Reliable spectrum sensing scheme based on dual detector with double-threshold for IEEE 802.22 WRAN

Abstract

In this paper, a reliable spectrum sensing (SS) scheme using dual detectors for IEEE 802.22 WRAN has been presented. In dual or double detectors, first one detector is energy detector (ED) with fixed threshold (FT), while second one is ED with adaptive double threshold (ADT). Numerical results shows that proposed reliable scheme improves detection performance and outperforms the cyclostationary based sensing method and adaptive SS by 12.9% and 15% at −8 dB signal-to-noise ratio (SNR), respectively. It also shows that the proposed scheme takes smaller detection time period than cyclostationary detection and adaptive SS scheme in the order of 5 ms and 0.8 ms at −20 dB SNR, respectively. Moreover, the scheme analyzes in conjunction with cooperative spectrum sensing (CSS) where each CRs work together in order to take final or global decision. It is observed that the proposed sensing scheme with CSS achieves spectrum detection performance in the order of 0.9 for SNR value of as low as −17.5 dB when numbers of CRs are ten.

Keywords

Cognitive radio networks energy detector fixed threshold double-threshold adaptive spectrum sensing cooperative spectrum sensing

1. Introduction

Day-by-day the numbers of mobile users are increasing, which will certainly create bandwidth crises due to limited spectrum availability. Cognitive radio is future technology, which is capable of solving the spectrum scarcity problem. In CR network, Unlicensed CR users use the unused licensed band of primary users (PU) while PU is not active. There are several methods to sense the spectrum of PU signal, such as matched filter detection, energy detection and cyclostationary feature detection [2,3,17,20,25]. Matched filter and cyclostationary feature detection, both techniques provide better performing results under low SNR in wireless communication systems (WCS). But, they require the prior information of PU’s signal. At the other end, energy detectors are the most common way of spectrum sensing because it does not require the prior information of PU’s signal and has low computational complexity. Sometimes this technique is also known as Blind spectrum sensing technique. However, it is well known that such a method does not perform well under low SNR. In [5], authors have proposed two-stage CR system, which consists of coarse and fine detection stages. But this system is not applicable for low level SNR signals. In [27], authors proposed another two-stage sensing technique, where first stage consists energy detector while second stage consists one-order feature sensing to detect weak signals. Further in [18], authors have proposed Two-stage spectrum sensing technique to improve detection performance. This technique carries two detectors, first stage consists energy detector and second stage consists cyclostationary detector to give better sensing performance, however it is computationally more complex and requires longer sensing time. In [9], authors have proposed another adaptive spectrum sensing scheme. In this scheme, out of two stages only one of the detection stage runs at a time, which is based on the estimated SNR. Due to the use of cyclostationary detector in [9] its implementation is complicated. However, to the best of available sources none of these technique focused on spectrum sensing failure problem [15].

In this paper, focus is on spectrum sensing failure problem, improved detection performance, and measured sensing time, which has been proposed in a reliable spectrum sensing scheme in CRN. The proposed spectrum sensing scheme considers dual detectors, which shows two-stages, first stage detector implies ED with fixed threshold (ED_FT), whereas second stage detector implies ED with adaptive double-threshold (ED_ADT) to enhance the detection performance at a fixed decided probability of false alarm ( $P_{f}$ ) i.e. 0.1.

In the first stage, energy detector detects the PU signal and calculates signal energy (X). Then compares with certain FT (γ), if X is greater than or equal to γ, the channel is declared to be busy, otherwise, ED_ADT is performed sensing operation in the second stage. The adaptive threshold (λ) of second stage detector compares with signal energy (X), if X is greater than or equal to ADT (λ), shows channel is occupied else unoccupied and can be used by CU users.

The selections of ADTs ( $λ_{1}$ and $λ_{2}$ ) are based on upper and lower boundaries of the noise uncertainty range [21]. We analyze the performance of propose sensing scheme in terms of probabilities of detection ( $P_{d}$ ), probability of error ( $P_{e}$ ) and SS time (T). Thus, numerical results show that propose detection scheme optimizes detection performance and lesser sensing time. The thresholds γ and λ, that improves the $P_{d}$ under this approach, at a fixed $P_{f}$ i.e. 0.1.

