Performance Analysis of Dual-Hop UAV-Assisted mmWave Links Considering Orientation Fluctuations

In emergency scenarios, infrastructure of wireless networks is usually damaged and becomes out of service. Therefore, Unmanned Aerial Vehicles (UAVs) have been widely nominated as an alternative to provide prompt and efficient wireless connectivity. To this end, UAV-assisted communication systems are recently being under investigation. In this paper, the focus is on UAV-assisted dual-hop links in which the source, relay and destination can be either ground-based or aerial nodes. Specifically, the paper analyzes the performance of these links in terms of the outage probability (OP) and the bit error rate (BER) considering eight different setups of dual-hop UAV-assisted links operating over the millimeter wave (mmWave) band. Unlike others, the performance analysis is conducted considering practical models of the channel fading, path loss, antennas gain and UAVs’ fluctuations. A generalized mathematical framework is followed to obtain the cumulative distribution function (CDF) and the probability density function (pdf) of the overall signal-to-noise ratio (SNR), which are utilized to characterize closed form expressions for the average OP and BER for all proposed setups. Analytical results are validated by Monte Carlo simulations which investigate the role of many setup parameters including the number of antenna elements, the fluctuation intensity, the transmit power and the modulation order. Moreover, results indicate that increasing the number of aerial entities in the link negatively affects its performance due to the impact of the fluctuations on the directional antennas in the mmWave band.


I. INTRODUCTION
An Unmanned Aerial Vehicle (UAV) is a pilot-less aerial vehicle which can be controlled either remotely from a point on the ground or by an onboard computer [1].This emerging technology has been initially used for various military and security applications such as border surveillance, reconnaissance operations, targeting, monitoring, strike, The associate editor coordinating the review of this manuscript and approving it for publication was Adao Silva .airfield security, and battlefield damage assessment [2], [3], [4].Later on, due to the advances in computing power, artificial intelligence, availability of general purpose software and many other forms of technological advancement, UAVs have been applied in civilian, industrial, public missions and cost effective commercial applications [5], [6], [7], [8], [9], [10], [11].
Among the different UAVs' applications, exploiting UAVs for providing wireless connectivity in emergency scenarios, which include natural disasters, military attacks and public events [12], has gained an increasing attention.The role of UAVs in such applications is to deploy an efficient and prompt communication system which can provide the desired connectivity [13].For example, UAVs can be utilized as a flying base stations to assist overloaded ground base stations in congested areas [14].In addition, UAVs can be employed to build UAV-assisted links to replace damaged terrestrial networks due to natural disasters [15].It is worth highlighting that communication systems are essential to support emergency management facilities.As rebuilding the destroyed local communication infrastructures may take a long time, it is very necessary a find a suitable alternative to maintain the connectivity between the rescue teams and the affected communities [16].Therefore, the idea of deploying UAV-assisted links in wireless communication systems has been presented to allow for emergency management teams and relief organizations to establish temporary networks, ensuring seamless communication and coordination during critical times.Additionally, the mobility of UAVs and many other features allow for flexible positioning and adaptive coverage, making them particularly suitable for dynamic emergency scenarios.
One of the main limitations of involving UAVs in communication systems is the continuous UAV's fluctuations as a result of the wind impact or the movement of the internal mechanical motors.Such fluctuations affect the antennas' orientation, which poses a serious challenge for communications systems especially those operating on the millimeter wave (mmWave) band.This is mainly because mmWave-based links are very sensitive to antennas misalignment errors that can be casued by UAVs' fluctuations.It is worth mentioning that antennas' misalignment due to orientation fluctuations directly affect the amount of the received power, which is also negatively reflected on other performance aspects including the error performance and outage rate.
Although the performance of UAV-assisted links has been widely investigated in literature, few studies has considered the impact of UAVs' orientation fluctuations.As such, this paper addresses the impact of orientation fluctuations on the performance of UAV-assisted dual-hop mmWave links which are used in emergency scenarios.To this end, eight different setups of UAV-assisted dual-hop links have been considered in which the source, relay and destination can be either aerial or ground node.The performance is characterized in terms of the Outage Probability (OP) and the average Bit Error Rate (BER) at the destination node, taking into account practical models of the channel fading, path loss and antennas gains.Moreover, closed form expressions of both OP and BER are derived following a solid generalized mathematical framework for the eight different system setups considered.Analytical and simulation results are explored to depict the impact of the different configuration parameters, such as the number of antenna elements, fluctuation intensity, transmit power and modulation order, on the performance of the eight different system setups of the dual-hop UAV-assisted mmWave links.An initial version of this work is included in our previous work [17] which is limited to outage analysis of UAV-assisted links.The contributions of this paper are summarized as follows • The impact of UAVs' orientation fluctuations on the performance of UAV-assisted mmWave-based dual-hop links is investigated considering practical models of channel fading, path loss and antennas' gains.
• A generalized mathematical framework is presented to characterize both the probability density function (pdf) and the cumulative distribution function (CDF) of the received signal-to-noise ratio (SNR) for eight different setups of the dual-hop UAV-assisted mmWave-based systems.
• Using the developed mathematical framework, closedform expressions of The end-to-end OP and average BER considering the eight different setups.
• Simulation results are depicted to show the impact of the different operational parameters on both OP and BER.The investigated parameters including the number of antennas elements, fluctuation intensity, transmit power, and modulation order in all different system setups.The rest of this paper is organized as follows.In Section II, related works are discussed, while the system model is described in Section III, detailing the eight different setups of the dual-hop UAV-assisted systems.Section IV analyzes the performance of the considered system in terms of the end-to-end OP and the average BER.Simulation results are explored and the impact of the different factors are discussed in Section V. Finally, conclusions and future work are drawn in Section VI.

