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Abstract - Spectrum sensing become a tough task when cognitive radio (CR) user experiences deep shadowing, or fading and time varying nature of wireless communication channel. One of the major functions of CR is the fast and accurately spectrum sensing, this ensures the efficient utilization of the freely available wireless spectrum. We are presenting the cyclostationary feature based technique to detect the primary user, autocorrelation function is used to analyse and estimation of spectrum. In this paper we have investigating the probability of detection under different average SNR environments and for different sensing time in channel such as Nakagami-m and Nakagami-n fading channel. Since the feature detection is performed in time-domain, the real-time operation and low computational complexity can be achieved.
Keywords - Cognitive radio, spectrum sensing, cyclostationary feature, sensing time, probability of detection.
Cognitive radios (CR) are one of the recent techniques in wireless communication system for providing the solution of spectrum scarcity and, improving the utilization of unoccupied spread spectrum effectively . It is possible in the CR due to it changing transmissions and receptions parameters automatically; therefore some researchers give the name software defined radio with cognitive engine brain . Cognitive radios provide the opportunity to secondary user to access the unused frequency spectrum. Unlicensed users first sense the primary user's activities and access the spectrum holes if detected  . Therefore spectrum sensing is one of the main tasks in CR system; a great challenge of spectrum sensing for the cognitive radio has the ability to detect the presence of PU with the fast speed and precise accuracy .
Spectrum sensing technique currently focused on primary transmitter detection and they can be classified as matched filter detection, cyclostationary detection and energy detection  . Matched filter technique is one of the optimal techniques for signal detection in low SNR environments but it requires a former awareness of the primary user's signal that includes the modulation type and order, pulse shape, and packet format. Furthermore a matched filter needs an enthusiastic receiver for every primary user class and cannot be used for blind spectrum sensing. On the other hand an energy detector is most popular method , measuring only the received signal power, it does not require the former signals detector in spectrum sensing and signal recognition system. A considerable drawback is that an energy detector suffers from poor performance in low SNR scenarios and extremely faded environment . Periodicity of the signals characteristic is used to perform various signal processing tasks that includes detection, recognition and estimation of the received signals though computationally complex . A cyclostationary feature detector is favourable for spectrum sensing in low SNR scenarios and extremely faded environment due to its robustness against the feature of uncertainty in noise power .
In experiments, it has been seen that Nakagami fading is supported the local path loss and can be represented in most of the environments .Nakagami distribution is special case of Rayleigh and negative exponential distribution for a particular value of fading parameter .
In this paper, we have developed a new simulation model to study the performance of cyclostationary based spectrum sensing (CS-SS) over Nakagami m and Nakagami n fading channels. Our works in this paper are as follows:-
Analyzing the cyclostationary feature and exhibit the periodicity charactiristics.
Evaluating the cyclostationary feature based detector performance of a single CR user in terms of probability of detection and false alarm probability.
Consequence of fading parameter are analyzing over the probability of detection of a CR user.
Effect of different sensing time are also investigating over the detection probability.
Imapct of channel SNR on sensing performance is signify
The organization of the paper is as follows, in section II, the system model is consider and described. Cyclostationary based feature detector is discussed and derived the formula for false alarm probability and detection probability in AWGN channel and fading channels. The simulation results and discussion are summarized in section III. Section IV concluded with the scope of future work in this relation.
We are considering a single CR consists of the cyclostationary feature based detector in multipath communication system. CR makes the hard decision binary '0' or '1' by comparing with predetermined threshold. In the receiver the signals received from different multipath are averaging and auto-correlate to detect for making decision for hypothesis '0' or '1'. The system model is presented in fig (1).
Fig.1. System model of single CR user in multipath wireless communication.
