Performance evolution of ED-based spectrum sensing in CR over Nakagami-m/shadowed fading channel with MRC reception

Internet of things contains the hefty number of devices with diverse types of communication interfaces. Therefore, these devices act as a source of interference to the primary users in the absence of appropriate collision detection technique. Spectrum sensing is the important function of cognitive radio and energy detector is the most popular technique used for spectrum sensing. Detection of the availability of unused spectrum for the secondary user becomes difficult when the channel is affected by composite multipath/shadowed fading. In this paper, analytical expressions of average probability of detection and average area under the receiver operating characteristic over Nakagami-m/log-normal with maximum ratio combining diversity are derived using Gaussian-Hermite integration approximation. In addition, an optimized threshold has been incorporated to overcome the problem of spectrum sensing even at low signal-to-noise ratio. To verify the correctness of exact results and derived analytical expressions, Monte Carlo simulations are incorporated.     

Performance of MRC receiver over Hoyt/lognormal composite fading channel

In this article, mixture gamma (MG) distribution is used for analysing the performance of L-Hoyt/lognormal composite fading channel. To overcome small-scale fading effect, micro-diversity using maximum ratio combining (MRC) is used at the receiver. Due to mathematical complexity, performance analysis of composite (L-Hoyt/lognormal) fading models is not present in closed form. The analytical expressions for the performance measure are derived in the form of received signal-to-noise ratio (SNR). The impact of system parameters on the energy detector (ED) performance is studied in terms of receiver operating characteristic (ROC) and area under the ROC curve (AUC). Further, the detection threshold parameter is optimised by minimising the total probability of error for L-Hoyt/lognormal channel. The accuracy of the proposed closed-form expressions is validated by comparing all the results with the Monte-Carlo/exact simulations.     

Performance analysis of spectrum sensing techniques over TWDP fading channels for CR based IoTs

In this paper, the performance of spectrum sensing techniques over two wave diffused power (TWDP) fading channels has been investigated for CR based IoT devices. The ubiquitous objects based on IoTs with cognitive capabilities are the future that would enable intelligent decisions to achieve any time, any place, interference-free and on-demand services. In this work, new closed-form expressions in terms of Marcum-Q function and Whittaker function for the spectrum detection probability over TWDP fading channels have been derived for different sensing techniques. The expressions are then used to optimize the decision threshold for IoT sensor nodes describing the optimal behavior of sensing over TWDP channels. The error probabability and Receiver Operating Characteristic (ROC) curves have been plotted and the operating point and limiting values of threshold for optimal performance have been identified. The performance loss of traditional energy detection (ED), cyclostationary based detection (CSD) and matched filtering detector (MFD) has been analyzed. The analytical results thus obtained are validated through monte-carlo simulations.     

Performance analysis of shadowed-Rice fading channel with cooperative spectrum sensing

In this paper, the performance analysis of wireless communication system over shadowed-Rice (SR) composite fading channel has been investigated and analysed. The unified analytical expressions of the average symbol error probability (ASEP) for several coherent and non-coherent modulation schemes separately with different constellation sizes are derived for composite fading channel under two different fade mitigation methods, with maximal ratio combining (MRC) microdiversity (Method 1) and MRC applied over the composite fading channel (Method 2). Furthermore, an asymptotic analysis is carried out and a closed-form expression of the ASEP with Method 2 is presented. Analytical expressions of the corresponding average probability of energy detection (PD) are formulated for both the methods. Finally, the derived PD expression is utilised to analyse the performance of cooperative system assuming erroneous feedback channel. Analysis of optimisation of detection threshold as well as number of cognitive users to minimise the total error rate is also carried out. The closed-form expressions are validated by comparing them with exact numerical results and Monte Carlo simulation.     

Signal Detection in Cognitive Radio Networks over AWGN and Fading Channels

In this paper, we consider the problem of spectrum sensing based on energy detection method in cognitive radio over wireless communication channels when users experiences fading and nonfading effects. The closed-form analytical expressions for the detection probability are derived over nonfading additive white Gaussian noise channel, Rayleigh, Rician and Nakagami-m fading channels. The detection probability involving Marcum-Q function is replaced by closed-form expression. The probability distribution function of fading channels is used to obtain the expressions for detection probability. The new derived numerical results are simulated under various parameters.     

