For reliable and robust high data-rate communication for various wireless applications including the emergency disastrous situations, temporary mass events, and even in military applications, promptly deployable flying base stations such as unmanned aerial vehicles (UAVs) have gained significant research attention as they are capable to provide high data-rates with improved capacity and coverage, targeted for beyond fifth generation (5G) communications(Zhan et al., 2011; Mozaffari et al., 2019). UAVs are broadly categorized into low altitude platform (LAP) and high altitude platform (HAP) based on their size and operating range. The LAPs are situated only few hundred meters above the earth surface, however, the HAPs are usually situated in stratosphere around 17–25 km (km) altitude from the earth surface. As the HAP situates in stratosphere, the wind velocity is low and atmospheric turbulence is negligible, hence, the HAP can be in quasi-static position and is capable to provide ubiquitous connectivity (Kurt et al., 2021). Due to the enhancement in communications technologies, lightweight composite materials, improved efficiency of solar panels and antenna, HAP became an viable aerial network component for various communication applications. The HAPs can be deployed easily and rapidly, their maintenance is easy, and having moderate operational cost than satellite which makes them economically feasible (Fidler et al., 2010; Kurt et al., 2021). Various technological trends of HAPs and their applications in wireless communications have been seen in (d’Oliveira et al., 2016). On the other hand, free-space optics (FSO) has been proven as an efficient replacement to radio-frequency (RF) due to its high operational bandwidth with improved capacity to fulfill the increasing demand of high data-rates for present and future wireless communication networks. FSO operates in unlicensed band, having low cost and easy deployment, and provides high-speed line-of-sight (LoS) communication (Singya et al., 2020; Trichili et al., 2020). The FSO links provide high data-rate secured transmission than the RF links, however requires LoS communication. Further, atmospheric turbulence and weather issues are more severe in terrestrial mobile communication which limits the FSO link’s performance. In such situations, RF links provide more robust communication to mobile users (MUs) than the FSO links. Thus, a hybrid system which can utilize the high data-rate capability of FSO links and the reliable transmission through RF links to terrestrial MUs has gained significant research attention (Trichili et al., 2021).

Various HAP networks like HAPCOS and CAPANINA in Europe, Helicos in USA, SkyNet is Asia, etc. have been deployed successfully for broadband data transmission to a larger distance (in hundreds of km). A considerable work on HAP networks have been seen in the literature. In (Vaiopoulos et al., 2013), authors proposed a HAP assisted setup for WiMAX orthogonal frequency division multiplexing (OFDM) transmission and derived the outage probability. In (Fidler et al., 2010), authors have shown various field trials to and from HAP using optical links to provide high data-rates. In (David et al., 2004), various considerations for inter-HAP optical link design are shown. In (Parthasarathy et al., 2014), channel modeling of inter-HAP optical link is proposed. In (Shibata et al., 2020), a gigabit HAP system for mobile communications is proposed. An HAP assisted ground to satellite uplink FSO/RF system is proposed in (Swaminathan et al., 2021) with Gamma-Gamma and shadowed-Rician fading for FSO and RF links, respectively, and various performance measures are derived. In (Singya and Alouini, 2021), an HAP assisted downlink hybrid FSO/RF based multiuser multiantenna terrestrial communication system is proposed, where the FSO link is characterized with the Gamma-Gamma distribution with pointing error impairments and Nakagami-m distribution is preferred for RF links. For the performance analysis, analytical expressions of outage probability, asymptotic outage probability, ergodic capacity, effective capacity, and generalized average symbol-error-rate (ASER) expressions of hexagonal-quadrature amplitude modulation (QAM), cross-QAM, and rectangular QAM are derived. (Liu et al., 2020) focuses on amplify-and-forward (AF) based HAP assisted satellite-terrestrial communication with Gamma-Gamma and Rayleigh distributions for the FSO and RF links, respectively, and obtained the outage probability. In (Antonini et al., 2006), capacity and efficiency of FSO link between the satellite and HAP are obtained for its feasibility. In (Gao et al., 2021), optimization of an intelligent reconfigurable surface assisted HAP network is proposed for downlink communication to terrestrial MUs.

