Comparative Study of Bayesian and Energy Detection Including MRC Under Fading Environment in Collaborative Cognitive Radio Network

The most important component of Cognitive Radio Network (CRN) is to sense the underutilised spectrum efficiently in fading environment for incorporating the increasing demand of wireless applications. The result of spectrum sensing can be affected by incorrect detection of the existence of Primary User (PU). In this paper, we have considered Collaborative spectrum sensing to maximise the spectrum utilisation of Cognitive Radio (CR) user. We proposed a new architecture and algorithm that shows the step by step spectrum sensing procedure using Energy detection and Bayesian detection in collaborative environment for an optimal number of users. This algorithm also includes Maximal Ratio Combining (MRC) diversity techniques in fusion centre to make a final decision under fading condition. The simulation result shows the significant optimisation of detection performance with less misdetection for large number of users. It is also observed that MRC produces better results in collaborative manner under Nakagami-m, Rayleigh and Normal fading. Finally in this paper, we have analysed the relative performance of different wireless channels for various SNR levels and from that analysis it concludes that ED technique works better in high SNR and BD technique works for low SNR. Keywords—Maximal Ratio Combining; Collaborative spectrum sensing, Fading and Shadowing; Data fusion centre; Receiver operating characteristics; False alarm rate


INTRODUCTION
Modern and advanced wireless communication services are becoming scarce resources because of high data rate devices, which communicate by using electromagnetic waves.Due to fixed spectrum, nowadays this is a hard job to provide efficient bandwidth for the increasing demand [1].Cognitive Radio Network (CRN) has become as a solution of limited spectrum problem by providing dynamic spectrum access with increasing number of users in current and future wireless communication [2].In CRN, licensed users are known as Primary User (PU) and unlicensed users are known as Secondary User (SU) where SU's are responsible to sense the occupied spectrum and use it without any interruption by giving highest priority to PU [3].This electromagnetic wave media is highly disposed to noise and it is tough to detect the exact transmitted signal.In presence of noise, miss detection may occur at SU.In case of misdetection, SU's senses the existence of signal power but in reality it may be just noise, or SU senses no primary signal in transmitting mode but in reality it is.So the presentation of CRN based on how finely and reliably a SU detects the unused spectrum and utilise it by CR users without interferences.
Spectrum detection can be done by using different techniques like, Neyman-Pearson Detection (NPD), Matched Filter (MF), Cyclostationary Detection, Energy Detection (ED) and Bayesian Detection (BD) etc. [4]- [7].In [8], Matched Filter also known as coherent detection which can improve sensing performance by requiring less observation time and samples.Sensing of MF depends on prior knowledge about PU like modulation technique, packet structure and carrier synchronisation and timing devices of CR that is complicated to implement [9], [10].In [11], Cyclostationary detection technique is used for detecting cyclostationary feature of PU signal.It also requires partial knowledge of PU and can easily distinguish transmitted signal from noise.This technique requires complex calculation, which is studied in [9].ED is the simplest way for sensing unknown deterministic primary signal with low complexity.It also refers as non-coherent detection, which can be implemented in both frequency and time domain that need no prior knowledge of PU [12].BD is used to reduce the misdetection probability for a given large false alarm rated by incorporating likelihood ratio test which works better in low SNR than ED [13 ].
In this paper, we have considered the energy detection and Bayesian detection to optimise the efficient sensing in cooperative environment and to optimise total error rate.In real life, it is very challenging to estimate correct movement of PU and sense the hidden terminal independently due to fading or different obstacles like building, tree, tower etc. with high saturation loss.Collaborative Spectrum Sensing (CSS) is an intelligent and smart approach for combating multipath fading and shadowing with optimum numbers of SU [14]- [17].In CSS, all CR users perform local measurement independently about existence or not existence of PU to make a binary decision and then forward the decision to a central Data Fusion Centre (DFC).DFC combines those decisions and makes a final decision [18].Different conventional diversity techniques are used to combine the independent decision which are discussed in [19] and [20].In this paper, we have considered Maximal Ratio Combining (MRC) scheme with Energy and Bayesian detection.When MRC is used, channel state information of PU is needed in DFC with a normalised weight and then is added by linear combiner.www.ijacsa.thesai.orgThis paper has improved the work of [21].This work demonstrates a clear comparison between local and collaborative sensing and has proposed a new scheme of MRC with ED to maximise spectrum detection within hidden terminal in collaborative environment.In wireless communication, fading is natural due to multipath propagation and shadowing.So, researchers are focused on detection performance over different fading channels [22], [23].Performance of ED over Nakagami-m and Rician fading is discussed in [22].The aim of this paper is to optimise the collaborative spectrum sensing by considering ED and BD over different fading channels like Rayleigh, Nakagami-m and Normal or Gaussian fading under MRC technique.It also analyses the performance of BD and ED based on SNR label.
The remainder of this work is structured as: Section 2 presents the structure of a signal model and mathematical formulation about ED and BD in local sensing.In Section 2, different fading channels characteristics like Nakagami-m, Rayleigh and Gaussian with tradition MRC is formulated with a new face.A complete algorithm, corresponding flowchart and proposed architecture of our collaborative spectrum sensing system are also deliberated in this section.Section 3 discusses about the simulation results with required parameter and gives an analysis of access opportunity of collaborative CRN.Final conclusion is given in Section 4.

