Exploiting User Clustering and Fixed Power Allocation for Multi-Antenna UAV-Assisted IoT Systems

Internet of Things (IoT) systems cooperative with unmanned aerial vehicles (UAVs) have been put into use for more than ten years, from transportation to military surveillance, and they have been shown to be worthy of inclusion in the next wireless protocols. Therefore, this paper studies user clustering and the fixed power allocation approach by placing multi-antenna UAV-mounted relays for extended coverage areas and achieving improved performance for IoT devices. In particular, the system enables UAV-mounted relays with multiple antennas together with non-orthogonal multiple access (NOMA) to provide a potential way to enhance transmission reliability. We presented two cases of multi-antenna UAVs such as maximum ratio transmission and the best selection to highlight the benefits of the antenna-selections approach with low-cost design. In addition, the base station managed its IoT devices in practical scenarios with and without direct links. For two cases, we derive closed-form expressions of outage probability (OP) and closed-form approximation ergodic capacity (EC) generated for both devices in the main scenario. The outage and ergodic capacity performances in some scenarios are compared to confirm the benefits of the considered system. The number of antennas was found to have a crucial impact on the performances. The simulation results show that the OP for both users strongly decreases when the signal-to-noise ratio (SNR), number of antennas, and fading severity factor of Nakagami-m fading increase. The proposed scheme outperforms the orthogonal multiple access (OMA) scheme in outage performance for two users. The analytical results match Monte Carlo simulations to confirm the exactness of the derived expressions.


Introduction
In recent years, unmanned aerial vehicles (UAVs) have been studied and recommended for possible applications in the Internet of Things (IoT) due to their prominent features related to low-cost implementation and high flexibility [1][2][3][4][5]. As one of the effective system models, a UAV-mounted relay can be easily employed, since it provides a flexible coverage area in comparison with conventional fixed relays and increases the network capacity [6]. For UAV-enabled/assisted ground communications, a UAV relay could be a wirelessly-powered device since it harvests energy from the radio signals received from a nearby base station to improve energy efficiency (EE) [7]. The authors in [7] presented the closed-form expressions to showcase two main system performance metrics such as ergodic capacity and outage behavior by enabling both amplify-and-forward (AF) and Although [25][26][27][28][29][30][31][32][33] studied the benefits of the multi-antenna approach to enhancing performance at destinations of a wireless system, it is still a crucial problem for in-depth analysis to provide more guidelines in the design of effective antenna selection for UAVaided IoT systems in practice. The main contributions of this paper are summarized as follows • We provide two practical scenarios of the multi-antenna relay to evaluate a UAV-aided IoT system that can be implemented while the system still leverages the advantage of a multi-antenna UAV. Compared with the traditional multiple input multiple output (MIMO) techniques, we prefer the antenna selection approach to reduce the cost of design and the complexity of signal processing. While Figure 1 exhibits the way that the relay leverages Maximum Ratio Transmission for signal transmission, the antennaselection approach in Figure 2 inherently enjoys the merits of reducing hardware complexity and cost. • Nakagami-m fading is suitable for characterizing a wide class of fading channel conditions for UAV links. Therefore, we focus on UAVs with the analysis of the Nakagami-m fading model rather than Rayleigh's fading model, which was applied in lots of previous studies. In addition, the two-user scenario of NOMA needs to evaluate the performance when the fixed power allocation is adopted. To confirm the superiority of those schemes, the closed-form expressions for the outage probability and closed-form approximation of the ergodic capacity are derived. • The outage probability for the multiple-antenna UAV is compared in cases with/ without direct links, NOMA, and OMA to evaluate the effectiveness of the UAV equipped with multiple antennas. We investigate the impacts of the transmit signal-tonoise ratio (SNR) and the number of antennas on the outage probability and ergodic capacity. From these results, one can choose a suitable number of antennas and SNR threshold to balance the demand for performance and the cost of design. The rest of this paper is organized as follows. Section 2 institutes the system model. In Sections 3 and 4, the closed-form outage probability is derived for Figures 1 and 2, respectively. Sections 5 and 6 show the ergiduc capacity analysis for Figures 1 and 2, respectively. Section 7 shows simulation results. Finally, conclusions are drawn in Section 8.  Notation: Vectors are symbolized by bold-faced letters, e.g., x, . F specifies the Frobenius norm, (.) T and (.) H denote the normal and Hermitian transpose, respectively; Pr(.) denotes the probability operator; E{.} is the Expectation operator; K n (.) is the so-called Bessel function; the probability density function (PDF) and the cumulative distribution function (CDF) of a random variable X are represented as F X (.) and f X (.), respectively.

