II. STRUCTURES OF ENERGY DETECTOR AND PREAMBLE DETECTOR

The main goal of CR is to correctly identify the presence and absence of PU and allows the SUs to utilize the unused spectrum if it is not used by PUs. Under binary hypothesis testing, we consider the occurrence of two input events in observing signal x _i in some observation interval denoted by [Reference Lehtomäki, Vartiainen, Vuohtoniemi and Saarnisaari19]

(1) $$\eqalign{H_0 &: x_i = n_i \cr H_1 &: x_i = s_i + n_i,}$$

where i = 1, 2, 3, … N is number of samples. H ₀ represents the hypothesis that the observation vector consists of noise. H ₁ represents the hypothesis that the observation vector consists of noise and signal. The noise component n _i is assumed to be Additive White Gaussian random variable which is independent and identically-distributed (i.i.d) with zero mean normal distribution with variance n _i ~ ${\cal N}(0,\,\sigma^{2})$ , and s _i is the signal.

A) Energy detector

ED is non-coherent detector which detects the presence of signals by simply squaring its energy and comparing that energy around the carrier frequency with a certain threshold. The ED consists of a quadrature receiver with y _I and y _Q representing samples from In-phase and Quadrature branch, respectively. The samples after passing the squaring device, output of the integrator is denoted by

(2) $$y_I = y_Q = \left({1 \over N_0}\right)\int^T_0 r^2(t)\,dt,$$

where r(t) is input signal, N ₀ is noise spectral density.

Within observed sensing period, test statistic ED can be approximated as Y _ED  = y _I  + y _Q . At the observation time t, decision variable Y _ED will be compared with a detection threshold of ED denoted by λ ^ED . Threshold value is set to meet the target probability of false alarm p _fa according to the noise power. In the case of p _fa , the detector classifies the channel as busy when the actual channel is free. Probability of detection (p _d ) is the probability of correctly detecting the presence of PU when the actual channel is in busy state. The expression for p _fa and p _d can be given as [Reference Park9]

(3) $$p_{fa}^{ED}= 1 - F_{\chi}\left({\lambda^{ED} \over \sigma^2},2n_T\right),$$

where F _χ is cumulative distribution function (CDF) of standard chi-square random variable with k degree of freedom, n _T is the number of bits during the observation interval T, and has a variance σ = 1,

(4) $$p_{d}^{ED}= {\cal Q}\left(\sqrt{\psi_{ED}},\sqrt{{\lambda^{ED} \over \sigma^2}}\right),$$

where ${\cal Q}$ is generalized Marcum-Q function with non-central chi-square distribution of non-centrality parameter $s^{2}= \psi_{ED} = n_{T}(SNR)$ .

ED is a robust, universal detector which can be deployed in all systems without requiring any prior knowledge of the type of underlying modulation scheme employed. Also, ED is more energy efficient in terms of energy consumption and ED's computational complexity is lower than the most of the detectors. However, ED is inherently less reliable at low SNR and noise uncertainty condition.

B) Preamble detector

For coherent detection of signals, the sensing node has to attain time synchronism with the ongoing transmission. In packet-based systems, the process of acquiring time synchronism is facilitated by the transmission of a preamble in front of every packet, typically consisting of repetitions of a sequence of known symbols. The receiver performs a correlation of the known sequence with the received signal with varying time offsets. At the offset corresponding to time synchronism, the correlation is high due to the processing gain resulting from the repetition of the known symbols. This high correlation is both indicative of the signal presence and provides an estimate of the time offset. This carrier-sense based CCA using the correlation of the known preamble with the received signal is called PD [Reference Shin, Ramachandran and Roy10].

In simple terms, PD [Reference Shin, Ramachandran and Roy10,Reference Nagaraj, Khan, Schlegel and Burnashev20] performs correlation of the known signal, thus the high processing gain due to correct offset gives higher reliability than ED. However, for the successful operation of PD, it consumes a high amount of power. Hence, PD is also considered as power hungry detector. Also, the computational complexity of PD is much higher than ED.