However, a significant work is witnessed on various hybrid FSO/RF systems in the literature. (Bhatnagar and Arti, 2013) considers a hybrid RF/FSO based satellite-terrestrial communication system, where Gamma-Gamma and shadowed-Rician distributions are considered for the FSO and RF links, respectively. Further, analytical ASER expression for M-ary phase-shift keying (MPSK) and asymptotic results are obtained. (Zedini et al., 2016) focuses on a hybrid FSO/RF system with Nakagami-m and Gamma-Gamma fading for the RF and FSO links, respectively, and the analytical expressions of ergodic capacity, outage probability, and bit-error-rate (BER) of binary phase-shift keying (BPSK) are derived. (Chen et al., 2019) covers energy harvesting in hybrid FSO/RF system by obtaining the outage probability. An FSO/RF based satellite-terrestrial communication system is considered in (Ahmad et al., 2017), where satellite is connected through the optical feeder link and provides RF connectivity to terrestrial users, and various performance measures are derived for analysis. (Zedini et al., 2020) focuses on an FSO/RF based satellite-terrestrial communication system with Gamma-Gamma distributed uplink optical feeder link and shadowed-Rician distributed downlink RF terrestrial users links, and ergodic capacity, outage probability, and BER expressions of BPSK are derived. In (Sharma et al., 2019), switching-based FSO/RF system is proposed and various performance measures are obtained. (Lee et al., 2020) focuses on the data throughput maximization for UAV based FSO/RF system. Further, in (Singya et al., 2020), ASER performance of various higher order complex QAM schemes is obtained for a mixed RF/FSO system with outdated channel state information. In (Xu and Song, 2021) and (Xu and Song, 2020), hybrid RF/FSO based communication systems are considered, where RF link is characterized with κ − μ distribution and the FSO link is characterized with the M - distribution with pointing error impairments. For performance analysis, outage probability, asymptotic outage probability, ergodic capacity, and ABER results are obtained. In (Xu and Zhang, 2021), a hybrid RF/FSO based deep space communication system is considered, where exponentiated Weibull and Nakagami-m distributions are considered respectively for the FSO and RF links; and outage probability, ergodic capacity, and ABER of MPSK are derived.

In the literature, some papers have discussed FSO based multi-hop communication systems. In (Datsikas et al., 2010; Zedini and Alouini, 2015; Ashrafzadeh et al., 2020), authors have analyzed the performance of multi-hop FSO systems. (Altubaishi and Alhamawi, 2019) focuses on the capacity analysis of a multi-hop FSO/RF system. In (Wang et al., 2015), authors have discussed the performance of multi-hop exponentiated Weibull distributed FSO system. However, above discussed multi-hop works focus only on generalized FSO systems without including HAP networks.

On the other hand, HAPs are having a wide 500 km radius footprint as recommended by International Telecommunication Union (ITU) (ITU-Radiocommun, 2000). Further, most of the HAP assisted projects have smaller coverage area and combining multiple HAPs can provide coverage to even entire country. For example, authors in (Miura and Oodo, 2001) and (Milas et al., 2003) have proposed respectively 16 and 18 HAPs configurations to provide coverage to entire Japan and Greece. However, only few works focus on the performance of multi-hop HAP/LAP assisted communication system. In (Yang et al., 2018), outage probability of LAP assisted RF/FSO/RF multi-hop system is derived. In (Sharma et al., 2016), authors have evaluated the performance of inter-HAP FSO communication system. Authors in (Michailidis et al., 2018) have discussed the performance of a three-hop HAP assisted RF/FSO/RF communication system. The above discussed works are summarized in Table 1 in details. The various considerations, channel models, and derived performance metrics are shown in Table 1 which are compared with our work (highlighted in bold letters) to show the novelty of our work.

As discussed above, we have seen significant works on dual-hop hybrid FSO/RF based systems. However, very limited work is seen on HAP assisted multi-hop hybrid FSO/RF scenario. Motivated with this, in this work, a highly reliable, robust, and high capacity long distance multiple serial HAPs assisted mixed FSO/RF multiuser multiantenna communication system is proposed. In the proposed system, end-to-end (e2e) long distance communication is completed through high bandwidth, high capacity FSO links established between the earth station (ES) to HAP and between multiple serial HAPs situated several hundred kilometer apart, and finally to the terrestrial MUs through the RF links via multiantenna array deployed at the final HAP. The intermediate HAPs are performing selective decode-and-forward (DF) relaying. Atmospheric turbulence of the ES to HAP link is modeled with Gamma-Gamma fading along with the pointing error impairments. As HAP situates at 20 km altitude, negligible atmospheric turbulence exists hence, only pointing error is considered for the inter HAP links. A multiantenna array is deployed at the HAP and Nakagami-m fading is considered for the RF links. Further, opportunistic user scheduling is performed for the best user selection. From this prospective, the major contributions of this work are as follows:

• For the performance analysis, individual link’s outage probability and overall outage probability are derived and the impact of pointing error, FSO detection type, MU selection, number of antennas, and RF fading severity are observed on the outage performance.

