Advanced Energy Sensing Techniques Implemented Through Source Number Detection for Spectrum Sensing in Cognitive Radio

  • Sagarika Sahoo
  • Tapaswini Samant
  • Amrit Mukherjee
  • Amlan Datta
Conference paper
First Online:
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 332)

Abstract

The world of wireless technology is been one of the most progressive and challenging aspects for the users and providers. It deals with the wireless spectrum whose efficient use is of foremost concern. These are improved by the cognitive radio users for their noninterference communication with the licensed users. Spectrum holes detection and sensing is a dynamic time variant function which is been modified using the proposed source number detection and energy detection. Energy detection technique is implemented so as to compare the thresholds of the channels dynamically, and source detection method is used for predicting the number of channels where the energy detection is to be performed. The simulation results show the optimization and reduced probability of miss detection considering the change in threshold.

Keywords

Cognitive radio Source number detection Energy detection Spectrum sensing 
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1 Introduction

Spectrum sensing has so far been identified as the step of crucial importance in the process of the cognition cycle and the most important function for the establishment of cognitive radio network that principally emphasizes on sensing the spectrum environment accurately and determines whether the primary user is active or not over a specific band reliably [1]. Therefore, in order to guarantee noninterference with the primary user, cognitive radio must detect very weak signals [2].

In this paper, the bootstrap-based source number detection (SND) technique is applied for spectrum sensing in cognitive radio networks (CRN). A novel test source number estimation method based on bootstrap is proposed. From the simulation results, it is seen that the proposed bootstrap-based source detection procedure can provide satisfied detection performance while only requires the optimal likelihood ratio and threshold compared with the existing methods.

Using simulations, we show that when the observations of number of sources at the sensors are added on the threshold dramatically falls yielding to control in likelihood ratio to improve condition of missed detection (P m ).

It is clear from Fig. 1 that the predictor unit initially observes n − 1 previous sensing frames that can be used to predict the succeeding nth sensing frames.
Fig. 1

Frame of sensing structure for cognitive radio

2 Energy-based Detection

Energy detection is one of the sub-optional signal sensing techniques which has been hugely used in radio communications [3, 4]. The detection process can be performed in time domain as well as in frequency domain. Figure l shows the energy detection process with the hypotheses as follow:
$$ H_{0} : \, Y\left[ n \right] = W\left[ n \right] \quad {\text{presence of signal}} $$
(1)
$$ H_{t} : \, Y\left[ n \right] = X\left[ n \right] \, + \, W\left[ n \right]\quad {\text{absence of signal}} $$
(2)
here, n = 1,…M; where M is the window under observation
Here, X[n] denotes the sample of the target signal having certain power ‘u’ and W[n] is noise sample that is assumed to be additive white Gaussian noise (AWGN) having zero mean and variance same as the signal power ‘u’ (Fig. 2).
Fig. 2

The process of energy detection. a Spectrum sensing through energy detection. b Implementation in time domain. c Implementation in frequency domain

