TY - JOUR
AU - Tamaghna, Acharya,
AB - Abstract Spectrum sensing (SS) is often considered to be one of the highly challenging issues in cognitive radio networks (CRNs), which is being extensively investigated to solve the growing problem RF spectrum scarcity in the next-generation wireless networks. Recently, spectrum prediction assisted cooperative spectrum sensing (CSS) is emerging as an effective way of SS, enabling efficient utilization of two critical resources of SS: time and energy. In this paper, we evaluate the reliability of hidden Markov model (HMM)-based CSS in CRNs, in the presence of random malfunctioning of secondary user (SU) nodes participating in the process. In view of the poor performance of the CSS, especially at low signal-to-noise ratio (SNR) values, we propose a new scheme to detect the possible presence of faulty nodes in the CSS system with high accuracy and quarantine them to maintain the reliability of the spectrum prediction process. The proposed scheme suggests a novel integration of the forward algorithm of HMM with fuzzy-C means clustering technique to design a robust spectrum prediction assisted CSS in CRNs. Simulation results confirm that our scheme delivers a significantly improved receiver operating characteristics compared to a prominent scheme even in the presence of high percentage of failure of SU nodes. 1. INTRODUCTION Next generation wireless networks are expected to overcome the growing problem of RF spectrum scarcity, to a great extent, by the possible implementation of the principle of Dynamic Spectrum Access [1], through Cognitive Radio [2] technology. A cognitive radio network (CRN) opportunistically utilizes the licensed spectrum of primary user (PU) for the unlicensed secondary users (SUs). One of the major tasks of CRN is spectrum sensing (SS) which is a technique to detect the presence of PU signal on the spectrum. A simple and useful method for SS is energy detection (ED) [3] where the energy of any PU signal is calculated and compared with a predefined threshold to determine the possible presence of the PU. However, the reliability of SS is affected severely by multi-path fading, shadowing and receiver uncertainty problems. Interference to PU is inevitable if SU node does not release its occupied spectrum due to failure in detecting PU’s presence. This leads to deterioration of the PU’s Quality of Service (QoS). Cooperative spectrum sensing (CSS) is a popular technique proposed to improve the reliability of the spectrum sensing operation by exploiting spatial diversity of the received PU signal at multiple SU or at single SU and its associated relay nodes. A survey of the various methods of CSS may be found in [4]. However, these spectrum sensing techniques consume significant amount of energy and time for sensing and subsequent processing of the sensed signal. To overcome these shortcomings, recently, prediction-based spectrum sensing technique [5–7] is emerging as a promising solution. Using this, the future PU state (active/idle) could be predicted with reasonable level of accuracy, by analyzing the past sensing outputs. This enables a SU node not to perform SS on PU channels, that are predicted to be busy, and thus, sensing time and energy can be reduced significantly. Furthermore, with successful prediction of spectrum occupancy pattern of a PU node, SU node, occupying the PU spectrum, can release it free before the PU resumes its transmission. Thus, the said interference to PU could be avoided to a great extent. A survey on the existing spectrum prediction techniques in CRN can be found in [8]. HMM-based spectrum prediction is considered to be one of the popular techniques. Reports of success of HMM-based prediction assisted CSS are largely based on the common presumption that all the SU nodes participating in the CSS process are functioning in the desired manner. However, sudden malfunctioning of one or more SU nodes is nothing but natural. But its impact on the accuracy of the spectrum prediction has not yet been fully explored in the open literature. For this, in our current study, the performance of hidden Markov model (HMM)-based spectrum predictor for CSS is evaluated in the presence of faulty nodes, forwarding useless random data on spectrum sensing to the fusion center (FC). Simulation result shows a significant degradation of system reliability at low signal-to-noise ratio (SNR) even with 20% faulty nodes. This motivates us to further investigate the problem of detection of faulty SU nodes for maintaining reliability of spectrum prediction technique in CRNs. 1.1. Related work HMM [9] is a statistical tool that has already found extensive applications in speech recognition, pattern recognition, computational molecular biology, finance etc. It is also explored in recent studies on CRNs in predicting true state (active/idle) of PU assuming the sensing channel between PU to SU, Markovian. In [10], the authors, possibly, first proposed a HMM-based spectrum prediction algorithm aiming to avoid the interference from and to the PUs caused due to conventional carrier sense multiple access (CSMA)-based spectrum access by SUs. In [11], the authors confirmed existence of Markovian chain through extensive real-time measurements in the paging band (928–948 MHz) and successfully predicted true states of the various sub-band within it. In [12], the authors proposed a fast spectrum detection algorithm using HMM where the samples of the wideband power spectrum density (PSD) are used as inputs to HMM predictor. In [13], the parameters, proposed by HMM, used for channel status prediction, were calculated statistically without using any training. In [14], a modified HMM-based single user prediction is proposed by the authors and their method was shown to be better than 1-nearest neighbor (1-NN)-based prediction. Thus, results of theoretical as well as experimental studies motivate us to consider HMM as our spectrum prediction model in the present study. In [15], the author employed HMM for blind spectrum sensing based on classification of multiple interferers where all signal, channel and noise