  This paper analyzes the unified performance of energy detection (ED) of
spectrum sensing (SS) over generalized fading channels in cognitive radio (CR)
networks. The detective performance of SS schemes will be obviously affected by
fading channel between communication nodes, and ED has the advantages of fast
implementation, no requirement of priori received information and low
complexity, so it is meaningful to investigate ED that is performed over fading
channels such as Nakagami-m channel and Rice channel, or generalized fading
channels such as \k{appa}-{\mu} fading distribution and {\eta}-{\mu} fading
distribution. The {\alpha}-\k{appa}-{\mu} fading distribution is a generalized
fading model that represents the nonlinear and small-scale variation of fading
channels. The probability density function (p.d.f.) of instantaneous
signal-to-ratio (SNR) of {\alpha}-\k{appa}-{\mu} distribution is derived from
the envelope p.d.f. to evaluate energy efficiency for sensing systems. Next,
the probability of detection model with Marcum-Q function has been derived and
the close-form detective expressions with moment generating function (MGF)
method are deduced to achieve sensing communications over generalized fading
channels. Furthermore, novel and exact closed-form analytic expressions for
average area under the receiver operating characteristics curve also have been
deduced to analyze the performance characteristics of ED over
{\alpha}-\k{appa}-{\mu} fading channels. Besides, cooperative spectrum sensing
(CSS) with diversity reception has been applied to improve the detection
accuracy and mitigate the shadowed fading features with OR-rule. At last, the
results show that the detection capacity can be evidently affected by
{\alpha}-\k{appa}-{\mu} fading conditions, but appropriate channel parameters
will improve sensing performance.
