I Introduction
The use of Unmanned Aerial Vehicle (UAV) networks is considered essential in a number of communication scenarios [1, 2, 3, 4, 5]. In wireless communications, Flying AdHoc Networks (FANETs) composed by multiple UAVs may be adopted to set up a communication network during a natural calamity [1, 6], defense applications, or to improve coverage as drone cells [1, 7]. In a FANET, UAV formations may be split into diverse coalitions according to distinct assignments. In intracoalition transmission, a drone must communicate with the coalition leader and must also establish communication with neighbor drones to schedule flight missions [8]. An effective data interaction in the UAV coalition is essential to keep the flight and mission performance [9]. Each UAV clusterhead (coalition leader) collects and delivers data from cluster members to the land controller [9, 10, 11]. Nevertheless, it is not easy to cover the whole network by onehop transmissions because of transmit power limitations of UAVs. To address this, a key approach is to employ relayassisted transmission or to modify the position and optimize UAV flights [9]. In fact, relaying can enhance the transmission rate and the coverage of systems without altering the UAV formation, which is key in UAV communications [9]. Therefore, relay selection protocols [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 64, 23] can be adapted and employed in FANETs, in which some UAVs are used as relays in scenarios with homogeneous or heterogeneous distances and pathloss between the UAVs.
In this context, the MultiWay Relay Channel (mRC) [14] includes the pairwise data exchange model formed by multiple twoway relay channels, which can be used by a pair of UAVs to establish communication with each other in intracoalition transmissions. The mRC also allows the full data exchange model, where each UAV receives information from the other UAVs. In fact, UAV relaying techniques can be improved by adopting multiway bufferaided protocols, where relay nodes can store information in their buffers [18, 24] before transmitting them to the destination. Moreover, the use of a UAV clusterhead as a central node with the same functions of the cloud in a Cloud Radio Access Network (CRAN) framework [15, 16, 17] may enhance UAV relaying schemes in FANETs. In the CRAN framework, the baseband processing often carried out at basestation (BSs), known as remote radio heads (RRHs), is centrally performed at a cloud processor aided by highspeed links, known as fronthaul links, between the cloud and the BSs [25].
This centralized processing facilitates interference suppression in wireless links and may be also adopted in FANETs. The BSs in the CRAN are denoted as remote radio heads (RRHs) as their action is commonly restricted to transmission and reception of radio signals [25]. The Maximum Minimum Distance (MMD), ChannelNorm Based (CNB) and Quadratic Norm (QN) relay selection criteria have been studied with maximum likelihood (ML) detection [15, 16, 12]. It is shown in [15, 12] that the MMD criterion minimizes the pairwise error pobability (PEP) and, consequently, the bit error rate (BER) in the ML receiver. However, CRAN based UAV relaying protocols in FANETs that employ such criteria and a recursive strategy that exploits timecorrelated channels often found in UAV communications have not been previously investigated in the literature.
In this work, we develop a CRANtype ClusterHeadDrivenBestLink (CHDBestLink) protocol for multipleantenna relaying systems with UAVs (FANETs), which chooses the best links among pairs of UAV sources (SVs) and UAV relays (RVs), optimizing the PEP, BER, average delay and MMD computation rate performances. We develop ML detectors for the UAV clusterhead and the nodes to detect the signals. We also propose a recursive MMD criterion and develop a relay selection algorithm for CHDBestLink, that tracks the evolution of channels over time and computes the MMD metrics only if the channels are considerably changed. Simulations depict the outstanding performance of the CHDBestLink protocol as compared to previously studied techniques. Thus, the main contributions of this letter are:

A CRANtype ClusterHeadDriven framework with joint detection at the UAV clusterhead and the nodes;

The CHDBestLink protocol for multipleantenna relaying systems with UAVs;

The recursive MMD relay selection algorithm.

An analysis of the proposed MWCBestUserLink scheme in terms of PEP, average delay and computational cost.
This paper is organized as follows. Section II presents the system model and the assumptions. Then, the proposed CHDBestLink protocol with the recursive MMD relay selection algorithm is presented in detail and analyzed in Sections III and IV, respectively. Section V depicts and examines the simulation results whereas Section VI draws the conclusions.