Note that the proposed system model and the analysis shown in this work is generalized. By considering number of HAPs N = 1, the multi-hop serial HAPs assisted mixed FSO/RF system can be converted into a dual-hop HAP assisted mixed FSO/RF system. By considering number of users U = 1, the performance of Uth terrestrial MU can be obtained. Further, all the parameters can be adjusted and the considered system model can be deployed for various specific applications.

Rest of the work is organized as follows: In Section II, proposed system model and channel model are discussed in detail. Various performance measures like outage probability, asymptotic outage probability, and generalized ABER are discussed in detail in Section III, Section IV, and Section V, respectively. Section VI discusses various theoretical and simulation results of the proposed system and conclusions from the obtained results are finally illustrated in Section VII.

Outage probability is one of the important performance measures and defines the probability of reaching the instantaneous e2e SNR below a fixed threshold (γ _th ). For the considered system, e2e instantaneous received SNR is shown in (7), hence the overall outage probability is given as P o γ t h = 1 − 1 − F γ H γ t h ︸ ES - HAP 1 − F γ H H γ t h N − 1 ︸ HAP - HAP 1 − F γ H M γ t h ︸ HAP - EU . (26)

Substituting the respective CDF values of the individual links in (26), we get P o γ t h = 1 − 1 − A G r + 1,3 r + 1 3 r , 1 B A 0 r μ r γ t h | ϱ 2 , 0 1 , ϱ 1 × 1 − 1 A 0 ϵ o 2 γ t h γ ̄ H n ϵ o 2 r N − 1 1 − U ∑ j , l C 0 C 2 − C 1 ϒ ( C 1 , C 2 γ t h ) . (27)

Using the binomial series expansion and after some mathematical computations, (27) can be solved as P o γ t h = A G r + 1,3 r + 1 3 r , 1 B A 0 r μ r x ϱ 2 , 0 1 , ϱ 1 − ∑ z = 1 N − 1 N − 1 z − 1 z 1 A 0 ϵ o 2 z γ t h γ ̄ H n ϵ o 2 z r + U ∑ j , l C 0 C 2 − C 1 ϒ C 1 , C 2 γ t h + U ∑ j , l ∑ z = 1 N − 1 N − 1 z − 1 z 1 A 0 ϵ o 2 z C 0 C 2 − C 1 1 γ ̄ H n ϵ o 2 z r γ t h ϵ o 2 z r ϒ C 1 , C 2 γ t h + A ∑ z = 1 N − 1 N − 1 z − 1 z 1 A 0 ϵ o 2 z γ t h γ ̄ H n ϵ o 2 z r G r + 1,3 r + 1 3 r , 1 B A 0 r μ r x ϱ 2 , 0 1 , ϱ 1 − A U ∑ j , l C 0 C 2 − C 1 ϒ C 1 , C 2 γ t h G r + 1,3 r + 1 3 r , 1 B A 0 r μ r x ϱ 2 , 0 1 , ϱ 1 − A U ∑ j , l ∑ z = 1 N − 1 N − 1 z − 1 z 1 A 0 ϵ o 2 z C 0 C 2 − C 1 1 γ ̄ H n ϵ o 2 z r γ t h ϵ o 2 z r ϒ C 1 , C 2 γ t h × G r + 1,3 r + 1 3 r , 1 B A 0 r μ r x ϱ 2 , 0 1 , ϱ 1 ] . (28)

Various insights on the system’s performance can be highlighted through the obtained outage probability (28). However, (28) is quite complex to decide the diversity order of the considered system. Hence, in this Section, we have conducted asymptotic analysis on the outage probability to obtain the diversity order. For this, the transmit SNR is assumed to tend to infinity. Therefore, at high SNR, (26) can be approximated as P o A γ t h ≈ F γ H A γ t h + N − 1 × F γ H H A γ t h + F γ H M A γ t h . (29)

