## On cyclostationary detectors in literature

Recently, I've been studying cyclostationary detectors. These methods of detecting the presence of a radio transmission seem to be quite popular in academic literature. On the other hand, I kind of glossed over them in my seminar on spectrum sensing. There were several reasons for that: one of them was certainly that I find the theory of cyclostationary signals and statistical spectral analysis hard to wrap my head around. Another reason was however that I couldn't find any papers that would describe a practical cyclostationary detector to sufficient enough detail to allow reproduction of published results. At the very least I wanted to compare its performance against other (non-cyclostationary) detectors in a laboratory experiment before writing about it in any depth.

Here are some of the problems I stumbled upon when trying to understand and reproduce results from scientific papers published on this topic. I don't want to point to any particular work. The example below is just a recent one that crossed my desktop (and happens to nicely illustrate all of the problems I write about). I encountered similar difficulties when reading many other research papers.

*(from Wireless Microphone Sensing Using Cyclostationary Detector presented at the INCT 2012 conference)*

Perhaps the most trivial thing that makes reading unnecessary hard is bad mathematical typesetting. It's sometimes bad enough that it is impossible to follow derivations without first rewriting them to a more consistent form. A part of the blame here goes to the publishers who are preferring manuscripts in Word. I have seen some beautiful articles produced in Word, but the fact is that it is much harder to mess up formatting in LaTeX. Not that it is impossible though. I have had to deal with my share of buggy LaTeX styles.

Another common problem that is simple to fix is inconsistent mathematical notation. For instance the constant *A _{c}^{2}/4* gets dropped somewhere in the middle of the derivation above. Also,

*x*might (or might not) mean two different things. I've heard people argue strongly that such trivial errors are of no concern, since obviously everyone in the field

*knows*what is meant by the author. The problem is that mathematical sloppiness creates confusion for readers that are not intimately familiar with the topic. Why even have a theoretical overview section in the paper then, if the assumption is that it the reader already knows it by heart?

After you manage to bite your way through the theoretical sections to the practical evaluation, it is surprisingly common that various parameters necessary to reproduce the results are left out. For instance, a lot of cyclostationary detectors use a method of estimating the cyclic spectrum called the FFT accumulation method. This method takes several parameters, for instance the sizes of two Fourier transforms that determine its time and frequency resolution. These are often omitted. Another omission is the exact waveform used to test the detector. The paper above gives only frequency deviation used by the wireless microphone, but not the nature of the modulation signal.

Having such difficulty reproducing results from papers based on pure numerical simulations is especially frustrating. I imagine the results are based on a few hundred lines of Matlab code which, if published, would quickly remove any doubts on how the results were obtained. However publishing source together with an article is still a rare exception.

Some of the difficulties I've been having are definitely due to my unfamiliarity with the field. As I keep studying the topic, some of the line of thoughts from the authors who wrote these papers become clearer and some mysteries on how they managed to come up with their results deepen. Undoubtedly some of my own writings aren't as clear, or error free, as I liked them to be. However there are literally hundreds of articles written on the topic of cyclostationary detectors and I'm continuously surprised how much time it is taking me to find a single reproducible example.

I sympathize with your frustration with technical papers on cyclostationary signal processing (CSP). I've been working in the area for nearly 30 years, and some of the papers you've had problems with may very well be mine. Lately, I'm trying to remedy this by creating a CSP blog. I started from the very beginning of the math, and haven't yet described in detail the detectors and estimators you are

seeking, but I'll get there. I'd appreciate it if you would give it a look some time.

Thanks!