The expression for p _fa and p _d of a PD can be given as [Reference Shin, Ramachandran and Roy10]

(5) $$p_{fa}^{PD}= 1 - F_{\chi}\left({\lambda^{PD} \over \sigma},2\right),$$

(6) $$p_d^{PD} = {\cal Q}\left(\sqrt{\psi_{PD}},\sqrt{{\lambda^{PD} \over \sigma^2}}\right),$$

where λ ^PD is the threshold setting for PD, the non-centrality parameter $s^{2}= \psi_{PD}=2n_{T}(SNR)$ is the output of the filters in in-phase, and quadrature branches at the correct offset. The correlation process of PD has a central chi-square distribution with 2 degree of freedom with a variance $(\sigma= \sqrt{n_{T}})$ .

III. PROPOSED SCHEME

Our proposed scheme is based on adaptive activation of energy efficient ED and reliable PD. As the first step of our proposed method, ED is used where it can easily make its own local decision. There are two thresholds λ₁ ^ED and λ₂ ^ED for the measured energy in the first step. If the sensed energy in the first step is between these two thresholds, the second step which involves the activation of PD is triggered to make an appropriate decision on the presence or absence of PU signal. Otherwise, the second step detector PD is not activated. In this way, we can enhance the detection performance and energy efficiency at the same time.

In our proposed scheme, when an SU confirms the presence or absence of the signal of PU, the second step PD detector is not activated at all; only the first step ED detector is sufficient to take the decision and increase the energy efficiency of our proposed scheme. The determination of double threshold values for ED is discussed in paper [Reference Zhu, Xu, Wang, Huang and Zhang14,Reference Peh, Liang, Guan and Zeng21]. For threshold setting, first, the boundary values $\bigtriangleup_{0}$ and $\bigtriangleup_{1}$ is defined according to the chosen false alarm probability of ED to determine the region of uncertainty. Based on $\bigtriangleup_{0}$ and $\bigtriangleup_{1}$ , the two threshold value λ₁ ^ED and λ₂ ^ED of ED is set accordingly. It should be noted that the region of uncertainty depends on the value of $\bigtriangleup_{0}$ and $\bigtriangleup_{1}$ chosen. If we choose the higher values for $\bigtriangleup_{0}$ and $\bigtriangleup_{1}$ , there is a greater region of uncertainty i.e. sensed energy is in between two thresholds values λ₁ ^ED and λ₂ ^ED . Hence, there is a higher chance of activation of second step detector PD and vice versa. The threshold setting λ₃ ^PD for PD is set according to the chosen false alarm probability which is the same false alarm probability of first step detector ED.

In step 1, if the sensed energy level by the SU is above threshold λ₂ ^ED , then decision D _i ‘11’ will be taken and it indicates the presence of a PU's signal i.e. condition H ₁₁ and if it is below threshold λ₁ ^ED , then decision D _i ‘00’ will be taken and it indicates the absence of a PU's signal i.e. condition H ₀₀. When the received energy of the PU's signal at the SU is between these two thresholds i.e. in the confused region then ED cannot take any decision D _i and further reports either ‘01’ or ‘10’ to FC to report uncertainty of the decision. For simplicity, it should be noted that ‘01’ or ‘10’ represents the same uncertainty of decision in our scheme. Now, the second step PD detector is activated. In the second step, the FC orders all the SUs to sense. The SUs sensing in the second step only need to report a one-bit decision; that is, ‘1’ means the presence of PU and ‘0’ means the absence of PU. Also, it should be noted that, in our proposed scheme, if SU is uncertain about the decision, it triggers the activation of second step PD to arrive at a concrete decision; the sensing result from the first step ED is no more considered and FC instructs all the SUs for sensing in the second step using reliable PD where the threshold is pre-defined for PD. Finally, the FC makes a decision by using a given hard decision fusion rule such as Majority, AND, or OR rule.