Corollary 1: By using the identities as shown in (34) and (35), asymptotic outage probability for the considered system is expressed as P o A γ t h ≈ A ∑ p = 1 3 r B γ t h A 0 r μ r ϱ 4 , p ∏ q = 1 q ≠ p 3 r Γ ϱ 4 , q − ϱ 4 , p ∏ q = 1 1 Γ 1 − ϱ 3 , q + ϱ 4 , p ∏ q = 2 r + 1 Γ ϱ 3 , q − ϱ 4 , p ∏ 3 r + 1 3 r + 1 Γ 1 − ϱ 4 , q + ϱ 4 , p + N − 1 A 0 ϵ o 2 γ t h γ ̄ H n ϵ o 2 r + 1 Γ m N t + 1 U m γ t h γ ̄ U U m N t . (30)

From (34), we observed that min ( ϵ 2 r , α r , β r ) is the dominant term of meijer-G function. Hence, the diversity order of the overall system is given as min ( ϵ 2 r , α r , β r , ϵ o 2 r , U m N t ) .

Proof: See the Appendix.

For various modulation schemes, a generalized ABER expression for the considered communication system can be given as (Zedini et al., 2020) P e = κ 2 Γ 1 / 2 ∑ p = 1 n 0 g p ∫ 0 ∞ x − 1 / 2 e − g p x P o γ d γ , (31) where n ₀, κ, and g _p are the selection parameters for various modulation schemes and their values are shown in Table 2.

Please note that by using the IM/DD, we can obtain the ABER performance of on-off keying (OOK), preferred commonly in practical FSO systems as it is flexible to laser nonlinearity with ease of use. Further, we have analyzed the ABER performance of various MPSK (including the BPSK) and MQAM schemes using the coherent heterodyne detection at FSO receivers. Now plugin (28) in (31), and performing various mathematical computations by using (Gradshteyn and Ryzhik, 2000, (3.351),(6.455),(7.813), (8.352)) to solve the integrals, the final generalized analytical ABER expression is derived as P e = κ 2 Γ 1 / 2 ∑ p = 1 n g p [ I 1 − I 2 + I 3 + I 4 + I 5 − I 6 − I 7 ] , (32) where I 1 = A F 1 1 2 , g p , I 2 = ∑ z = 1 N − 1 N − 1 z − 1 z A 0 ϵ o 2 z 1 γ ̄ H n ϵ o 2 z r Γ ϵ o 2 z r + 1 2 g p − ϵ o 2 z r + 1 2 , I 3 = U ∑ j , l C 0 C 2 − C 1 F 2 1 2 , g p , I 4 = U ∑ j , l C 0 C 2 − C 1 ∑ z = 1 N − 1 N − 1 z − 1 z A 0 ϵ o 2 z 1 γ ̄ H n ϵ o 2 z r F 2 ϵ o 2 z r + 1 2 , g p , I 5 = A ∑ z = 1 N − 1 N − 1 z − 1 z A 0 ϵ o 2 z 1 γ ̄ H n ϵ o 2 z r F 1 − ϵ o 2 z r + 1 2 , g p , I 6 = A U ∑ j , l C 0 C 2 − C 1 Γ C 1 F 1 1 2 , C 2 + g p − ∑ z 1 = 0 C 1 − 1 C 2 z 1 z 1 ! F 1 − z 1 + 1 2 , C 2 + g p , I 7 = A U ∑ j , l C 0 C 2 − C 1 ∑ z = 1 N − 1 N − 1 z − 1 z A 0 ϵ o 2 z 1 γ ̄ H n ϵ o 2 z r Γ C 1 × F 1 − ϵ o 2 z r + 1 2 , C 2 + g p − ∑ z 1 = 0 C 1 − 1 C 2 z 1 z 1 ! F 1 − ϵ o 2 z r − z 1 + 1 2 , C 2 + g p , (33) wherein F 1 ( ϕ 1 , ϕ 2 ) = ( ϕ 2 ) ϕ 1 − 1 G r + 1,3 r + 1 3 r , 1 [ B ϕ 2 ( A 0 ) r μ r x | ϱ 2 , 0 ϕ 1 , 1 , ϱ 1 ] and F 2 ( ϕ 1 , ϕ 2 ) = C 2 C 1 Γ ( C 1 + ϕ 1 ) C 1 ( C 2 + ϕ 2 ) C 1 + ϕ 1 2 F 1 ( 1 , C 1 + ϕ 1 ; C 1 + 1 , C 2 C 2 + ϕ 2 ) .

