Outage probability based on telecommunication range for multi-hop HALE UAVs

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.

The results of all previous studies, prove that the performance of the UAVs relay network is directly dependent on the propagation of relay signals. Therefore, in order to extend the telecommunication range, this study uses a multi-hop cascaded network comprising N-cooperative relaying HALE UAVs, and, for the worst-case scenario, proposes a statistical model based on how the telecommunication range affects the outage probability in an N-Rayleigh fading channel.
This unique study builds on existing results by making the following contributions. Exact expressions are presented to show the outage probability based on the telecommunication range in a multi-hop N-Rayleigh fading channel. Finally, the effect of rain, which is one of the most important factors of ambient conditions on the outage probability, is considered.
The rest of this paper is organized as follows. In Section 2, the problem statement and the reason for employing a cooperative relaying scenario for extended telecommunication range in HALE UAVs is presented. Section 3 introduces the system model and channel model under rainy conditions. Then, in Section 4, the statistical model based on the outage probability and exact expressions for the outage probability based on the telecommunication range in a multi-hop N-Rayleigh fading channel, are derived. Section 5 discusses the results of computer simulations. Finally, Section 6 concludes this paper and summarizes the key findings.

Problem Statement
Considering the geometrical model of Figure 1, and without taking into account constraints of characteristics of LoS link, such as the transmitted power and antenna gain, the following equations describe the maximum range in HALE UAVs [18,19]. Table 1 defines the parameters of the (1-7).  By making the  BOP small, the high altitude of the HALE UAV changes ̂ to a straight line and changes the crust of the sphere (i.e., CDE) to a circle with D as its center. Therefore: As depicted in Figure 2, (11) shows that the maximum telecommunication range and coverage (d max , r max ) is a function of the UAV altitude. Considering the typical values for a telecommunication link of HALE UAV, the maximum telecommunication range depend on the transmitted power, bit rate, required / 0 at the receiver, antenna gain, and channel noise [19].
from (12), the average power of the receiving signal in the ground station ( ) can be expressed as: ) 2 is the free-space signal propagation path loss for the wavelength (). Also Figure 3 shows the variation in the maximum telecommunication range against the required / 0 at the receiver. The simulation parameters are given in Table 2.   The results of the simulation in Figure 3 show that when required / 0 is reduced, the maximum telecommunication range is also reduced, especially at high frequencies. For example, the minimum required E b /N 0 at the receiver for QPSK modulation is 7.8 dB @ BER=10 -6 , for which the maximum telecommunication range is about 200 and 100 km at 2.4 and 5 GHz, respectively. Therefore, for an extended telecommunication range in HALE UAVs with the same link parameters, a cooperative relaying scenario should be used. The system model and channel model of this scenario are described below.

HALE UAV System and Channel Model 3.1. System Model
A multi-hop cooperative relaying technology enhances the spectral efficiency and extends the coverage of both cellular and ad-hoc wireless networks [21,22]. In cascade cooperative multi-hop relaying technology, the source and destination nodes communicate through a set of cooperating relay nodes in which the transmitted signals propagate through cascaded relay nodes in order to extend coverage for improving the performance of the network. The signal received at the relay is usually processed before being forwarded to the destination. There are several signal relaying protocols such as AF and DF [23]. Figure 4 shows N-cooperative relaying HALE UAVs.