parameters are unknown. In [16], the authors proposed a method that helps the FC to detect deterioration of the sensing performance without using the information of local sensing statistics. In [17], the authors compared between two channel status predictors using neural network based on multilayer perception (MLP) and HMM. By repeated simulations, they showed that HMM predictor is better than MLP-based predictor under dynamic traffic scenarios. In [18], a hidden bivariate Markov model (HBMM)-based SS was proposed and its dwelling time was analyzed using real-time measurements. Their results showed that HBMM-based detector could yield more accurate PU state estimation and prediction than standard HMM with high path loss and strong shadowing effects. In [19], the authors used HBMM for hard and soft fusion in collaborative spectrum sensing, based on the on-line estimation of HBMM parameters. Their scheme is independent of the predefined threshold or weights and hence better spectrum sensing result is achieved. In [20], the authors extended the idea of HBMM to higher order HBMM to take the advantages of both higher order and HBMM by which the prediction accuracy is significantly improved. In [21], the authors addressed the estimation problem of HMM by extending the expectation-maximization (EM) algorithm for estimating the primary user parameters in CRN. In [22], the authors used a non-stationary HMM (NS-HMM) for modeling the time-varying nature of PU traffic aiming to improve the accuracy of spectrum occupancy predictions. In [23], the authors used a HMM-based spectrum occupancy predictor using hard fusion rules. The prediction accuracy improvement is done in terms of prediction error by required threshold setting. In [24], the authors extended the number of hidden states in HMM and formulated the prediction problem as maximum-likelihood (ML) estimation by using a realistic measurement-based traffic model for industrial cognitive radio. In [25], the performance of an HMM-based spectrum occupancy predictor for energy-efficient CRN was studied over the 2.4 GHz ISM band using an indoor set up. In [26], the authors proposed a 2-D spectrum and power (harvested) sensing scheme to improve the PU detection performance in energy harvested CRNs. In [27], the authors considered a realistic scenario by assuming multiple power levels of PU node and used a continuous HMM (CHMM)-based blind spectrum sensing algorithm for detecting both the presence and the transmit power level of PU node. The reliability of spectrum estimation through CSS is very much vulnerable to possible attacks from malicious SU node(s) as well as malfunctioning SU nodes in the network. In [28], a robust malicious user prediction scheme was proposed for CSS enabled spectrum prediction scheme. In [29], the authors evaluated energy efficiency in the presence of malicious users in cooperative CRN. In [30], the authors proposed a contribution-based CSS where some nodes are malfunctioning due to locational disadvantage, multi-path fading or shadowing but they do not consider any hardware malfunctioning of the nodes. In [31], a Dempster–Shafer (D–S) theory-based CSS method was proposed to detect the SU nodes with hardware malfunctioning. But this scheme is shown to be suitable for systems with less than 30% faulty nodes. 1.2. Motivation The modeling of CRN in the presence of faulty nodes is important because hardware malfunctioning of one or more SU nodes is more likely in such networks as the hardware design for practical CR devices is yet to achieve a matured stage. In CSS, some nodes may supply erroneous data due to battery exhaustion, sudden malfunctioning of electronic circuits, ageing or in harsh weather conditions which introduce harmful effects on system performance. Degradation in the reliability of the system performance is significant and illustrated in Section 4. But making a provision at each SU node to check the health of its own hardware every time before the process starts may not always be feasible. This is also not an energy-efficient approach considering the fact that SU nodes are often driven by limited battery power. This scenario becomes more challenging as any node could start malfunctioning at any point during operation. So an efficient system should use some scheme where the FC checks continuously for the possible malfunctioning one or more nodes before using their inputs for CSS and also to exclude those faulty nodes for maintaining reliable system performance. Such a method should be sensitive enough so that it could detect the presence of faulty SU nodes when their number is very small. Also it should ensure robustness of the CSS when the number of faulty nodes is high. To the best of our knowledge, none of the previous studies on spectrum prediction using HMM considered this issue. 1.3. Contribution The specific contributions of this paper may be summarized as follows: A simulation study is carried out to evaluate the performance of HMM-based spectrum predictor for CSS in a CRN considering the presence of random number of faulty nodes, forwarding unreliable data on spectrum sensing to the FC node. A novel scheme is proposed to identify faulty SU node(s) with high probability in an HMM-based CSS system and exclude them from the CSS process to maintain reliability of the CSS. The novelty of the proposed scheme lies in the combination of the forward algorithm [32], used in HMM, and fuzzy-C means (FCM) clustering [33] technique in designing a highly sensitive and robust scheme for faulty node detection in CRNs. Further, our scheme does not require any knowledge of the fading statistics of the various wireless channels involved in the CSS and power adaptation strategy used by the SU nodes in forwarding their sensed signals to the FC. Complexity of the proposed scheme is also analyzed. Extensive simulation results are presented to quantify the robustness and sensitivity of our proposed scheme, especially in the low SNR regime, and to compare its performance with a prominent recent solution. The rest of the paper is organized as follows. Section 2 describes our system model for CSS. Besides, some preliminaries about HMM and principles of its application in PU spectrum prediction is also described. Our proposed HMM-based spectrum prediction scheme is presented in Section 3. In Section 4, simulation results are presented. Finally, the paper is concluded in Section 5. 