Ii System Model
The system is a multiway multipleantenna MultipleAccess BroadcastChannel (MABC) relay network composed by a number of clusters (pair of SVs and ) and half duplex (HD) decodeandforward (DF) RVs, ,…,, where and are finite positive integer numbers and may be different from . The number of pair of SVs and the number of RVs in the UAV formation depend on the kind of mission. These SVs and RVs may be fixedwing UAVs, that must keep a continuous progressive motion to stay aloft, or rotarywing UAVs such as quadcopters, that can move in any direction as even as to stay stagnant in the air [2]. In a CRAN structure, the SVs typify mobile users, the RVs typify RRHs and the UAV clusterhead typifies the cloud. The UAV clusterhead is fixed and has higher processing and buffering capacity than the other UAVs. The SVs have antennas to transmit or receive and each RV antennas, where is a finite positive integer number, all of them used for reception () and out of antennas are chosen from each RV employed for transmission (), where is a finite positive integer number and , composing a spatial multiplexing network. Therefore, the higher
the superior the network performance, as it increases the degrees of freedom. Besides, the higher
the superior the network performance as it increases the number of receive antennas at the RVs. Nevertheless, if and are increased, this leads to a higher computational cost. Thus, there is a tradeoff between network performance and computational cost, when and are increased. The chosen RVs employ clusterhead buffers to store or extract packets in each time slot. A clusterhead buffer with size packets is used on demand for each cluster, as illustrated in Fig.1. In the uplink (MA phase), a cluster is chosen to transmit packets to a chosen RV for reception. Then, the signal is decoded by the clusterhead processor, XORtype PLNC is performed on the decoded data and the resulting symbols are stored in their clusterhead buffers. In the downlink (BC phase), two RVs and are chosen to send packets from the particular clusterhead buffer to the chosen cluster. In most conditions the choice of only one RV in the downlink is enough for a fair performance. Nevertheless, by choosing two RVs, the chance of combining the links associated with the chosen RVs increases the degrees of freedom of the network and, thus, enhances its performance. The network could choose more than two RVs to further enhance its performance, however the computational cost would be considerably increased for a high value of . In this study, for simplicity, we employ the mRC pairwise data exchange model, but the full data exchange model may be adopted in future studies.Iia Assumptions
The energy sent in the uplink from each SV to the chosen RV for reception () equals that transmitted in the downlink from the chosen RV(s) for transmission to the SVs (). Thus,
. Non reciprocal channels and mutually independent zero mean complex Gaussian random channel coefficients, which are stationary for the time of one time slot and change independently from a time slot to another, are considered. The transmission is structured in data packets, where the order of the packets is inserted in the preamble and the primary order is recovered at the destination. Pilot symbols for estimation of channel state information (CSI) and network signaling are also inserted in the preamble. In each time slot
, the central node (the UAV clusterhead) decides whether a cluster or the RVs must transmit, through a feedback channel. Global CSI at the UAV clusterhead is supplied by network signaling. Besides, each RV has information concerning its and links. The use of a UAV clusterhead as a single central node and its buffers leads to a higher control overhead. Nevertheless, it minimizes the average delay and the complexity, as a unique central node decides which nodes transmit (instead of all destination nodes) and the packets related to a cluster are stored in only its particular clusterhead buffer rather than being spread in the buffers of all RVs. This study focus on the ideal case where the fronthaul links (between the UAV clusterhead and RVs) have unconstrained capacities and RVs can reliably convey their data to the clusterhead processor. Realistic systems with capacityconstrained fronthaul links [25] may be studied in future works.IiB System Description
Considering the worst case scenario, where UAVs can fly at ultralow altitude (5m  15m) and, consequently, without the presence of the Line of Sight (LoS) component (Rayleigh fading), the channel model may be aproximated to that of ground wireless sensor networks [26]. The channel matrix includes largescale fading, arising from the pathloss of signal as a function of distance and shadowing by large objects such as buildings and hills, effects of largescale fading, associated with the propagation parameters of the signal over far away distances, and the Rayleighdistributed and smallscale fading effects, resulting from the constructive and destructive interference of the multiple signal paths between the transmitter and receiver [27]. Thus, the quadratic norm of is given by
(1) 
where denotes each SV or (), refers to each RV (), is a constant determined by the carrier frequency, antenna gain and other system characteristics, is the pathloss parameter, denotes a channel matrix associated with the links modeled by mutually independent zero mean complex Gaussian random coefficients and the respective distance between and .
