**Measurement below noise floor**

Measuring gated-CW pulses in the frequency domain is not straightforward especially when dealing with weak signals. The most easy way consists in using a spectrum analyzer as a demodulator to get the envelope of the pulses. However, even using a very high grade Automatic Spectrum Analyzer (ASA), there are some strong limitations if no external trigger is used.

We will demonstrate here that peak power measurement can even be carried out below the noise floor as soon as the spectrum analyzer has been fully characterized and modeled.

## Recommended setup and measurement parameters

In order to carry out weak signal measurements, the spectrum analyzer has to be used in 0 SPAN mode and triggered with the arbitrary wave generator (AWG) that delivers the gated-CW pulses. Then the ASA Resolution Band Width (RBW) has to be set to its optimal value.

As seen on this figure, a too large RBW (blue curve) leads to a high noise floor and to a reduced signal-to-noise ratio. A too small RBW (green curve) leads to a distortion of the envelope and to a under-estimation of its magnitude. As already addressed in our __Good Practice Guidance__, the optimal RBW (orange curve) for

the worst case (rectangular pulse) is given by RBW [MHz] = 3000 / FWHM [ns] where FWHM is the Full Width Half Maximum of the pulse.

## Peak power assessment of ultra weak signals

For that purpose we have averaged the signal on 256 consecutive samples. The signals of interest has been especially chosen to not satisfy the recommendation of presenting a peak power at least 10 dB over the noise floor power. Indeed, we have used signals with a peak power ranging from ASA noise floor + 4 dB down to ASA noise floor â€“ 10dB! For the purple curve, the actual signal peak power presents almost the same value than the noise power (-90.8 dBm). When a power is doubled, it leads to an amount of 3 dB which corresponds to the signal-to-noise ratio that is expected for that purple curve. The observed signal-to-noise ratio is indeed of only 2.2 dB.

With a model (dotted blue curve on Fig. below) based on Monte-Carlo simulations we have perfectly retrieve the measured signal-to-noise ratios presented above. Moreover, we have shown that accurate peak power measurements can be carried out even when signal peak power is of the same order of magnitude than noise power.

To get a more complete review on this subject please refer to our application note on __Frequency-domain pulse measurement__ where we show than from a very standard use to the most comprehensive use of the same spectrum analyzer with same gated-CW signals, a gain of 40 dB can been reached in terms of sensitivity!

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