MATLAB: How to specify ‘nsamp’ for an oversampled Orthogonal Frequency Division Multiplexing (OFDM) signal

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In the Help Documentation on 'AWGN Channel' in Communication Toolbox, the section 'Describing the Noise Level of an AWGN Channel' mentions that:

SNR = EbNo + 10*log10(k) – 10*log10(nsamp)

I have a system that simulates Orthogonal Frequency Division Multiplexing or OFDM. I am oversampling my input data from [1 -1 1 1] to [1 -1 0 0 0 0 1 1]; how would I specify 'nsamp' in the SNR equation given that there is oversampling in the OFDM modulation.

Should 'nsamp' be 2 in this situation?

Best Answer

In the time domain, four symbols are modulated by four different cosine frequencies (or OFDM tones); they are then added together to make an OFDM signal. This process can be accomplished by using an IFFT since the symbols are essentially the coefficients x(k)'s in the Fourier Transform since they are multiplied times a cosine. In order to "recover" the corresponding time signal, the IFFT is taken of the symbols.

There are a number of considerations such as inserting zeros to make a frequency guard band or reorganizing the symbols to make them symmetric (to produce a real time signal).

In any case, 'nsamp' should be set to Nfft/Np, where Nfft is the number of OFDM tones (e.g., 64) and Np is the number of non-zero tones (usually smaller than Nfft). This assumes that the output of each modulator (before OFDM frame assembly) is not oversampled. Note that this interpretation of nsamp is not the one given in the documentation, but it is the right formulation for OFDM.

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Hi Ali,

please try to run the following code:

%%Setup
% Define parameters.
M = 16;                 % Size of signal constellation
k = log2(M);            % Number of bits per symbol
n = 3e4;                % Number of bits to process
nsamp = 1;              % Oversampling rate
hMod = modem.qammod(M); % Create a 16-QAM modulator
%%Signal Source
% Create a binary data stream as a column vector.
x = randint(n,1); % Random binary data stream
% Plot first 40 bits in a stem plot.
stem(x(1:40),'filled');
title('Random Bits');
xlabel('Bit Index'); ylabel('Binary Value');
%%Bit-to-Symbol Mapping
% Convert the bits in x into k-bit symbols.
xsym = bi2de(reshape(x,k,length(x)/k).','left-msb');
%%Stem Plot of Symbols
% Plot first 10 symbols in a stem plot.
figure; % Create new figure window.
stem(xsym(1:10));
title('Random Symbols');
xlabel('Symbol Index'); ylabel('Integer Value');
%%Modulation
y = modulate(modem.qammod(M),xsym); % Modulate using 16-QAM.
%%Transmitted Signal
ytx = y;
%%Channel
% Send signal over an AWGN channel.
EbNo = 10; % In dB
snr = EbNo + 10*log10(k) - 10*log10(nsamp);
ynoisy = awgn(ytx,snr,'measured');
%%Received Signal
yrx = ynoisy;
%%Scatter Plot
% Create scatter plot of noisy signal and transmitted
% signal on the same axes.
h = scatterplot(yrx(1:nsamp*5e3),nsamp,0,'g.');
hold on;
scatterplot(ytx(1:5e3),1,0,'k*',h);
title('Received Signal');
legend('Received Signal','Signal Constellation');
axis([-5 5 -5 5]); % Set axis ranges.
hold off;

After you have run the code you should have the following variables in your workspace:

whos
  Name            Size             Bytes  Class           Attributes
    EbNo            1x1                  8  double                    
    M               1x1                  8  double                    
    h               1x1                  8  double                    
    hMod            1x1                     modem.qammod              
    k               1x1                  8  double                    
    n               1x1                  8  double                    
    nsamp           1x1                  8  double                    
    snr             1x1                  8  double                    
    x           30000x1             240000  double                    
    xsym         7500x1              60000  double                    
    y            7500x1             120000  double          complex   
    ynoisy       7500x1             120000  double          complex   
    yrx          7500x1             120000  double          complex   
    ytx          7500x1             120000  double          complex

Please compare these values with yours in order to hunt down the issue.

I hope I could help,

Friedrich

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