Eyidayo Adebola

Unified analysis of energy detectors with diversity reception in generalised fading channels

In this paper, the authors present a novel moment generating function-based technique to unify the performance evaluation of an average energy detector for detecting unknown deterministic signals over generalised fading environments (including the η-μ, κ-μ, α-μ, K, G and KG generalised fading distributions) with diversity reception. Specifically, the authors exploit a known exponential-type integral representation for the generalised Marcum Q-function Qv (a, b) that is valid for any ratio of a/b but for positive integer order v to greatly simplify the task of finding the statistical expectations over the fading signal-to-noise ratio random variables in the computation of the average detection probability metric. This new approach leads to a very compact and an elegant solution for many practical cases of interest including the independent but non-identically distributed fading statistics and/or arbitrarily correlated diversity branches in maximal-ratio combining, square-law combining and square-law selection diversity receivers. The authors’ numerical results also show that the performance of average energy detector is superior to the classical total energy detector with the increasing number of samples owing to the noise averaging effect. We have also demonstrated the versatility and utility of the proposed analytical framework to investigate the impact of dissimilar mean signal strengths, fading parameters, time-bandwidth product, diversity order and signal combining techniques on the receiver operating characteristics of diversity energy detectors in a myriad of fading environments that had heretofore resisted simple solutions.

On the Dirac Delta Approximation and the MGF Method for ASER Analyses of Digital Communications over Fading Channels

Two distinct methods are applied to derive tighter closed-form approximations for the average symbol error rate (ASER) of a multitude of coherent and differentially coherent digital modulations (with/without diversity) in different fading environments. The first approach relies on the Dirac delta function approximation of a generalized function g(x)=xc-1 exp(-ax) to eliminate the need for integration, while the second method exploits a tight exponential-type approximation for the Gaussian probability integral to express the ASER in terms of only the moment generating function (MGF) of received signal-to-noise ratio (SNR) random variable.

Asymptotic analysis of digital modulations in κ–μ, η–μ and α–μ fading channels

This study derives several new and simple closed-form approximations for the average symbol error rate (ASER) and outage probability performance metrics of digital communication systems (with/without diversity receivers) impaired by additive white Gaussian noise and fading. These approximations utilise the coefficients of the Poincare series expansion for the probability density function (PDF) of signal-to-noise ratio (SNR) random variable in conjunction with Mellin transform of the conditional error probability and/or its auxiliary functions to generalise some of the known asymptotic ASER/outage probability expressions to a wider range of modulation schemes and different types of propagation environments (including κ–μ, η–μ and α–μ fading channels). A new class of asymptotic approximations for the ASER/outage probability is also derived (based on a normalised asymptotic PDF of SNR) that is considerably better than the conventional high-SNR approximation although both techniques need only the first non-zero term of the Maclaurin (if exists) or the Poincare series expansion of the channel PDF. The authors’ also investigate the utility/efficacy of Welch–Satterthwaite and Moschopoulos approximations for yielding accurate predictions of the ASER in the low-SNR regime for different fading environments. Closed-form approximations for the ergodic (average) channel capacities of different types of fading channels with/without diversity reception are also derived.

Partial area under the receiver operating characteristics curves of diversity-enabled energy detectors in generalised fading channels

A known exponential-type integral representation for the generalised Marcum-Q function Qv (a, b) is exploited (which is valid for integer order v but for any ratio of a/b) to unify the performance evaluation of the partial area under the receiver operating characteristics curve (partial AUC) metric of average energy detectors with diversity reception in a myriad of fading environments (including the η − μ, κ − μ, α − μ, K, G and KG generalised fading distributions). This new metric facilitates the comparison of two different energy detectors within a specified detection threshold range and can also be used to compute the total AUC as a special case. The numerical results also show that the partial AUC performance of an average energy detector is superior to that of the classical total energy detector with the increasing sample size owing to the noise averaging effect. The new analytical framework also facilitates the investigation of the effects of dissimilar fading parameters and/or signal strengths, diversity order and diversity combining techniques on the partial AUC performance of energy detectors.

On the Ergodic Secrecy Rate of Cooperative Decode-and-Forward Relay Networks

In this article, we develop a unified analytical framework for investigation of the ergodic secrecy rates of cooperative decode-and-forward relay networks in a myriad of fading environments. We utilized an exponential-type integral representation for the logarithmic function to derive an approximate expression for the ergodic secrecy rates of cooperative decode-and-forward relay networks only in terms of the moment generating function (MGF) of signal-to-noise ratio (SNR). We show that cooperative relays can be exploited to enhance the wireless physical layer security of the classical Wyner wire-tap channel. Numerical results are presented to investigate the impact of channel fading statistics, location of the relays, number of eavesdroppers as well as power allocation on the achievable ergodic secrecy rate.