We further propose CSS with proposes reliable SS scheme to further improve the reliability and detection performance of cooperative decision. Here, all the CRs perform local observation by using two-stage SS detectors. The thresholds are selected as per the value of the noise uncertainty at each CR user. If the collected energy value falls between or outside the two thresholds, the local decision will be made and reported to the fusion center (FC) in the form of binary bit i.e. either 0 or 1. The FC will make a final decision using hard decision OR rule. In the propose model we have used OR rule because it has better detection performance when the number of cooperating CR users is large [1], and provides slightly better performance at low $P_{f}$ [23].

The novelty of this paper that under reliable SS scheme we consider two-stages for detecting the PU signal, first stage carries ED_FT which takes lesser sensing time and makes fast processing. While second stage based on ED_ADT which mitigates sensing failure problem. Final resultant of both stages provide well perform at low SNR levels, reduce computational complexity, and improve detection performance as well.

The rest of the paper is organized as follows: Section 2 presents system description. Section 3 describes proposed system model. Section 4 shows the numerical results and analysis. Finally, Section 5 concludes the paper.

2. System description

There is a mathematical expression to detect the PU signal by using following hypothesis for received signal [11,25], $x (n) = \{\begin{matrix} w (n), & H_{0}, \\ s (n) h (n) + w (n), & H_{1} . \end{matrix}$ (1) $x (n)$ shows signal received by each CR user. $s (n)$ is the PU licensed signal, $w (n)$ shows AWGN (additive white Gaussian noise) with zero mean i.e. $w (n) \sim N (0, σ_{w}^{2})$ and $σ_{w}^{2}$ is noise variance, $h (n)$ is the gain of Rayleigh fading channel where wireless channel is Rayleigh exist between the PU and the CR users. $H_{0}$ is the null hypothesis, shows the absence of PU and $H_{1}$ is the alternative hypothesis, shows that PU is present.

2.1. Energy detector

Energy detector plays an important role in CRN in order to detect PU signal due to its simplicity and easy to implement [24]. It measures the energy of PU signal and compares it to a threshold (γ) in order to determine whether the PU signal is present or absent. To determine signal energy there is a mathematical formulation given as [6], $X = \frac{1}{N} \sum_{n = 1}^{N} {| x (n) |}^{2},$ (2) where $x (n)$ shows received PU signal, N shows number of samples and X shows the energy of $x (n)$ . The value of threshold is set to meet the desired target $P_{f}$ as per the power of noise signal. The probability of detection $P_{d}$ can be also identified. The expression for $P_{d}$ and $P_{f}$ can be defined as [16], $\begin{array}{rclr} P_{d} = Q (\frac{λ - N (σ_{S}^{2} + σ_{ω}^{2})}{\sqrt{2 N {(σ_{S}^{2} + σ_{ω}^{2})}^{2}}}), & (3) \\ P_{f} = Q (\frac{λ - N σ_{ω}^{2}}{\sqrt{2 N σ_{ω}^{4}}}), & (4) \end{array}$ where $σ_{ω}^{2}$ and $σ_{S}^{2}$ are the noise variance and signal variance, respectively. $Q ()$ denotes Gaussian tail probability Q-function. The total error rate is the addition of the probability of false alarm ( $P_{f}$ ) and the probability of missed detection alarm ( $P_{m}$ ). Thus, the total error rate is given by $P_{e} = P_{f} + (1 - P_{d}),$ (5) where $(1 - P_{d})$ shows the probability of missed detection alarm ( $P_{m}$ ).

2.2. Adaptive double-threshold scheme for spectrum sensing

Most of the ED [28] are based on fixed single threshold scheme, in which detected PU signal compares with threshold in order to identify whether PU is present or not. These kind of EDs are appearance difficulty when noise uncertainty increases for a CR and thus degrades its sensing reliability, Moreover, this may not be optimum in case of low SNR where the performance of fixed single threshold (γ) based detector can vary from the targeted performance metrics substantially.

In [4], authors have shown the curve of PU signal and noise signal in which authors discussed that detection of PU signal from noise signal is easy if both signals do not overlap to each other. Suppose detector receives PU signal then it declares $H_{1}$ i.e. channel is occupied, and if gets noise signal it declares $H_{0}$ i.e. channel is unoccupied. But, if PU signal and noise both intersects to each other then it is very difficult to sense desired signals. The area between $λ_{1}$ and $λ_{2}$ , known as confused region [4]. $λ_{1}$ is called upper bound and $λ_{2}$ is lower bound.

