Simulating noise in OFDM

Question

I'd like to simulate a certain $E_s/N_0$ in a baseband OFDM MATLAB modem to generate SER curves.

I randomize 50 QAM symbols with $N$ subcarriers each in frequency domain, add null frequencies (guard bands) to each symbol, perform IFFT and then add CP. Then I convolve the "time domain" symbols with a certain channel with taps of my choice and then I want to add noise, but I'm not sure about how to normalize it so that I obtain the correct SNR as generally reported in theoretical curves.

I get funky results with just MATLAB's agwn function with the measured flag.

Answer 1

In theory, all you'd need to do is add Gaussian noise of the appropriate variance. Without seeing your code and without knowing what "funky" means, I would check for:

• when you do the convolution, scale the result by $\Delta t$, the time differential
• make sure the FFT scaling that Matlab performs is not throwing you off

One thing you can do, which is simple but not very elegant, is to add the noise to each symbol after the FFT in the receiver, but before running any decision rule on them. You can simply add one sample of complex noise of variance $N_0$ to each symbol; since you control their average energy, you can get any SNR you want.

Answer 2

You shouldn't do a measurement with only one OFDM symbol at first. Instead create some random data, perform QAM modulation, devide QAM symbols array in $N$ OFDM data blocks and make OFDM symbols. Then add CP and paste it together to form a frame. Now you can calculate its power,

$P_{signal} = 1 \div (N \cdot N_{FFT})\sum {s^2} $

estimate PAPR, add some noise to model frame spread over AWGN channel. Choose SNR of interest, you know your signal's power, so you can calculate power of noise to be added to satisfy SNR value you've choosen.

$P_{noise} = 10^{-SNR/10} \cdot P_{signal}$

Create complex-value noise with $randn$ function and scale it with

$\sigma = \sqrt{P_{noise}}/{\sqrt{2}}$

and then add noise to your signal.

After that if you perform OFDM demodulation and than QAM demodulation you'll achive BER you're expecting to be for SNR you've choosen. If you want to have more precise measurement, do this routine for some times for one value of SNR and make average statistic. If you want to plot really good curves you need $1e+5...1e+6$ bits to measure BER for one SNR value. You can construct frame from about 5000...20000 bits (its common length for LDPC decoder used e.g. in the latest DVB-T, as I remember) and do measurements in $for$ loop. I advice you to generate random data at every iterarion.

So I don't see any problem in FFT normalization or with anything else. You construct a frame, estimate its power and insert noise according to average signal's power and SNR you want to achive.

Oh, I've forgotten. If you use only part of subcarriers during modulation, you should scale noise power as

$P_{noise} = P_{noise} \cdot N_{used} \div N_{FFT}$

to match the band where signal really exists and noise band.