II. RELATED WORKS
Many previous studies have been directed to investigate the performance of UAV-assisted links considering different models of single-hop UAV-assisted links such as Air-to-Ground (AG) [18], [19], Ground-to-Air (GA) [20] and Air-to-Air (AA) [21].In [18], using Wireless InSite Software, the received signal strength (RSS) and root mean square delay spread (RMS-DS) of multi-path components are analyzed for different UAV heights in AG links considering different environments, such as urban, suburban, rural, and over sea.In [19], real measurements have been obtained for AG channel propagation considering a flying UAV in an open area.In [20], authors provide a method of channel prediction during GA communication to avoid the blockage at 28 GHz.Channel modeling of AA link has been conducted in [21] where Rice model is extended to include multipath effects induced by UAVs' altitude.Other simplified models of GG, GA, AG and AA single-hop links are adopted in [22].In another work, the performance analysis for a UAV-assisted downlink system using Free Space Optical (FSO) links has been investigated utilizing the Málaga distribution to characterize the effect of atmospheric turbulence in [23].However, none of these models adopted for single-hop links have considered the antennas' fluctuations caused by UAV(s) vibrations [24].
Dual-hop UAV-assisted links have been proposed as a solution to overcome some of the challenges associated with the single-hop links especially the problem of the limited communication range and blockage.Many works have focused on analysing the performance of dual-hop UAVassisted links including optimizing the used communication technology (FSO or radio frequency (RF)), the mode of relaying system (one-way relaying or two-way relaying), the relaying protocol (amplify-and-forward (AF) or decodeand-forward(DF)).For example, authors in [25], [26], and [27] present a dual-hop UAV-assisted systems using FSO communication technology.In [25], the performance of the proposed relaying system is studied under the AF relaying protocol while authors in [26] consider the DF relaying protocol.Differently, the impact of antenna orientation has been considered for GAG UAV-assisted link operating on FSO in [27], where the channel distribution is obtained and utilized to obtain the OP.
Other set of works has focused on analysing the mmWavebased dual-hop UAV-assisted systems.In [28], an efficient UAV-relaying method for mmWave-based links is proposed where the UAV gradually adjusts its path to approach the optimal location.In [29], the focus is on optimizing the UAV position, analog beamforming, and power control to maximize the achievable rate in a full-duplex UAV relaying network.To achieve better performance considering different environments, many researches tend to use hybrid systems of RF/FSO, such as [30] that presents the ergodic sum rate analysis of a UAV-based communication system with mixed RF/FSO channels.More related work is reported in [31] where the pdf and CDF of the SNR are derived for the GAG UAV-assisted dual-hop mmWave-based links considering the UAVs' antennas fluctuations.
In all of the above discussed works (summarized in Table 1), analysis of dual-hop UAV-assisted links have not considered the UAVs' vibrations except [27], [30], [31].However, works conducted in [27] and [30] consider the impact of the fluctuations on the FSO link, which is different from the RF case.Also, all of these works [27], [30], [31] are limited to the case of GAG setup which represents a special case of UAV-assisted links.To the best of our knowledge, there are no previous works that investigate the impact of the orientation fluctuations of UAV-assisted dual hop mmWave-based links.Therefore, this work comes to complement the research efforts in this direction by analyzing the impact of the orientation fluctuations on the OP and BER.