Using single threshold, detection between noise and PU signal is difficult under confused region. To overcome this problem we considered adaptive two threshold scheme to define the local decision at the CR user as following logic function rule (LR), $LR = \{\begin{matrix} H_{0} = 0, & X ⩽ λ_{2}, \\ H = M, & λ_{2} < X < λ_{1}, \\ H_{1} = 1, & λ_{1} ⩽ X . \end{matrix}$ (6) M is the quantization decision and X denotes received PU signal energy by CR user.

Fig. 1.

Confused region is divided into four equal parts using quantization method.

There is another double thresholds based scheme proposed by [22], to reduce the average number of sensing bits to the receiver. But, the deductions are achieved at the expense of some sensing performance loss which is sensing failure problem. In order to remove this problem successfully, two thresholds $λ_{1}$ and $λ_{2}$ are used to help the decision of the CR. In Fig. 1, two-bits are using by quantization process to divide confused region into four equal parts such as ( $λ_{2} A–AB–BC–C λ_{1}$ ), where $λ_{2}$ , A, B, C and $λ_{1}$ are sub-thresholds (ST) and their values are defined as $\begin{array}{rclr} ST = \{\begin{matrix} A = λ_{2} + D, \\ B = A + D, \\ C = B + D, \\ λ_{1} = C + D, \end{matrix} & (7) \\ D = \frac{(Upper bound - Lower bound)}{No . of quantization intervals} = \frac{(λ_{1} - λ_{2})}{4}, & (8) \\ M = \{\begin{matrix} 00, & λ_{2} < X ⩽ A, \\ 01, & A < X ⩽ B, \\ 10, & B < X ⩽ C, \\ 11, & C < X < λ_{1} . \end{matrix} & (9) \end{array}$

Now, the false alarm probability ( $P_{f}$ ) of conventional ED with single threshold can be calculated as [16] $P_{f} = Q (\frac{λ - N σ_{ω}^{2}}{\sqrt{2 N σ_{ω}^{4}}}),$ (10) where $Q ()$ is known as Gaussian tail probability Q-function, and noise variance is represented by $σ_{ω}^{2}$ . Given the target false alarm probability $\overline{P_{f}}$ , the threshold λ can be calculated as $λ = Q^{- 1} (\overline{P_{f}}) \times \sqrt{2 N σ_{ω}^{4}} + N σ_{ω}^{2},$ (11) where $Q^{- 1} ()$ denotes the inverse Gaussian tail probability Q-function. Assuming that the noise uncertainty in the wireless network environment is defined as $[1 / ρ σ_{ω}^{2}, ρ σ_{ω}^{2}]$ , where ρ is a constant parameter that computes the size of the uncertainty and $ρ > 1$ . In the proposed double threshold decision, the value of maximum noise variance shows the value of upper threshold $λ_{1}$ and the value of minimum noise variance shows the value of lower threshold $λ_{2}$ . Hence $\begin{array}{rclr} λ_{1} = Q^{- 1} (\overline{P_{f}}) \times \sqrt{2 N ρ σ_{ω}^{4}} + N ρ σ_{ω}^{2}, & (12) \\ λ_{2} = Q^{- 1} (\overline{P_{f}}) \times \sqrt{2 N / (ρ σ_{ω}^{4})} + N / (ρ σ_{ω}^{2}) . & (13) \end{array}$

Suppose that $x_{i}$ is the normalized version of received sample $x (n)$ , the cumulative distribution function (CDF) of the ED_ADT, can be calculated as $f_{Y_{i}} (y) = Pr (| x_{i} |^{2} ⩽ y^{(2 / p)}) .$ (14)