2. SYSTEM MODEL AND PRELIMINARIES 2.1. Network model An HMM-based spectrum prediction approach to assist CSS is considered here. The network under consideration consists of a single PU and K SU nodes where an arbitrary subset of SU nodes in the CRN are malfunctioning. The energy values accumulated at FC is used for training of the HMM parameters and then it runs spectrum prediction algorithm. All the SU nodes are collocated in between PU node and FC node. In other words, the distance between PU node to any SU node and FC node to the SU node is much larger than the distance among the SU nodes as shown in Fig. 1. Here, every SU node is sensing for the possible presence of PU signal, via sensing channel, and forwards the received signal to the FC via reporting channel at regular intervals. For reporting, SU nodes are assumed to access a common control channel using time division multiple access (TDMA). Next, the FC node calculates the energy of a predefined set of samples of the sensed signal received from corresponding SU nodes. Figure 1. View largeDownload slide System model with a fixed PU node and collocated SU nodes where some nodes are malfunctioning. Figure 1. View largeDownload slide System model with a fixed PU node and collocated SU nodes where some nodes are malfunctioning. Finally, the spectrum prediction decision taken by the FC node. In addition, the reliable/faulty status of SU nodes is broadcast to them via a feedback channel as shown in Fig. 1. The overall spectrum prediction operation of the system consists of two phases. In Phase I, before deployment, the HMM parameters are trained continuously during an off-line training period at FC node by the sensing results of reliable SU nodes only. In Phase II, after deployment, the spectrum of interest is being sensed by SU nodes in a cooperative manner and their sensing results are being sent to the FC node. Thus, HMM parameters are trained on-line at regular interval by the sensing results of the SU nodes which are considered to be reliable by our algorithm at FC. The list of necessary symbols used in our subsequent discussion is shown in Table 1 for the convenience of readers. Table 1. List of necessary symbols used in our CSS model and their descriptions Symbol Description of the symbol K Total number of SU nodes hs Sensing channel fading coefficient hr Reporting channel fading coefficient dsi Distance between PU and ith SU node dri Distance between ith SU node and FC node δ Path loss exponent xpu PU signal Ns Number of samples sensed Ts Sensing duration fs Sampling frequency Ppu Transmission power of PU node Psu Transmission power of SU node us Noise in the sensing channel ysu PU signal received at SU node yfc Received signal at FC from SU node Efc Energy of the received signal at FC node ur Noise in the reporting channel Symbol Description of the symbol K Total number of SU nodes hs Sensing channel fading coefficient hr Reporting channel fading coefficient dsi Distance between PU and ith SU node dri Distance between ith SU node and FC node δ Path loss exponent xpu PU signal Ns Number of samples sensed Ts Sensing duration fs Sampling frequency Ppu Transmission power of PU node Psu Transmission power of SU node us Noise in the sensing channel ysu PU signal received at SU node yfc Received signal at FC from SU node Efc Energy of the received signal at FC node ur Noise in the reporting channel Table 1. List of necessary symbols used in our CSS model and their descriptions Symbol Description of the symbol K Total number of SU nodes hs Sensing channel fading coefficient hr Reporting channel fading coefficient dsi Distance between PU and ith SU node dri Distance between ith SU node and FC node δ Path loss exponent xpu PU signal Ns Number of samples sensed Ts Sensing duration fs Sampling frequency Ppu Transmission power of PU node Psu Transmission power of SU node us Noise in the sensing channel ysu PU signal received at SU node yfc Received signal at FC from SU node Efc Energy of the received signal at FC node ur Noise in the reporting channel Symbol Description of the symbol K Total number of SU nodes hs Sensing channel fading coefficient hr Reporting channel fading coefficient dsi Distance between PU and ith SU node dri Distance between ith SU node and FC node δ Path loss exponent xpu PU signal Ns Number of samples sensed Ts Sensing duration fs Sampling frequency Ppu Transmission power of PU node Psu Transmission power of SU node us Noise in the sensing channel ysu PU signal received at SU node yfc Received signal at FC from SU node Efc Energy of the received signal at FC node ur Noise in the reporting channel 2.2. Spectrum sensing model The sensing channel between PU and SUi and reporting channel between SUi and FC are modeled as Rayleigh flat fading with fading coefficients hsi and hri, respectively, where i={1,2,…,K}. They are assumed to be circularly symmetric complex Gaussian (CSCG) random variables such that hsi∼CN(0,dsi−δ) and hri∼CN(0,dri−δ), dsi is the distance between PU node to ith SU node, dri is the distance between ith SU node to FC node and δ is the path loss exponent. The feedback channel is assumed to be ideal. Let xpu(n) represent the PU signal which follows CSCG distribution with zero mean and variance E[|xpu(n)|2]=1. So the signal received by ith SU node can be written as ysui(n)=ΘPpuhsixpu(n)+usi(n),∀i∈{1,2,…,K} (1) for n={1,2,…,Ns}, where Ns=Tsfs is the number of samples, Ts is the sensing duration, fs is the sampling frequency and Ppu be the transmission power of PU node. Θ is a binary indicator to represent presence/absence of the PU signal where Θ=1 means PU is active (binary hypothesis ℋ1) and Θ=0 means PU is idle (binary hypothesis ℋ0). usi(n) is additive independent and identically distributed (i.i.d.) CSCG random sequence representing noise signal at ith SU with zero