The decision D _i in the first step when ED is active is given as:

(7) $$D_i = \hbox{if} \left\{\matrix{O_i \lt \lambda_1^{ED},\hfill & H_{00}\hfill\cr \lambda_1^{ED} \leq O_i \leq \lambda_2^{ED},\hfill & H_{10}\,\hbox{or}\,H_{01}\hfill \cr O_i \geq \lambda_2^{ED},\hfill & H_{11}\hfill} \right.$$

In the second step, when the PD is activated, we find the decision variable V from Y _PD over M offset bits. Y _PD is the output from the PD receiver. Variable V is compared with PD threshold λ₃ ^PD to decide the presence or absence of PU signal.

The decision D _i in the second step when PD is active is given as:

(8) $$D_i=V=Y_{PD}^m \left\{\matrix{0 \hfill & 0 \leq \sum\limits_{i=1}^{N-K} O_i \leq \lambda_3^{PD} \hfill \cr 1 \hfill &\sum\limits_{i=1}^{N-K} O_i \gt \lambda_3^{PD} \hfill}, \quad m = 1, \ldots M,\right.$$

where m = 1, … M is the varying time offset bits where the PD receiver performs a correlation of the known sequence with the received signal.

The FC makes a final decision based on a voting rule. In this paper, we have considered widely used hard decision voting rule, ‘K out of N rule’. In this rule, the presence of PU is declared, if K SUs out of total N SUs declare the presence of PU. Similarly, the absence of PU is declared if K SUs out of total N SUs declare the absence of PU. The procedural flow of our proposed scheme block diagram is shown in Fig. 1.

Fig. 1. Procedural flow of proposed scheme.

Based on above discussion, we can say that our proposed scheme is energy efficient than PD as in our scheme the second step PD is only triggered when the O _i of first step ED lies in the confused region. The detection performance of our proposed scheme is higher as compared with ED due to the involvement of reliable PD. Since the involvement of cooperative PD is only triggered if the O _i values lies in confused region, we can say that the computational complexity of our proposed scheme is higher than ED and lower than PD i.e. in between ED and PD. Thus, making our proposed scheme as both energy efficient than PD and reliable than ED.

Algorithm 1 First Step Algorithm-Activation of Non-cooperative ED

Algorithm 2 Second Step Algorithm-Activation of Cooperative PD

A) False alarm and detection probabilities of proposed adaptive method

The use of double thresholds for ED allow the probabilities of false alarm and miss detection to be set arbitrarily low at the expense of an increased uncertainty region. This means that when the region of uncertainty increases, there is a involvement of reliable PD which keeps the low probabilities of false alarm and miss detection in the system. When the ED detector is active in first step, the false alarm probability $p_{fa,Step1}^{ED}$ , probability of no false alarm $p_{No \hbox{-}fa,Step1}^{ED}$ , probability of detection $p_{d,Step1}^{ED}$ , and miss detection probability $p_{m,Step1}^{ED}$ concerned with double thresholds of ED are given as follows:

(9) $$\eqalign{p_{fa,Step1}^{ED}&=\,P\{O_i \gt \lambda_2^{ED}\vert H_{00}\}\cr &=\,1 - F_{\chi}\left({\lambda_2^{ED} \over \sigma^2},2n_T\right),}$$

(10) $$\eqalign{p_{No-fa,Step1}^{ED}&=\,P\{O_i \leq \lambda_1^{ED}\vert H_{00}\} \cr &=\,1-\left(1 - F_{\chi}\left({\lambda_1^{ED} \over \sigma^2},2n_T\right)\right),}$$

(11) $$\eqalign{p_{d,Step1}^{ED}&=\,P\{O_i \gt \lambda_2^{ED} \vert H_{11}\} \cr &=\,{\cal Q}\left(\sqrt{\psi_{ED}},\sqrt{{\lambda_2^{ED} \over \sigma^2}}\right),}$$