In Eq. (14), p is an arbitrary constant, has value two. The zero-mean primary signal $s (n)$ with average power $σ_{S}^{2}$ is independent of the circularly symmetric complex Gaussian noise $w_{i} (n)$ with variance $σ_{w}^{2}$ , and $h_{i} (n)$ denotes the Rayleigh faded channel that is independent of $w_{i} (n)$ . Hence, $| h_{i} (n) |$ is Rayleigh distributed with variance $σ_{h}^{2} / 2$ . Thus, the probability distribution function (PDF) of the ED_ADT detector for $H_{j}$ (where $j = 0, 1$ ) is given as $f_{Y_{i} | H_{j}} (y) = [\frac{2 \times y^{((2 - p) / p)}}{p}] \times f_{| x_{i} |^{2} | H_{j}} (y^{(2 / p)}),$ (15) where $f_{| x_{i} |^{2} | H_{0}}$ and $f_{| x_{i} |^{2} | H_{1}}$ are exponentially distributed as follows $\begin{array}{rclr} f_{| x_{i} |^{2} | H_{0}} (y) = exp [- y], y ⩾ 0, & (16) \\ f_{| x_{i} |^{2} | H_{1}} (y) = [\frac{1}{(1 + γ)}] \times exp [- \frac{y}{(1 + γ)}], y ⩾ 0 . & (17) \end{array}$

Note that $y = (σ_{h}^{2} \times σ_{S}^{2}) / σ_{n}^{2}$ is the average signal-to-noise ratio (SNR) of the sensing channel. Finally, by using Eqs (15) and (16) we have $f_{Y_{i} | H_{0}} (y) = [\frac{2 \times y^{((2 - p) / p)}}{p}] \times exp [y^{(2 / p)}], y ⩾ 0 .$ (18)

Now the probability of false alarm for ED_ADT will be calculated as $\begin{array}{rclr} P_{f}^{ED_ADT} = \int_{λ_{2}}^{+ \infty} f_{Y_{i} | H_{0}} (y) d y, & (19) \\ P_{f}^{ED_ADT} = \int_{λ_{2}}^{+ \infty} [\frac{2 \times y^{((2 - p) / p)}}{p}] \times exp [y^{(2 / p)}] d y, & (20) \\ P_{f}^{ED_ADT} = exp (- λ_{2}^{2 / p}) . & (21) \end{array}$

Using Eqs (15) and (17), the probability distribution function (PDF) of the ED_ADT detector for $H_{1}$ is computed as $f_{Y_{i} | H_{1}} (y) = [\frac{2 \times y^{((2 - p) / p)}}{p \times (1 + γ)}] \times exp [- \frac{y^{(2 / p)}}{(1 + γ)}], y ⩾ 0 .$ (22)

Now the probability of detection for ED_ADT can be obtained as $\begin{array}{rclr} P_{d}^{ED_ADT} = \int_{λ_{2}}^{+ \infty} f_{Y_{i} | H_{1}} (y) d y, & (23) \\ P_{d}^{ED_ADT} = \int_{λ_{2}}^{+ \infty} [\frac{2 \times y^{((2 - p) / p)}}{p \times (1 + γ)}] \times exp [- \frac{y^{(2 / p)}}{(1 + γ)}] d y, & (24) \\ P_{d}^{ED_ADT} = exp (- \frac{λ_{2}^{2 / p}}{1 + γ}) . & (25) \end{array}$

Similarly, the total error rate ( $P_{e}$ ) for ED_ADT can be calculated as $P_{e}^{ED_ADT} = P_{f}^{ED_ADT} + (1 - P_{d}^{ED_ADT}),$ (26) where $(1 - P_{d}^{ED_ADT})$ shows the probability of missed detection alarm ( $P_{m}^{ED_ADT}$ ). If detected signals fall inside any one of the quantized interval, it will generate its respective decimal values (DV) as $DV = \{\begin{matrix} If M = 00, & respective decimal value – 0; \\ If M = 01, & respective decimal value – 1; \\ If M = 10, & respective decimal value – 2; \\ If M = 11, & respective decimal value – 3 . \end{matrix}$ (27)

Equation (27) shows the decimal values (DV), which are compared with threshold ( $λ_{1}$ , $λ_{2}$ and λ) to make local decision at a fixed $P_{f}$ i.e. 0.1. Outside the confused region it produces binary bit i.e. either 0 or 1 depends on signal position.

3. Proposed system model

Fig. 2.

Proposed model: Dual detectors for spectrum sensing. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/JHS-150521.)

Algorithm 1.