Performance optimisation of RF energy harvesting relay-based interweave/underlay cognitive radio network

This paper investigates the performance of energy harvesting (EH) relay-based interweave/underlay cognitive radio network. The relay employs amplify and forward (AF) technique along with time-switching relaying protocol (TSR) for EH. Based on sensing accuracy, we derive an expression for optimisation of charging duration TSR parameter and sensing duration for maximising throughput of interweave cognitive radio (CR). Based on sensing efficiency, throughput and outage probability for underlay CR is analysed considering the interference temperature constraints and optimal power distribution parameter at secondary user (SU) terminals. Variations in the sum-rate and detection probability are considered in terms of cumulative distribution functions (CDF) of the terminal Signal to Noise Ratios (SNRs). We prove that erogodic sum-rate is maximised in underlay CR case, when interference power distribution parameter is half across the SU terminals. The optimised values of switching-time ratios have been derived analytically for both interweave and underlay CR. The results thus obtained are compared by taking symmetrical and asymmetric channels between SU terminals. Analytical results are validated through Monte-Carlo simulations to confirm the accuracy of the derived expressions.     

Optimized cooperative spectrum sensing network analysis in nonfading and fading environments

The proposed cooperative spectrum sensing (CSS) network is equipped with multiple antennas and an improved energy detector (IED) scheme at each cognitive radio (CR). Each CR in the network receives the information about the primary user (PU) in the form of binary decisions at multiple antennas. Diversity technique called selection combining (SC) scheme is used at multiple antennas to select the maximum value of sensing information present at multiple antennas. Finally, sensing information will be passed to the fusion center (FC) through reporting channel, and the final decision about PU is made at FC using fusion rules. Initially, we have derived the novel missed detection probability expressions for AWGN channel, Rayleigh, and Rician fading environments. Later, the closed form of optimized expressions for proposed CSS network parameters are derived to achieve an optimal performance. The closed form of optimized expressions such as number of CR users (N_opt ), normalize threshold value (λ_n,opt ), and an arbitrary power of the received signal (p_opt ) are derived under various fading environments. The performance is evaluated using complementary receiver operating characteristics (CROC) and total error rate curves. The MATLAB‐based simulations are evaluated with the strong support of theoretical expressions. Finally, various simulation parameters such as sensing channel SNR, the error rate in reporting channel, threshold value, and number of antennas at each CR are considered in the simulation to show the effect on the performance of proposed CSS network.     

Capacity limits of spectrum‐sharing systems over hyper‐fading channels

Cognitive radio (CR) with spectrum‐sharing feature is a promising technique to address the spectrum under‐utilization problem in dynamically changing environments. In this paper, the achievable capacity gain of spectrum‐sharing systems over dynamic fading environments is studied. To perform a general analysis, a theoretical fading model called hyper‐fading model that is suitable to the dynamic nature of CR channel is proposed. Closed‐form expressions of probability density function (PDF) and cumulative density function (CDF) of the signal‐to‐noise ratio (SNR) for secondary users (SUs) in spectrum‐sharing systems are derived. In addition, the capacity gains achievable with spectrum‐sharing systems in high and low power regions are obtained. The effects of different fading figures, average fading powers, interference temperatures, peak powers of secondary transmitters, and numbers of SUs on the achievable capacity are investigated. The analytical and simulation results show that the fading figure of the channel between SUs and primary base‐station (PBS), which describes the diversity of the channel, does not contribute significantly to the system performance gain. Copyright © 2011 John Wiley & Sons, Ltd.     

Hard and softened combination for cooperative spectrum sensing over imperfect channels in cognitive radio networks

Recently, cognitive radio (CR) access has received much attention to overcome spectrum scarcity problem. Spectrum sensing methods are often used for finding free channels to be used by CR. In this paper, the problem of cooperative spectrum sensing will be investigated in CR networks over realistic channels. This problem is not clarified until now by taking into account the error effect on the decision reporting. The analytical expressions of the hard and softened one bit and two bits hard combination scheme for cooperative spectrum sensing will be derived. These expressions are investigated to compare with simulation results. The analysis and simulation results show that the performance of cooperative spectrum sensing is limited by the probability of reporting errors. Moreover, it is shown that there is a significant performance loss when a final decision regarding to primary user’s (PU) state made at the fusion depends on a set of local spectrum sensing information that are distorted by imperfect reporting channels during transmission. The probability of detection is degraded due to imperfect reporting channel by 16.5% and 12.2% with one bit hard combination and softened two bits hard combination, respectively. To reduce this performance loss, Amplify and Forward (AAF) relying mechanism will be proposed. The probability of detection is improved by 8% and 9.3% with one bit hard combination and softened two bits hard combination, respectively using AAF relaying mechanism.     

