Shumon Alam

Unified analysis of energy detection of unknown signals over generalized fading channels

Reliable spectrum sensing is the very task upon which the entire operation of cognitive radio rests. Blind sensing of spectral-holes using a radiometer (energy detectors) is one of the solutions that have been proposed for enabling opportunistic spectrum access. This article revisits the problem of energy detection of an unknown deterministic signal over a myriad of fading environments. Specifically, a new approach (based on the canonical series representations of the generalized Marcum Q-function of real order in conjunction with the derivatives of the moment generating function of signal-to-noise ratio) is proposed to analyze the performance of maximal-ratio combining (MRC) and square-law combining (SLC) energy detectors with independent but non-identically distributed (i.n.d) fading statistics, including Rice and mixed-fading channels. Our analytical framework is also capable of treating the Nakagami-m channels with non-integer fading severity indices as well as halfodd integer values for the time-bandwidth product u. Many of these cases were either intractable with the classical probability density function/contour integral approaches, or that heretofore had resisted simple/computationally efficient solutions. Selected numerical results are also provided for the receiver operating characteristic (ROC) of MRC and SLC diversity energy detectors over Rice and Nakagami-m channels.

Further results on area under the ROC curve of energy detectors over generalized fading channels

A simple measurement to analyze the signal detectors performance is desirable. Although, receiver operating characteristic (ROC) curve has long been used for characterizing system performance, area under the ROC curve (AUC) measurement provides meaningful insights of the system performance. Signal detectors performance can be characterized simply by average AUC, since average AUC varies from 0.5 to 1. In the worst case scenario, the detectors performance can be no less than 0.5 and the best can be 1. In this paper simple expression of average AUC is developed based on the kth order derivative of the moment generating function (MGF) over the generalized fading channels for no-diversity and several diversity cases. Simplified expressions are derived for maximum ratio combing (MRC), square-law combing (SLC) diversity schemes and a simple CDF based single integral expression is developed for selection combining (SC) technique. Examples are given considering the Nakagami-m and Rice channels. Our approaches are simple and analytical results are even shown using the half integer bandwidth-time product (u) and the half integer Nakagami-m fading index. Different factors affecting energy sensing has been analyzed, which can be readily used for other applications such as cognitive radio.

Further results on the energy detection of unknown deterministic signals over generalized fading channel

In this article, we consider the performance of energy detection in composite multipath/shadowing fading environment. We also investigate the mitigation of the effect of these fading components on detection performance with the use of diversity techniques. Single channel, maximum ratio combining (MRC), square law combining (SLC), and square-law selection (SLS) diversities are analyzed using the rapidly convergent canonical series representation of Marcum Q-function with derivatives of moment generating function (MGF) of signal-to-noise ratio (SNR) of composite channel. On the other hand, the selection diversity combining (SDC) is analyzed using single integral of cumulative distribution function (CDF) of SNR. In all cases, we model the composite channel fading using the G-distribution which has been shown to be more accurate in representing the Suzuki and Nakagami-Lognormal distributions than K and KG and in closed formed compared to single integral expression for Rice-Lognormal distribution. Using this framework, we found out that the performance of energy detection does not degrade significantly at low and moderate shadowing conditions and that diversity detection greatly mitigates the effect of shadowing on detection performance with MRC giving the best performance, followed by SLC and then SDC or SLS depending on the average channel SNR, number of samples and level of shadowing. To the best of our knowledge, such a simple framework and resulting novel observations have never been reported before.

An intrusion detection technique based on continuous binary communication channels

Choosing Intrusion Detection Systems (IDSs) is difficult owing to the availability of different IDS techniques, the nature of attacks and the inability of IDS techniques to guarantee total security. The use of Intrusion Prevention Systems (IPSs) as a first line of defence does not prevent all attacks, so IDSs are needed as a second line of defence. Anomaly and signature-based techniques are the main approaches employed by IDSs. This new IDS technique is based on two main anomaly detection techniques: statistical and predictive pattern generation techniques. This IDS will detect both known and unknown attacks using signature-based and anomaly techniques.

Energy detector's performance analysis over the wireless channels with composite multipath fading and shadowing effects using the AUC approach

In this paper, energy detectors performance over the wireless channels with composite multipath fading and shadowing effects is analyzed using the area under the receiver operating characteristic (ROC) curve (AUC) in contrast to the conventional ROC measurement. AUC is a single statistical parameter which can be used to describe energy detectors performance more meaningfully. An energy detector may not see the transmitter due to the shadowing and fading. Generalized-K (KG) distribution is considered to describe the composite effects because of its simplicity than the other available models such as the Nakagami-lognormal distribution. The analysis is then extended to the cases with diversity receptions including maximal ratio combining (MRC), square law combining (SLC), and selection combining (SC) as the representative of diverse receiver combining techniques. The developed framework is very simple and the analytical results could be used readily to design energy detection based cognitive radio network. Energy detectors performance analysis with the AUC parameter over the composite effects is new and thus this work contributes significantly in the wireless communications areas.