III. SYSTEM MODEL
A dual-hop communication link is considered in this work, where a source node (S) transmits data towards a destination node (D) via a relay node (R).Being a UAV-assisted link implies that nodes S, R and D can be either ground-based or aerial nodes.As such, eight different system setups can be formed by different combinations of aerial and ground nodes, as depicted in Fig. 1, named as AAA, AAG, GAA, GAG, GGG, AGG, GGA and AGA.In all of these notations, the first, second and third letters represent S, R and D, respectively, where A refers to an aerial node while G refers to a ground node.For example, the AAG setup represents a dual-hop system where S and R are both aerial nodes represented by two UAVs while D is a ground node.For all setups, the distances on both hops are assumed identical and denoted by L. Also, as the considered link is operating on the mmWave band, directional antennas are utilized at the three nodes.Each of nodes S and D is equipped by a single directional antenna to communicate with R, while R utilizes two directional antennas to communicate with both S and D separately.
Our work will start by showing the single-hop studies and equations that introduced in [31] before extending them to the dual-hop relaying system.A general formula of the SNR for a single hop is given as follows: where ℓ − ℓ ′ signifies the considered hop (S − R or R − D), ζ is the channel fading power, P ℓ is the transmit power, h(L) is the path loss, G ℓ−ℓ ′ the overall antennas' gain of the considered link, and σ 2 is the noise power.It is worth to mention here that the transmitted power from all nodes is considered identical and denoted by P. Based on (1), the transmitted signal is affected by channel fading (smallscale propagation effects), path loss (large-scale propagation effects) and antennas' gains.In what follows, we describe the model adopted for each of these effects.

A. PATH LOSS
The adopted model for path loss is based on the recent 3GPP report [32], which expresses the path loss in dB over an aerial distance L, h dB (L), as follows where h b is the average building height of the area (in meters), and f c is the carrier frequency.It should be highlighted here that this path loss model is valid for UAV's altitude less than 150m.

B. CHANNEL FADING
Among the different channel fading models, Nakagami fading model has been widely accepted to represent the small-scale channel propagation effects in the mmWave band due to its agreement with real channel measurements [21].
In Nakagami model, the channel power ζ is distributed according to the Gamma distribution.As such, the pdf of ζ is given as where m is the Nakagami fading parameter and (.) is the Gamma function.

C. ANTENNA GAIN
The last varible in the SNR formula ( 1) is G ℓ−ℓ ′ which represents the gains of the two antennas (transmit and receive antennas) of the considered hop ℓ − ℓ ′ (i.e., AA, AG, GA or GG), which is represented by their product, i.e., G ℓ−ℓ ′ = G ℓ G ℓ ′ .In our work, the antennas are assumed to be uniform square array antennas, each of N × N elements.The spacing between the elements in both x-and y-directions are set to λ/2 where λ is the wavelength.Also, the progressive phase shifts in both x and y directions are set to zeros.The gain of the antenna (either transmit or receive antenna) depends on the type of the node carrying the antenna (i.e.either A or G).

1) ANTENNA GAIN OF AERIAL NODES
The radiation gain of a directional antenna is usually represented by the orientation angles of the antenna in x and y directions, denoted by φ ℓx and φ ℓy , respectively.From the 3GPP report [32], the angles, φ ℓx and φ ℓy , are combined to form other two angles denoted by φ ℓ and ϕ ℓ and expressed as follows For an aerial node, both φ ℓx and φ ℓy are actually random as a result of the random hovering vibrations.As such, both angles are assumed to be Gaussian distributed, i.e. φ ℓx ∼ N (φ ′ ℓx , σ 2 ℓo ) and φ ℓy ∼ N (φ ′ ℓy , σ 2 ℓo ).Based on [33], the array radiation gain is expressed as follows G ℓ (φ ℓx , φ ℓy ) = G 0 (N ℓ )G a (φ ℓx , φ ℓy )G e (φ ℓx , φ ℓy ), (5) where G a is an array factor, G e is the single element radiation pattern and G 0 is a constant defined later.From the 3GPP, the single element radiation pattern, G e,3dB = 10 × log 10 (G e ) of each single antenna element is obtained as follows where φ e3dB = 65 and ϕ e3dB = 65 are the vertical and horizontal 3D beam waves, respectively, G max = 8 dB i is the maximum directional gain of the antenna element, F m = 30dB is the front-back ratio, and G SL = 30 dB is the side-lobe level limit.The array factor G a (φ ℓx , φ ℓy ) for a square array of N 2 elements can be obtained as follows Finally, G 0 is computed utilizing the relation below which ensures that the radiated power from transmit antennas is kept the same: More details on the element and array radiation pattern are provided in [33] and [34].