System Model
We consider a downlink multiple-antenna UAV-aided IoT system, as shown in Figure 1. In this scenario, a base station (BS) wants to transfer the information to K users, in which two users in the group are located in separated clusters. The user U k could be a strong user or a weak user (k = 1, 2, 3, . . . , K). The BS works with different frequencies assigned to these clusters following OMA. To evaluate the performance of a particular cluster, we refer to the strong user U 1 and the weak user U 2 with the help of an AF-based UAV (R), as illustrated in Figure 1. It is noted that the multiple users served by BS are divided into many groups, and each group contains two users. In addition, the BS and two users are equipped with a single antenna, and the UAV (relay) R is equipped with N antennas. In the IoT system, multiple-input multiple-output (MIMO) techniques can be employed to mitigate the detrimental effects of unavoidable fading when the base station uses multiple antennas for transmitting and receiving signals. Although using the MIMO technique could be a promising way to improve the capacity and system performance, the transceivers need multiple radio frequency (RF) chains leading to higher power consumption and higher hardware complexity. In this article, we design antenna selection (AS) schemes applied at the BS to reduce the number of RF chains and still maintain the advantages of MIMO systems. Perfect channels state information (CSI) is assumed to be available at the BS. In addition, we assume that the fading channels are distributed over Nakagami-m channels, which are usually characterized by channels connected to UAV.
The channel coefficients between BS and R are denoted by the 1 × N matrix where each element h n R with fading parameter m R is called independent and identically distributed (i.i.d.), and the expectation E h n R 2 = λ R width n ∈ {1, 2, . . . , N}. Likewise, the channel coefficients between R and two users ( Following the NOMA principle and in order to provide more user fairness, we assume that h U 2 2 > h U 1 2 , a 2 > a 1 with a 1 and a 2 are the power allocation coefficients and a 1 + a 2 = 1 [40,41]. In this article, we just focus on the analysis of two users located in a particular cluster and assume the performance at other clusters is similar. The BS transmits the superposition coding signal, which is combined by two signals x 1 and x 2 to R and two users in phase 1. The expectations of signals x 1 and x 2 are assumed that E x 2 1 = E x 2 2 = 1 in which E[.] is called the expected operator. Hence, the transmitted signal expression at BS is given byx where x 1 and x 2 are the messages for U 1 and U 2 , respectively. We assume that n R , n RU i , n U i denotes the additive white Gaussian noise (AWGN) with mean power N 0 .

The Outage Performance of Figure 1
The received signals at U 1 , U 2 and R are, respectively, given by and where P S is the transmit power and v R ∈ C N×1 is the receive beamforming vector at the R. By employing the maximum ratio combining (MRC) scheme, each user U 1 and U 2 employs in [42].
In the second phase, R transmits the signal x R =Ḡy R to both U 1 and U 2 , whereḠ denotes the amplifying gain at relay, i.e., where P R denotes the transmit power of the relay. Without loss of generality, we assume that the transmit power at R is equal to the transmit power of the BS, i.e., P R = P S = P. Therefore, the received signals at U i (forwarded by R) are given by [43]: By employing the Maximum Ratio Transmission (MRT) scheme, the relay obtains the following beamforming vector k i ∈ N×1 to steer the signal in the direction of two users U 1 and U 2 with [42,44].
To calculate the instantaneous signal-to-interference-plus-noise ratio (SINR) of the two phases, let us define the average transmit SNR, ρ = P N 0 and the random variables (RVs) There are two phases of signal processing in the NOMA system. In the first phase, other signal components are treated as interference by U 2 while decoding their own message x 2 . The SINR is used to decode the signal x 2 with a direct link given by Similarly, the instantaneous SINR at U 1 to detect x 2 is given as After SIC, we assume the perfect SIC is at the receiver side. Therefore, the received SNR at U 1 to detect its own message x 1 is written as In the second phase, the instantaneous SINR at U 2 relating to link R → U 2 is calculated by applying the same procedure as the first phase and is thus given by Considering the link R → U 1 , the instantaneous SINR at U 1 to detect x 2 and the instantaneous SNR at U 1 to detect its own data x 1 are, respectively, given by and Based on the selection combination, the instantaneous SINRs at U 2 and U 1 could be given as [45]γ Based on the quality of service of two users, their target SINRs can be determined. Each user has its own the SNR threshold, ε th i = 2 2R i − 1, i ∈ {1, 2} where R 1 is the target rate at U 1 to detect x 1 and R 2 is the target rate at U 1 to detect x 2 . For simplicity, we assume the SNR thresholds of U 2 and U 1 are both equal, i.e., ε th 1 = ε th 2 = ε th .