Propose reliable SS detector scheme

3.1. Reliable spectrum sensing scheme

Figure 2 illustrates the proposed system model of dual detectors for SS scheme carries two detectors. First stage consists of energy detector (ED) with single threshold, and second stage consists of energy detector with adaptive double-threshold (ED_ADT) scheme. If ADT scheme is used in the first stage, it will take somewhat more time to sense PU signal, while ED takes lesser time to detect PU signal. But under spectrum sensing failure problem, it does not perform well. That’s why in second stage we have used ADT based ED. Algorithm 1 for reliable SS scheme.

Probability of false alarm of dual detectors will be $\begin{array}{rclr} P_{F}^{Dual_detector} = P_{r} \times P_{f}^{ED} + (1 - P_{r}) \times P_{f}^{ED_ADT}, & (28) \\ P_{F}^{Dual_detector} = P_{r} (P_{f}^{ED} - P_{f}^{ED_ADT}) + P_{f}^{ED_ADT} . & (29) \end{array}$

Probability of detection of dual detectors will be $\begin{array}{rclr} P_{D}^{Dual_detector} = P_{r} \times P_{d}^{ED} + (1 - P_{r}) \times P_{d}^{ED_ADT}, & (30) \\ P_{D}^{Dual_detector} = P_{r} (P_{d}^{ED} - P_{d}^{ED_ADT}) + P_{d}^{ED_ADT}, & (31) \end{array}$ where $P_{d}^{ED}$ and $P_{d}^{ED_ADT}$ are the probability of detection throughout of ED and ED_ADT detector respectively, $P_{f}^{ED}$ and $P_{f}^{ED_ADT}$ are the probability of false alarm of ED and ED_ADT detector, respectively. $P_{r}$ is the probability factor that a channel would be reported to energy detector and therefore, the probability that a channel would be reported to ED_ADT detector will be $(1 - P_{r})$ . $P_{r}$ dependents on SNR of the channels to be sensed i.e. if $P_{r} < 0.5$ shows channel is very noisy, and $P_{r} ⩾ 0.5$ shows channel is less noisy or has a good SNR. Hence, the overall probability of false alarm and probability of detection directly depend on $P_{r}$ ( $0 ⩽ P_{r} ⩽ 1$ ).

3.2. First stage (ED_FT)

Figure 3 shows the internal architecture of ED with single threshold (γ). Here, input PU licensed signal received by square law device, which shows detected signal energy (X) and compared with single threshold to make a final decision to determine whether the PU is present or absent, $X = \frac{1}{N} \sum_{n = 1}^{N} {| x (n) |}^{2} .$ (32)

First stage local decision rule (LF) used by energy detector with single threshold is given by $LF = \{\begin{matrix} 1, & γ ⩽ X, \\ 0, & X < γ . \end{matrix}$ (33)

3.3. Second stage (ED_ADT)

Fig. 3.

Internal architecture of energy detector with Single threshold (ED). (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/JHS-150521.)

This is a simple kind of a circuit of ED except threshold. In this model we used adaptive threshold instead of fixed threshold as used by first stage. Suppose PU signal is not detected by first stage then the second stage detector will try to detect PU signal. Figure 4 depicts internal model of ED with ADT in which firstly square law device (SLD) receives the sensed PU signal and computes signal energy (X). On the basis of value of X, ED_ADT choses appropriate threshold and compare with X to decide PU is present or absent. Further SLD, there are two parts, in upper part if detected energy values (X) are greater than or equal to $λ_{1}$ , it will show $H_{1}$ (signal presented), or less than $λ_{2}$ show $H_{0}$ (signal absent). But, if detected energy values (X) fall between $λ_{1}$ and $λ_{2}$ then it consider lower part and follow quantization process to produce its respective decimal values ( $DV$ ) as shown in Eq. (27) under the consideration that $P_{f}$ should be 0.1.

Fig. 4.

Internal architecture of energy detector with adaptive double-threshold (ED_ADT). (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/JHS-150521.)