Channel Model
A HALE UAV telecommunication channel is expected to be Ricean in its general form, i.e., the Rice distribution can be employed to describe the statistics of the channel [5]; hence, the telecommunication channel model can be expressed as follows [24]: In (15), h LOS is the free-space LoS response and h NLOS is the response due to the scattered waves (NLoS). K is the Ricean factor, and expresses the relative power of the direct and scattered components of the received signal, and provides an indication of the link quality. In the case of = 0, a Rayleigh distribution describes the channel, whereas a very large value of K, i.e., → ∞, implies the presence of a Gaussian channel.
Moreover, the rain is confined to the first 2.5-5 km of the atmosphere depending on the latitude [25]. Hence, an EM wave propagating in the troposphere is directly affected by rain. An important conclusion of this explanation is that multipath signals are observed, even in unobstructed LoS links during rain, but they are not observed during clear-sky conditions. Hence, the h channel can be expressed by (16): In (16), ℎ is a deterministic, non-fading LoS response, and is a stochastic response of the scattered waves owing to rain.
is the Ricean factor, and directly refers to the rainy conditions. In a heavy rainfall environment, → 0 and channel ℎ is approximately equal to ℎ . In this situation, the channel h is modelled Rayleigh fading. Empirically, the Ricean factor ( ) is given as [26,27] This empirical relationship between the Ricean factor K r (in dB) and the rainfall rate (in mm/h) is dependent upon factors such as the elevation, frequency, polarization, climate, and environment. In the worst case, → 0, ( increase), and the channel ℎ is described by a Rayleigh distribution. Rain primarily contributes to signal attenuation, and the rain attenuation L r is empirically obtained by using the specific rain attenuation L r (dB/km) [28,29], which is defined as (18).
In (18), d r is the total rainy path length and is geometrically obtained, H r is the effective rain height, H R is the altitude of the HALE UAV, θ is the elevation angle of the HALE UAV platform, and the values of the empirical regression coefficients a r and b r depend on the climatic zone, the transmission frequency, and the polarization. The rain attenuation is significant at frequencies above 10 GHz, where the wavelength and raindrop size (about 1.5 mm) are comparable, so the attenuation is quite large. Thus, HALE UAV-based communication systems operating in the Ka and V frequency bands are susceptible to rain; their L and S frequency-band counterparts are not susceptible to rain. Therefore, the channel model in the system model shown in Figure 4 is an N-Rayleigh channel, where its statistical model is explained below.

Statistical Model Based on Outage Probability
The model of attenuation for an N-Cooperative relaying HALE UAV link, as shown in Figure 4, is given as: In (19), L f is the total signal attenuation, that is defined as an "N-Rayleigh" random variable, and L i is the signal attenuation for each link that defines a Rayleigh distributed random variable with a probability density function (pdf) of ( ) = 2 (− In (20) and (21), the Meijer G-function is a generalized hypergeometric function, and is defined using a contour integral representation: . However, the outage probability is defined as the probability that the received instantaneous SNR on the destination is lower than the SNR threshold. In other words, thus, from (25) the outage probability is: Therefore, F L f (d, l f ) is the cumulative density function (CDF) of the N-Rayleigh distribution. By applying (21), we get: The expansion of the  Figure 5 shows the telecommunication range with the number of cooperative relays against outage probability in a multi-hop link comprising N-cooperative relaying HALE UAVs. The simulation shows that as the telecommunication range increases, the more the outage probability (P outage ) increases; however when both the telecommunication range and the number of relays increase, P outage decreases.

Results and Discussion
For example, for a specified telecommunication range (i.e., 100 km), the outage probability decreases from approximately 0.9 to 0.2 when the number of cooperative relays from N=1 to N=5 increases. Therefore, by the increasing number of relays in this scenario, in addition to increasing the telecommunication range, the outage probability (P outage ) also decreases.
Moreover, Figure 6 shows that in rainy conditions and with a fixed number of relays, whenever both the rate of rainfall and telecommunication range increases, P outage increases. When the rain rate (R r ) increases, SNR decreases; however, the effect of ℎ increases. Because of the considerable attenuation at frequencies above 10 GHz in rainy conditions, with increasing rain rate, the maximum telecommunication range of HALE UAV from the source to destination decreases yet, hence, the outage probability increases.

Conclusion
UAVs as an aerial communications platform is expected to an important role in future communication systems. Increasing telecommunication range with the cooperative relaying is one of the UAV-aided wireless communication applications which discussed in this paper. Cooperative relaying simultaneously extends the range and improves the link connectivity; however, the transmitted power does not change. In this study, increasing telecommunication range for a multi-hop cascaded network comprising N-cooperative relaying HALE UAVs analyzed. We first studied the geometric model for the HALE UAV telecommunication range and showed that for increasing telecommunication range in HALE UAV with the same link parameters, especially at high frequencies, a cooperative relaying scenario should be used. Next, we proposed a system model and channel model under rainy conditions. It was shown that an N-Rayleigh fading channel will be created. Finally, we proposed a statistical model based on the effect of telecommunication range on the outage probability in an N-Rayleigh fading channel. An issue that has been highlighted in this paper is that, in the N-Rayleigh fading channel, when the telecommunication range increases, so too will the P outage , whereas when both the telecommunication range and the number of relays sincreases, P outage decreases significantly.