Complementary Receiver Operating Characteristics Research Articles

Spectrum sensing performance of wireless cognitive radio sensor network with hard‐decision fusion over generalizedα−μfading channels

SummaryThe analysis of spectrum sensing performance of energy detection (ED)‐based wireless cognitive radio sensor network (ED‐WCRSN) with hard‐decision combining (HDC) is presented in this paper. Particularly, several network parameters are derived to estimate the performance of ED‐WCRSN, considering channel errors, noise, and generalized fading. In the considered network, first, cognitive radio sensor (CRS) senses a primary user (PU), gets sensing data, and then uses an ED to make a local binary decisions about PU's active or inactive status. In both sensing and reporting channels, the channel error probability is also taken into account. Next, HDC technique is used at control center (CC) to combine the locally obtained decisions, and a final decision about the status of the PU is made. To do so, first, the expression for the novel and analytical, which incorporates noise and fading, detection probability in a CRS is derived and validated using Monte Carlo simulations in MATLAB and using an experimental setup. Then, utilizing derived mathematical expressions, closed‐form expressions of an average error rate (AER), optimal numbers of CRSs, and detection thresholds under noisy and fading conditions are developed. The substantial influence of channel and network factors is assessed using receiver operating characteristics (ROC), complementary ROC, and AER. Finally, the impacts of channel and network parameters on ED‐WCRSN performance are explored. For numerous parameters of the considered network, the optimal values detection threshold and number of CRSs are also found.

Optimization Analysis of Cooperative Spectrum Sensing System over Generalized $$\kappa -\mu $$ and $$\eta -\mu $$ Fading Channels

This paper presents, optimization analysis of energy detection based cooperative spectrum sensing system (CSSS) with hard-decision combining. Several system parameters are optimized to evaluate an optimal performance theoretically over noisy and generalized fading channels. In particular, wireless environments with noise plus $$\kappa -\mu $$ and $$\eta -\mu $$ fading are considered in the sensing channels. More precisely, each secondary user (SU, also called as cognitive radio user) depend on an energy detector (ED). The SU collects the signal from the primary user (PU), is given as input to the ED, and the energy of the signal is calculated for making a binary decision locally. The locally obtained decisions are combined using hard-decision combining and a final decision about position of the PU is made. In this work, the novel mathematical expressions for detection probability of a single SU is derived first, subject to noise plus fading and validated by using Monte Carlo simulations. Next, we develop theoretical frame works for optimization analysis of CSSS using derived mathematical expressions. The channel error probability is considered in both sensing and reporting channels. Further, we derive closed-form optimal expressions of number of SUs and detection threshold subject to generalized fading and optimal values are calculated. Through receiver operating characteristics (ROC), complementary ROC and total error rate, system performance is evaluated for the significant influence of channel and network parameters. Finally, the influence of the generalized fading severity parameters, the signal-to-noise ratio (SNR), the number of SUs, the detection threshold, and the channel error probability on the performance of CSSS is also investigated.

Optimized cooperative spectrum sensing network analysis in nonfading and fading environments

SummaryThe 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 (Nopt), normalize threshold value (λn,opt), and an arbitrary power of the received signal (popt) 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.

Performance improvement of energy detector in cognitive radio using SECp diversity combining technique over fading channel

In this paper, performance of energy detector is analysed over Rayleigh fading environment using different diversity combining techniques. The channel is considered as Independent and Identically Distributed (IID). The closed form expressions for probability of detection using Switch and Stay Combining (SSC) as well as switch and examine combining using post examining selection (SECp) are derived. The performance is compared using the curves of probability of detection for different Signal to Noise Ratio (SNR). Probability of false alarm versus probability of misdetection curves is also compared. These curves are called complementary Receiver Operating Characteristics (ROC) curves. For dual diversity system, SECp is a modified form of SSC. Unlike SSC, when all the paths are tested and none of them has an acceptable SNR, the SECp combiner selects the path having highest SNR. So energy detector's detection performance in a dual diversity system is improved using SECp which is analysed here.

Performance improvement of energy detector in cognitive radio using SECp diversity combining technique over fading channel

In this paper, performance of energy detector is analysed over Rayleigh fading environment using different diversity combining techniques. The channel is considered as Independent and Identically Distributed (IID). The closed form expressions for probability of detection using Switch and Stay Combining (SSC) as well as switch and examine combining using post examining selection (SECp) are derived. The performance is compared using the curves of probability of detection for different Signal to Noise Ratio (SNR). Probability of false alarm versus probability of misdetection curves is also compared. These curves are called complementary Receiver Operating Characteristics (ROC) curves. For dual diversity system, SECp is a modified form of SSC. Unlike SSC, when all the paths are tested and none of them has an acceptable SNR, the SECp combiner selects the path having highest SNR. So energy detector's detection performance in a dual diversity system is improved using SECp which is analysed here.