mean and unit variance. The received signals at the SU nodes are forwarded via a common reporting channels using TDMA to the FC node. Hence, the signal sensed by SUi received at FC node via a common reporting channel in the ith TDMA slot will be yfci(n)=Psuhriysui(n−Ns)+uri(n),∀i∈{1,…,K} (2) where n={(Ns+1),(Ns+2),…,2Ns}, Psu be the transmission power of SU node, uri(n) is also additive i.i.d. CSCG random sequence representing noise at FC node corresponding to ith SU with zero mean and unit variance. Hence, energy of the received samples at FC corresponding to ith SU may be written as Efci=∑n=Ns+12Ns|yfci(n)|2,∀i∈{1,2,…,K} (3) Now these calculated energy values at FC node are used as input to HMM (based spectrum predictor) as shown in Fig. 2. Figure 2. View largeDownload slide Block diagram of HMM-based spectrum prediction method in cooperative CRN. Figure 2. View largeDownload slide Block diagram of HMM-based spectrum prediction method in cooperative CRN. 2.3. Hidden Markov model The received energy values are the observed states values for HMM. As mentioned earlier, the original PU state will be either 0 for PU idle or 1 for PU active. Since, this state is not directly available to SUs due to wireless channel fading and noises, so it is considered as the hidden state value for HMM as shown in Fig. 3. Figure 3. View largeDownload slide Hidden Markov model with observed and hidden sequences for T time slots. Figure 3. View largeDownload slide Hidden Markov model with observed and hidden sequences for T time slots. 2.3.1. Definition of HMM The formal definition of HMM is considered as a tuple λ=(π,A,B) [32], where π={πi} is termed as the set of initial state distribution parameters which is defined as πi=P[q1=Si],1≤i≤N (4) satisfies the condition ∑i=1Nπi=1 and πi≥0 where qt is the state at time t, N is the total number of states and S={S1,S2,…,SN} is the set of distinct states of the system under consideration. The state transition matrix A={aij} is defined as aij=P[qt+1=Sj|qt=Si],1≤i,j≤N (5) where aij≥0 for all i,j and ∑j=1Naij=1 for 1≤i≤N. The observation matrix B={bj(m)} is defined as bj(m)=P[vmatt|qt=Sj],1≤j≤N,1≤m≤M (6) satisfies the conditions bj(m)≥0 and ∑m=1Mbj(m)=1 for 1≤j≤N, where M is the number of observation symbols and V={v1,v2,…,vM} is the set of possible observations. For spectrum prediction model, M=2 is considered. v1 is considered as 0 (PU is idle) and v2 is considered as 1 (PU is active). All the necessary symbols used in HMM model and their description are shown in Table 2. Table 2. List of necessary symbols used in HMM model and their descriptions. List of parameters used Description of the symbol T Length of the observation sequence N Number of states M Number of observation symbols S={S1,S2,…,SN} Set of distinct states in the system V={v1,v2,…,vM} Set of possible observations qt State at time t A State transition matrix B Observation matrix π Initial state distribution O={O1,O2,…,OT} Observation sequence Z={z1,z2,…,zT} Hidden state sequence λ=(π,A,B) Set of all HMM parameters List of parameters used Description of the symbol T Length of the observation sequence N Number of states M Number of observation symbols S={S1,S2,…,SN} Set of distinct states in the system V={v1,v2,…,vM} Set of possible observations qt State at time t A State transition matrix B Observation matrix π Initial state distribution O={O1,O2,…,OT} Observation sequence Z={z1,z2,…,zT} Hidden state sequence λ=(π,A,B) Set of all HMM parameters Table 2. List of necessary symbols used in HMM model and their descriptions. List of parameters used Description of the symbol T Length of the observation sequence N Number of states M Number of observation symbols S={S1,S2,…,SN} Set of distinct states in the system V={v1,v2,…,vM} Set of possible observations qt State at time t A State transition matrix B Observation matrix π Initial state distribution O={O1,O2,…,OT} Observation sequence Z={z1,z2,…,zT} Hidden state sequence λ=(π,A,B) Set of all HMM parameters List of parameters used Description of the symbol T Length of the observation sequence N Number of states M Number of observation symbols S={S1,S2,…,SN} Set of distinct states in the system V={v1,v2,…,vM} Set of possible observations qt State at time t A State transition matrix B Observation matrix π Initial state distribution O={O1,O2,…,OT} Observation sequence Z={z1,z2,…,zT} Hidden state sequence λ=(π,A,B) Set of all HMM parameters 2.3.2. HMM-based spectrum prediction Given an observation sequence O={O1,O2,…,OT}, where Ot∈{v1,v2}∀t={1,2,…,T} and given model parameters λ=(π,A,B), Viterbi algorithm [32] is used to uncover the hidden state sequence Z={z1,z2,…,zT} which is most likely to generate the observation sequence O, where T is the length of observation sequence. The objective of HMM predictor is to predict the future state zT+1 based on the past observations. To get the best result, HMM parameters are trained both in off-line and then on-line processes at regular intervals. Once the training is complete, the joint probability of observing the sequence O followed by an idle PU state P(O,0|λ) and an active PU state P(O,1|λ) at the future time slot (T + 1) are calculated. The state of future time (T + 1) is predicted according to the following rule: IfP(O,0|λ)≥P(O,1|λ)→OT+1=0(PUisidle).IfP(O,0|λ)<P(O,1|λ)→OT+1=1(PUisactive). (7) 2.3.3. HMM training Baum Welch Algorithm [32] is used for training process, which iterates between expectation and maximization step to find HMM parameters λ=(π,A,B) such that probability P(O/λ) is maximized, given an input sequence O={O1,O2,…,OT}. It is presumed that there are no faulty nodes present in the system during off-line training process but during on-line training process some nodes may not function reliably. So, if during the on-line training process, if some faulty observation sequences are mixed, then values of the model parameters A and B will be different. As a result, the estimation of the hidden states are more likely to mismatch with its real states. Hence, spectrum prediction for zT+1 state is also likely to be less accurate. This is also illustrated in Fig. 3. 