How to Calculate power spectral density using USRP data?

Question

I wanted to plot a graph between Average power spectral density(in dbm) and the frequency (2.4 GHZ to 2.5 GHZ).

The basic procedure i used earlier for power vs freq plot was to store the data generated by "usrp_specteum_sense.py" for some time period and then taking average.

Can i calculate PSD from the power used in "usrp_spectrum_sense.py"?
Is there any way to calculate PSD directly from usrp data?
Is there any other apporch which can be used to calculate PSD using USRP for desired range of frquency??

PS: I recently found out about the psd() in matplotlib, can it be use to solve my problem??

Answer 1

I wasn't 100% sure whether or not to mark this question a duplicate of Retrieve data from USRP N210 device ; however, since the poster of that question was very confused and so was his question, let's answer this in a concise way:

What an SDR device like the USRP does is give you digital samples. What these are is nothing more or less than what the ADC (Analog-to-Digital converter) makes out of the voltages it sees. Then, those numbers are subject to a DSP chain that does frequency shifting, decimation and appropriate filtering. In other words, the discrete complex signal's envelope coming from the USRP should be proportional to the voltages observed by the ADC. Thanks to physics, that means that the magnitude square of these samples should be proportional to the signal power as seen by the ADC.

Thus, the values you get are "dBFS" (dB relative to Full Scale), which is an arbitrary measure relative to the maximum value the signal processing chain might produce.

Now, notice two things:

• As seen by the ADC is important. Prior to the ADC there's
  • an unknown antenna with a) an unknown efficiency and b) unknown radiation pattern illuminated from an unknown direction,
  • connected to a cable that might or might not perfectly match the antennas impedance, and that might or might not perfectly match the USRP's RF front-end's impedance,
  • potentially a bank of preselection filters with different attenuations,
  • a low-noise frontend amplifier, depending on the device/daughterboard with adjustable gain, with non-perfectly flat gain over frequency
  • a mixer with frequency-dependent gain,
  • baseband and/or IF gain stages and attenuators, adjustable,
  • baseband filters, might be adjustable,
  • component variances in PCBs, connectors, passives and active components, temperature-dependent gain and intermodulation, as well as
  • ADC non-linearity, frequency-dependent behaviour.
• proportional is important here, since after sampling, there will be
  • I/Q imbalance correction,
  • DC/LO leakage cancellation,
  • anti-aliasing filtering prior to
  • decimation,
  • and bit-width and numerical type changing operations.

All in all, the USRPs are not calibrated measurement devices. They are pretty nice, and if chose the right one for your specific application, you might just need to calibrate once with a known external power source feeding exactly your system from antenna to sampling rate coming out at the end, at exactly the frequency you want to observe. After knowing "ok, when I feed in x dBm of power, I see y dBFS, so there's this factor (xy) dB between dBFS", you now have calibrated your device for exactly one configuration consisting of

• hardware models and individual units used, including antennas and cables,
• center frequency,
• gain,
• filter settings,
• decimation/sampling rate

Note that doing such calibrations, especially in the 2.4 GHz ISM band will require a "RF silent" room – it'll be hard to find an office or lab with no 2.4 GHz devices these days, and the reason why these frequencies are free for usage is that microwave ovens interfere; and then there's the fact that these frequencies tend to diffract and reflect on building structures, PC cases, furniture with metal parts... In other words: get access to an anechoic chamber, a reference transmit antenna and transmit power source, and do the whole antenna system calibration dance that results in a directivity diagram normally, but instead generate a "digital value relative to transmit power" measurement. Whether or not that measurement is really representative for how you'll be using your USRP in a lab environment is very much up for your consideration.

That is a problem of any microwave equipment, not only the USRPs – RF propagation isn't easy to predict in complex environments, and the power characteristics of a receiving system isn't determined by a single component, but by the system as a whole in exactly its intended operational environment. Thus, calibration must require you either know your antenna, cable, measurement frontend, digitizer and DSP exactly and can do the math including error margins, or that you calibrate the system as a whole, and change as little as possible afterwards.

So: No. No Matlab function in this world can give meaning to numbers that isn't in these numbers – for absolute power, you'll need to calibrate against a reference.

Another word on linearity: A USRP's analog hardware at full gain is pretty sensitive – so much sensitive that operating eg a WiFi device in the same room would be like screaming in its ear, blanking out weaker signals, and driving the analog signal chain into non-linearity. In that case, not only do the voltages observed by the ADC lose their linear relation to the voltages inserted at the antenna port, but also, and that is usually worse, amplifiers become mixers, so unwanted intermodulation introduces energy in spectral places where there was none. So make sure you operate your device in a place where you make the most of your signal's dynamic range without running into nonlinearities.