Cognitive radio network with coordinated multipoint joint transmission

Cognitive radio (CR) is considered to be a promising technology for future wireless networks to make opportunistic utilization of the unused or underused licensed spectrum. Meanwhile, coordinated multipoint joint transmission (CoMP JT) is another promising technique to improve the performance of cellular networks. In this paper, we propose a CR system with CoMP JT technique. We develop an analytical model of the received signal‐to‐noise ratio at a CR to determine the energy detection threshold and the minimum number of required samples for energy detection–based spectrum sensing in a CR network (CRN) with CoMP JT technique. The performance of energy detection–based spectrum sensing under the developed analytical model is evaluated by simulation and found to be reliable. We formulate an optimization problem for a CRN with CoMP JT technique to configure the channel allocation and user scheduling for maximizing the minimum throughput of the users. The problem is found to be a complex mixed integer linear programming. We solve the problem using an optimization tool for several CRN instances by limiting the number of slots in frames. Further, we propose a heuristic‐based simple channel allocation and user scheduling algorithm to maximize the minimum throughput of the users in CRNs with CoMP JT technique. The proposed algorithm is evaluated via simulation and found to be very efficient.     

Modelling and Performance Analysis of Energy Detector Over Weibull–Shadowed Fading Channel with Application to Cooperative Sensing

In this work, we investigate and analyse the performance of the energy detector over Weibull–Shadowed composite fading channel. To this end, we have derived the novel expressions for the probability of detection (PD) and the average area under the receiver operating characteristic curve (AUC). Furthermore, the asymptotic analysis of such performance metrics has been carried out and the simpler and closed-form expressions of the PD and the average AUC have been proposed with maximal ratio combining, equal gain combining, and selection combining diversity schemes. Finally, the derived results have been applied to cooperative system considering erroneous channel between secondary users and a fusion center. The derived expressions are valid for both integer and non-integer values of the multipath and shadowing parameters. The derived analytical results are corroborated by both exact numerical results and Monte-Carlo simulations, and it is shown that the performance of cooperative system not only depends on the parameters of composite fading distribution but also on the erroneous feed-back channel.     

Cross‐layer optimization for full‐duplex cognitive radio network with cooperative spectrum sensing

In this paper, the cross‐layer optimal design of multihop ad hoc network employing full‐duplex cognitive radios (CRs) is investigated. Firstly, the analytical expressions of cooperative spectrum sensing performance for multihop CR networks over composite fading channels are derived. Then, the opportunistic throughput and transmit power of CRs are presented based on the derivation of false alarm and missed detection probability. Finally, a multiobjective optimization model is proposed to maximize the opportunistic throughputs and minimize the transmitting power. Simulation results indicate that Pareto optimal solution of sensing duration, decision threshold, and transmit power can be achieved by cross‐layer multiobjective optimization, it can balance the conflicts between different objective functions and reap the acceptable outcomes for multihop CR network.     

Adaptive Decode-and-Forward Protocol Based Cooperative Spectrum Sensing in Cognitive Radio with Interference at the Secondary Users