2.4. FCM clustering FCM [33] is a data classification method between similar type of objects where a hard decision threshold between the data is unavailable. In this method, similar type of data is separated to two or more clusters based on the requirement. One may argue on the applicability of the Fuzzy Logic-based tool in CSS in view of its real-time nature. It may be noted that some recent papers [34, 35] have already studied the scope of fuzzy logic in CSS. In our proposed faulty SU node detection algorithm, due to the dynamic nature of the channel parameters such as noise, fading and SU node positions, it is difficult to find a closed form expression for the decision threshold between reliable SU nodes and faulty SU nodes in terms of the probability values generated by our proposed algorithm. So, instead of using a static decision threshold, a FCM-based clustering algorithm is used to differentiate between them. Details of the algorithm can be found in Section 3. In the next section, how to detect those faulty sequences and the corresponding faulty nodes and maintain the reliability of the HMM parameters are explained in details. 3. FAULTY NODE DETECTION IN HMM-BASED CSS FOR CR NETWORKS As seen from Section 1.2, though HMM-based spectrum prediction in CRNs is well investigated, the challenge of maintaining the reliability of the spectrum prediction in the presence of faulty nodes has not yet received due attention from the researchers, despite its practical importance. As mentioned earlier, in [31], the authors report reliable system performance only in the presence of moderate percentage of faulty nodes in CRN. This may be due to a fixed decision threshold selection approach adopted to differentiate between faulty and healthy nodes in the network ignoring dynamics of the CSS environment due to fading nature of the sensing and reporting channels involved in the process. Thus the problem of designing a faulty node detection scheme in CSS with greater robustness remains open. In this section, we present a detailed description of our highly sensitive faulty node detection scheme to be used in HMM-based spectrum prediction process in cognitive radio networks, especially in low SNR environment. The novelty of our proposed scheme may be summarized in two parts: (i) considering application of the forward algorithm of HMM [32], for determining the probability value of the PU state sequence observed at any SU node (healthy or faulty) and (ii) using FCM technique for segregating faulty SU nodes from healthy ones using these probability values and dynamic decision threshold selection mechanism. Besides, the scheme neither asks for the information on the fading statistics of the sensing and reporting channels used in the CSS, nor the power adaptation strategy adopted by the SU nodes participating in the spectrum prediction process. For the ease of readability, our proposed scheme is described in the following five steps. It is also illustrated in Fig. 4. Algorithm 1 Faulty Node Detection in HMM-based CSS For CR Networks Input HMM parameters λ=(π,A,B), Received observation sequences O={O1,O2,…,OT} at FC, Most reliable SU node. Output Modified HMM parameters, The future PU state zT+1, Set of reliable SU nodes U(K−F)R, Set of faulty SU nodes UFF. Initialization: HMM parameters, Most reliable SU node. 1 Calculate ZTemp from OTemp using Viterbi Algorithm. 2 Calculate P(O/λ) using Forward Algorithm. 3 Clustering of U=(U1,U2,…,UK) using Fuzzy C-means Clustering algorithm. 4 if ( n(UK−FR=1) then 5 go to Step 1 6 Estimate λ=(π,A,B) using the observation sequence O={O1,O2,…,OT} values of the U(K−F)R cluster set 7 Predict ZT+1 using most reliable node of U(K−F)R set 8 return λ=(π,A,B), ZT+1, U(K−F)R, UFF Input HMM parameters λ=(π,A,B), Received observation sequences O={O1,O2,…,OT} at FC, Most reliable SU node. Output Modified HMM parameters, The future PU state zT+1, Set of reliable SU nodes U(K−F)R, Set of faulty SU nodes UFF. Initialization: HMM parameters, Most reliable SU node. 1 Calculate ZTemp from OTemp using Viterbi Algorithm. 2 Calculate P(O/λ) using Forward Algorithm. 3 Clustering of U=(U1,U2,…,UK) using Fuzzy C-means Clustering algorithm. 4 if ( n(UK−FR=1) then 5 go to Step 1 6 Estimate λ=(π,A,B) using the observation sequence O={O1,O2,…,OT} values of the U(K−F)R cluster set 7 Predict ZT+1 using most reliable node of U(K−F)R set 8 return λ=(π,A,B), ZT+1, U(K−F)R, UFF Algorithm 1 Faulty Node Detection in HMM-based CSS For CR Networks Input HMM parameters λ=(π,A,B), Received observation sequences O={O1,O2,…,OT} at FC, Most reliable SU node. Output Modified HMM parameters, The future PU state zT+1, Set of reliable SU nodes U(K−F)R, Set of faulty SU nodes UFF. Initialization: HMM parameters, Most reliable SU node. 1 Calculate ZTemp from OTemp using Viterbi Algorithm. 2 Calculate P(O/λ) using Forward Algorithm. 3 Clustering of U=(U1,U2,…,UK) using Fuzzy C-means Clustering algorithm. 4 if ( n(UK−FR=1) then 5 go to Step 1 6 Estimate λ=(π,A,B) using the observation sequence O={O1,O2,…,OT} values of the U(K−F)R cluster set 7 Predict ZT+1 using most reliable node of U(K−F)R set 8 return λ=(π,A,B), ZT+1, U(K−F)R, UFF Input HMM parameters λ=(π,A,B), Received observation sequences O={O1,O2,…,OT} at FC, Most reliable SU node. Output Modified HMM parameters, The future PU state zT+1, Set of reliable SU nodes U(K−F)R, Set of faulty SU nodes UFF. Initialization: HMM parameters, Most reliable SU node. 1 Calculate ZTemp from OTemp using Viterbi Algorithm. 2 Calculate P(O/λ) using Forward Algorithm. 3 Clustering of U=(U1,U2,…,UK) using Fuzzy C-means Clustering algorithm. 