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I am a little unsure about the generation of a additive white Gaussian noise, so I would appreciate to hear from you if I`m doing it correctly.

My goal is to generate the time-domain noise correspondent to a noise floor of -135 dbm/Hz

The procedure I`m adopting is the following:

1 - Convert the noise floor in dbm/Hz to Watts/Hz
2 - Get the average total power from the PSD.
3 - Generate the Gaussian noise with this average total power
4 - Take the FFT of the Gaussian noise and estimate the periodogram to verify whether it is indeed generating the noise with the correct PSD

Here is how I do the 4 steps above:

1 - \begin{align} S_\text{watts} = \left(10^{\frac{S_\text{dBm}}{10}}\right)10^{-3} \end{align} where $S_\text{watts}$ is the PSD in Watts/Hz and $S_\text{dBm}$ is the PSD in dBm/Hz.

2 - Average total power is given by $$ P_n = S_\text{watts} B ,$$ where $B$ is the Bandwidth

3 - Generate the randn MATLAB function multiplied by $\sqrt{P_n}$.

4 -
4.1 Take the FFT of the signal, let`s say, $X(k)$.
4.2 Get the Energy Spectral Density (ESD) as $\frac{\left| X(k) \right|^2}{N}$
4.3 Get the PSD by simply dividing the ESD by $N$ (the FFT length) 4.4 I do not simply plot the $10 \log_{10}\left(\text{PSD} 10^3\right)$, since I believe this would plot the PSD in dBm/subcarrier. Instead of this, I plot $10 \log_{10}\left(\frac{\text{PSD}}{\text{tone spacing}} 10^3\right)$, in attempt to get the plot as dBm/Hz.

The code below is what I am using. Please, indicate if I`m doing any mistake.

clear all clc bandwidth = 106e6; % in Hz sampleFrequency = 2*bandwidth; % in Hz noiseFloor = -135; % in dBm/Hz awgnPsd = (10.^(noiseFloor/10))*1e-3; % in Watts/Hz noisePower = awgnPsd*2*bandwidth; % in Watts % Generate noise signal: N = 4096; % signal length nSymbols = 1000; % number of symbols with length N to be generated noise = randn(N,nSymbols)*sqrt(noisePower); % Verify PSD toneSpacing = sampleFrequency/N; % DFT tone spacing ESD = mean(abs(fft(noise,N)).^2)/N; % Energy spectral density PSD = ESD/N; % plot PSD figure plot(10*log10((PSD/toneSpacing)*1e3))
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  • $\begingroup$ An aside: if you want to create a discrete-time simulation of a voltage waveform that represents some power level, you need to take the impedance that the voltage is measured across into account. For RF communication applications, this is often 50 ohms. $\endgroup$ Commented Dec 8, 2013 at 2:16

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Here is a Matlab snippet that might help. You should be able to apply the result to your favorite PSD routine to see the dbm/Hz in the frequency domain.

% create complex noise with a desired dBm/Hz fs=1e6; % whatever you want N=1e5; % # samples of noise R=50; % ohms dbm_hz = -135; % goal bw = fs; % complex noise with BW = sample rate dbm = dbm_hz + 10*log10(bw); dbw = dbm - 30; watts = 10^(dbw/10); vrms = sqrt(watts * R); n = randn(N,1) + j*randn(N,1); n = vrms * n / std(n); meas_dbm_hz = 10*log10(sqrt(mean(n.*conj(n)))^2 / R) - 10*log10(bw) + 30
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