On the marginal area under the receiver operating characteristics of diversity energy detectors in generalized fading channels

In this article, we exploit an exponential-type integral representation for the generalized Marcum-Q function Qv(a,b) (which is valid for any ratio a/b) to unify the performance evaluation of the marginal area under the receiver operating characteristics curve (AUC) metric of average energy detectors with diversity reception in a myriad of fading environments (including the η-μ, κ-μ and α-μ generalized fading distributions). This new metric facilitates the comparison of two different energy detectors within a specified detection threshold range and can also be used to compute the total AUC as a special case. Our numerical results also show that the marginal AUC performance of an average energy detector is superior to that of the classical total energy detector with the increasing sample size due to the noise averaging effect. Our new analytical framework also facilitates the investigation of the effects of dissimilar fading parameters and/or signal strengths, diversity order and diversity combining techniques on the marginal AUC performance of energy detectors.

Chapter 14 – Analyzing the Ergodic Secrecy Rates of Cooperative Amplify-and-Forward Relay Networks over Generalized Fading Channels

Wireless physical layer security approaches can prevent eavesdropping without upper layer data encryption. However, such techniques are hampered by time-varying wireless channel conditions and they are typically feasible only when the legitimate partners in the Wyner’s wire-tap channel model have an advantage over the source-eavesdropper channels. Node cooperation is an effective strategy to overcome this challenge and enhance the performance of secure wireless communications. This chapter addresses secure wireless communications of a source-destination pair with the help of multiple cooperating amplify-and-forward relays in the presence of one or more eavesdroppers. The role of channel fading is characterized in terms of average (ergodic) secure communication rates. Overall, this work establishes the utility of node cooperation for improving secure wireless communications and provides a unified analytical framework for assessing the ergodic secrecy rates of cooperative amplify-and-forward relay networks in a generalized fading environment with independent but non-identically distributed channel fading statistics.

Cross-layer throughput optimization for delay and QoS constrained applications

In this article we recast the problem of throughput optimization in cross-layer architecture for delay sensitive applications. Unified mathematical framework was developed for maximizing user throughput in generalised wireless environment. The optimization variables adapted include symbol rate (at the application layer), packet length (at the MAC layer), constellation size (at the physical layer) and number of retransmissions of M-PSK digital modulation schemes. We derive optimization equations for each of the above degrees of freedom in closed-form which maximizes the throughput subject to a prescribed packet loss probability constraint. Interior-point optimization algorithm was used to solve the resultant constrained non-linear optimization problem. Numerical results reveal that no successful packet decoding is possible at very low average signal-to-noise (SNR) regime as the packet loss constraint is not met when channel condition is very bad irrespective of adaption. At moderately low SNR, it is sufficient to adapt packet length while keeping symbol rate fixed at the maximum value while joint optimization of both the number of retransmissions and the constellation size parameters while keeping the packet length at an appropriate value is required in the high average SNR regime, to achieve maximum throughput over a myriad of wireless fading environments. Results also showed that the tighter the packet loss constraint, the lower the throughput becomes.

Joint-design of PHY/MAC layers for throughput optimization

This article develops a unified analytical framework for maximizing the user throughput of a cooperative multi-relay network over generalized wireless channels using the symbol rate, packet length and constellation size of M-ary PSK/QAM digital modulation schemes as optimization variables. Optimization equations for each of the above degrees of freedom are derived in closed-form. A low-complexity discrete optimization algorithm for finding the “optimal” parameter-triplet is also developed to solve the resulting non-linear joint optimization problem. Numerical results reveal that it is sufficient to adapt the number of cooperating relay nodes as well as the symbol rate in the low SNR regime while a joint-optimization of both the packet length and the constellation size parameters is desirable in the high SNR regime to achieve the maximum throughput.

On the performance of energy detectors in generalized fading environments

In this article, we carryout performance analysis on energy detectors in myriads of generalized fading environments. We utilize a new “exponential-type” contour and finite-range integral representations for the generalized M-th order Marcum Q-function QM(α,β) when its real order M>0 is not necessarily an integer. The accuracy of the new alternative integral representation for Marcum Q-function is validated using various existing representations. The form of the proposed integral representations (valid for real order M) facilitates its utility in various applications such as the evaluation of the receiver operating characteristics (ROC) of Bartlett periodogram (with/without zero padding) and the partial area under the ROC curves metric of Bartlett periodogram with/without diversity combining in a myriad of fading environments.