In this Section, numerical values from the derived results are obtained and are validated through the simulations performed through Matlab by conducting 10⁸ realizations. The atmospheric turbulence of ES-HAP link is generated by the product of two generalized Gamma distributed random variables. The radial displacement parameter is considered to be Rayleigh distributed and is applied to (8) for pointing error impairments. Throughout the analysis, η = 1 is considered. Unity transmit power is considered at all the nodes and γ _th = 1 dB is considered for the analysis. Further, parameters related to various links are shown in Table 3 unless otherwise stated.

In Figure 3, analytical and simulation results of outage probability against transmit SNR are shown for all three links. In Figure 3A, analytical and simulation results of ES-HAP link are compared for both the IM/DD and heterodyne detection (Het. in figures) techniques for different atmospheric turbulence conditions based on various ground turbulence i.e. C n 2 ( 0 ) = 1.7 × 1 0 − 14 , C n 2 ( 0 ) = 5 × 1 0 − 13 , and C n 2 ( 0 ) = 1 × 1 0 − 12 , (in m^−2/3) respectively for weak, moderate, and strong ground turbulence conditions. Simulation results match well with the analytical results and validate the accuracy. From Figure 3A, we observe a significant improvement in outage performance while going from strong to weak turbulence for both the detection techniques. Also, heterodyne detection provides significant performance improvement than IM/DD due to its capability in handling turbulence effects more efficiently despite having implementation complexity (Zedini et al., 2016). For the performance analysis, a = 10 cm, ω _L = 50 cm, and σ = 10 cm are considered which corresponds to ϵ = 2.553. The same can be conducted for different values of ϵ by varying these selection parameters to show the impact of pointing error. In Figure 3B, analytical and simulation results of HAP-HAP link are compared for various values of ω _L /a which corresponds to different values of ϵ _o . Simulation results match well with the analytical results and validate the accuracy. Further, selection of appropriate values of a, ω _L , and σ results in an appropriate ϵ _o for desired system performance. Figure 3C compares the analytical and simulation results of HAP to terrestrial MUs link for different values of fading severity m, number of antenna N _t , and number of terrestrial users U. U = 1 gives the performance of uth terrestrial MU while increasing U gives the flexibility of user selection. Considering U = 1, m = 1, N _t = 1 as a reference case, we observe significant performance improvement while increasing m or N _t or both. However, increase in N _t gives better performance than increase in m. Increase in U provides the user selection flexibility and improves the outage performance further.

In Figure 4, analytical, simulation, and asymptotic results of overall system outage probability are compared for various values of U, m, and N _t while heterodyne detection is considered at FSO receiver. For the analysis, C n 2 ( 0 ) = 5 × 1 0 − 13 m − 2 / 3 is considered and ω _L /a = 5 for moderate pointing error (Figure 4A) and ω _L /a = 2 for severe pointing error (Figure 4B) are considered. Rest of the parameters are shown in Table 3. From Figure 4A, considering U = 1, m = 1, N _t = 1 as reference case, for an outage probability of 10^–2, approximately 8.7 and 11.7 dB gains are achieved while increasing m from one to two and N _t from 1 to 2, respectively. This indicates better performance with an increase in N _t than m by approximately 3 dB. Further, the gain is same throughout the SNR range except for U = 1, m = 2, N _t = 2 and U = 2, m = 2, N _t = 2 cases. For U = 2, m = 2, N _t = 2, there must be a significant performance improvement as shown in Figure 3C, however, only slight improvement is observed over U = 1, m = 2, N _t = 2. This is because the ES-HAP FSO link’s performance reaches to its saturation which limits the overall outage performance. Hence, no further performance improvement is achieved with the increase in U, m, and N _t beyond U = 2, m = 2, N _t = 2 case. In Figure 4B, ω _L /a = 2 is maintained for the FSO links for severe pointing error case. From Figure 4B, by considering U = 1, m = 1, N _t = 1 as reference case, we can observe a clear performance improvement for U = 1, m = 2, N _t = 1 or U = 1, m = 1, N _t = 2. For further increase in U, m, or N _t , we can observe slight improvement only in the low and medium SNR range. However, no such improvement can be seen at high SNRs and all the curves merge with each other. This is because the ES-HAP FSO link’s performance saturates early due to severe pointing error which limits the overall outage performance. Simulation results validate the analytical results presented in Figure 4. Further, asymptotic results on outage probability are also shown in Figure 4 which match with the outage results at high SNRs for all the considered cases and validates the high SNR approximation. Further, the diversity order of the overall system is obtained as min ( ϵ 2 r , α r , β r , ϵ o 2 r , U m N t ) .