4 if ( n(UK−FR=1) then 5 go to Step 1 6 Estimate λ=(π,A,B) using the observation sequence O={O1,O2,…,OT} values of the U(K−F)R cluster set 7 Predict ZT+1 using most reliable node of U(K−F)R set 8 return λ=(π,A,B), ZT+1, U(K−F)R, UFF 3.1. Proposed method Step 1: At first, the scheme selects the received observation sequence OTemp={O1,O2,…,OT} corresponding to any arbitrary SU node and calculates a temporary PU state sequence ZTemp={z1,z2,…,zT} corresponding to it using Viterbi algorithm. Let K be the total number of SU nodes in the system out of which a random set of F nodes is malfunctioning. The data received in any observation slot t ∀t∈{1,2,…,T} from the SU nodes at FC are denoted by Rkt∀k∈{1,2,…,K}. So after T time slot, each row of R, which is a K×T matrix, stores either the reliable observation sequence OR={OR1,OR2,…,ORT} or the faulty observation sequence OF={OF1,OF2,…,OFT}. Step 2: Now given the model λ=(π,A,B) (the HMM parameters used here are the obtained from the training procedure described in HMM training section earlier), our aim is to find P(Rkt/λ)∀k∈{1,2,…,K},t∈{1,2,…,T}, that is the probability (or likelihood) of observation sequence Okt={Ok1,Ok2,…,OkT} at kth SU node generated by that temporary state sequence ZTemp in the system. To find P(Rkt/λ) we have used Forward Algorithm [32]. The steps are described below. For t={1,2,…,T} and i={1,2,…,N} we define αkt(i)=P(Rk1,Rk2,…,Rkt,zt=qi|λ) (8) where αkt(i) is the probability of the partial observation sequence up to time t and qt is the state at time t for kth SU node. Now αkt(i) can be calculated recursively as follows: Initialization: Let αk1(i)=πibi(Rk1),1≤i≤N (9) Induction: For t=1,2,…,(T−1) compute αk(t+1)(j)=[∑i=1Nαkt(i)aij]bj(Rk(t+1)),1≤j≤N. (10) Termination: P(Rkt/λ)=∑i=1NαkT(i) (11) Step 3: The results are stored in a set Uk={u1,u2,…,uK} which is mixed with the probability values of reliable nodes and faulty nodes where uk=P(Rkt/λ)∀t∈{1,2,…,T} represents the probability value of the kth SU node. Now from this set Uk, it is required to find a threshold value Uth so that this set can be divided into two disjoint sets: U(K−F)R={U1R,U2R,…,U(K−F)R} one for reliable SU nodes and UFF={U1F,U2F,…,UFF} another for faulty SU nodes. But, it is an extremely difficult task to determine a unique Uth for reliable SU nodes because that Uth will be a dynamic one as it is function of channel parameters such as fading nature, noise, PU power and SU node positions which are random in nature. So instead of finding an analytical expression for the Uth, we choose FCM clustering to find two cluster centers CR and CF corresponding to reliable SU cluster set U(K−F)R and faulty SU cluster set UFF respectively where 0<|CR|,|CF|<1 and |CR|>|CF|. The value of Uk for kth SU node closer to cluster center is selected as a member of that cluster set means, if |CR−Uk|≤|CF−Uk| then Uk is selected as a member of U(K−F)R set; else Uk is considered as a member of UFF set. Now based on the decreasing probability values, the members of reliable SU node set U(K−F)R are rearranged and the topmost member in the list is considered as the most reliable (least probability of malfunctioning) SU node. Thus, the said process of dynamic thresholding does not depend upon some specific fading statistics of the channel. Hence, it is equally applicable if one considers other fading statistics like Rician and Nakagami fading [36]. Now from the next time slot, the observation sequence of the most reliable SU node is considered as the temporary observation sequence OTemp for calculating Ztemp as stated in Step 1. Step 4: Since in Step 1, an arbitrary SU node is selected to predict Ztemp, the node could be either reliable or faulty. This results in two cases: Case 1: If the SU node selected in Step 1 is reliable: then the algorithm can efficiently differentiate between the received data into two sets U(K−F)R and UFF, respectively, as stated in Step 3. The reason behind the probability values of all reliable SU nodes are clustered on the same set U(K−F)R and all faulty nodes on the set UFF is as follows. Since all reliable SU nodes are sensing the same PU spectrum and they are collocated, so their observed sequences Oi∀i∈{1,2,…,(K−F)} will be more correlated in nature. Hence, the temporary hidden state sequence ZTemp is calculated in Step 1 from most reliable SU node will be more similar to the original PU state sequence Zoriginal={z1,z2,…,zT}, where Zoriginal is the actual PU state sequence, hidden to SU nodes. Thus, P(Rkt/λ)∀k∈{1,2, . . . ,(K−F)}, which is the probability of all observed sequences to produce that hidden state sequence will be closer to each other. But for any faulty SU node, these probability values P(Rkt/λ)∀k∈{1,2,…,F} will be less than that of any reliable SU node as it is assumed to have no correlation with PU signal. Case 1 will also be repeated if the most reliable SU node of UR set sends reliable data in the next time slot. Case 2: If the SU node selected in Step 1 is faulty: then the algorithm results in only one member in U(K−F)R set. The rest of the members belongs to UFF set. This is because as selected observation sequence OTemp is faulty, the temporary PU state sequence ZTemp obtained from that observed SU node sequence will be uncorrelated with the original PU state sequence Zoriginal. As a result, all the probability values will be very less than that of the faulty SU node. Precisely, P(OTemp/λ)≫P(Ok/λ)∀k∈{1,2,…,(K−1)}. So after clustering, U(K−F)R set will have only one SU node and all the other SU nodes will be in the UFF set. So a checking condition is added in our algorithm. If the number of SU node in set U(K−F)R is one, then the members of the two sets are not updated and the algorithm selects the next most reliable SU node from set U(K−F)R (or selects another observation sequence of any arbitrary SU node if this condition arises in initial time slot) and the process continues again from the first step. If it is not one, then the members of the sets are updated with current values and the process continues. So the minimum number of SU nodes in the system must be greater than two. Case 2 will also be repeated if the most reliable SU node of U(K−F)R also starts malfunctioning in the next time slot. Step 5: The HMM parameters are trained using the observation sequences of the members of U(K−F)R set. The future PU state zT+1 is predicted using the observation sequence of that most reliable SU node sequence from U(K−F)R set by the prediction rule stated in Section 2. Finally, the predicted value of future PU state zT+1 is sent to the members of U(K−F)R set and an advisory report is sent to the members of UFF set about their malfunctioning, through the feedback channel. In the next time slot, the observation sequence corresponding to the most reliable SU node from U(K−F)R set is selected to generate again a temporary PU state sequence ZTemp and the above steps are repeated to update the members of the two set U(K−F)R and UFF in each time slot. Figure 4. View largeDownload slide Block diagram of our proposed method. Figure 4. View largeDownload slide Block diagram of our proposed method. 