1.4 Non-Cooperative Sensing
1.4.1 Feature Detection Strategies
The feature detection approaches assume that a PU is transmitting information to a primary receiver when a SU is sensing the primary channel band. The elaboration of sensing techniques that use some prior information about the transmitted signal is interesting in terms of performance.
In fact, feature detection algorithms employ knowledge of structural and statistical properties of PU signals when making the decision. Such properties include for example the cyclostationarity property, the autocorrelation property or the finite alphabet property.
1.4.1.1 Cyclostationarity Based Detection
The most known feature sensing technique is the CD [15]. Cyclostationary processes are ran- dom processes for which statistical properties such as mean and autocorrelation change periodi- cally as a function of time. The theory of cyclostationarity is relevant to various fields like telecom- munications, mechanics, biology, econometrics etc. [16]. For example, in mechanics, periodicity is due to gear rotation and in econometrics, it is due to seasonality. In telecommunications and radar applications periodicity is due to modulation, sampling, multiplexing and coding operations [16].
Wireless communication signals typically exhibit cyclostationarity at multiple cyclic frequen- cies that may be related to the carrier frequency, symbol, chip, code or hop rates, as well as their harmonics, sums and differences. These periodicities can be exploited to design powerful sensing algorithms for CRs. Cyclostationarity based detectors have the potential to distinguish among the PUs, SUs, and interference exhibiting cyclostationarity at different cyclic frequencies. Moreover, random noise commonly does not possess the cyclostationarity property. Cyclostationarity based detection has received a considerable amount of attention in the literature. Recent bibliography on cyclostationarity, including a large number of references on cyclostationarity based detection, is provided in [16].
The cyclic autocorrelation function at some lagland some cyclic frequencyαcan be estimated from samplesxby
ˆ
rl(x, α)= 1 p−l
p−l−1X
n=0
xn+lx∗ne−jαn l≥0 (1.6) wherep is the length of the PU signal in samples. The cyclic autocorrelations are non-zero for cyclostationarity based PU. This property is exploited to detect a PU by testing whether the ex- pected value of the estimated cyclic autocorrelation is zero or not. In [17], an optimum spectral correlation detector in stationary additive white Gaussian noise (AWGN) is presented. However, the scheme requires lot of information related to the PU like signal phase, modulation type and its parameters, such as carrier frequency, pulse shape and symbol rate, which makes the scheme im- practical. In [18], authors have proposed a generalized likelihood ratio test (GLRT) for detecting the presence of a cyclic frequency with an asymptotic constant false alarm rate (CFAR). Howe- ver, it may be desirable to test the presence of multiple cyclic frequencies to improve the detector performance. In [19], authors introduce a GLRT detector based on multiple cyclic frequencies, where the CFAR property is retained over the set of cyclic frequencies. It is particularly suitable for signals with multiple significant cyclic frequencies.
A GLRT may be obtained from the likelihood ratio test by replacing the unknown parameters with their maximum likelihood estimates. Assuming thatsis cyclic with cycle frequencyα,
ˆr=[Re{ˆrl1(α)}, ...,Re{ˆrlK(α)},Im{ˆrl1(α)}, ...,Im{ˆrlK(α)}] (1.7) denotes a 1×2K vector containing the real and imaginary parts of the estimated cyclic auto- correlations forK time delays at the cyclic frequency stacked in a single vector [18]. The GLRT statistic is given by [18]
ΥCD(x)=ˆrΣˆ−1ˆrT (1.8) whereΣˆ is an estimate of the covariance matrixΣ∼=cov{ˆr}[18].
