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 0.1 and a carrier frequency offset of 0.05.

ww_caf_16qam
Figure 1.
ww_caf_16qamrect
Figure 2.
ww_caf_2fsk
Figure 3.
ww_caf_4fsk
Figure 4.
ww_caf_8psk
Figure 5.
ww_caf_8pskrect
Figure 6.
ww_caf_amdsblc
Figure 7.
ww_caf_amdsbsc
Figure 8.
ww_caf_bpsk
Figure 9.
ww_caf_bpsk_man
Figure 10.
ww_caf_bpsk_man_bl
Figure 11.
ww_caf_bpskrect
Figure 12.
ww_caf_cpm
Figure 13.
ww_caf_dqpsk
Figure 14.
ww_caf_dqpskrect
Figure 15.
ww_caf_dsssbpsk
Figure 16.
ww_caf_dsssqpsk
Figure 17.
ww_caf_dssssqpsk
Figure 18.
ww_caf_gfsk
Fgiure 19.
ww_caf_gmsk
Figure 20.
ww_caf_msk
Figure 21.
ww_caf_ook
Figure 22.
ww_caf_ookrect
Figure 23.
ww_caf_qpsk
Figure 24.
ww_caf_qpsk_man
Figure 25.
ww_caf_qpsk_man_bl
Figure 26.
ww_caf_qpskrect
Figure 27.
ww_caf_sqpsk
Figure 28.
ww_caf_sqpskrect
Figure 29.
ww_caf_tone
Figure 30.

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

ww_caf_atsc_dtv_15dB_1
Figure 31.
ww_caf_cdma_30dB_1
Figure 32.
ww_caf_cdma_group_30dB_1
Figure 33.
ww_caf_wcdma_20dB_3
Figure 34.

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Author: Chad Spooner

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.

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