2) ANTENNA GAIN FOR GROUND NODES
Unlike the aerial node, the directional antenna installed at a ground node can be considered in a perfect alignment as it is not affected by fluctuations.Therefore, the antenna gain at a ground node can be computed using the same procedure followed for the aerial node while assuming φ ℓx ≃ 0 and φ ℓy ≃ 0, as follows

IV. SYSTEM PERFORMANCE ANALYSIS
In this section, the performance of dual-hop cooperative links of the considered setups is analyzed by quantifying two important metrics: the end-to-end OP and the average BER.

A. OP ANALYSIS
In general, OP is the probability that the channel capacity falls below a predefined threshold (C th ), which is mathematically expressed as follows or simply, OP can be defined as the probability that the SNR γ falls below a predefined threshold γ th as follows For a dual-hop systems, the OP is defined as the probability that the SNR of any of the two hops, i.e., S − R or R − D, falls below the outage threshold γ th .Therefore, P out can be expressed as follows where γ 1 and γ 2 represent the SNR of the S − R hop and the R − D hop, respectively, of the considered dual-hop system.Let us define γ min = min{γ 1 , γ 2 }.Therefore, The end-to-end OP can be rewritten as follows: Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
where F γ min (γ ) is the CDF of γ min , which can be expressed as follows [35]: where F γ 1 (γ ) and F γ 2 (γ ) represent the CDFs of the S − R hop and the R − D hop, respectively.Given the different channel effects encountered in different link types (i.e., AA, AG, GA, or GG) in the two hops, the CDF of each hop should follow the link type.In [31], three different closed form expressions of the CDFs of AA, AG and GA links, have been derived.Next, we will unify the representation of these CDFs in one generalized function that accommodate all of these link types and the GG link as well.Specifically, the CDF of the hop ℓ − ℓ ′ can be expressed as follows: where ν(., .) is the lower incomplete gamma function, and J ℓ i is defined as follows: where M (., .) the Marcum Q-function.The function J ℓ ′ j ℓ ′ can be computed by the same formula of J ℓ i ℓ with replacing i ℓ and ℓ by j ℓ ′ and ℓ ′ .The value of the parameter T ℓ is substituted as follows: and T ℓ ′ is computed using the same formula by replacing ℓ by ℓ ′ .The variable µ ℓ−ℓ ′ i ℓ ,j ℓ ′ is expressed as follows: where R ℓ−ℓ ′ i ℓ ,j ℓ ′ is given in (19), as shown at the bottom of the next page, where G ′′ 0 (N ) is given as follows: Finally, the OP of any of the considered eight setups can be expressed by substituting the proper CDFs corresponding to the considered setup in (14).For example, the OP of the AGA system setup can be computed by replacing F γ 1 and F γ 2 by the CDFs F A−G (γ th ) and F G−A (γ th ) in (14), which leads to the OP of the AGA system setup as depicted in (21), as shown at the bottom of the next page.OP formulas of other setups can be obtained in a similar procedure.

