Understanding and Using the Statistics of Communication Signals

A Gallery of Cyclic Correlations

For your delectation.

There are some situations in which the spectral correlation function is not the preferred measure of (second-order) cyclostationarity. In these situations, the cyclic autocorrelation (non-conjugate and conjugate versions) may be much simpler to estimate and work with in terms of detector, classifier, and estimator structures. So in this post, I’m going to provide surface plots of the cyclic autocorrelation for each of the signals in the spectral correlation gallery post. The exceptions are those signals I called feature-rich in the spectral correlation gallery post, such as DSSS, LTE, and radar. Recall that such signals possess a large number of cycle frequencies, and plotting their three-dimensional spectral correlation surface is not helpful as it is difficult to interpret with the human eye. So for the cycle-frequency patterns of feature-rich signals, we’ll rely on the stem-style (cyclic-domain profile) plots that I used in the spectral correlation gallery post.

The signals that are used to generate the plots are exactly the same as in the spectral correlation gallery post; see that post for details. On to the cyclic autocorrelation gallery. The first, and largest, set of objet d’art are simulated signals. These are followed by some surfaces for captured communication signals. The simulated digital signals feature symbol or bit rates of and a carrier frequency offset of .

Here are the cyclic autocorrelation functions for four captured signals: WCDMA, CDMA, ATSC-DTV, and CDMA-EVDO:

I'm a signal processing researcher specializing in cyclostationary signal processing (CSP) for communication signals. I hope to use this blog to help others with their cyclo-projects and to learn more about how CSP is being used and extended worldwide.
View all posts by Chad Spooner

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