My colleague Dr. Apurva Mody (of BAE Systems, IEEE 802.22, and the WhiteSpace Alliance) and I have received a patent on a CSP-related invention we call tunneling. The US Patent is 9,755,869 and you can read it here or download it here. We’ve got a journal paper in review and a 2013 MILCOM conference paper (My Papers [38]) that discuss and illustrate the involved ideas. I’m also working on a CSP Blog post on the topic.

The basic idea is that wideband signals typically possess a multitude of cycle frequencies, many of which are an order of magnitude or more smaller than the signal’s occupied bandwidth. The presence of these cycle frequencies can be detected by processing narrowband (relative to the signal bandwidth) components of the signal. So the entire signal does not have to be captured by a high-rate sampling process in order to assess at least some of its cyclostationarity.

If the cycle frequencies that we can see through these narrowband views of the signal (what we call *tunnels*) are unique to the signal, then we can detect the signal and recognize its modulation type without the burdens of (1) high-rate sampling and (2) the high cost of our beloved CSP algorithms when applied to large sets of such samples.

Let me know of your interest in this topic in the comments; feedback is helpful in determining my CSP-Blog post priorities.

Dear Dr.Spooner,

Thank you for this post. Unfortunately I can’t see the images in the Patent link, it seems like there are not included in the web page.

I am really interested in this idea, as I am working on cyclostationarity of multicarrier signals (5G waveforms). All of them have indeed multiple cyclic frequencies with very small magnitude compared to the fundamental frequencies. However, I can’t understand the reason behind this phenomenon, would you like to explain it further?

(a paper we submitted was rejected because one of the reviewers pointed that our CAF should be discrete in the cyclic frequency axis. It looks like if it is not as it has these several cyclic frequencies).

Thank you for bringing the problem with the images to my attention. I did find a way to download the entire document from the US Patent and Trademark Office website, and I’ve created a new link to that pdf file in the post. So you should be able to see all the figures in that file. The equations look a lot better too, in that pdf file.

Even though signals like LTE and, I suppose, 5G waveforms possess many cycle frequencies with low spectral correlation magnitudes compared to the PSD, the cycle-frequency parameter is still discrete. I think there are extensions to the usual theory of CSP that involve uncountable sets of cycle frequencies and perhaps even continuously variable cycle frequencies, but those extensions (usually? always?) require high-speed relative motion between the signal source and the receiver. So maybe your analysis of the spectral correlation function suffered from insufficient cycle-frequency resolution?

The general reason we see all those “weak” cycle frequencies is that the signal possesses several periodicities that have very different time scales. So you might see a high-rate OFDM signal combined with a low frame rate, and statistics of the overall signal are influenced by these elements mixing together. If you can send me your best write-up or published paper that describes the 5G waveforms (at the physical layer!) I might be able to provide a better answer in the future.

cmspooner @ ieee dot org