B. BER ANALYSIS
The average BER is another important performance metric for wireless communication systems.In our considered dualhop UAV-assisted communication setups, it is clear that the BER at S and D nodes are identical in all proposed setups.Hence, the BER analysis can be calculated at just one node, say D. Consider the bit block transmitted from S is denoted by b, received at R as b, and finally received at D as b.Therefore, the average BER at D, denoted by BER SD , can be expressed as By substituting e SR and e RD that represent error vectors in the data transmitted from node S to node R and from node R to node D, respectively, the equation can be rewritten as follows The last line of (23) states that the event e SR ⊕ e RD ̸ = 0 occurs only when the bits in the error vectors.This case can be further expanded due to the fact the two hops are independent as follows: As e SR and e RD are two independent error events [35], (24) can be simplified as follows: which can be rewritten as follows where α S−R and α R−D represent the BER in the link S − R and R − D, respectively.For a coherent PSK modulation scheme, the average BER over a fading channel for the link ℓ − ℓ ′ can be expressed as follows [36]: where erf(•) is the error function, γ , while δ, and ω can be determined respectively as follows: The pdf f γ ℓ−ℓ ′ (γ ) is the probability density function of γ th at ℓ − ℓ ′ and it can be computed as follow: Accordingly, ( 27) can be rewritten as follows: By solving the integral in (31) [37, eq.4.3.8],α ℓ−ℓ ′ can be expressed in a closed from expression as follow: where 2 F 1 (., .; .) is the hyber-geometric Gauss function.Finally, the average BER SD can be obtained by substituting α ℓ−ℓ ′ from (32) for both links in (26).

V. SIMULATION RESULTS
In this section, the results of Monte Carlo simulation for our proposed dual-hop UAV-assisted mmWave system setups in terms of the two metrics; the end-to-end OP and the average BER are explored and discussed.A set of simulation parameters are set to fixed values which are listed in Table 2. Results are explored in figures for the system setups 32524 VOLUME 12, 2024 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.AAG, AGA, GAA, GGA, AGG, GAG, AAA, and GGG, respectively, in the following subsections.

A. OP RESULTS
In this subsection, the end-to-end OP (P out ) versus γ th is explored in Fig. 2 to Fig. 9 for all setups considered.Each of these figures includes three sub-figures that investigate the impact of the transmit power P, the number of antenna elements N and the UAV's vibration intensity σ 2 o .In the first sub-figures (a) in Fig. 2 -Fig.9, N and σ 2 o are fixed to N = 4 and σ 2 0 = 1 • , respectively, while three different values of the transmit power P are assumed P = −10, 0 and 10 dBm.From these results, the impact of transmit power can be clearly observed, where the increase in transmit power reduces the OP.For example, at γ th = 10 dB for AAG setup, OP is decreased from 10 −1 to 10 −4 when the transmit power increases from 0 to 10 dB.The same behaviour can be observed in all other setups, which is mainly due to the increase of the received signal power as the transmit power increases.
In the second sub-figures in all figures (i.e., sub-figures (b) in Fig. 2 -Fig.9), the impact of varying the number of antenna elements on the OP is depicted.To this end, both P and σ 2 o are fixed to P = 20dBm and σ 2 o = 1 • , respectively, while three different values of the number of antenna elements N are assumed N = 4, 8 and 12.It is worth mentioning that all entities in all setups are equipped by identical antenna type and size.Based on these results, it can be realized that increasing the number of antenna elements N at each entity will reduce the OP.This can be referred to the fact that increasing the antenna elements will improve the received SNR at each hop, and thus, the link outage will be reduced, as depicted in all setups with different extents.
The last set of OP results are included in the third subfigures (c) in Fig. 2 -Fig.9, which are dedicated to show is clear that increasing the vibration intensity has a negative impact represented by increasing the OP for all system setups (except for the GGG system setup).This is mainly because of UAVs' vibration will contribute to waste some of the transmit power which will not reach the receiver.As such, the amount of the received power will be reduced, and hence, the OP will increase.It is worth mentioning that vibration intensity has no impact in the GGG setup (Fig. 9-(c)) as no UAVs are involved in this setup.

B. BER RESULTS
The BER results for all setups considered are depicted in Fig. 10-Fig.17, with the same order of OP results.A general observation can be noted in all BER figures is that the average BER decreases as the transmit power increases.This common behaviour between all investigated setups is mainly because increasing the transmit power will improve the SNR, therefore, the BER is decreased.The impact of changing the modulation order M on the overall BER is shown in the first sub-figures (a) in Fig. 10 -Fig.17  As expected, in all setups, increasing the modulation order will increase the BER in both hops, which is mainly due to increasing the bits per symbol transmitted each time.The average BER increases as it can be clearly noted in the results.
In the sub-figures (b) in Fig. 10 -Fig.17, the average BER versus the transmit power is plotted at different numbers of antenna' elements for all system setups.Both M and σ 2 o are fixed to M = 8 and σ 2 o = 1 • , respectively, and three different value of the number of the antenna elements are assumed N = 4, 8 and 12. Unlike the impact on the OP, increasing the number of antenna elements N leads to improve the average BER, which is mainly due to increases the received SNR at the destination resulted from the larger number of antenna elements used.
In the third sub-figures (c) in Fig. 10 -Fig.17 both M and N are fixed to M = 8 and N = 4, respectively, where three different values of the vibration intensity σ 2 o = 1 • , 3 • and 5 • are considered.A clear negative impact of increasing the vibration intensity σ 2 o on the system performance appears, which is mainly due to losing the alignment between antennas due to the UAVs' vibrations.