If detected energy values (X) fall outside or between $λ_{1}$ and $λ_{2}$ , then the proposed ED_ADT model generates value of m or n with the help of Eqs (6), (9) and (27), respectively, $\begin{array}{rclr} m = \{\begin{matrix} 0, & X ⩽ λ_{2}, \\ 1, & λ_{1} ⩽ X, \end{matrix} & (34) \\ n = DV, λ_{2} < X < λ_{1}, & (35) \end{array}$ where m is the output values of upper part and n is the output value of lower part. After that values of m and n are added using adder, $Y = (m + n) .$ (36)

Finally, using Eqs (34), (35) and (36) the local decision (LS) of second stage or ED_ADT is expressed as $LS = \{\begin{matrix} 1, & λ ⩽ Y, \\ 0, & Y < λ . \end{matrix}$ (37)

Equation (37), equating the resultant value (Y) to threshold (λ) to maintain overall system probability of false alarm ( $P_{f}$ ) 0.1. If Y is greater than or equal to λ then signal is present otherwise absent.

3.4. Cooperative Spectrum Sensing with propose reliable SS detector

CSS technique is used to mitigate shadowing and fading in order to improve sensing performance of both local sensing performance and global sensing performance in a CRN [10,13,19,29]. Here all CRs are using two-stage spectrum sensing scheme to sense PU signal. Once all CRs have taken the local decision individually, they send their local decisions in the form of binary bit i.e. 0 or 1 to the FC over error free orthogonal channels to take final decision. In Fig. 5, let there are k numbers of CRs, all of them transmit local decision $L_{i}$ to a common single FC.

Fig. 5.

CSS technique with proposed reliable SS detector scheme. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/JHS-150521.)

Finally, FC combines the binary bit decisions of all CRs where each CR have proposed scheme i.e. two-stage detectors, and makes global decision to show presence or absence of PU signal as follows $\begin{array}{rclr} F = \sum_{i = 1}^{k} L_{i}, & (38) \\ L_{i} = \{\begin{matrix} 1, & γ ⩽ X_{i} or λ ⩽ Y_{i}, \\ 0, & X_{i} < γ or Y_{i} < λ . \end{matrix} & (39) \end{array}$

In Eq. (39), F is the sum of the all local decisions $L_{i}$ from the CRs. The FC considers a hard decision OR rule to decide whether PU signal is present or not. The hard decision OR rule states that a signal is present only and only if any of the CRs sense a signal. As per the hard decision OR rule if Y is greater or equal to 1, then signal is detected and if Y is smaller than 1, then signal is not detected. The mathematical expression can be written as $\begin{array}{rclr} FC = \{\begin{matrix} 0, & \sum_{i = 1}^{k} L_{i} < 1, \\ 1, & \sum_{i = 1}^{k} L_{i} ⩾ 1, \end{matrix} & (40) \\ FC = \{\begin{matrix} F < 1, & H_{0}, \\ F ⩾ 1, & H_{1} . \end{matrix} & (41) \end{array}$

Finally, Eq. (41) shows the global or final result of FC. Now, the performance of overall proposed system can be analyzed via $P_{F}$ and $P_{D}$ . Hence, using hard decision OR rule in CSS, the total probability of false alarm ( $P_{F}$ ) of the FC can be expressed as follows $\begin{array}{rclr} P_{F} = P_{r} {F ⩾ 1 | H_{0}} = P_{r} {\sum_{i = 1}^{k} L_{i} ⩾ 1 | H_{0}}, & (42) \\ P_{F} = 1 - \prod_{i = 1}^{k} (1 - P_{f, i}) . & (43) \end{array}$

Similarly, using hard decision OR rule in CSS, the total probability of detection alarm ( $P_{D}$ ) of the FC can be expressed as follows $\begin{array}{rclr} P_{D} = P_{r} {F ⩾ 1 | H_{1}} = P_{r} {\sum_{i = 1}^{k} L_{i} ⩾ 1 | H_{1}}, & (44) \\ P_{D} = 1 - \prod_{i = 1}^{k} (1 - P_{d, i}) . & (45) \end{array}$

$P_{f}$ is the probability of false alarm of individual CR’s and $P_{d}$ probability of detection alarm of individual CR’s [18], $\begin{array}{rclr} P_{f} = P_{f}^{F} + (1 - P_{f}^{F}) \times P_{f}^{S}, & (46) \\ P_{d} = P_{d}^{F} + (1 - P_{d}^{F}) \times P_{f}^{S}, & (47) \end{array}$ where $P_{f}^{F}$ and $P_{f}^{S}$ are the probability of false alarm of first stage and second stage detector, respectively. $P_{d}^{F}$ and $P_{f}^{S}$ are the probability of detection alarm of first stage and second stage detector, respectively. Algorithm 2 for CSS technique with proposed reliable SS detector scheme.