A. Signal model of local spectrum sensing
The main goal of spectrum sensing is to increase efficient use of spectrum hole and monitor the channel continuously to provide primary user precedence.In this paper, two most popular detection techniques is used like Energy detection and Bayesian detection to maximise the accessibility in an occupied channel based on SNR estimation.For binary signal detection two hypothesis are chosen to specify a decision rule about the presence or absence of PU that is referred as statistical decision.By following the term of signal the detection problem is solved using following hypothesis function [16],

{
Where denotes as Null hypothesis that indicate there is no signal without noise, indicate that primary user is in operation mode that produce the result of presence of primary user.
In cognitive radio network, we consider N number of secondary users for spectrum sensing and each user senses the spectrum hole independently.For i th secondary user that is independently and identically distributed [24], local spectrum sensing is determined by following the signal model including two hypothesis [21],

{
Where is denotes as received signal for primary user's transmitted signal at i th secondary user and follows the Gaussian random process with zero mean and variance .At the signal detector the sample sequence set of secondary users refers as iϵ{1,2,3, …, N}, is additive noise that produce null hypothesis and indicate that there is no primary user.
is the complex factor of channel gain between transmitter and receiver.The term indicates that primary user is detected with hypothesis.

B. Local spectrum sensing using Energy detection
Energy detection is also known as non-coherent detection that can detect the signal energy by ignoring the structure of the signal.In case of unknown feature of a signal, energy detection could make better result.In Figure 1, energy detection technique collects transmitted signal bandwidth in specified sensing interval t i .Received Sampling signals are prefilled using Bandpass filter and then square them using magnitude squaring device.Squared signals are integrated with respect to specified time interval to measure the test statistics.In this energy detection, process test hypothesis is compared with predefined threshold value µED , which is measured based on signal noise, energy and sampling size.Functionally test statistics is given by [25], ∑ where, = test statistics, M = sampling size of received signal.
In this case, an efficient decision rule is introduced by comparing predefined threshold with test statistics where that varies only two random variable set {0, 1} that produce the hypothesis (j=0,1).Formally the decision rule is given by, ……………if µED,i< V(y) ……………if µED,i> V(y) where, , , www.ijacsa.thesai.org= Power budget at Primary user.
To determine the efficient measurement of test statistics it is very important to identify the number of sample and threshold value, that are calculated based on two important detection probability parameters and . is denoted as probability of detection and is denoted as probability of false alarm.Threshold and efficient sample size is measured by given equations [25], where, = SNR for ith SU, ⁄ , = One sided power spectral density.
Since PU is surrounded by different fading and obstruction, it is very tough to make a correct spectrum sensing decision with respect to ) and .A correct dicision matrix is given in Table 1 according to Figure 2 that produces the result about existence or not existence of PU.
where, u = the time-bandwidth product = TW , = threshold value for ith secondary user, , is the generalised Marcum-Q function which is formulated as [23], ∫ And is modified Bessel function of the u-1 order.Therefor using this function the probability of detection for the i th user can be written as, Therefore, Probability of misdetection is given as, , And statistical calculation of false alarm is written as, , , ⁄

