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Cooperative relaying increases telecommunication range, improves the connectivity, and increases the reliability of data transmission; however, the transmitted power does not change. This paper analyzes the extended telecommunication range of a multi-hop cascaded network comprising N-cooperative relaying high-altitude long endurance (HALE) unmanned aerial vehicles (UAVs) under ambient conditions. A notable ambient condition is rain, which causes signals to scatter in different directions; hence, one should model the communication channel for HALE UAV as a Rayleigh channel. This paper proposes a statistical model that is based on the effect of the telecommunication range on the outage probability in an N-Rayleigh fading channel. The simulation results show that as the telecommunication range increases, the outage probability (Poutage) also increases, whereas when both the telecommunication range and the number of relays increase, Poutage decreases. An issue that has been highlighted in this paper is that, by increasing number of relays from N=1 to N=5 the telecommunication range increases and Poutage about 40% decreases. Moreover, in rainy conditions and with a fixed number of relays, when both the intensity of rainfall and telecommunication range increases, Poutage increases. For example by increasing rate of rain (Rr) from 1mm/h to 100 mm/h, Poutage increases around 30% in 100 Km with two relays. [ABSTRACT FROM AUTHOR]