Closed-form energy-based signal detection analysis in presence of a Lomax fading channel in full hyper-Rayleigh regime

Abstract

The presented research examines the energy-based spectrum sensing problem of a signal transmitted over a wireless communication channel with severe fading. To account for the most challenging propagation conditions, a recently developed Lomax wireless channel model was utilized, which exhibits hyper-Rayleigh characteristics over the entire range of possible parameter values. For the channel model under consideration, the existence of the specific hyper-Rayleigh regimes (i.e., weak, strong, and full) are identified asymptotically and studied numerically for a finite signal-to-noise ratio. For the most severe fading conditions, the system’s performance was assessed in terms of the average probability of detection, receiver operating characteristics, and area under the curve. These metrics were derived in closed-form for the cases of Maximum Ratio Combining at the receiver and without diversity reception. The obtained expressions were analyzed via numerical and statistical simulation as functions of system and channel parameters, including the sensing base, average signal-to-noise ratio, and scale parameter for the signal-to-noise probability distribution. The results from numerical simulations were compared with existing regulations specified in the 5G standard for energy-based detection in medium access procedures.