C. COMPARISON OBSERVATIONS
Although all UAV-assisted setups have a common behaviour of both BER and OP versus any of the investigated operational parameters, they are affected in different extents, and there are some general observations that can be made based on both BER and OP results for all setups considered.First, comparison among all setups reveals that increasing the number of aerial entities degrades the performance in terms of both OP and BER.This is mainly due to the vibrations of the hovering aerial nodes that cannot be eliminated.As mentioned earlier, vibration will directly affect the antennas' orientation, which significantly impacts the received SNR in mmWave-based links.Therefore, it is clear from the OP and BER results that the results of AAA setup has the worst performance as compared to other setup.Also, the results of GGG attain the best performance among all others.Specifically, setups that have one aerial entity (i.e., AGG, GAG, GGA) attain lower outage rate and higher average BER than setups that include two aerial entities (i.e., AAG, AGA and GAA).However, one can ask about the reason of including aerial nodes as the performance gets worse.Here, it is worth highlighting that dual-hop UAVassisted links come to create a link between two nodes that cannot be connected on the ground.Also, the mathematical framework and the results in this study provide a tool for the system designer to evaluate the performance, and hence, select the best system setup.

VI. CONCLUSION
This paper has investigated the performance of dualhop UAV-assisted mmWave-based links using decode-andforward protocol.As nodes can be either aerial or ground nodes, eight different system setups, which represent all possible node combinations of UAV-assisted dual-hop links, have been considered and analyzed.The analysis has presented a generalized closed-form expressions for both probability distribution function and cumulative density function of the signal-to-noise ratio for all possible single-hop links (AA,AG, GA and GG), which have been used to formulate the end-to-end OP and the average BER for all proposed setups.Analytical and Monte Carlo simulation results have shown the impacts of the transmit power, the number of antenna elements, the modulation order and the UAV's vibration intensity of on the outage and error performance.This paper offers the possibility of finding the optimal values of the link parameters and provides an extensive reference for engineering practice in the field of UAV-assisted mmWave links.
Extending this work can include analyzing other performance aspects such as channel capacity, secrecy capacity and wireless coverage.Future work may by energy harvesting, which can be a interesting extension of this work.Also, employing artificial intelligence tools for optimizing the performance of UAV-assisted links can be investigated in future studies.

FIGURE 2 .FIGURE 3 .FIGURE 4 .
FIGURE 2. The end-to-end OP of the AAG setup versus γ th showing (a) The impact of P (b) The impact of N and (c) The impact of σ 2 o .

FIGURE 5 .FIGURE 6 .FIGURE 7 .FIGURE
FIGURE 5.The end-to-end OP of the GGA setup versus γ th showing (a) The impact of P (b) The impact of N and (c) The impact of σ 2 o .

FIGURE 9 .FIGURE 10 .FIGURE 11 .FIGURE 12 .
FIGURE 9.The end-to-end OP of the GGG setup versus γ th showing (a) The impact of P (b) The impact of N and (c) The impact of σ 2 o .

FIGURE 13 .FIGURE 14 .FIGURE 15 .
FIGURE 13.The BER of the GGA setup versus the transmit power showing (a) The impact of M (b) The impact of N and (c) The impact of σ 2 o .
for all system setups.Both N and σ 2 o are fixed to N = 4 and σ 2 o = 1 • , respectively, while three different values of the modulation order M are considered M = 2, 4 and 8.

FIGURE 16 .FIGURE 17 .
FIGURE 16.The BER of the AAA setup versus the transmit power showing (a) The impact of (b) The impact N and (c) The impact of σ 2 o .

TABLE 1 .
Summary of related works.