The spectrum sensing performance at a particular frequency band can be formulated by the binary hypothesis H0 when primary user's signal is absent and another hypothesis H1 uses for primary user's signal present in the spectrum. Therefore our focus of spectrum sensing is to decide between the following two hypotheses,
y(t) is the received signal at the cognitive receiver, s(t) is the transmitted signal of the primary user and h is the gain of the channel. n(t) is the noise added in the transmitted signal due AWGN and fading channels.
CYCLOSTATIONARY FEATURE DETECTION TECHNIQUE
In wireless communication most modulated signals are carried with sinusoidal carriers, pulse trains, repeating codes, hopping sequences, cyclic prefixes, and signals are characterized as cyclostationary because their mean value and autocorrelation functions exhibit periodicity . Autocorrelation shows the degree of similarity between two signals, if the signals are same waveforms result gives the high amount of correlation. In practice, most primary signals contain deterministic feature, as a result we can utilize these feature and correlate the signals in time domain. Now we examine the autocorrelation detection in detail and evaluate its spectrum sensing performance.
Consider a complex deterministic signal s(t) and expressed as:
Where a is the envelope, f0 is the frequency and is the initial phase.
When the modulated signals are transmitted through the channel, the received signal:
y (t) =s (t) +n (t) .... (2)
The correlation between the original signal y(t) and corresponding y(t-T) is performed by the multiplying these two signals. By using the correlation characteristics, we define the test statics of the correlation signals (CS) as:
Where the factor (2N+1) is the number of signal computed after the autocorrelation.
denotes the observation time to sense the spectrum.
Spectrum sensing analysis:
The functional block diagram of the proposed technique is shown in fig (2). It is the technique in which the autocorrelation is taken for a certain number of samples. In practice, autocorrelation of the same waveforms we get the maximum amount of correlation, for a fixed time interval we search the peak of the correlation and compare it with the predetermined decision threshold . If detected peak is below than predetermine threshold then it assumed that the licensed spectrum is free and if the peak is above the threshold it is declared as the spectrum is occupied by the primary user.
Fig. 2. Block diagram of cyclostationary feature based spectrum sensing technique.
The cyclostationary feature based spectrum sensing technique can be implemented as shown in fig (2). For large observation sample N, pdf of the for both hypothesis H0 and H1 can be approximated by circularly symmetric complex Gaussian distributions, according to central limit theorem .
Where represent the circularly symmetric complex Gaussian distribution with mean and variance.Therefore, under H0 , the envelope of , r is Rayleigh distributed according .
Where I0(.) is the zeroth order modified Bessel function and A2 stands for a non-centrality parameter. For a particular threshold ï¬ the commutative density function (CDF) of the envelope under different hypothesis over AWGN channel are respectively given :
Where Q(.) is the generalized Marcum Q-function  .
To observe whether the primary user is present or not, we have to search peak value of within a period. When maximum selection diversity is employed
Where L is the number of diversity branches.
Under H0 and given variants, the false alarm probability for variable ,can be evaluated as-
Similarly the detection probability over AWGN can be obtained as
Now taking L=1,
For calculating the probability of detection, we can first specify the probability of false alarm and fix the corresponding value of threshold ï¬ from equation (10). For a fixed number of samples N the probability detection can be evaluated by substituting the ï¬ in equation (11).
Since probability of false alarm is not dependent upon the SNR because of under H0 no primary signal is present. Probability of detection given in equation (11) is written as a function of instantaneous SNR, ϒ, when h is varying due to fading.
In equation (12), the generalized Marcum-Q function can be represented in a circular contour integral. Therefore ,
Where - is the circular contour of radius r that encloses the origin. The singularities of the integrand are Z=0 and Z=1 therefore radius of the contour within the range of 0 to 1.
We are taking the fading channels, therefore the SNR of the received signal varies randomly and average probability of detection can be written as-
Where is the moment generating function (MGF) of SNRand E (.) is the expectation.