3.2. Complexity analysis In our proposed algorithm, two tools are used, HMM and FCM clustering. In Step 1, Viterbi algorithm is used to uncover the hidden state sequence from observation sequence using HMM parameters. The complexity of it depends upon the number of states N and the number of observation sequence T which is O(N2T) [32]. As N=2 in our scheme, so the complexity is in the order of O(T). In Step 2, forward algorithm is used to calculate the probability of observation sequence generating the temporary state sequence. For calculating each probability values, N2T [37] multiplications are required. As there are K number of SU nodes in our model, so total KN2T multiplications are required. So the complexity of this algorithm is found to be O(KT) as N=2. In Step 3, FCM clustering is used to differentiate between reliable SU nodes and faulty SU nodes. This algorithm runs in Θ(KC2P) [38] where C is the number of clusters and P is the dimension of the data point. Hence, the complexity is bounded by O(KC2P). In our method, the number of clusters is two and the dimension of the data is one. So the complexity is reduced in O(K). However, in [38], the authors further showed that this complexity can be reduced to Θ(KCP) with a modified version of FCM. Step 4 requires only one comparison. If the comparison results yes then our scheme is repeated from the first step. If L is the number of times the algorithm runs in the loop, the complexity of the loop with be L times of the overall complexity of each iteration of the loop. However, with a large number of simulations, it is found that the algorithm runs the loop only for 1–3 times because it is highly unlikely that the most reliable SU node starts malfunctioning in subsequent time slot. So L=1 is taken in our analysis. In Step 5, the training of HMM parameters is done by Baum Welch algorithm. Forward–Backward (FB) algorithm is used for the estimation of HMM parameters in this technique which has a time complexity O(N2T) [37] for both forward (as stated earlier) and backward algorithm. So it is also O(T). Therefore, the total complexity of the proposed scheme is O(T)+O(KT)+O(K)+O(T). Now as K and T are both non-negative integers, so the overall complexity of this algorithm is reduced to O(KT). 4. SIMULATION RESULTS In order to validate the efficiency of the proposed method, we simulate our algorithm in MATLAB. All the necessary parameters and their corresponding values used in our simulation are listed in Table 3. The PU arrival rate is assumed to follow Poisson Distribution with mean μp=30 and variance σp2=1 and the idle durations are exponentially distributed with mean μe=70 and variance σe2=1 with probability of PU occupying the spectrum being 30%. The observation history length is set as T=100 and number of samples per observation is set as N=50. Necessary parameters of the HMM under consideration are initialized as follows: πini=[0.5 0.5],Aini=[0.50.50.50.5], Bini=[0.5⋅⋅⋅0.50.5⋅⋅⋅0.5]2×100. Table 3. List of necessary parameters and their values. Name of the Parameter Value Total sampling interval 100 Path loss exponent 3.5 No of samples send per instance per SU node 50 Mean of PU arrival rate of Poisson distribution 30 Variance of PU arrival rate of Poisson distribution 1 Mean of PU idle durations of exponential distribution 70 Variance of PU idle durations of exponential distribution 1 Percentage of PU presence 30% The observation history length 100 Range of received SNR values 0dB to −22dB Name of the Parameter Value Total sampling interval 100 Path loss exponent 3.5 No of samples send per instance per SU node 50 Mean of PU arrival rate of Poisson distribution 30 Variance of PU arrival rate of Poisson distribution 1 Mean of PU idle durations of exponential distribution 70 Variance of PU idle durations of exponential distribution 1 Percentage of PU presence 30% The observation history length 100 Range of received SNR values 0dB to −22dB Table 3. List of necessary parameters and their values. Name of the Parameter Value Total sampling interval 100 Path loss exponent 3.5 No of samples send per instance per SU node 50 Mean of PU arrival rate of Poisson distribution 30 Variance of PU arrival rate of Poisson distribution 1 Mean of PU idle durations of exponential distribution 70 Variance of PU idle durations of exponential distribution 1 Percentage of PU presence 30% The observation history length 100 Range of received SNR values 0dB to −22dB Name of the Parameter Value Total sampling interval 100 Path loss exponent 3.5 No of samples send per instance per SU node 50 Mean of PU arrival rate of Poisson distribution 30 Variance of PU arrival rate of Poisson distribution 1 Mean of PU idle durations of exponential distribution 70 Variance of PU idle durations of exponential distribution 1 Percentage of PU presence 30% The observation history length 100 Range of received SNR values 0dB to −22dB In off-line training period, the HMM parameters are trained 500 times for the rest of our simulations. The performance of the proposed method is evaluated in terms of probability of detection Pd and probability of false alarm Pfa for a given SNR. They are defined as Pd=P(FCpredictsℋ1|originallyPUisactive) (12) Pfa=P(FCpredictsℋ1|originallyPUisidle) (13) The objective is to get higher Pd value for lower values of Pfa which is a measure of reliable system performance. The SNR of the sensed signal reported by SUi is calculated at FC using Equation (2). Since SUs are assumed to be collocated with respect to PU and FC, average SNR of the signals forwarded by different SUs are considered to be the same at FC. Figure 5 shows the performance