# Channel modeling of a waveguide for calculation of BER, SNR and data rate.

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Arslan Ahmed Sohoo on 20 Jun 2022
Answered: Abhimenyu on 1 Dec 2023
I have simulated a waveguide and obatined the s parameters etc. Now i want to model a channel in Matlab and characterize the waveguide. i want to find the SNR, BER, and channel capacity.
How can i use the s-parameters obtained from CST, to characterize the waveguide in Matlab?
My task is to calculate the data rate vs length. (attached figure)
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### Answers (1)

Abhimenyu on 1 Dec 2023
Hi Arslan,
I understand that you want to use the S-parameters obtained from CST, to characterize the waveguide in MATLAB. The S-parameters (also called S-matrix or scattering parameters) represent the linear characteristics of RF electronic circuits and components. From the S-parameter matrix, you can calculate characteristics of linear networks such as gain, loss, impedance, phase group delay etc.
To use the S-parameters obtained from CST, you need to import them into MATLAB using the sparameters function. This function creates an rfdata.data object that contains the S-parameter data and the corresponding frequency vector.
Please follow the example code given below to understand the manipulation of the S-parameters and to obtain “data-rate vs length” graph:
% Import S-parameters from CST
s = sparameters('sparams.s2p'); % sparams.s2p is the file name of the S-parameter data from CST
% Plot the S-parameters on a Smith chart
rfplot(s);
% Convert the S-parameters to an equivalent impulse response using "s2tf" function
[num,den] = s2tf(s);
%Convert the transfer function to impulse response using "impz" function for the convolution in
%channel propagation
[h,t] = impz(num,den);
% Developing the channel model(values are assumed)
% Generate a modulated signal
fs = 1e6; % sampling frequency
fc = 100e3; % carrier frequency
M = 4; % modulation order
data = randi([0 M-1],1000,1); % random data
x = pskmod(data,M,pi/M); % phase shift keying modulation
x = x.*exp(1i*2*pi*fc*(0:length(x)-1)/fs); % upconversion
% Apply the channel impulse response to the signal
y = filter(h,1,x); % or y = conv(h,x);
% Add noise to the signal
snr = 10; % signal-to-noise ratio in dB
y = awgn(y,snr,'measured');
% Demodulate the signal
y = y.*exp(-1i*2*pi*fc*(0:length(y)-1)/fs); % downconversion
y = pskdemod(y,M,pi/M); % phase shift keying demodulation
% Calculate the SNR using the "snr" function of MATLAB
snr_est = snr(y,x); % estimate the SNR
%Calculate bit error rate using "berconfint" function of MATLAB
[ber,~] = berconfint(length(data),sum(y~=data)); % estimate the BER with 95% confidence interval
bw = fs/2; % bandwidth of the channel
% estimate the channel capacity
C = bw * log2(1 + snr_est)
% Plot the data rate versus length
L = 1:10; % length of the waveguide in meters
R = c*L; % data rate in bits per second
semilogy(L,R); % plot on a log-scale
xlabel('Length (m)');
ylabel('Data rate (bps)');
title('Data rate vs length for the waveguide');
The above code will provide “Data rate vs length for the waveguide” plot. The Signal-to-noise ratio and bit-error-rate are calculated using the MATLAB functions “snr” and “berconfint” respectively. The channel capacity is estimated using the standard formula :
C= Bandwidth* log2(1+SNR)
Please refer to the below mentioned MATLAB documentation links to understand more on “sparameters”,snr andberconfint” respectively:
I hope this helps to resolve the query.
Thanks,
Abhimenyu
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