Length of observation samples:
Sensing time in spectrum sensing is defined as the time consumed to sense the spectrum whether it is occupied by primary user or free. Sensing time is depends upon the number of observation length of the samples. Cyclostationary feature based spectrum detection are observe for different data length are presented in fig (6). For short observation length it is complicated to distinguish between noise and the signal, on the other hand for longer observation it is easier to detect the signal of the primary users. But this exercise is time consuming and makes the real time execution more terrible.
A.Nakagami-n fading channels:
In this fading, channel is complex Gaussian with non-zero mean and with the direct line of sight (LOS) path. The envelope r = |h| is rician distributed. In such case, the signal strength follows the rician distribution; the pdf of will be given as ,
Where is the Rician factor.
Averaging this over Rician fading channel can be obtained by equation (16) to equation (11). Then ,
For k=0 the expression approaches to the Rayleigh distribution.
B. Nakagami-m fading channels:
Nakagami-m fading is another generalized fading channel in multipath wireless communication. Nakagami fading is defined by parametric gamma function for its rapid fading in high frequency long distance propagation. In wireless communication Nakagami fading is characterized as:
Nakagami fading paramete m shows the severence of fading channel.
m ranges from 1/2 to ∞.
For special case of m=1, the distribution reduces to Rayleigh distribution and for m=0.5 it becomes one sided Gaussian distribution.
For m=∞, the distribution become no fading with AWGN.
Power of the Nakagami distribution follows the gamma distribution.
The pdf of for Nakagami distribution will be given as ,
Where m is the Nakagami fading parameter, Ó¶ (.) is the Gamma function and ï€ is the average value of SNR.
IV. Results and Discussions
In this section, numerical and simulation results are presented to analyse the spectrum sensing performance based on our proposed technique. Fig. (3) and fig. (4) shows the receiver operating curve for fading channel at average SNR of 5 dB and m=1, Probability of false alarm taken in the range of 0 to 1 and measure the corresponding probability of detection. Fig (3) shows the ROC curve for Rician fading channel for different value of Rician parameter k=0, 1, 2, 3, from result it has been seen that as fading parameter increases the effect of fading decreases and probability of detection increases. Rayleigh channel characteristic is achieved for rician parameter k =0 and noticed the most severance of fading channel.
Fig.3. ROC curve (Pd Vs Pf) for different rician fading channel parameters at average SNR 5 dB.
Fig.4. Performance of single cognitive user for different weibull fading channel parameter at average SNR 5 dB.
Fig (4) depicted the performance of single cognitive user in the Nakagami-m fading channel for different fading parameters m considered. In simulation we have taken m=1, 2, 3, 4, 5 are taken; from the result it has been clear that the sensing performance is better in Nakagami-n fading channel.
Fig (5) depicted the performance of Nakagami m and Nakagami n channel in different SNR environment, taking the observation samples 50 and corresponding sensing time........
Nakagami n parameters are considered 0 and 2 and at fading parameter 0 it characterized the Rayleigh fading channel, and Nakagami m parameter is set at m=2. We observe that cyclostationary detection perform better for Nakagami n channel as compared to nakagami m channel. The result is compared to the energy detection based spectrum sensing ,
and we achieved better result in cyclostationary feature detection technique.
Fig (6) shows the performance of CR at different observation length and therefore different sensing time. From result it has been observe that, to achieve better detection performance in fading channel the length of observation samples should be large, but it has a significantly drawback is to increase in sensing time.
Fig.5. Pd Vs average SNR for different fading channel (N=50, Pf 0.1).
Fig.6. Pd Vs Observation length for different fading channels (average SNR is considered 5 dB).
In this paper, we have focused on the cyclostationary based spectrum sensing technique and autocorrelation function used for analyse the spectrum. Since the sensing time is most important parameter in the wireless communication, and that are discussed in our paper. Probability of detection is measured for fading channels under different SNR environments and for different sensing time is measured. It is analysed that for low SNR condition the observation length should be larger, therefore sensing time would be high and for high SNR condition we are getting high probability of detection.