Oluwatobi Olabiyi

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.

Closed-form evaluation of area under the ROC of cooperative relay-based energy detection in cognitive radio networks

In this article, we develop a closed form evaluation of the area under receiver operating characteristics (ROC) curve (AUC) when employed in the analysis of cooperative amplify-and-forward (CAF) relay-based energy detection. The developed analytical expression for AUC results into finite kth order derivative of the moment generating function of the end-to-end signal-to-noise ratio. The resulting closed-form expressions can be easily generalized across different fading channels and multi-relay system. We first consider a single amplify-and-forward (AF) relay based sensing and later extend the framework to multi-relay system. Both options of maximum ration combining (MRC) and square-law combining are analysed. We found out that direct sensing performs better than single relay sensing under certain scenario. However, the sensing performance is greatly enhanced when both direct and relay based sensing are combined to form a CAF relay detection system. Also, we show that MRC CAF relay sensing outperforms their corresponding SLC CAF relay sensing.

Further results on the performance of energy detector over generalized fading channels

Cognitive radio network requires an efficient and effective means of detecting holes in the spectrum. Energy detection is one of the solutions that have been proposed for enabling opportunistic spectrum access. In this article, we present yet other simplified unified approaches to the analysis of performance of the energy detector under different fading channels. One is based on the kth order derivative of the moment generating function (MGF) of the fading channel and the other is based on the kth moment of the output SNR of the receiver of energy detector. Both methods are derivatives of two complementary alternative series representations of Marcum-Q function using the Laguerre polynomial recently developed by [12]. Due to its faster rate of convergence, we employ the form with kth derivative of MGF of SNR of fade distribution in our computational analysis. However, the same proposed framework is easily applicable to the form requiring kth moment of SNR of fading channel. The method presented is applicable to common multipath fade distribution (e.g., Rayleigh, Rice and Nakagami-m channels) and composite multipath/shadowing fade distribution. It also has the capability of providing results for fractional fading index, m and half-integer time-bandwidth product, u. Selected numerical results are also provided for the receiver operating characteristics (ROC) of single channel, MRC and SLC diversity energy detectors over Rice channels.

Performance evaluation of cooperative cognitive radio networks with data/decision fusion

In this article, we develop an analytical framework for performance evaluation and comparison between decision and data fusion rules for cooperative relay based cognitive radio networks. Our unified analytical formulas for the data fusion rules are sufficiently general to tackle generalized stochastic channel models with independent but non-identically distributed (i.n.d) link statistics. We also derive a unified expression for computing the effective detection and false alarm probabilities for multi-relay networks with k-out-of-N decision fusion rules (which includes “AND”, “OR”, and the “Majority-Rule” as special cases). While the decision fusion rule yields a slightly better performance than the data fusion rule with a single cooperating relay, we observe that the performance of data fusion schemes lie in between the extremes of “AND” and “OR” rules of decision fusion for multi-relay networks. The maximal-ratio combining (MRC) based data fusion rule outperforms the square-law combining (SLC) counterpart, as anticipated. However, a different value of “k” in the k-out-of-N decision fusion rule outperforms others depending on the system parameters. As such, an adaptive decision fusion rule will more advantageous than a decision fusion rule with a fixed k value.

Improving the Spectral Efficiency of Adaptive Modulation in Amplify-and-Forward Cooperative Relay Networks with an Adaptive ARQ Protocol

This paper investigates the effectiveness of a cross-layer design that combines adaptive modulation (AM) at the physical layer with an adaptive truncated automatic repeat request (ARQ) protocol at the data link layer to maximize the throughput of cooperative amplify-and-forward (CAF) relay networks under prescribed delay and/or error performance constraints. A by-product of our proposed analytical framework, that involves evaluation of the marginal moment generating function (MGF) of the end-to-end signal-to-noise ratio (SNR), for computing the average throughput and average packet error rate performance metrics is the unification and generalization of existing studies on cross-layer combining of AM and truncated ARQ for non-cooperative diversity systems to generalized fading channels. Our analytical methodology is motivated by the fact that the MGF of end-to-end SNR for multi-relay CAF networks is either available in the research literature (for certain fading environments) or it can be computed much more conveniently than its PDF, while the desired marginal MGF can be evaluated efficiently using a multi-precision Laplace inversion formula of an auxiliary MGF function. The efficacy of an adaptive Rmax (maximum retransmission limit) strategy over the classical fixed Rmax scheme is also examined.

Ergodic capacity analysis of cooperative amplify-and-forward relay networks over generalized fading channels

This paper presents two new methods for evaluating the ergodic channel capacities of cooperative non-regenerative multirelay networks in a myriad of fading environments and under three distinct source-adaptive transmission policies: i optimal rate adaptation with a fixed transmit power; ii optimal joint power-and-rate adaptation; and iii truncated channel inversion with fixed rate. In contrast to the previous related works, our proposed unified analytical frameworks that are based on the moment generating function and/or the cumulative distribution function of end-to-end signal-to-noise ratio allow us to gain insights into how power assignment during different transmission phases, relay node placement, fade distributions, and dissimilar fading statistics across the distinct communication links impact the ergodic capacity, without imposing any restrictions on the channel fading parameters. Copyright

Extending the capability of energy detector for sensing of heterogeneous wideband spectrum

Reliable spectrum sensing is the very task upon which the entire operation of the cognitive radio rests. Energy detection is one of the solutions that have been proposed for enabling opportunistic spectrum access but its capability has limited sensitivity, no resolution and requires high sampling rate when employed in the detection of wideband heterogeneous spectrum. This article proposes a solution that can extend the capability of traditional energy detector to wideband sensing with improved performance. The solution involves the use of parallel detection circuitry with each tuned to different frequencies. The decision of each detection circuit can then be used to create a spectral map of the entire spectrum. This introduces some resolution component and improved sensitivity based on the number of parallel circuits and bandwidth of each detection circuit. Since the bandwidth of the incumbent signal is generally not known a priori, there is possibility that it spans across multiple detectors. The detection of such wideband signal can be achieved by either data or decision fusion of the results of each narrowband detector. We show that the use of parallel multi-channel detection can greatly enhance the detection of wideband signal compared to averaging while improving the resolution and sensitivity of energy detection of wideband spectrum. Numerical results have been shown for representative cases and careful review of previous works reveals that these have never been considered in literature.

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.