C. Local spectrum sensing using Bayesian Detection
Bayesian detection method is used in a prior statistics of PU movement and signalling information of PU to improve the throughput of SU sensing to utilise the unused spectrum.Bayesian detector works as a likelihood ratio test detector, which can make better performance in low and high SNR in binary hypothesis testing.Decision of the testing will produce by comparing this likelihood ratio with predefined threshold which is shown in Figure 3.
The main goal of Bayesian detector is to reduce the cost or risk for making the incorrect decision.Expected minimise cost expression is defined as, C = C1|0 P(C1|0) + C0|1 P(C0|1) + C1|1 P(C1|1) + C0|0 P(C0|0) (10) where, Cab(a = 0, 1 and b = 0, 1) is the estimation of the cost that can make a detection statistics with binary hypothesis test.According to decision rule a clear cost matrix with detection probability is given in Table 2.For the two hypothesis testing with prior information, the likelihood ratio test is formulated as [26], (11) Then the likelihood ratio is compared with threshold of Bayesian detection that is suitable to derive optimal detector,

H1 H0
Where Bayesian detector is used to minimise the Bayesian cost to maximise spectrum utilisation.This function is related to false alarm probability and correct decision probability, Max P(H0) (1-Pfa) + P(H1) Pd where, , ̅ is refers as probability density function for different fading channels.
In case of Nakagami-m fading channel, the probability density function is given by, Therefore, average probability of detection over Nakagamim fading by following equation ( 7) is formulated as [23], where, m is shape parameter of Nakagami-m channel The probability density function for Rayleigh fading channel is, , where,  is scale parameter of Rayleigh distribution And in case of Normal or Gaussian fading channel, the probability density function is, where, β is the expectation of the distribution and is the variance of the normal distribution We can calculate the spectrum detection probability over Rayleigh and Normal fading channel to apply the corresponding PDF equation ( 16) and (17) in equation (7).www.ijacsa.thesai.org

E. Sensing under fading channels in collaborative environment including MRC a) Formulation:
For collaborative spectrum environment, we have considered N number of secondary users to sense the occupied spectrum to get an efficient result.In collaborative CRN, N number of SU senses the spectrum individually in a specified time interval to detect the real state of PU. Figure 4, determine PU activity with occupied states D = {d1, d2,…… …, dT}, for specified time interval states t = {1, , …… …, T }.But, for the hidden spectrum hole SU generates its observation sequence O = {o1, o2, … … …, oT}, based on their local detection procedure.This observation set represent sensing information about the existence of not existence of PU in transmission mode.All SU transmit their observation information to DFC using local sensing method.Then DFC makes the final decision whether the SU finally transmit or not.For N number of collaborative user where N= 1, 2, 3,…,N m, the probability of detection in DFC is written as [21], The probability of false alarm for collaborative detection is written as, ( ) To make an effective detection result DFC use different diversity method to combine the given sensing form all SU.One of the most popular diversity schemes is maximum ratio combining scheme.In this work, we proposed a collaborative environment with MRC diversity in different fading channels.The DFC collects all information and combine them using linear combiner.In MRC diversity, the complex envelop of received signal for individual branches of SU is formulated as [27], where, = composite channel achievement in fading, = weighted factor for each channel, ∑ = compound envelop of received signal, ∑ ̃ = complex envelop of received noise.
Then the detection hypothesis is expressed as, To maximise the detection statistics in collaborative sensing, MRC technique introduce an instantaneous SNR that is indicated as .In DFC, this is calculated by summarising given all individual secondary users SNR using linear combiner.That is, ∑ Therefore, we can write the detection probability under MRC method as, This equation will used to express the detection probability over Nakagami-m, Rayleigh and Normal fading channels by using equation (15).For Nakagami-m fading the detection probability under MRC is mathematically calculated as, And b) System Algorithm: To understand the working procedure of our system a wellorganised and smart algorithm is introduced.This algorithm shows the step by step spectrum sensing procedure using BD and ED in collaborative environment for an optimal number of users.This algorithm also includes MRC diversity technique in DFC to make a final decision (Algorithms 1 to 3).www.ijacsa.thesai.org

Local sensing
Step 2: For N individual users.
Step 3: Select the received signal and filter the signal locally at each user.
Step 4: Perform PU detection method (Energy detection or Bayesian detection).
Step 5: Take independent decision using local ED or BD based on SNR level using algorithm 2 and 3.
Step 6: Report independent sensing decision Hj to DFC.

Final decision in DFC
Step 6: DFC produces the final result using MRC under Nakagami-m, Rayleigh and Normal Fading channels.
Step 7: Estimate and for independent user for equation (20) Step 8: Compute .
Step 12: Match V(y) with or .
Step 13: If V(y) is greater than threshold value then DFC makes H 1 as a final result else produce H 0 .
Step 13: Compute , and under different fading channel using MRC.
Step 14: Calculate and to evaluate Collaborative sensing proficiency under fading channels using MRC.