Outage Probability at U 2
According to [46,47], the cumulative distribution functions (CDF) of the RVs X i , Y and Z i , respectively, are given by and the probability density function (PDF) of the RVs X i , Y and Z i , respectively, are given by where are the parameters of multipath fading , respectively. Then, the outage probability at U 2 can be given bȳ Proposition 1. The closed-form expression of the outage probability at user U 2 can be given bȳ Proof of Proposition 1, see Appendix A.

Outage Probability at U 1
Similarly, the outage probability at user U 1 can be computed bȳ Proposition 2. The closed-form expression of the outage probability at user U 1 can be computed bȳ where ϕ = ε th a 1 ρ Proof. Here,B 1 is calculated asB Next,B 2 is calculated as With the help of Equations (1.111), (3.471.9) [48] and after some manipulations, we haveB Substituting (22) and (19) into (17), the expression of (18) can be obtained.

Remark 1.
Although derivations of outage behavior are complicated, we still realize that channel parameters and the number of transmit antennas can be the main factors affecting the system performance. For example: in (18), the outage behavior relies on m, N.

The Outage Performance of Figure 2: Separated Antenna Selection Approach
In Figure 2, each user follows the antenna selection scheme itself. This way, the performance of each user can be maximized as expected. We will present how Figure 2 is different from Figure 1 in terms of outage performance. In addition, Figure 3 shows the block diagram of the antenna selection for Figure 2. We assume the MRC method from BS to R and the optimal antenna from R to two users by the transmit antenna selection method.  By employing the antenna-selection technique for separated users, the received signal at each U i is first written as

Best Antenna Serving U 1
In this case, the BS selects the ideal antenna to obtain the highest performance at U 1 . When U 2 performance is assured owing to greater normalized channel gain and the source chooses an appropriate antenna to serve U 1 , this method can maximize the system's performance. The chosen antenna, represented by n * 1 , may therefore be written as According to (23), the equivalent instantaneous end-to-end SINR of U 1 can be written as In addition, the PDF and CDF ofZ n * i can be re-expressed as and From (25) and (26), we can write the expression of P I I 1 as in (29) where Proposition 3. The approximated closed-form expressions of the outage probability for U 2 with Figure 2 is given byP Proof of Proposition 3, see Appendix B.

Best Antenna Serving U 2
The source BS will select the ideal antenna in Figure 2 to get the highest performance dedicated to U 2 . When the U 1 performance is uncertain owing to high interference levels and/or unfavorable channel conditions, this method can maximize the system's performance. The source then favors a suitable antenna to serve U 2 . The chosen antenna, represented by n * 2 , may be written as Thus, the received SINR at U 2 to detect x 2 is given bȳ The outage probability of U 2 for AF-NOMA is Similarly, by solving P I I 1 , P I I 2 can be obtained as Although the design of Figure 2 costs less, the system working with Figure 1 still provides higher diversity characterization. We pay attention to examining other system performance metrics, i.e., ergodic capacity.
Proof of Proposition 4, see Appendix C.

Figure 2: Ergodic Capacity Analysis
Ergodic Rate of U 2 : On the condition that U 2 can detect x 2 , the achievable rate of U 2 can be written as C I I 2 = E 1 2 log 2 1 +γ n * RU 2 ,x 2 . The EC of U 2 can be obtained in the following proposition.

Proposition 5.
The closed-form expression of approximated C I I 2 for U 2 is given by where φ k = cos 2k−1 2K π .
Although obtaining a closed-form formula for C I I 2 is challenging, we can acquire an accurate approximation for it. We may obtain (44) by using Gaussian-Chebyshev quadrature Equation (25.4.38) [49].
The proof is finished.

Simulation Results
In this section, we set m = m U 1 = m U 2 = m R = m RU 1 = m RU 2 and numerically simulate some theoretical results to show the outage performance. In particular, the main parameters can be seen in Table 2. In addition, the Gaussian-Chebyshev parameter is selected as D = J = K = 100 to yield a close approximation.

