I am trying to emulate the SFO effect for OFDM system, I did it using linear interpolation as shown [HERE][1]  . That can be explained as if I have the time domain signal $s_n$ representing the output of ifft (let’s ignore the noise and the guard interval), so the SFO can be inserted using linear interpolation.  Below is the code I made for that, and the resulted rotated signal without compensating the SFO. 

    clc; clear all; close all;
    n_sym = 10;  % The number of symbols
    N = 1024;    % The symbole length 
    mod = 4;     %the modulation order 
    len= n_sym* log2(mod)*N;  %Lenght of whole data (N * Number of symbol* M)
    
    
    %This part will generate binary vector as per length entered by user
    data=floor(rand(1,log2(mod)*len)+0.5);
    %Mapping of binary data
    mapper_out = qammod(bi2de(reshape(data,[],log2(mod))), mod,'UnitAveragePower', true);
    % Take the iFFt operation after S/P operation 
    sn = ifft(reshape(mapper_out,N,[]));
    
    %===== Here using interpolation to add 1 ppm SFO =====
    for sy = 1 : size(sn,2)
        S_y = sn(:,sy);       %Taking every symbol separatly
        for nn = 1 : length(S_y)-1 
            X_te(nn) = S_y(nn) + (nn*(S_y(nn+1) - S_y(nn))/1e6);   %Doing linear interpolation with 5ppm
        end 
            X_te2(:,sy) = [S_y(1); X_te.'];                 %[x[1];  x[nn]]
    end 
      out = fft(X_te2);  out = out(:);  %P/S
    
      %===Calculate the BER 
    data_rec = qamdemod(out, mod); 
    b_rec = reshape(de2bi(data_rec,log2(mod)),[],1).';
    [BER_1 Ratio_1] = biterr(b_rec(1:68),data(1:68))
    %========== 
    
    figure;plot(real(out),imag(out),'b+');title('constellation with and without  Sampling Frequency Offset'); hold on; 
    plot(real(mapper_out),imag(mapper_out),'r+','LineWidth',3); 

[![enter image description here][2]][2]

The problem is that, when adding an SFO effect of 1 ppm, the signal is completely rotated as shown in the above figure, and the BER cannot be recovered at all as shown in the above code. However, when having 1 ppm SFO, it’s expected to have little bit similar constellation to the ideal signal, and the BER performance is supposed to be almost 0.  

**Update**

Normally, the added SFO effect into the signal $x[n]$ as following:

$y\left [ n \right ] = x\left [ n \right ] + n \times \frac{x\left [ n + 1 \right ] - x\left [ n \right ]}{10^6}$

The dominator is $10^6$ means that 1 ppm is added. Assuming the length of the symbols is $N = 1024$, so the maximum added SFO will be 1024 too. 
On the other hand, if we can normalize the added SFO by $N$ to have the maximum added SFO 1ppm, the above equation will be: 

$y\left [ n \right ] = x\left [ n \right ] + n \times \frac{x\left [ n + 1 \right ] - x\left [ n \right ]}{N \times 10^6}$ 

Unfortunately, the rotation is still very big and the signal is completely deteriorated. 


  [1]: https://dsp.stackexchange.com/questions/62857/how-to-emulate-sample-frequency-offset-for-ofdm-in-matlab/62858?noredirect=1#comment176083_62858
  [2]: https://i.sstatic.net/86fgw.jpg