Performance analysis of energy detector over generalised wireless channels in cognitive radio

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University London.This thesis extensively analyses the performance of an energy detector which is widely employed to perform spectrum sensing in cognitive radio over different generalised channel models. In this analysis, both the average probability of detection and the average area under the receiver operating characteristic curve (AUC) are derived using the probability density function of the received instantaneous signal to noise ratio (SNR). The performance of energy detector over an ŋ --- µ fading, which is used to model the Non-line-of-sight (NLoS) communication scenarios is provided. Then, the behaviour of the energy detector over к --- µ shadowed fading channel, which is a composite of generalized multipath/shadowing fading channel to model the lineof- sight (LoS) communication medium is investigated. The analysis of the energy detector over both ŋ --- µ and к --- µ shadowed fading channels are then extended to include maximal ratio combining (MRC), square law combining (SLC) and square law selection (SLS) with independent and non-identically (i:n:d) diversity branches. To overcome the problem of mathematical intractability in analysing the energy detector over i:n:d composite fading channels with MRC and selection combining (SC), two different unified statistical properties models for the sum and the maximum of mixture gamma (MG) variates are derived. The first model is limited by the value of the shadowing severity index, which should be an integer number and has been employed to study the performance of energy detector over composite α --- µ /gamma fading channel. This channel is proposed to represent the non-linear prorogation environment. On the other side, the second model is general and has been utilised to analyse the behaviour of energy detector over composite ŋ --- µ /gamma fading channel. Finally, a special filter-bank transform which is called slantlet packet transform (SPT) is developed and used to estimate the uncertain noise power. Moreover, signal denoising based on hybrid slantlet transform (HST) is employed to reduce the noise impact on the performance of energy detector. The combined SPT-HST approach improves the detection capability of energy detector with 97% and reduces the total computational complexity by nearly 19% in comparison with previously implemented work using filter-bank transforms. The aforementioned percentages are measured at specific SNR, number of selected samples and levels of signal decompositionMartyrs Foundatio

Entropy and Energy Detection-based Spectrum Sensing over F Composite Fading Channels

In this paper, we investigate the performance of energy detection-based spectrum sensing over F composite fading channels. To this end, an analytical expression for the average detection probability is firstly derived. This expression is then extended to account for collaborative spectrum sensing, square-law selection diversity reception and noise power uncertainty. The corresponding receiver operating characteristics (ROC) are analyzed for different conditions of the average signal-to-noise ratio (SNR), noise power uncertainty, time-bandwidth product, multipath fading, shadowing, number of diversity branches and number of collaborating users. It is shown that the energy detection performance is sensitive to the severity of the multipath fading and amount of shadowing, whereby even small variations in either of these physical phenomena can significantly impact the detection probability. As a figure of merit to evaluate the detection performance, the area under the ROC curve (AUC) is derived and evaluated for different multipath fading and shadowing conditions. Closed-form expressions for the Shannon entropy and cross entropy are also formulated and assessed for different average SNR, multipath fading and shadowing conditions. Then the relationship between the Shannon entropy and ROC/AUC is examined where it is found that the average number of bits required for encoding a signal becomes small (i.e., low Shannon entropy) when the detection probability is high or when the AUC is large. The difference between composite and traditional small-scale fading is emphasized by comparing the cross entropy for Rayleigh and Nakagami-m fading. A validation of the analytical results is provided through a careful comparison with the results of some simulations.Comment: 30 pages, 11 figures, 1 table, Submitted to IEEE TCO

Average Rate of Downlink Heterogeneous Cellular Networks over Generalized Fading Channels - A Stochastic Geometry Approach

In this paper, we introduce an analytical framework to compute the average rate of downlink heterogeneous cellular networks. The framework leverages recent application of stochastic geometry to other-cell interference modeling and analysis. The heterogeneous cellular network is modeled as the superposition of many tiers of Base Stations (BSs) having different transmit power, density, path-loss exponent, fading parameters and distribution, and unequal biasing for flexible tier association. A long-term averaged maximum biased-received-power tier association is considered. The positions of the BSs in each tier are modeled as points of an independent Poisson Point Process (PPP). Under these assumptions, we introduce a new analytical methodology to evaluate the average rate, which avoids the computation of the Coverage Probability (Pcov) and needs only the Moment Generating Function (MGF) of the aggregate interference at the probe mobile terminal. The distinguishable characteristic of our analytical methodology consists in providing a tractable and numerically efficient framework that is applicable to general fading distributions, including composite fading channels with small- and mid-scale fluctuations. In addition, our method can efficiently handle correlated Log-Normal shadowing with little increase of the computational complexity. The proposed MGF-based approach needs the computation of either a single or a two-fold numerical integral, thus reducing the complexity of Pcov-based frameworks, which require, for general fading distributions, the computation of a four-fold integral.Comment: Accepted for publication in IEEE Transactions on Communications, to appea

Area under ROC curve of energy detection over generalized fading channels

A fast and reliable detection scheme is essential in several wireless applications such as radar and cognitive radio systems. Energy detection is such a method as it does not require a priori information of the received signal while it exhibits low implementation complexity and costs. Since the detection capability of ED is largely affected by the effects of multipath fading, this paper is devoted to a thorough analysis of energy detection based spectrum sensing over generalized fading conditions. To this end, analytical expressions are firstly derived using the area under the receiver operating characteristic curve (AUC) under additive white Gaussian noise. This analysis is subsequently extended to the case of generalized fading conditions characterized by k - μ and η - μ fading distributions. The offered results are novel and are employed in analyzing the corresponding performance. It is shown that fading phenomena result to detrimental effects on the performance of spectrum sensing since the deviation between severe and non-severe conditions is rather substantial