The same reasoning applies to and its quadratic norm is given by
(2) 
In each time slot, the network may work in two modes: "MultipleAccess" (MA) or "BroadcastChannel" (BC). Therefore, depending on the relay selection metrics (presented in Section III), the network has two options: a) MA mode: The chosen cluster transmits packets (one packet per each antenna) straight to the chosen RV ; and b) BC mode: and transmit packets from the clusterhead buffers to the chosen cluster. If the relay selection algorithm decides to function in the MA mode, the signal transmitted by the chosen cluster ( and ) and received at (the RV chosen for reception) is structured in an vector described by
(3) 
where is an vector with symbols transmitted by () and other symbols transmitted by (), is a matrix of and links and is the zero mean additive white complex Gaussian noise (AWGN) at . Observe that is composed by square submatrices of dimensions as given by
(4) 
Considering perfect synchronization, we employ the ML receiver at the clusterhead processor:
(5) 
where is each of the possible vectors of transmitted symbols ( is the number of symbols in the constellation used). The ML receiver computes an estimate of the vector of symbols transmitted by the SVs . Alternative suboptimal detection techniques could also be considered in future work [29, 30, 31, 32, 33, 34, 73, 36, 37, 38, 39, 40, 41, 46, 47, 48, 49].
By performing XOR type PLNC, only the XOR outputs, that result in packets, are stored with the information: "the bit transmitted by is equal (or not) to the corresponding bit transmitted by ". Thus, the bitwise XOR is employed:
(6) 
and the resultant symbol is stored in the clusterhead buffer. Therefore, an advantage of employing XOR is that only packets are stored in the clusterhead buffer, rather than . In contrast, if the relay selection algorithm decides to work in the BC mode, the signal transmitted by the RVs chosen for transmission ( and ) and received at and is structured in an vector given by
(7) 
where is a vector with symbols, , , represents the matrix of and links, and is the AWGN at or . Note that is chosen among submatrices of dimensions contained in as given by
(8) 
The ML receiver is also employed at the chosen cluster:
(9) 
where denotes the possible vectors with symbols. Therefore, the vector of symbols sent by is calculated at by employing XOR type PLNC:
(10) 
It is also employed at to compute the vector of symbols transmitted by :
(11) 
An estimate is used rather than in (5) and (9) with the ML receiver for imperfect CSI. We remark that is calculated as =+
, where the variance of the mutually independent zero mean complex Gaussian
coefficients is described by ( and ) [15], in which in the MA phase, and in the BC phase. Channel and parameter estimation [60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74] and resource allocation techniques [75] could be considered in future work in order to develop algorithms for this particular setting.Iii Proposed CHDBestLink Protocol and Relay Selection Algorithm
The network in Fig. 1 employs the CHDBestLink protocol, which in each time slot works in the MA or BC mode. The MMDbased relay selection algorithm, when functioning, must calculate the metrics associated with different submatrices associated with the uplink channels and distinct submatrices associated with the downlink channels, where , to choose the best cluster, the best RV(s) and the mode of operation, in each time slot (high computational complexity). When a chosen cluster composed by two SVs communicates with each other, the others remain silent. Differently from [15, 16], where the MMDbased relay selection algorithm is employed for scenarios with timeuncorrelated channels and the MMD metrics are computed in each time slot, we consider scenarios where the UAVs are hovering over a specific area with low mobility, leading to possible timecorrelated channels. Therefore, the MMD metrics are computed in the inicial time slot and the best RV(s) are chosen based on these metrics. Then, the MMD metrics are computed again only when it is observed that the channels have been considerably changed from the last time these metrics were computed. Thus, with the proposed recursive MMD, the MMD computation rate (number of time slots the MMD metrics are computed divided by the total number of time slots) is reduced. In the following, the protocol operation is detailed.