In this paper a novel multiple-user cooperative spectrum sensing scheme (MCSS) based on hybrid relay is proposed to achieve the spatial diversity gain in detection of the primary user (PU) in a cognitive radio (CR) network. A practically important case where co-channel interference signals are present at the network is considered for the analysis. Closed-form expressions of detection probability \((\hbox {P}_{\mathrm{d}})\) and false alarm probability \((\alpha )\) for the proposed adaptive decode-and-forward based multiple-user cooperative spectrum sensing scheme (ADF-MCSS) using energy detector over Rayleigh fading sensing channels is derived in presence of co-channel interference at the secondary user which is far away from the PU. Further we extend the concept of two user amplify-and-forward (AF) and decode-and-forward (DF) cooperative spectrum sensing schemes in multiple-user scenario (i.e. AF-MCSS and DF-MCSS) over Rayleigh fading channels when the secondary user (which is far away from PU) is affected by interference. Closed-form expressions of AF-MCSS and DF-MCSS schemes over a Rayleigh fading channels are also evaluated and compared with that of proposed ADF-MCSS in presence of interference signals at the secondary user. Further the performance analysis of AF-MCSS, DF-MCSS and ADF-MCSS schemes are compared with the existing non-cooperative spectrum sensing schemes in presence of interference at the secondary user. Our analysis is validated by numerical and simulation results for multiple-user CR network. The impact of number of cooperative relays, SNR in sensing channel, energy of interference signal, false alarm on detection probability in proposed ADF, AF and DF schemes is shown.     

基于解码转发CR-NOMA协同系统物理层安全性能分析

分析了认知无线电（Cognitive Radio,CR）非正交多址（Non-orthogonal Multiple Access,NOMA）网络中的物理层安全性能。考虑到现有窃听者,支持NOMA的CR通过Nakagami-m信道以解码转发协作模式传输数据。为了分析CR-NOMA物理层安全性能,通过连接中断概率和安全中断概率的闭式表达式来评估CR-NOMA的安全性能。此外,通过蒙特卡罗模拟仿真以验证推导出的分析结果,并深入分析了参数对系统性能的影响。     

Performance of an energy detector over η-μ/lognormal composite channel with cooperative sensing

The η-μ/lognormal composite distribution corresponds to a physical realistic scenario where the multipath effect is characterised by well-known η-μ generalised model and shadowing effect is captured by the lognormal (LN) distribution. In this work, an approximate closed-form of η-μ/LN distribution is derived using Gauss-Hermite (GH) integration. Further, the derived probability density function is utilised to develop the closed-form expression as well as infinite series representation of the average probability of energy detection (PD) and average area under the receiver operating characteristics curve (AUC) along with their respective upper bound of the truncation error. Maximal ratio combining (MRC) microdiversity technique is applied over η-μ/LN composite fading model and then its average PD is derived. In order to reduce the total probability of error, the optimisation of the detection threshold parameter is done. The result clearly shows the significant improvement in the detection probability when the optimised threshold parameter is used. Further, an extensive analysis of the optimisation of the cooperative spectrum sensing (CSS) over η-μ/LN distribution with ‘v-out-of-U’ rule at fusion center assuming erroneous feedback channels is also carried out. The closed-form expressions are validated by comparing them with exact results and Monte Carlo simulation.     

Detection performance of cooperative spectrum sensing with hard decision fusion in fading channels

In this paper, we investigate the detection performance of cooperative spectrum sensing (CSS) using energy detector in several fading scenarios. The fading environments comprise relatively less-studied Hoyt and Weibull channels in addition to the conventional Rayleigh, Rician, Nakagami-m and log-normal shadowing channels. We have presented an analytical framework for evaluating different probabilities related to spectrum sensing, i.e. missed detection, false alarm and total error due to both of them, for all the fading/shadowing models mentioned. The major theoretical contribution is, however, the derivation of closed-form expressions for probability of detection. Based on our developed framework, we present performance results of CSS under various hard decision fusion strategies such as OR rule, AND rule and Majority rule. Effects of sensing channel signal-to-noise ratio, detection threshold, fusion rules, number of cooperating cognitive radios (CRs) and fading/shadowing parameters on the sensing performance have been illustrated. The performance improvement achieved with CSS over a single CR-based sensing is depicted in terms of total error probability. Further, an optimal threshold that minimises total error probability has been indicated for all the fading/shadowing channels.     