Modelling and performance evaluation over Nakagami-m/log-normal fading environments

In this paper, we present the closed-form expressions of composite Nakagami-m/log-normal (NL) fading channel by Holtzman approximation. The obtained expressions are used to derive the important performance parameters of wireless communications systems. These performance matrices are amount of fading (AF), outage probability (PO), average channel capacity (CC) and average symbol error probability (ASEP) of coherent modulation comprising binary orthogonal, antipodal, M-ary phase shift keying (M-PSK) and M-ary pulse amplitude modulation (M-PAM). Furthermore, energy detection (ED) is one of the ways to determine whether the signal is present or not. The performance of ED is studied in terms of complementary receiver operating characteristics (CROC) curve. To verify the correctness of our analysis, the derived closed-form expressions are corroborated via exact result and Monte Carlo simulations.

The effect of Weibull fading channel on cooperative spectrum sensing network using an improved energy detector

This paper analyses the performance of proposed cooperative spectrum sensing (CSS) network in Weibull fading environment. First, we have derived the novel analytic expressions for probabilities of missed detection and false alarm in Weibull fading channel, assuming an improved energy detector (IED), selection combining diversity scheme and multiple antennas at each cognitive radio (CRs). Next, performance is analyzed using complementary receiver operating characteristics curves, total error rate, average channel throughput, and network utility function curves for the proposed CSS network. The optimal performance of CSS network is achieved by optimizing the CSS network parameters. The closed form of expressions for the optimum value of number of CRs, arbitrary power of received signal, and detection threshold at each CR are derived using OR-Rule and AND-Rule at fusion center (FC). The average channel throughput and network utility function analysis are evaluated using $$k=1+n$$ and $$k=N-n$$ fusion rules at FC. Finally, the impact of several network parameters such as, multiple antennas at each CR (M), number of CRs (N) in CSS network, Weibull fading parameter (V), arbitrary power of received signal (p), and sensing channel SNR ( $${\bar{\gamma }})$$ on the performance of proposed CSS network are investigated using the simulation results. The performance comparison between conventional energy detector and an IED has been highlighted with the simulations.

MGF Approach Based Analysis Of Energy Detection In <sub> K -M</sub> Shadowed Fading Channels And Diversity Receivers

In this paper, the performance of Energy Detection (ED) over K-M shadowed fading channel is investigated using the Moment Generating Function (MGF) of the received Signal-to-Noise Ratio (SNR). The K-M shadowed is a generic composite fading channel of K- M fading and which represents the impact of multipath in line-of sight (LoS) communication scenario and Nakagami - m distribution. The study is then extended to include Maximal Ratio Combining (MRC), Square Law Combining (SLC), and Square Law Selection (SLS) diversity receivers. The simulation and numerical results for the Complementary Receiver Operating Characteristics (CROC) and average Area under the CROC (CAUC) curves are given for different scenarios and compared with some previous works. These results show an improvement in the overall detection capability of ED is noticed when the diversity receptions are employed. In contrast to previous works which are limited by the values of the fading parameters, the proposed approach is not restricted by any condition.

A novel LMS-BLM algorithm for AF relays based cooperative wireless networks

Wireless communication networks are usually affected by channel impairments such as multi-path fading effects, shadowing, noise, etc. Therefore, techniques to mitigate wireless channel impairments, to improve the quality and spectral efficiency of communication over wireless channels are indispensable. Thus, amplify and forward (AF) relays based cooperative wireless networks are considered in this study for their capability to reduce the effects of fading caused by multipath propagation. Moreover, most studies on relay networks assume perfect channel state information at the receiver (CSIR), but in reality, due to the nature of wireless channels, little information is known on both the channel state information (CSI) and original transmitted signal at the receiver. Therefore, our main contribution is based on proposing a novel algorithm that combines the least mean square (LMS) algorithm and Bayesian linear model (BLM) detector for their low implementation complexity and feasibility. Analytical and theoretical simulations on receiver operating characteristics (ROC), complementary ROC, mean square errors (MSE) learning curves, optimum threshold and probability of error are presented. The results have shown that the proposed algorithm is effective and can provide higher detection performance in the current and next generation wireless networks where multiple relays strategy is applied.