Algorithm 2.

CSS using proposed reliable SS detector scheme

4. Numerical results and analysis

In the proposed system model, we are assuming total number of samples (N) are 1000, $P_{f} = 0.1$ , $P_{r}$ is 0.5, and SNR values varies from −20 dB to 0 dB. QPSK modulation is considered in Rayleigh fading channel.

The probability of detection describes how often PU is susceptible to potential interference from the CR. In CRN, $P_{d}$ is one of the important parameter in order to calculate the performance of system. According to IEEE 802.22 WRAN standard the value of $P_{d}$ should be as maximum as possible under the constraint of probability of false alarm.

Figure 6 exhibits the graph between $P_{d}$ and SNR of the proposed scheme with other two existing schemes. It is found that proposed scheme yields better results and the detection performance is improved by 12.9% and 15% as compare to cyclostationary based sensing method and adaptive spectrum sensing at −8 dB SNR, respectively.

Fig. 6.

Probability of detection vs. SNR at $P_{f} = 0.1$ with $N = 1000$ , QPSK modulation scheme and Rayleigh fading channel. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/JHS-150521.)

Figure 7 shows that the proposed scheme has minimum error rate as compared to other two existing schemes, i.e. 0.1 at −8 dB SNR.

Receiver Operating Characteristics (ROC) curve is illustrates in Fig. 8. ROC curve shows the relationship between probability of false alarm and probability of detection alarm [26] of a SS method under several SNR values for propose scheme. For $P_{f} = 0.1$ and $SNR = - 10 dB$ , probability of detection is in the order of 0.9, which is the SS requirement of IEEE 802.22 [7,8].

The SS time defines the total time taken by CR user to detect PU signal. Suppose SS time is increased then PU can utilize its spectrum in a better manner and the limit is decided that CR cannot interfere throughout that much of time. More PUs will be detected if more the SS, due to this the level of interference will be less. The SS time is directly related to the number of samples received by the CR user. The more sensing time is devoted to detecting, the less sensing time is available for transmissions and hence degrading the CR throughput. This is known as the sensing efficiency problem [12] or the sensing-throughput trade-off [14] in SS.

Fig. 7.

Total error probability vs. SNR at $P_{f} = 0.1$ with $N = 1000$ , QPSK modulation scheme and Rayleigh fading channel. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/JHS-150521.)

Fig. 8.

ROC Curves for energy detector and ED_ADT based spectrum sensing detector under different SNR values. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/JHS-150521.)

Fig. 9.

Spectrum sensing time vs. SNR with $N = 1000$ , QPSK modulation scheme and Rayleigh fading channel. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/JHS-150521.)

Figure 9 shows the graph of spectrum sensing time versus SNR. The proposed scheme requires lesser sensing time than the existing proposed schemes. It is observed that there is an inverse relation between SS time and SNR. As SNR increases, sensing time decreases. At −20 dB SNR, proposed scheme requires sensing time around 48.2 ms whereas cyclostationary and adaptive SS based sensing methods require around 53.2 ms and 49.0 ms, respectively, $T_{Dual_detector} = T_{ED} + T_{ED_ADT},$ (48) where $T_{Dual_detector}$ is total time taken by dual detectors for SS time. $T_{ED}$ and $T_{ED_ADT}$ are the ED and ED_ADT detectors SS time, respectively. Therefore, the ED detector sensing time can be calculated as $T_{ED} = E [K_{1}] \times T_{1},$ (49) where $E [K_{1}]$ denotes the mean number of channels reported to ED detector $T_{1} = \frac{N_{E}}{2 \times W} .$ (50)

$T_{1}$ is the mean sensing time for each channel, in which $N_{E}$ is the number of samples during the observation interval and W is the channel bandwidth. $K_{1}$ is a random variable which follows a binomial distribution, depends on number of sensed channels M and probability factor $P_{r}$ that a channel would be reported to the ED detector. Hence, the detection time of the energy detection is $T_{ED} = M \times P_{r} \times T_{1} .$ (51)