Algorithm 2 Steps to calculate local sensing using Energy detection
Step 1: SU takes the received signal and pass through BPF Step 2: Estimate Power Spectral Density (PSD).
Step 3: Integrate PSD and determine fixed threshold using parameters.
Step 5: Compare and , for , produce H 1 otherwise produce H 0 .

Algorithm 3 Steps to calculate local sensing using Bayesian detection
Step 1: SU takes the received signal at specified sensing time.
Step 2: Set prior probability parameters.
Step 5: Set cost estimation matrix.
Step 6: if , then produce H 1 otherwise produce H 0 .

III. SIMULATION AND RESULT
This section is about the performance of detection in collaborative environment under different fading channels like Rayleigh, Normal and Nakagami-m using MRC.In addition, we also compare the performance between Energy detection and Bayesian detection based on specified SNR.

A. Simulation parameters
To estimate the collaborative performance under fading channel using MRC, the numerical simulation parameters followed by Energy and Bayesian detection are considered in Table 3.

B. Simulation Results
In the simulation result section, Receiver Operating Characteristics (ROC) curves are used to recognise the access probability of collaborative sensing by measuring the interchange between and against the different SNR levels.This segment delivers simulation and analytical results to verify and compare the ROC curves in sensing condition.All figures show that theoretical results are very close to simulation result.Therefore we can say that more than 95% confidence level is achieved.
Figure 5 shows the impact of collaborative detection for different numbers of users.It indicates that probability of collaborative detection will increases at a large number of users with fewer false alarms.Figure 6 demonstrates against for various sampling rates.It has been observed for the figure that the detection probability rises with a large number of sampling.
Figure 7 shows the performance of Rayleigh fading under MRC using Bayesian detection.Though for the increased number of antenna MRC works better, but the ROC curve for collaborative with MRC produce superior detection than local sensing.Therefore using Table 4 we can say that Bayesian detection works in low SNR under Rayleigh fading where M = 200.www.ijacsa.thesai.orgIn Figure 8, the effects of MRC under Rayleigh fading are studied using Energy detection.It is observed that collaborative MRC produces more effective result for higher SNR range.From these two figures, it observed that Normal fading channel start detection for low SNR in BD and produces better access probability for collaborative MRC where ED starts working at high SNR, and produces efficient detection against sensitive false alarm in collaborative environment.
In Table 4, relative performance of Nakagami-m, Rayleigh and Normal or Gaussian fading are given for different SNR level using BD and ED.Findings from this tables are-Collaborative MRC produces a better output of access probability for all channels, Bayesian Detection works better at Nakagami-m fading for Low SNR values and Energy detection works better at Rayleigh fading for High SNR values.

Fig. 2 .
Fig. 2. Block diagram of detection hypothesis integral calculation of detection probability makes high complexity we can represent the formula as series function of Marcum-Q function,

Fig. 3 .
Fig. 3. Process flow diagram of Bayesian detection sensing under fading channel In wireless communication system, fading occurs due to multipath propagation and shadowing.Measurement of detection performance of energy detection and Bayesian detection over fading channel is very important to meet the spectrum sensing challenges to improve transmission performance.Probability of detection in fading condition is measured using following equation,

Fig. 4 .
Fig. 4. Block diagram of proposed Collaborative detection using MRC detection and false alarm probability under MRC can be expressed by,

Algorithm 1
Steps to estimate Collaborative Spectrum Sensing under different fading channels using MRC Initial Step Step 1: Cognitive Radio user received transmitted signal independently trough specified sensing period with N = 1, 2, 3, … …, Nm no-cooperative SU.

Figures 9
Figures 9 and 10 show a clear comparison of the performance of detection between Bayesian and Energy detection under Nakagami-m fading.These show that Nakagami-m fading gives better detection than Rayleigh fading for same estimation.

Figures 11 and 12
Figures 11 and 12 manifests the ROC curves for Normal fading under Bayesian and Energy detection, which shows the effects of increasing number of antennas with MRC to estimate optimum detection by considering sensitive false alarm rate.

TABLE III .
PARAMETERS FOR EVALUATE ENERGY AND BAYSIEN DETECTION UNDER DIFFERENT FADING USING MRC