Investigating Frequency Offsets on OFDM Transceiver Performance

[O.J.]

Homework Statement

I am simulating an OFDM transceiver using MATLAB. I am trying to investigate the effect of frequency offsets on the system performance by measuring different offsets against their respective bit error rate with a SNR of 10 dB.

Homework Equations

All equations and variables are presented in the code. I am uncertain as to what is the fundamental frequency though but I used 1/T (where T is the symbol period without guard time of each subcarrier).

The Attempt at a Solution

Here is my code:

%% OFDM Model (CP and GT) with AWGN at different SNR's

% NOTE! OFDM Parameters used in WiMAX are found in the ebook page 42!
%% OFDM parameters
Tu = 0.001; %symbol period for each subcarrier
N = 128; %number of carriers
R = 1/8; %guard time ratio (WiMAX standard)
G = Tu*R; %guard time
Ti = Tu + G; %OFDM symbol period
T = Ti/N; %original symbol period
fi = 1/Ti; %symbol rate of each datastream
f = fi*N;
Q = 8; %sampling frequency factor (should be chosen such that Q*R = whole number)
Fs = Q*f; %sampling frequency
z = 4*N;
t = 0:1/Fs:(z*Ti-1/Fs); %simulation period (upper limit should
%be an integer K ==> K*N*Ti -1/Fs
%% TRANSMITTER
%generate message
L = length(t)/Q;
M1 = round(rand(1,L));
tn = 0:Q/Fs:(z*Ti-1/Fs);

%using BPSK (mapping 0's to -1's)
M=2*M1-1;

stem (tn,M); %plot the original message (BPSK)
xlabel('Time (seconds)');
ylabel('Digital Message Signal (in discrete bits)');
title ('Message vs Time');

%S/P conversion
A = reshape(M,N,L/N);

%modulate each subcarrier using IFFT
B = ifft(A);

%P/S conversion
C = reshape(B,1,L);

%oversample by a factor of Q (DAC ~)
D=ones(Q,1)*C;
D=conj(D(:)');

%guard time insertion
i=1;
k=1;
for t0=1:L;
for t1=1:R*Q;
D(1,k*Q-R*Q+i)=0;
i=i+1;
end
k=k+1;
i=1;
end

%cyclic prefix insertion
j=1;
i=Q-R*Q+1;
k=1;
a=1;
for f = 1:length(C);
for g = 1:R*Q;
D(:,Q*k-R*Q+j) = D(:,a);
j=j+1;
a=a+1;
end
j=1;
a=1+k*Q;
k=k+1;
end
plot (t,D); %plot the OFDM signal
xlabel ('Time (seconds)');
ylabel ('OFDM Signal');
title ('OFDM Signal (with guard time & cyclic prefix) vs Time');

%% Add frequency offset
SNR = 10;
index=1;
f0 = 1/Tu;
S = zeros(2,10);
BER = 0;
BER1 = 0;
per = 0;
N_max = 100;
h = modem.pskdemod(2,pi);

for tr = 0:0.05:0.5
D1 = D*exp(2*pi*sqrt(-1)*per*f0);
for tk = 1:N_max
%% RECEIVER
%undersampling (ADC ~) removing Tg and CP
Dn = awgn(D1, SNR,'measured');
E = zeros(1,L);
i = 1;
j = 1;
for t0=1:L;
E(1,i) = Dn(1,j);
i=i+1;
j=j+Q;
if j>Q*L
j=j-1;
end
end
%S/P
F = reshape(E, N, L/N);
%demodulation
G = fft(F);
%P/S
Mr = reshape(G, 1, L);
Mr = real(Mr);

%BPSK Demodulation
M2 = demodulate(h,Mr);

%comparing the received and the sent message (0's & 1's)
bit_error = length(find(M1~=M2));
BER = bit_error/length(M2);
BER1 = BER1+BER;

end

S(1,index) = BER1/N_max;
S(2,index) = per;
per = per + 0.05;
index = index + 1;
BER1 = 0;
BER = 0;
end

semilogy(S(2,:),S(1,
xlabel ('Normalized frequency offset')
ylabel ('Bit Error Rate')
title ('BER vs Frequency Offset')
grid on

 

[KataKoniK]

First of all, great job on simulating an OFDM transceiver using MATLAB! It's great to see your interest and effort in investigating the effect of frequency offsets on system performance.

To answer your question about the fundamental frequency, it is defined as the lowest frequency component in a waveform. In the case of OFDM, the fundamental frequency is equal to the inverse of the symbol period (1/T). This is because in OFDM, the subcarriers are spaced at intervals of 1/T, which means they have a frequency spacing of 1/T.

In your code, you have correctly used 1/T as the fundamental frequency. However, I would recommend using a variable to represent this value instead of a comment, as it will make your code more readable and easier to modify in the future.

Overall, your code looks good and your approach of varying the frequency offset and measuring its effect on the bit error rate is a good way to investigate the system performance. One suggestion I would make is to also plot the theoretical bit error rate curve for comparison, as this can help validate your simulation results.

Keep up the good work and continue exploring different aspects of OFDM!