shift_tx;
% Generate channel estimate at the Rx
channel_rx = (randn(num_samples, 1) + 1i * randn(num_samples, 1)) / sqrt(2);
% Apply Doppler shift to the channel at the Rx
doppler_shift_rx = exp(1i * 2 * pi * doppler_frequency * t.');
channel_rx = channel_rx .* doppler_shift_rx;
% Add small variations to the channel estimates
variation = 0.1; % Adjust the variation level as desired
channel_tx = channel_tx + variation * (randn(num_samples, 1) + 1i * randn(num_samples, 1));
channel_rx = channel_rx + variation * (randn(num_samples, 1) + 1i * randn(num_samples, 1));
% Plot the channel estimates
time = (0:num_samples-1) / sampling_rate;
figure;
subplot(2, 1, 1);
plot(time, abs(channel_tx));
xlabel('Time (s)');
ylabel('Magnitude');
title('Channel Estimate at Tx');
subplot(2, 1, 2);
plot(time, abs(channel_rx));
xlabel('Time (s)');
ylabel('Magnitude');
title('Channel Estimate at Rx');
In this example, we generate channel estimates at both the “Tx and Rx using complex Gaussian random processes. We then apply a Doppler shift to the channels to introduce a varying fading effect. Small variations are added to the channel estimates to make them similar but not identical. Finally, the channel estimates are plotted to visualize the fading characteristics.
You can adjust the coherence time, sampling rate, Doppler frequency, and variation level according to your requirements.
I hope the above information helps resolve your query.
Thanks
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