Dictionary-based reconstruction of the cyclic autocorrelation via ℓ1-minimization for cyclostationary spectrum sensing

One of the main enablers of dynamic spectrum access is fast and reliable spectrum sensing. Acquiring the occupation status of a spectral band can be accomplished in different ways, one of which is called cyclostationary spectrum sensing. The aforementioned method exploits the prior knowledge of periodicities inherent in most man-made signals for the purpose of detecting their presence in a set of sample data. One prerequisite for the detection is the knowledge of the signal´s cyclic autocorrelation (CA), which can be estimated from a finite amount of time-domain samples. This work introduces a new method for estimating the CA using a very small amount of time-domain samples, i.e. a short observation time. This is accomplished by modeling the desired CA vector using a custom dictionary describing its known properties and recovering it by solving a convex optimization problem.