The sensing is performed to make certain if any activity of the primary user for a particular band of frequency occurs, as suggested by binary hypothesis testing, and that can be mapped as [5-7]:
$$ \begin{aligned}& N_{0} {:}{\text{ The idle primary user}} \hfill \\ & N_{ 1} {:}{\text{ The working primary user}} \hfill \\ \end{aligned} $$
The presence or absence of primary signal has been given by \( N_{1}^{\text{PN}} \) where i = 0 is the absence and i = 1 shows the presence. Given CN i N, which is sensing and making the decision on the basis of that hypothesis modeled structures are used which is the below conditional probabilities:
$$ P_{m} = p\left( {N_{0}^{\text{CN}} \left| {N_{1}^{\text{PN}} } \right.} \right) $$
(3)
$$ P_{\text{fa}} = P\left( {N_{1}^{\text{CN}} |N_{0}^{\text{PN}} } \right) $$
(4)
where P m denotes probability of missed detection and P fa as probability of false alarm. The signal which is consequently received at any particular instance say jth is given by:
$$ y_{j} = \, h_{j;1} a^{\text{PN}} + h_{j;2} a^{\text{CN}} + n_{j } $$
(5)
and where the channel between the primary user is denoted by h j;1 and the jth secondary user, and h j;2 is the channel between jth secondary user and any other secondary user with setting channel property as Rayleigh distribution. a PN is a primary network signal, including the primary user symbol transmission and a CN includes the transmitted symbols from any active secondary user. The cognitive user sensed signals are obtained when the cognitive system is performing spectrum sensing (H CN 0), demonstrated with the following condition:
$$ y_{j} = \left\{ {\begin{array}{*{20}l} {h_{j,2} a^{\text{CN}} + n_{j} } \hfill & {N_{0}^{\text{PN}} } \hfill \\ {h_{j,1} a^{\text{PN}} + h_{j,2} a^{\text{CN}} + n_{j} } \hfill & {N_{1}^{\text{PN}} } \hfill \\ \end{array} } \right., $$
(6)
And at the time when spectrum sensing operation being idle, the initial model leads to:
$$ {\text{y}}_{j} = \left\{ {\begin{array}{*{20}l} {n_{j} } \hfill & {N_{0}^{\text{PN}}} \hfill \\ {h_{{j,1^{{a^{\text{PN}} }} }} + n_{j} } \hfill & {N_{1}^{\text{PN}} } \hfill \\ \end{array} } \right., $$
(7)
Now, the false alarm probability and detection probability can be expressed as follow:
$$ \begin{aligned} Q_{{d,{\text{SLC}}}} = &\;Q_{mK} \left( {\sqrt {2\gamma_{\text{slc}} } ,\sqrt \lambda } \right) \\ Q_{{d,{\text{SLC}}}} = &\;\frac{{\Gamma \left( {mK ,\frac{\lambda }{2}} \right)}}{{\Gamma (mK)}} \\ \end{aligned} $$
(8)
where \( \gamma_{\text{slc}} = \sum\nolimits_{k = 1}^{K} {\gamma_{k} } \), y k is the SNR received at kth cognitive user. To converse to a selection like correlation metric and/or negentropy metric, diverse measurements are utilized [8]. These are further adapted to measure the inverse gaussianity of the identified signal [9, 10]. The inverse gaussianity measured is compared with the threshold that has been presumed, as a result, the decision regarding the primary signal in the frame is within the sensing period (Fig. 3).
Fig. 3

Probability of detection (theoretical) versus probability of false alarm

The choice made is executed to rest of frames that are sensed. The graph shows probability of detection (theoretical) versus probability of false alarm for 1,000 simulations using the standard formula of error function.

3 Bootstrap-based Detection (Parametric and Nonparametric Resampling Method)

The common assumption of Gaussian data seems to lead to some variant of the statistic, as shown, irrespective of the source detection scheme is based on hypothesis tests or information theoretic criteria,
$$ \frac{{\left( {\prod_{j = k}^{P} l_{i} } \right)^{{(1/\left( {p - k + 1} \right))}} }}{{\frac{1}{p} - k + 1\sum\nolimits_{i = 1}^{p} {l_{i} } }}\quad \quad k = 1, \ldots ,p - 1 $$
(9)
which is the ratio of the geometric mean to the arithmetic mean of the smallest sample eigenvalues [11, 12]. This can be accomplished by considering the following set of hypothesis tests for determining the number of sources:
$$ \begin{array}{*{20}c} {H_{0} {:} \lambda _{1} = \cdots = \lambda_{p} } \\ \vdots \\ {H_{k} {:} \lambda_{k + 1} = \cdots = \lambda_{p} } \\ \vdots \\ {H_{p - 1} {:} \lambda_{p - 1} = \lambda_{p} } \\ \end{array} $$
(10)
with corresponding alternatives K k , not H k , k = 0,…,p − 2. Acceptance of H k leads to the estimate q = k. A practical procedure to estimate starts with testing and proceeds to the next hypothesis test only on rejection of the hypothesis currently being tested. Upon acceptance, the procedure stops, implying all remaining hypotheses are true. The procedure is outlined in Table 1.
Table 1

Hypothesis test procedure used for determining the number of sources

Step 1

Set \( k = 0 \)

Step 2

Test \( H_{k} \)

Step 3

If \( H_{k} \) is accepted then set \( \hat{q} = k \) and stop

Step 4

If \( H_{k} \) is rejected and \( k < p - 1 \) then set \( k \leftarrow k + 1 \)

and return to step 2. Otherwise set \( \hat{q} = p - 1 \) and stop

4 Proposed Method

In the proposed method, the primary sources are been estimated through bootstrap-based SND in the initial stage and the optimization is been performed on the basis of number of sources in the later.