To detect the cyclostationary over the received signal we make the choice of the statistical test proposed by Dandawate and Giannakis [15]. This test uses the asymptotic properties of the cyclic autocorrelation function estimates. It has been shown in [15] that under hypothesisH0, regardless of the distribution of the input data, the distribution ofT(x)converges asymptotically to a central χ2distribution with2pdegrees of freedom wherepis an integer withp≥1. This makes it possible to analytically calculate the probability of false alarm for a large enough observation lengthT for a given threshold. This leads to an asymptotically constant false alarm rate test. UnderH0, one can write :
Tlim→∞ΥCD(x)=χ22p (1.9) Hence, the (asymptotic) probability of false alarm for this detector with thresholdγCDis given by
PF A,CD=1−G
³γCD 2 , K
´
(1.10) whereG(.)is the (lower) incomplete gamma function [20].
The main advantage of the cyclic autocorrelation function is that it differentiates the noise energy from the modulated signal energy. Therefore, a CD can perform better than other detectors in discriminating against noise due to its robustness to the uncertainty in noise power. However, it is computationally complex and requires a significantly long observation time.
1.4.1.2 Autocorrelation Based Detection
Many communication signals contain redundancy, introduced for example to facilitate syn- chronization, by channel coding or to circumvent inter-symbol interference. This redundancy oc- curs as non-zero average autocorrelation at some time lagl. Based on the system model given in Section 1.3, the autocorrelation function at some laglcan be estimated from :
ˆ
rl(x)= 1 p−l
p−l−1X
n=0
xn+lx∗n l≥0 (1.11)
Any signal except for the white noise case will have values of the autocorrelation function different from zero at some lags larger than zero. Although some might be exactly zero depending on the zero crossings. In practice, this simplistic view will be obscured by the fact that we have to estimate the autocorrelation function locally on stochastic signals and noise. This will inevitably generate spurious values that are not accounted above. The autocorrelation function is proportional to the received signal variance and its use in spectral sensing is therefore also dependent on either knowing the variance of the noise without signal or deriving reliable estimates of the variance based on long signal observations. If we assume that the noise level is constant, then the observed variance of the received signal is lower bounded by the noise itself. Several options for deriving the noise variance or some average received signal variance are open.
In [21], authors have proposed an autocorrelation-based detector for orthogonal frequency division multiplexing (OFDM) signals. OFDM has developed into a popular scheme for wide- band digital wireless. This detector is limited to the case when the PU is using OFDM. Another autocorrelation-based detector was proposed in [22]. This detector relies on the fact that the au- tocorrelation function of the oversampled communication signal exhibits non-zero values at non- zero lags, whereas for the white noise (i.e., no signal) these values will be zero. We present in this section a summary of the autocorrelation-based detector given in [22].
To detect the existence/non existence of a signal we use functions of the autocorrelation lags where the autocorrelation is based on (1.11). Therefore, the autocorrelation-based decision statistic is given by [22]
ΥAD(x)=
XL l=1
wlRe{ˆrl} ˆ
r0 (1.12)
where the number of lags,L, is selected to be an odd number. The weighting coefficientswlcould be computed to achieve the optimal performance. They are given by
wl=L+ 1 +|l|
L+ 1 (1.13)
With decision thresholdγAD, the probability of false alarm of this detector is
PF A,AD=Q
γAD
"
γAD2 p + 1
2p XL
l=1
w2l
#−12
(1.14)
whereQis the generalized Marcum Q-function [20].
1.4.1.3 Other Feature Sensing Methods
Other feature spectrum sensing methods include matched filtering and multitaper spectral es- timation. Matched filtering is known as the optimum method for detection of PUs when the trans- mitted signal is known [23]. The main advantage of matched filtering is the short time to achieve a certain probability of false alarm or probability of a miss detection [24] as compared to other me- thods that are discussed in this section. However, matched filtering requires the CR to demodulate received signals. Hence, it requires knowledge of the PUs signaling features such as bandwidth, operating frequency, modulation type and order, pulse shaping, frame format, etc. Multitaper spec- tral estimation is proposed in [25]. The proposed algorithm is shown to be an approximation to maximum likelihood power spectral density (PSD) estimation. For wideband signals it is nearly optimal. Although the complexity of this method is less than the maximum likelihood estimator, it is still computationally demanding.