(12) $$\eqalign{p_{m,Step1}^{ED}&=\,P\{O_i \leq \lambda_1^{ED}\vert H_{11}\} \cr &=1-\left({\cal Q}\left(\sqrt{\psi_{ED}},\sqrt{{\lambda_2^{ED} \over \sigma^2}}\right)\right).}$$

The probabilities of uncertainty under H ₀ and H ₁ are denoted by $\bigtriangleup_{0}$ and $\bigtriangleup_{1}$ , respectively, and are given by

(13) $$\eqalign{\bigtriangleup_{0}&=\,P\{\lambda_1^{ED} \lt O_i \leq \lambda_2^{ED}\vert H_{00}\} \cr &=\,1-p_{fa,Step1}^{ED} - p_{No-fa,Step1}^{ED},}$$

(14) $$\eqalign{\bigtriangleup_{1}&=\,P\{\lambda_1^{ED} \lt O_i \leq \lambda_2^{ED}\vert H_{11}\} \cr &=\,1-p_{d,Step1}^{ED} - p_{m,Step1}^{ED}.}$$

As we know in our proposed scheme, when the ED in first step is uncertain about the decision, it will trigger the activation of cooperative PD in second step. When the PD detector is active in second step, the false alarm probability $p_{fa,Step2}^{PD}$ , probability of no false alarm $p_{No-fa,Step2}^{PD}$ , probability of detection $p_{d,Step2}^{PD}$ , and miss detection probability $p_{m,Step2}^{PD}$ concerned with PD are given as follows:

(15) $$\eqalign{p_{fa,Step2}^{ED}&=\,P\{V \gt \lambda_3^{PD}\vert H_{0}\}\cr &=\,1 - F_{\chi}\left({\lambda_3^{PD} \over \sigma},2\right),}$$

(16) $$\eqalign{p_{No \hbox{-}fa,Step2}^{ED}&=\,P\{V \leq \lambda_3^{PD}\vert H_{0}\} \cr &=\,1-\left(1 - F_{\chi}\left({\lambda_3^{PD} \over \sigma},2\right)\right),}$$

(17) $$\eqalign{p_{d,Step2}^{PD}&=\,P\{V \gt \lambda_3^{PD}\vert H_{1}\} \cr &=\,{\cal Q}\left(\sqrt{\psi_{PD}},\sqrt{{\lambda_3^{PD} \over \sigma^2}}\right),}$$

(18) $$\eqalign{p_{m,Step2}^{PD}&=\,P\{V \leq \lambda_3^{PD}\vert H_{1}\} \cr &=\,1-\left({\cal Q}\left(\sqrt{\psi_{PD}},\sqrt{{\lambda_3^{PD} \over \sigma^2}}\right)\right),}$$

since we have used K out of N rule for the second step i.e. when the PD is active, the cooperative probabilities of false alarm $p_{Coop \hbox{-}fa,Step2}^{PD}$ and cooperative detection probabilities $p_{Coop \hbox{-}d,Step2}^{PD}$ can be respectively obtained as follows:

(19) $$p_{Coop \hbox{-}fa,Step2}^{PD} = \sum\limits_{K}^{N} \left(\matrix{N \cr K} \right) (1-p_{fa,Step2}^{PD})^{N-K} (p_{fa,Step2}^{PD})^K,$$

(20) $$p_{Coop \hbox{-}d,Step2}^{PD} = \sum\limits_{K}^{N} \left(\matrix{N \cr K} \right) (1-p_{d,Step2}^{PD})^{N-K} (p_{d,Step2}^{PD})^K.$$

The overall probability of detection for our adaptive activation of ED and PD scheme can be given as

(21) $$p_{d}^{ov} = p_{d,Step1}^{ED} + \bigtriangleup_{1} p_{coop-fa,Step2}^{PD}.$$

