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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
Energy Detection of Unknown Signals over Cascaded Fading Channels
Energy detection is a favorable mechanism in several applications relating to
the identification of deterministic unknown signals such as in radar systems
and cognitive radio communications. The present work quantifies the detrimental
effects of cascaded multipath fading on energy detection and investigates the
corresponding performance capability. A novel analytic solution is firstly
derived for a generic integral that involves a product of the Meijer
function, the Marcum function and arbitrary power terms. This solution
is subsequently employed in the derivation of an exact closed-form expression
for the average probability of detection of unknown signals over *Rayleigh
channels. The offered results are also extended to the case of square-law
selection, which is a relatively simple and effective diversity method. It is
shown that the detection performance is considerably degraded by the number of
cascaded channels and that these effects can be effectively mitigated by a
non-substantial increase of diversity branches.Comment: 12 page
Communication in a Poisson Field of Interferers -- Part I: Interference Distribution and Error Probability
We present a mathematical model for communication subject to both network
interference and noise. We introduce a framework where the interferers are
scattered according to a spatial Poisson process, and are operating
asynchronously in a wireless environment subject to path loss, shadowing, and
multipath fading. We consider both cases of slow and fast-varying interferer
positions. The paper is comprised of two separate parts. In Part I, we
determine the distribution of the aggregate network interference at the output
of a linear receiver. We characterize the error performance of the link, in
terms of average and outage probabilities. The proposed model is valid for any
linear modulation scheme (e.g., M-ary phase shift keying or M-ary quadrature
amplitude modulation), and captures all the essential physical parameters that
affect network interference. Our work generalizes the conventional analysis of
communication in the presence of additive white Gaussian noise and fast fading,
allowing the traditional results to be extended to include the effect of
network interference. In Part II of the paper, we derive the capacity of the
link when subject to network interference and noise, and characterize the
spectrum of the aggregate interference.Comment: To appear in IEEE Transactions on Wireless Communication
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
Distributed Nonparametric Sequential Spectrum Sensing under Electromagnetic Interference
A nonparametric distributed sequential algorithm for quick detection of
spectral holes in a Cognitive Radio set up is proposed. Two or more local nodes
make decisions and inform the fusion centre (FC) over a reporting Multiple
Access Channel (MAC), which then makes the final decision. The local nodes use
energy detection and the FC uses mean detection in the presence of fading,
heavy-tailed electromagnetic interference (EMI) and outliers. The statistics of
the primary signal, channel gain or the EMI is not known. Different
nonparametric sequential algorithms are compared to choose appropriate
algorithms to be used at the local nodes and the FC. Modification of a recently
developed random walk test is selected for the local nodes for energy detection
as well as at the fusion centre for mean detection. It is shown via simulations
and analysis that the nonparametric distributed algorithm developed performs
well in the presence of fading, EMI and is robust to outliers. The algorithm is
iterative in nature making the computation and storage requirements minimal.Comment: 8 pages; 6 figures; Version 2 has the proofs for the theorems.
Version 3 contains a new section on approximation analysi
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