Parameters Notation Values
The power allocation coefficient The fading severity parameter m 2 Target rates SINR ε th 2 (dB) The average power In Figure 4, we examined the outage probability versus SNR and the number of antennas. The figure shows that the outage probability for User 2 is lower than that for user 1. Although the outage probability for both users tends to decrease linearly and quickly, the outage probability for User 2 still keeps a value of around 10 0 in the SNR range from 0 to 10 dB. In particular, when the number of antennas increases from 1 to 3, the outage probability for both users is reduced. This implies that the more antennas, the more reliable the system.  In Figure 5, we present the outage probability versus SNR and fading severity factor m. Similar to Figure 4, the outage probability for User 2 is also lower than that for User 1. The outage probability for both users decreases quickly as SNR increases. For impacts of m on the outage probability, it is observed from the figure that the larger the value of m, the higher the slope of the outage probability curves. This can be explained based on (15) and (17). Figure 6 plots the outage probability versus power allocation coefficient a 2 . The figure shows that the outage probability for User 2 decreases in the case of increasing a 2 . However, this is the opposite for User 1 where the outage probability increases linearly when a 2 increases. In addition, the outage probability for two users tends to decrease since the number of antennas increases. In Figure 7, we present the relationship between the outage probability and SNR for scenarios with and without direct links between BS and users for Figure 1. It is evident that the outage probability for User 2 consistently remains lower than that for User 1. Furthermore, when there is no direct link between BS and users, the outage probability for User 1 is higher compared to User 2. The absence of a direct link leads to a higher outage probability compared to scenarios with a direct link. Interestingly, as the value of m increases from 1 to 2, the outage probability for both users, in cases with or without direct links, consistently improves.  Figure 8 presents the outage probability as a function of SNR in dB in cases of NOMA and OMA schemes. It is observed from the figure that the outage probability for User 2 and NOMA is lower than that for OMA in both cases where the number of antennas is 1 and 2. However, this is the opposite for User 1 where the outage probability for OMA is lower than that for NOMA. In general, the outage probability curves decrease quickly as SNR increases. In Figure 9, the ergodic capacity versus SNR in different cases of antennas (i.e., n = 1, 3, 5) was investigated. The figure shows that the ergodic capacity of User 2 increases gradually in the SNR range of 0 to 20 dB. However, this tends to remain constant during the SNR range of 20 to 30 dB. For User 1, the ergodic capacity increases rapidly as SNR varies from 10 to 30 dB. In addition, the number of antennas also causes a change in the ergodic capacity. Specifically, the higher the number of antennas, the larger the ergodic capacity. However, the impact of the number of antennas on the ergodic capacity for User 2 is insignificant, particularly in the SNR range of 20 to 30 dB. Next, Figure 10 demonstrates that the performance of two users in Figure 1 is better than that of the users Figure 2 in terms of outage probability. The main reason is that Figure 1 still exhibits higher diversity, although Figure 1 requires a higher design cost. The demand for low-cost design for some applications of the Internet of Things would prefer the benefits of Figure 2. Figure 11 presents the inclusion of simulation data for comparative analysis, serving to verify the accuracy of the obtained analytical results. Additionally, a comparison is made between the ergodic capabilities of the proposed system in Figures 1 and 2. Specifically, User 2 demonstrates a higher ergodic capacity in Figure 1 compared to Figure 2 within the low and moderate SNR regions. However, User 1 achieves a superior ergodic capacity over Figure 2 across a wide range of SNR values. Remarkably, in the medium and high SNR ranges, User 2's achievable capacity converges to a constant because interferences in the instantaneous SINRs at User 2 rise as the average SNR increases. Conversely, the interferences experienced by User 1 intensify as the average SNR rises, as demonstrated in Equations (36), (39), (44) and (48). Consequently, it is evident that the ergodic capacity of User 2 in Figure 1 outperforms that of User 2 in Figure 2.  Lastly, Figure 12 illustrates the variation of the ergodic capacity as the number of antennas increases, ranging up to 10. Notably, User 1 exhibits a higher ergodic capacity compared to User 2. The ergodic capacity demonstrates a proportional relationship with the number of antennas. However, for User 2, this capacity remains nearly constant when the number of antennas exceeds 4. This observation suggests that the impact of the number of antennas on User 1 is greater than that on User 2. This can be explained based on (36) and (39).

Conclusions and Future Work
This paper has presented two practical schemes of multiple-antennas UAV-aided IoT systems. Closed-form expressions for the outage probability were studied to confirm Figure 1 with a higher superiority of outage performance compared with Figure 2. We also provide performance analysis for the system by deriving a closed-form approximation of the ergodic capacity in Figure 1. The numerical results show that a weak user (User 2) achieves a lower probability than a strong user (User 1). The outage probability without direct links is lower than that with direct links. The IoT relying on the NOMA scheme is superior to that using the OMA scheme. The performance of the system increases when the number of antennas increases. These findings are a basic background for investigating the performance of the NOMA system with multiple antennas. In future work, reconfigurable intelligent surface-based UAVs could be studied to improve the performance of IoT users. In the future, we will combine UAV NOMA with changeable intelligent surfaces to increase system performance metrics even more.

Conflicts of Interest:
We have also no conflict of interest to disclose.

Appendix B
Proof of Proposition 3. The outage probability of U 2 with Figure 2 is calculated as Let t = x − θ max ρ → t + θ max ρ = x → dt = dx; then,P I I 1 is given bȳ Using Newton's binomial, i.e., (a + x) k = ∑ k v=0 k v x v a k−v and Equation ( With the aid of Equation ×K q−c+1 2 µ R µ RU 1 aθ max (θ max ρ 2 + 1) .

(A10)
The proof is completed.