As I have found out, their is no way to find the actual pdf and its parameters (like mean and variance) when primary signal is exist in cyclostationary spectrum sensing. So how do I define analytic expression for the Probablity of detection if it exists.
I think the answer to your question will depend on the cyclic features of the signal you're trying to detect (and presumably identify). In short, the modulation of the signal you're trying to detect makes a difference, as well as noise and any Rayleigh fading.
I found these two papers that might be worth a read to start out. The first URL shows the abstract of a PhD thesis, but not the thesis text. It does sound like what you're looking for, in the sense that it describes all of the impairments you might encounter in the process. You probably need to contact the author to get the full text.
The second URL is an ieeexplore paper (which requires membership which your school probably has). It provides the full text. In this paper, they describe a technique that allows detection without prior knowledge of the signal characteristics. However, the probabilities of detection using this technique are also a function of the signal modulation. They call this "blind" spectrum sensing. As you might expect, any modulation scheme that includes strong peaks will be easier to sense that a "more polite" modulation.
http://www.ee.ucla.edu/events/events-archive/2013/wideband-cyclostationary-spectrum-sensing-and-modulation-classification
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6784529
@Albert
Thanks for the reply.
I am looking for the genralised derivation of probablity of detection for cyclostationary detection. I ahve found some thesis which says that it is not possible to derive those for genralised expression rather they have derived for particular case. So i want to make sure that is it really not possible or their might be some expression for that.
@svetla
Thanks for the reply
I am looking for generalized. Your reference defines for a particular case.
A closed form of the detection probability for a Ciclostationary Single Cycle Detector can be found in the following paper: "Cooperative Cyclostationary Spectrum Sensing in Cognitive Radios at Low SNR Regimes" No a priory knowledge about PU signal is required in this analysis
http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=5502481&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F5497983%2F5501741%2F05502481.pdf%3Farnumber%3D5502481
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