A performance study of energy detection for dual-hop transmission with fixed gain relays: area under ROC curve (AUC) approach

In this paper, energy detectors performance is investigated for the blind (fixed gain) amplify & forward (AF) dual-hop relay networks using the area under the receiver operating characteristic curve (AUC) metric. Different from the well-known receiver operating characteristics (ROC) metric, AUC is a single statistical parameter which can be used to describe and compare performance of different types of energy detectors. In this article, we derive closed-form AUC expressions for the fixed-gain AF relay networks over the Rayleigh fading channels. The analysis is then extended to the maximum ratio combing (MRC) and square-law combing (SLC) diversity detectors for a dual-hop but multi-relay systems. Our analytical framework and the closed-form AUC expression is based on the kth order derivatives of the moment generating function (MGF) of the combiner output signal-to-noise ratio (SNR).

Energy detector's performance evaluation in a relay based cognitive radio network: Area under the ROC curve (AUC) approach

In this paper, energy detectors performance is analyzed for the two-hop relay network using the area under the receiver operating characteristic (ROC) curve (AUC) in contrast to the ROC based analysis. AUC provides summary measures for the performance of a system. It provides meaningful performance analysis as it varies only from 0.5 to 1. In the worst case scenario, the practical detectors performance can be no less than 0.5 and the best can be 1. A simple generalized AUC framework is developed based on the canonical series representations of the generalized Marcum Q-function of real order in conjunction with the kth order derivative of the moment generating function (MGF) of signal to noise ratio (SNR) of the channel. The framework is then applied to analyze the energy-detection performance for single and multiple two-hop relay networks. For multiple two-hop relay networks, the receiver combining techniques are analyzed in particular maximum ratio combining (MRC) and square-law combining (SLC) as the representative of various combining techniques. Different factors such as the sampling number, number of relays and fading severity influencing the energy sensing have been analyzed. Proposed approach is simple in terms of computation and performance analysis and the results can be used readily for selecting proper cognitive radio operating parameters. Also the solution is capable of handling the half odd-integer bandwidth-time product (u) and the half odd-integer Nakagami-m fading severity index (m).

Accurate approximations for the symbol error probability of cooperative non-regenerative relay systems over generalized fading channels

In this article, we present a unified approach for the asymptotic analysis of symbol error rates for two-hops cooperative non-regenerative multi-relay networks over a myriad of stochastic channel models. The analysis can be also extended to other types of cooperative strategies and multi-hop networks without much difficulty. The proposed moment generating function (MGF) framework is also sufficiently general to encapsulate all types of coherent and non-coherent digital modulation schemes. In addition to simplifying the computation complexity of average symbol error rate (ASER) for cooperative amplify-and-forward (CAF) diversity schemes treated in the literature, we also provide accurate ASER approximations for many fading environments that heretofore had resisted a simple solution. The accuracy of our approximations has been validated with closed-form formulas that are available for specific fading environments (e.g., Rayleigh and Nakagami-m channels) and via computer (Monte Carlo) simulations.

Optimizations of cooperative spectrum sensing with reporting errors over myriad fading channels

This paper investigates the energy detection based cooperative spectrum sensing (CSS) and develops a generalized error rate with reporting errors at the fusion center (FC) for decision fusion and provides optimization schemes by developing optimized voting rule (k-out-of-N) and energy-detection threshold over myriad fading channels. The optimization scheme is based on the Bayesian criterion (BC) where BC risk is formulated as the total error rate (sum of the weighted false alarm and missed detection probability) at the fusion center. The BC risk factor is minimized for optimizing the operating parameters. A fast sensing scheme is also explored with the optimum voting rule by satisfying the target error rate. This work has presented simple framework with reporting errors for decision fusion and the resulting observations are new. Our studies enhance the existing theoretical knowledge of co-operative spectrum sensing over myriad fading channels and will be useful for actual implementation of cooperative relay systems.

A unified framework for the performance analyses of diversity energy detectors over fading channels

This paper revisits the problem of energy detection of an unknown deterministic signal over a myriad of fading environments. Specifically, a new analytical approach based on six alternative series representations of the generalised Marcum Q-function of real order in conjunction with moments or derivatives of the Moment Generating Function of Signal-to-Noise Ratio SNR is proposed to analyse the performance of Maximal-Ratio Combining MRC and Square-Law Combining SLC energy detectors with independent but non-identically distributed i.n.d fading statistics. Our analytical framework is sufficiently general, and capable of handling half-odd integer values for the time-bandwidth product and non-integer fading severity indices for the Nakagami-m fading environment, as well as i.n.d Rice and mixed fading scenarios. Many of these cases were either intractable with the classical probability density function/contour integral approaches, or had resisted a simple/computationally efficient solution. Selected numerical results are also provided for the Receiver Operating Characteristic ROC of MRC and SLC diversity-based energy detectors over Rice and Nakagami-m channels.