Figure 4 shows the detection of number of sources through an additional feedback to the traditional energy detection scheme which includes threshold V(t) and the output of energy detector.
Fig. 4

Energy sensing through source number detection

The shortcomings of the traditional spectrum sensing along with its optimization have been modified [13] which includes improper access of the spectrum efficiently and not being able to identify the presence or absence of PU [14]. To alleviate this problem, the primary sources are efficiently detected using SND technique and spectrum sensing is performed with the proposed energy-based scheme [15]. The overall model has been modified with detection of spectrum while the primary user and CR user work simultaneously.
$$ \begin{aligned} & T_{i,j} = l_{i} - l_{j} , \\ & {\text{where}}\;i = k + 1 \ldots p - 1\;{\text{and}}\;j = \, i + 1, \ldots ,p \\ \end{aligned} $$
(11)
These differences will be small when both li and lj are considered to be noise eigenvalues but relatively large if any one or both of l i and l j are source eigenvalues. The pair wise comparisons represented in a hypothesis testing framework gives
$$ H_{ij:} \lambda_{i} = \lambda_{j} $$
(12)
$$ \begin{array}{*{20}c} {K_{{ij:}} \lambda _{i} \ne \lambda _{{j,}} } \\ {{\text{where}}\;i = k + 1, \ldots , p - 1\;{\text{and}}\;j = i + 1, \ldots ,p} \\\end{array}$$
(13)
The hypotheses H k can be reformulated as intersections between the pairwise comparisons
$$ H_{k \, } = \bigcap\limits_{i}^{j} {H_{ij} } \quad {\text{and}} $$
(14)
$$\begin{array}{*{20}c} K_{k} = \bigcup\limits_{i}^{j} {K_{ij} } \\ {\text{where}}\; \, i = \, k + 1, \ldots . \, p - 1\;{\text{and}}\; \, j = \, i + 1, \ldots ,p \\ \end{array} $$
(15)
One of the most popular approaches for composite hypotheses testing stands to be the generalized likelihood ratio test. By their maximum likelihood estimates, the GLRT replaces any unknown parameters. The GLRT can generally have the form
$$ \hat{T}\left( {X_{N} } \right) = \frac{{f_{1} \left( {X_{N} ;\hat{\theta }_{1} } \right)}}{{f_{0} \left( {X_{N} ;\hat{\theta }_{0} } \right)}}\left\{ \begin{gathered} > \tau ,\,{\text{accept}}\;{\rm H}_{1} \hfill \\ < \tau ,\,{\text{accept}}\;{\rm H}_{0} \hfill \\ \end{gathered} \right., $$
(16)
where \( \hat{\theta }_{1} \) is the MLE of . \( {\theta }_{1} \) assuming H 1 is true, and \( \hat{\theta }_{0} \) is the MLE of \( {\theta }_{0} \) assuming H 0 is true.

As in the simple hypotheses, the threshold \( \tau \) is found from the nominal value of the probability of false alarm P fa.

5 Simulation and Discussion

The simulated results as performed is shown to using information theoretic criteria which can detect the primary users or source transmitters signal and then the spectrum sensing is carried out using bootstrap-based energy detection and optimization is performed as shown in Fig. 5. As shown in Fig. 5, the graph shows the number of sources versus their corresponding likelihood and threshold.
Fig. 5

Source detection for primary transmitting signals

As shown in Fig. 5, the increase in number of primary sources corresponds to decrease in likelihood ratio of miss detection and also the decrease in threshold. Here, the threshold is getting reduced because of increasing number of primary sources, i.e., increase in number of primary channels implies decrease in overall selection of threshold for cognitive receiver in the time domain. There will be change in power levels for different channels as per the application and cognitive receiver is selecting the optimum threshold among all the channels. Here, the numbers of sources are calculated by comparing the likelihood and threshold of the generating signal which is 10.

6 Conclusion

In the proposed method, the likelihood of probability of miss detection is been improved with varying threshold. Here, the number of channels is considered with respect to the SND and accordingly the energy detection of individual channels is being considered. The output of the simulated graphs shows the optimum number of sources by changing the number of primary sources and the number of cognitive receivers. In practical cases, we can select the number of primary users and energy detection statistics according to the applications of different spectrum channels by cognitive users.

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Copyright information

© Springer India 2015

Authors and Affiliations

  • Sagarika Sahoo
    • 1
  • Tapaswini Samant
    • 1
  • Amrit Mukherjee
    • 1
  • Amlan Datta
    • 1
  1. 1.School of Electronics Engineering, KIIT UniversityBhubaneswarIndia

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