Multiple Antenna-Aided Cascaded Energy and Matched Filter Detector for Cognitive Radio Networks

A new multiple antenna-aided cascaded energy and matched filter detector (MCEM) for cognitive radio networks is proposed. Our proposed scheme is equipped with multiple receive antennas employing energy efficient energy detector (ED) and reliable matched filter (MF) to mitigate the channel fading and increase the detection performance of the secondary users (SUs). Partial decisions are first made by using cascaded energy and matched filter detector (CEM) at each antenna and then the final collaborative decision is made based on those partial decisions. The probability of detection/false alarm of the proposed scheme is presented in terms of the complementary receiver operating characteristics (ROCs). The performance of MCEM scheme is explored via MATLAB simulations that implement the clear channel assessment (CCA) modules for IEEE 802.15.4. Simulation results showed that our proposed MCEM scheme improves the detection performance and is more energy efficient as compared to CEM scheme employing single antenna and other conventional schemes.

On Performance of Weighted Fusion Based Spectrum Sensing in Fading Channels

Cognitive radio (CR) is a promising technology for efficient utilization of underutilized spectrum since it is able to detect the occupancy of primary users (PUs) in the different parts of the spectrum. As the sensing channel uncertainties limit the reliability of the spectrum sensing decision, cooperation among multiple CR users is often used to improve the spectrum sensing decision. In this paper, the performance of single CR user based spectrum sensing and cooperative CR user based spectrum sensing (CSS) has been assessed in several channels such as AWGN, log-normal, Hoyt (or Nakagami-<i>q</i>), Rayleigh, Rician (or Nakagami-<i>n</i>), Nakagami-<i>m</i>, and Weibull channels. The performance of two spectrum sensing schemes based on assigning weights to CR users such as (a) weighting according to sensing channel preference and (b) weighting according to the value of decision statistic is evaluated. The performance comparison between two weighting schemes under several fading channels has been made. The performance of proposed CSS has been illustrated through complementary receiver operating characteristics (CROC) for different fading channels. The effects of weighting factors (<i>k</i> and <i>R_f</i>) on overall missed detection performance are shown. The performance of CSS with OR-logic fusion as a special case is also presented for comparison purpose.

Orthogonality and Cooperation in Collaborative Spectrum Sensing through MIMO Decision Fusion

This paper deals with spectrum sensing for cognitive radio scenarios where the decision fusion center (DFC) exploits array processing. More specifically, we explore the impact of user cooperation and orthogonal transmissions among secondary users (SUs) on the reporting channel. To this aim four protocols are considered: (i) non-orthogonal and non-cooperative; (ii) orthogonal and non-cooperative; (iii) non-orthogonal and cooperative; (iv) orthogonal and cooperative. The DFC employs maximum ratio combining (MRC) rule and performance are evaluated in terms of complementary receiver operating characteristic (CROC). Analytical results, coupled with Monte Carlo simulations, are presented.

How well do response changes of striate neurons signal differences in orientation: a study in the discriminating monkey

Just-noticeable differences (JNDs) in orientation were measured in 2 monkeys using a temporal same-different task, with stationary rectangular gratings as stimuli, and compared to those of humans tested in the same setup. The JNDs of one monkey (1.5 degree) were similar to those of humans; those of the other monkey were larger (5.8 degrees). We recorded from V1 neurons in these monkeys while they were performing the orientation discrimination with the same stimuli and under the same conditions as used in the behavioral testing. In order to determine how small a difference in orientation the V1 neurons can, in these conditions, signal reliably by small changes in firing rate, we performed 2 different receiver-operating characteristic (ROC) analyses. One ROC analysis was performed on the number of spikes evoked by the first of the 2 stimulus presentations as a function of the orientation of this stimulus. Neural JNDs derived from the neurometric curve were obtained in this way for 50 cells. In the second ROC analysis, the difference in the number of spikes evoked by the 2 stimuli presented in succession during 1 trial was analyzed as a function of orientation difference between the 2 stimuli. Neural JNDs were obtained by this procedure for 21 cells. These 2 complementary ROC analyses yielded very similar results. Also, the results were similar for the 2 monkeys. A minor fraction of V1 cells can reliably signal difference in orientation as small as 2.5 degrees, but none could signal differences smaller than 2 degrees. Our results also showed that the neural JND obtained by the ROC analysis depends on the duration of the interval during which spikes are counted. In these experiments, this duration could be chosen rather precisely, because the reaction times of the 2 monkeys were measured. Also, our results showed that the neural JND depends on the point of the tuning curve at which the measurement is made and is smallest when this is done on the steepest part of the tuning curve. Finally, our results show that the discriminative capacity of V1 neurons does not depend so much on each of the tuning characteristics--bandwidth, response strength, and variability--as on the combination of these factors.