Similarly, the overall probability of no false alarm and false alarm for our scheme can be respectively given as

(22) $$p_{No \hbox{-}fa}^{ov} = p_{No-fa,Step1}^{ED} + \bigtriangleup_{0} p_{No-fa,Step2}^{PD}$$

(23) $$\eqalign{p_{fa}^{ov} &=\, 1-p_{No-fa}^{ov}\cr &=\,p_{fa,step1}^{ED} - \bigtriangleup_{0} (1-p_{fa,Step2}^{PD})}$$

IV. NUMERICAL RESULTS

Our simulation was conducted in MATLAB to investigate the performance of our proposed scheme. Additive White Gaussian Noise is imposed on the original signal x _i either for H ₀ or H ₁ condition. We assumed that there exists an error-free control channel available between the SUs and the FC for sending local decisions and observational values O _i of the confused region. For a fair comparison of our proposed scheme, we compared our scheme with conventional ED where only a single threshold based on the probability of false alarm of ED is defined for decision making process and double threshold using ED method of [Reference Zhu, Xu, Wang, Huang and Zhang14].

The receiver operating characteristics (ROC) curves of our proposed scheme as compared with other schemes is shown in Fig. 2. The ROC curve is obtained with SNR = 5 dB, Number of cooperative SUs = 6, $\bigtriangleup_{0} = \bigtriangleup_{1} = 0.1$ , time bandwidth product u = 5. As we can clearly see from Fig. 2, our proposed scheme has the higher detection performance compared with double threshold method using ED and conventional ED methods. Our scheme takes the advantage of reliable activation of PD at the second step if the decision from first step using ED is uncertain.

Fig. 2. ROC of proposed adaptive activation of ED and PD detector scheme.

Figure 3 shows the cooperative probability of detection curves against different SNR values when $\bigtriangleup_{0} = \bigtriangleup_{1} = 0.01$ . Figure 3 is plotted using $\bigtriangleup_{0} = \bigtriangleup_{1} = 0.01$ , SNR values ranges from −10 dB to 10 dB, number of cooperative SUs = 6, p _fa is set at 0.1, time bandwidth product u = 5. It is clear from Fig. 3 that our proposed adaptive activation of ED and PD scheme is better in detecting PU signal than the other schemes at different SNR ranges. Even at −10 dB SNR value, our scheme is clearly able to detect the PU signal. The scheme using double threshold ED and conventional ED suffer greatly at low SNR region due to the fact that the energy detector is highly susceptible to the noise uncertainty at the low SNR. The uncertainty of the decision in the confused region by first step ED detector activates the second step which is back-off by reliable PD detector in our scheme. Hence, our proposed scheme performance is superior to all other schemes. It should be noted that detection performance of PD is obviously higher and is almost equal to “1” as shown by the reference [Reference Shin, Ramachandran and Roy10], hence it is not shown in our simulation results.

Fig. 3. Comparison of probability of detection of our proposed scheme with other methods at different SNR when $\bigtriangleup_0 = \bigtriangleup_1 = 0.01$ .

Figure 4 shows the cooperative probability of detection curves against different SNR values when $\bigtriangleup_{0} = \bigtriangleup_{1} = 0.1$ . Figure 4 is plotted using $\bigtriangleup_{0} = \bigtriangleup_{1} = 0.1$ , SNR values ranges from −10 dB to 10 dB, number of cooperative SUs = 6, p _fa is set at 0.1, time bandwidth product u = 5. As we increase the uncertainty region, the second step detector PD is triggered to make the reliable detection. Hence it is clear from Fig. 4, that in our proposed adaptive activation of ED and PD scheme, PD is activated most of the time. so, the detection probability is higher for our scheme over all ranges of SNR as compared with other schemes.

Fig. 4. Comparison of probability of detection of our proposed scheme with other methods at different SNR when $\bigtriangleup_0= \bigtriangleup_1 = 0.1$ .

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.