degradation of our system with increasing number of faulty nodes in the system with respect to different received SNR scenarios, for Pfa=0.1. It can be seen that Pd value decreases as the system has more number of faulty nodes for any fixed received SNR value. At SNR=−10dB and 20% faulty nodes, the decrease of Pd value is found to be 21% from the case of no faulty node. It is evident that the Pd value decreases for increasing number of faulty nodes in the system as by increasing the number of faulty nodes, the system has more faulty data for the training process. So the updated HMM parameters are not reliable. Pd value also decreases for decreasing values of received SNR because with decreasing SNR values, the probability that some of the reliable SU nodes are detected to be faulty and vice versa increases. This results degradation of the Pd value. Figure 5. View largeDownload slide Performance degradation of our system at different received SNR conditions with increasing number of faulty nodes for Pfa=0.1. Figure 5. View largeDownload slide Performance degradation of our system at different received SNR conditions with increasing number of faulty nodes for Pfa=0.1. In Fig. 6, we compare single faulty node detection sensitivity of our proposed method vs method in [31] for different received SNR values where total number of SU nodes = 10. Faulty node detection sensitivity is defined as the ratio between the number of correct detection of faulty nodes and the number of trial in our simulation. It can be seen, for SNR=−12dB, detection rate is nearly 48% as compared with [31], where it is almost 33%. The reason behind the performance improvement our scheme is that in [31], the authors used a static threshold for detecting faulty nodes. But, in our method, we use a dynamic threshold which is capable of detecting single faulty nodes with greater reliability. Figure 6. View largeDownload slide Single faulty SU node detection sensitivity curves of our proposed method vs method in [31] for different SNR (dB) conditions; Pfa=0.1, the total number of SU nodes = 10. Figure 6. View largeDownload slide Single faulty SU node detection sensitivity curves of our proposed method vs method in [31] for different SNR (dB) conditions; Pfa=0.1, the total number of SU nodes = 10. In Fig. 7, faulty SU nodes detection accuracy of the proposed method is shown for different percentage of faulty nodes existing in the system with total number of SU nodes as a parameter, received SNR=−10dB and Pfa=0.1. Faulty SU nodes detection accuracy is defined as the ratio of total number of faulty nodes detected by the proposed method to the total number of faulty nodes actually existing in the system. It can be observed that as the percentage of faulty nodes are increasing in the system, the detection accuracy decreases because increase in faulty nodes implies decrease in the number of reliable nodes. Since only reliable nodes are used for achieving high Pd, through spectral diversity, decrease in reliable nodes decreases Pd. As we increase the total number of SU nodes in the system, the detection performance is improved because the system has more reliable data for training of the HMM parameters. The detection accuracy decreases by 23% as the number of faulty nodes is increased from 20% to 80% for total number of SU nodes = 60. Figure 7. View largeDownload slide Faulty SU node detection accuracy vs. different percentages of faulty SU nodes curve for different number of SU nodes for received SNR=−10dB and Pfa=0.1. Figure 7. View largeDownload slide Faulty SU node detection accuracy vs. different percentages of faulty SU nodes curve for different number of SU nodes for received SNR=−10dB and Pfa=0.1. For better understanding of the improvement of our proposed method, Fig. 8 illustrates the receiver operating characteristics (ROC) curve which compares our proposed method with that in [31], with the number of faulty nodes as a parameter. It can be seen that for Pfa=0.1 and 10% faulty nodes in the system, the improvement of Pd value is about 14% than the method in [31]. But for same value of Pfa and 40% faulty nodes in the system, almost 56% improvement of Pd value can be achieved than the method in [31], which indeed shows effectiveness of our system over [31]. Our ROC curve maintains much better level of reliability even for 80% faulty nodes in the system compared to [31] with 40% faulty nodes. The reason that the method in [31] losses its robustness when percentage of faulty nodes are more than 30% is due to their faulty-node detection method. Their method is based on the evidence from the other cooperative SU nodes. As they have set the evaluation threshold 0.5, so if the percentage of faulty users are less than 30%, this method maintains it reliability. But if number of faulty users are increasing, the individually calculated evidences of the faulty users become higher and the method fails to maintain its robustness. In our method, instead of setting a fixed threshold, a dynamic clustering method is used so that even if the percentage of faulty SU nodes is more than 30%, this algorithm still maintains reliable spectrum prediction in the system. Figure 8. View largeDownload slide ROC curves comparison of our proposed method vs method in [31] for received SNR(dB) is in between −22dB and −10dB. Figure 8. View largeDownload slide ROC curves comparison of our proposed method vs method in [31] for received SNR(dB) is in between −22dB and −10dB. 5. CONCLUSION In this paper, we have evaluated HMM-based CSS in the presence of random faulty nodes in CRNs. Degradation in PU spectrum prediction accuracy, due to training of HMM parameters by such a set of SU nodes, is quantified under low SNR scenario. 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TI - Faulty Node Detection in HMM-Based Cooperative Spectrum Sensing For Cognitive Radio Networks
JF - The Computer Journal
DO - 10.1093/comjnl/bxx127
DA - 2018-10-01
UR - https://www.deepdyve.com/lp/oxford-university-press/faulty-node-detection-in-hmm-based-cooperative-spectrum-sensing-for-w10Zj3KjaT
SP - 1468
VL - 61
IS - 10
DP - DeepDyve
ER -