Similarly, the ED_ADT detector sensing time can be calculated as $T_{ED_ADT} = E [K_{2}] \times T_{2},$ (52) where $E [K_{2}]$ denotes the mean number of channels reported to ED_ADT detector $T_{2} = \frac{N_{ED_ADT}}{2 \times W} .$ (53)

$T_{2}$ is the mean sensing time for each channel, in which $N_{ED_ADT}$ is the number of samples during the observation interval. Where, $K_{2}$ is a random variable which follows a binomial distribution, depends on parameters M and $(1 - P_{r})$ , where $(1 - P_{r})$ is the probability factor that a channel would be reported to the ED_ADT detector. Hence, the detection time of ED_ADT detector is $T_{ED_ADT} = M \times (1 - P_{r}) \times T_{2} .$ (54)

Thus, the overall spectrum sensing time is calculated by substituting Eqs (51) and (54) in Eq. (48) as $\begin{array}{rclr} T_{Dual_detector} = M \times P_{r} \times T_{1} + M \times (1 - P_{r}) \times T_{2}, & (55) \\ T_{Dual_detector} = M \times [P_{r} \times T_{1} + (1 - P_{r}) \times T_{2}] . & (56) \end{array}$

Equation (56) shows the final mathematical expression of overall spectrum sensing time for dual defectors.

Fig. 10.

Probability of detection vs. threshold values at $SNR = - 6 dB, - 8 dB, - 10 dB, - 12 dB$ , with $N = 1000$ , QPSK modulation scheme and Rayleigh fading channel. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/JHS-150521.)

In Fig. 10, we have plotted the probability of detection ( $P_{d}$ ) versus threshold value (λ) plots for different SNR values such as −6 dB, −8 dB, −10 dB and −12 dB, it is seen that there is an inverse relationship between ( $P_{d}$ ) and threshold for a fixed value of SNR. Observe Fig. 10, if SNR increases, probability of detection also increases with respect to threshold. The maximum value of probability of detection is approximately 1.0 throughout the range of threshold (λ) at −6 dB SNR. It shows that the proposed reliable SS scheme based detector can detect PU signal at −6 dB SNR for $N = 1000$ and $λ = 3.0$ .

In Fig. 11, we have plotted the probability of detection ( $P_{d}$ ) versus SNR plots for different number of cooperative CR users $k = 3, 4, 5, 6, 7, 8, 9, 10$ , $P_{f} = 0.1$ and $N = 1000$ . It can be concluded from Fig. 11 that the value of probability of detection increases with increase in the value of SNR for different number of CRs. The probability of detection is maximum for $k = 10$ , it’s implies that for $N = 1000$ and $P_{f} = 0.1$ , only ten CR users are required for deciding the presence of the PU by using the two-stage spectrum sensing scheme. When $k = 10$ , $P_{f} = 0.1$ and $SNR = - 17.5 dB$ approximately, the proposed SS model can achieve probability of detection value 0.9, which is the SS requirement of IEEE 802.22 [7,8].

Fig. 11.

Probability of detection vs. SNR at $P_{f} = 0.1$ with $N = 1000$ , total CR users $k = 3, 4, 5, 6, 7, 8, 9, 10$ , QPSK modulation scheme and Rayleigh fading channel. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/JHS-150521.)

5. Conclusion

In this paper, a dual detector for spectrum sensing in CRN has been proposed. This scheme reduces computational complexity as well as longer sensing time and overcomes sensing failure problem. Numerical results show that proposed reliable SS based two-stage detectors scheme outperforms other two existing schemes, by 12.9% and 15% at −8 dB SNR. It is also shown that the proposed scheme has lesser sensing time than cyclostationary detection and adaptive SS scheme in the order of 5 ms and 0.8 ms at −20 dB SNR respectively and it has also been implemented with CSS scheme, it further shows that when $k = 10$ , and $P_{f} = 0.1$ proposed detector is able to detect PU licensed signal at −17.5 dB SNR. Finally, results conclude that the proposed scheme exhibits better performances than existing schemes.

Footnotes

Acknowledgements

The authors wish to thank their parents for supporting and motivating for this work because without their blessings and God’s grace this was not possible. This paper is a tribute to all peoples who lost their life in Uttarakhand disaster in July 2013.

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