Multi-channel energy detection under phase noise: analysis and mitigation

For the development of highly integrated, flexible and low-cost cognitive radio (CR) devices, simple transceiver architectures, like direct-conversion receiver, are expected to be deployed and provide viable radio frequency (RF) spectrum sensing solutions for practical implementation. Yet, this can be very challenging task especially if spectrum sensing and down-conversion are conducted over multiple RF channels simultaneously for improved efficiency in channel scans. Then, the so-called dirty RF problem that degrades link performance of traditional transmission systems starts to be influential from spectrum sensing perspective as well. The unavoidable RF impairments, e.g., oscillator phase noise in direct-conversion receiver, could generate crosstalk between multiple channels that are down-converted simultaneously, and thus considerably limit the spectrum sensing capabilities. Most of the existing spectrum sensing studies in literature assume an ideal RF receiver and have not considered such practical RF hardware problem. In this article, we study the impact of oscillator phase noise on energy detection (ED) based spectrum sensing in multi-channel direct-conversion receiver scenario. With complex Gaussian primary user (PU) signal models, we first derive the detection and false alarm probabilities in closed-form expression. The analytical results, verified through extensive simulations, show that the wideband multi-channel sensing receiver is very sensitive to the neighboring channel crosstalk induced by oscillator phase noise. More specifically, it is shown that the false alarm probability of multi-channel energy detection increases significantly, compared to the ideal RF receiver case. The exact performance degradation depends on the power of neighboring channels as well as statistical characteristics of the phase noise in the deployed receiver. In order to prevent such performance degradation in spectrum identification, an enhanced energy detection technique is proposed. The proposed technique calculates the leakage power from neighboring channels for each channel and improves the sample energy statistics by subtracting this leakage power from the raw values. An analytical expression is derived for the leakage power which is shown to be a function of power spectral levels of neighboring channels and 3-dB bandwidth of phase noise process. Practical schemes for estimating these two quantities are discussed. Extensive computer simulations show that the proposed enhanced detection yields false alarm rates that are very close to those of an ideal RF receiver and hence clearly outperforms classical energy detection.     

Energy Detection in Hoyt/Gamma Fading Channel with Micro-Diversity Reception

Spectrum sensing is the important function of cognitive radio and energy detection is the most popular technique used for spectrum sensing. Detection of the availability of unused spectrum for the secondary user becomes difficult when the channel is affected by composite multipath/shadowed fading. In this paper, the performance analysis of an Energy Detector in Hoyt/gamma composite fading channel with Maximum Ratio Combining employing micro-diversity is analyzed. Analytical expressions for performance parameters, i.e., the average probability of detection and the average area under the receiver operating characteristics curve are evaluate. The effect of diversity on the performance of energy detector is also studied. Monte-Carlo simulation results have verified the accuracy of the proposed analysis.     

Diversity Analysis of Peaky FSK Signaling in Fading Channels

Error performance of noncoherent detection of on-off frequency shift keying (OOFSK) modulation over fading channels is analyzed when the receiver is equipped with multiple antennas. The analysis is conducted for two cases: 1) the case in which the receiver has the channel distribution knowledge only; and 2) the case in which the receiver perfectly knows the fading magnitudes. For both cases, the maximum a posteriori probability (MAP) detection rule is derived and analytical probability of error expressions are obtained. Numerical and simulation results indicate that for sufficiently low duty cycle values, lower error probabilities with respect to FSK signaling are achieved. Equivalently, when compared to FSK modulation, OOFSK with low duty cycle requires less energy to achieve the same probability of error, which renders this modulation a more energy efficient transmission technique. Also, through numerical results, the impact of number of antennas, antenna correlation, duty cycle values, and unknown channel fading on the performance are investigated.     

Cooperative Cognitive Radio Networks: New Approach for Detection Accuracy Analysis Under Impaired Channels

The quality of the reporting channel and the relaying mechanism play a significant role in cooperative spectrum sensing (CSS). However, these factors are frequently overlooked when it comes to discussing the performance of CSS in cognitive radio (CR) networks. In this work we investigate the performance of a relay-based CSS approach proposed for CR applications. Specifically, we analyze the detection accuracy of a CR network considering channel impairments, amplify-and-forward relying protocol, and a selection combining scheme. First, a closed form expression for the average false alarm probability is derived. Then, the probability density function (PDF) of the end-to-end signal-to-noise ratio (SNR) is obtained and a closed-form expression for the average detection probability at high SNR applications is derived. The sensing and the reporting channels are assumed to be subjected to independent and identically distributed Rayleigh fading. The PDF approach is used in our analysis. This approach is not easily tractable as it involves higher orders of Bessel functions. However, an approximated polynomial representation of a first-order modified Bessel function of the second kind makes this task possible. The results obtained validate the derived closed form expressions and show the importance of considering reporting channel statistics and relaying mechanism for accurate performance analysis of the CSS in CR networks.