A review on spectrum sensing for cognitive radio: challenges and solutions <s> Cyclostationary Detection <s> As a continuation of Part I, the spectral correlation function is presented for a variety of types of digitally modulated signals. These include digital pulse-amplitude, pulse-width, and pulse-position modulation, and various types of phase-shift keying and frequency-shift keying. The magnitudes of the spectral correlation functions are graphed as the heights of surfaces above a bifrequency plane, and these graphs are used as visual aids for comparison and contrast of the spectral correlation properties of different modulation types. <s> BIB001 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Cyclostationary Detection <s> It is shown that the cyclostationarity attribute, as it is reflected in the periodicities of (second-order) moments of the signal, can be interpreted in terms of the property that allows generation of spectral lines from the signal by putting it through a (quadratic) nonlinear transformation. The fundamental link between the spectral-line generation property and the statistical property called spectral correlation, which corresponds to the correlation that exists between the random fluctuations of components of the signal residing in distinct spectral bands, is explained. The effects on the spectral-correlation characteristics of some basic signal processing operations, such as filtering, product modulation, and time sampling, are examined. It is shown how to use these results to derive the spectral-correlation characteristics for various types of man-made signals. Some ways of exploiting the inherent spectral redundancy associated with spectral correlation to perform various signal processing tasks involving detection and estimation of highly corrupted man-made signals are described. > <s> BIB002
This cyclostationarity can be extracted by the spectral-correlation density (SCD) function BIB002  BIB001 . For a cyclostationary signal, its SCD function takes nonzero values at some nonzero cyclic frequencies. On the other hand, noise does not have any cyclostationarity at all; that is, its SCD function has zero values at all non-zero cyclic frequencies. Hence, we can distinguish signal from noise by analyzing the SCD function. Furthermore, it is possible to distinguish the signal type because different signals may have different nonzero cyclic frequencies. In the following, we list cyclic frequencies for some signals of practical interest  BIB001 . When source signal x(t) passes through a wireless channel, the received signal is impaired by the unknown propagation channel. In general, the received signal can be written as  where * denotes the conjugate, α denotes the cyclic frequency for x(t), H( f ) is the Fourier transform of the channel h(t), and S x ( f ) is the SCD function of x(t). Thus, the unknown channel could have major impacts on the strength of SCD at certain cyclic frequencies. Although cyclostationary detection has certain advantages (e.g., robustness to uncertainty in noise power and propagation channel), it also has some disadvantages: (1) it needs a very high sampling rate; (2) the computation of SCD function requires large number of samples and thus high computational complexity; (3) the strength of SCD could be affected by the unknown channel; (4) the sampling time error and frequency offset could affect the cyclic frequencies.