Fast Auto-correlation

Intro

Frank of radiorauch fame put together an excellent page (and some code) on performing real-time auto-correlation with GNU Radio and the USRP.

Unfortunately the code no longer works with the new version of GNU Radio, so I upgraded it and wrote some block definitions so that it could be used as a graphical sink in GRC (GNU Radio Companion).

Please refer to Frank's page for the gory details. Suffice to say that his FAC (Fast Auto-Correlation) implementation exploits the Wiener Khinchin theorem, which in this context essentially means that if you take the FFT of the power spectrum of a signal (i.e. two FFTs), "we have a particularly fast way of calculating auto-correlations" - Frank.

GRC Block

Auto-correlation of a W-CDMA downlink channel, showing the pilot channel's radio frames repeating every 10ms:

[File:CDMA_FAC.png|800px]

In GRC, the blocks as such:

[File:GRC-FAC.png]