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On the Theory of Cyclostationary Signals

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... Figure 4 gives the theoretical and experimental ROC curves of the CFD on a 16-QAM signal in a Gaussian channel with a SNR = −11 dB. The theoretical curve is generated by Equation (33) and the experimental curve is obtained by Monte Carlo simulations. We can note through these results the similarity between the two curves. ...
... P d performance curve as a function of SNR. The theoretical curve obtained according to Equation(33) and the experimental one coincide. ...
... ( ) can be approximated as shown below and mentioned by [43,44]: ...
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... In accordance with the fact that noise is Wide-Sense Stationary (WSS) with zero correlation while modulated signals are cyclostationary with spectral correlation due to the replication of signal periodicities [11,13], hence the PUs signal can be isolated from noise signal. A scalar waveform x(t) is known to be either spectrally self-coherent or conjugate selfcoherent at a frequency a if the cyclic autocorrelation function (spectral correlation function) [3,12,15], i.e., the correlation between x(t) and x(t) shifted in frequency by a, is nonzero for some delay s [2] i.e., ...
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... The basic timesmoothing and frequency-smoothing methods of spectral correlation analysis were introduced in [8] and proof of their equivalence was given in [9] and [10]. Methods which more fully exploit the computational efficiency of the FFT, namely, the FFT accumulation method (FAM) and the strip spectral correlation analyzer (SSCA) were introduced in [11] and discussed in [13] and [14]. ...
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