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}-μ fading distribution and η-μ fading distribution. The α-\k{appa}-μ 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 α-\k{appa}-μ 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 α-\k{appa}-μ 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 α-\k{appa}-μ fading conditions, but appropriate channel parameters will improve sensing performance.