Iiia Relay selection metric
For each cluster (with and ), in the first step, the metric related to the links of each square submatrix (associated with ), is calculated in the MA mode:
(12) 
where , , and are tentative vectors with symbols and . This metric is calculated for each of the (combination of in ) possibilities, for each submatrix . In the second step, the ordering is performed on and the smallest metric is stored:
(13) 
In the third step, the ordering is performed on and the largest metric is obtained:
(14) 
where . After finding for each cluster , the ordering is performed and the largest metric is stored:
(15) 
Therefore, the cluster and that fulfil (15) are chosen to receive packets from the chosen cluster. In the fourth step, for each cluster the metrics , related to each submatrix (associated with each pair and ), are computed for BC mode:
(16) 
where , and , and , and are tentative vectors formed by symbols and . This metric is calculated for each of the possibilities, for each submatrix . This reasoning is also applied in the fifth step, to calculate the metric . In the sixth step, the metrics and are compared and the smallest one is stored:
(17) 
After finding for each pair of submatrices and , the ordering is performed and the largest metric is obtained:
(18) 
In the seventh step, after finding for each pair of RVs, the ordering is performed and the largest metric is stored:
(19) 
where . After finding for each cluster , the ordering is performed and the largest metric is stored:
(20) 
Therefore, the cluster and the RVs and that fulfil (20) are chosen to transmit at the same time packets stored in the particular clusterhead buffer to the chosen cluster. The estimated channel matrix is considered in (12) and (16), rather than , if we assume imperfect CSI.
IiiB Observing the channels
At each time slot, the protocol observes if the channels change considerably in relation to the last computed MMD metrics:
(21) 
where is the channel matrix associated with the chosen RV when the MMD metrics were computed at the last time and is the channel matrix associated with the same RV but in the present time slot. Moreover, if , in which , the protocol considers that the channels have not changed so much and decides that the last computed MMD metrics can be reused for relay selection. Otherwise, it computes again the MMD metrics, as described in Subsection III. A. Additionally, a designer might consider precoding and beamforming techniques [50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 66, 67, 45, 42, 43, 44] to help mitigate interference rather than open loop transmission.
IiiC Choice of the transmission mode
After calculating and (or observing the channels and deciding to reuse the last computed metrics), the metrics are compared and we choose the transmission mode:
where , is the total number of packets stored in the clusterhead buffers, is a finite integer non negative metric that when reduced increases the chance of the protocol to work in BC mode, leading to smaller average delay.
Iv Analysis: Pairwise Error Probability
The PEP suposes an error event when is transmitted and the detector calculates an incorrect (where ), based on the received symbol [12, 13]. In [15, 16] an approach is proposed to analyze the PEP worst case of the MultiWay Cloud Driven BestUserLink (MWCBestUserLink) protocol. In this work, this approach is used to calculate the PEP worst case of the proposed CHDBestLink. Considering , in MA mode, and , in BC mode, and , an expression for computing the PEP worst case with cooperative transmissions (CT) in each time slot is described by
(22) 
where is the smallest value of and the
function is the probability a standard normal random variable takes a value greater than its argument. The proposed CHDBestLink with the MMD criterion chooses the channel matrix
that minimizes the PEP worst case as given by(23) 
This strategy can be employed for each of the square submatrices in a non square matrix (composed by multiple square submatrices). In [15], a proof shows that the MMD relay selection criterion by maximizing the minimum Euclidian distance between different vectors of transmitted symbols minimizes the BER in the ML receiver of MWCBestUserLink [15] and, consequently, also of CHDBestLink.
V Simulation Results
This section presents the simulation results of the proposed CRAN type CHDBestLink, using the recursive MMDbased relay selection algorithm, and the existing BufferAided MultiWay MaxLink (MWMaxLink) [13] and MWCBestUserLink [15] protocols adapted to UAV relaying, with the MMDbased relay selection algorithm and the ML receiver. The Monte Carlo simulation method is performed. Binary Phase Shift Keying (BPSK) signals are adopted and remark that higher order constellations may be studied elsewhere. The MMD computation rate is given by the number of time slots the MMD metrics are computed divided by the total number of time slots. The time a packet takes to arrive at the destination after it is sent by the SV is considered to calculate the average delay [28]. Thus, the delay is the amount of time slots the packet resides in the buffer. These protocols were tested for a set of values and packets is enough to ensure excellent performance. Perfect and imperfect CSI and symmetric unit power channels ( ) are considered. For simplicity, homogeneous distances and pathloss are considered and the SVs and RVs are spread with distinct positions but the RVs have almost the same distances and pathloss as the SVs. Moreover, timeuncorrelated and timecorrelated channels (in scenarios where the UAVs are hovering over a specific area with low mobility) are employed. With timecorrelated channels, the channel matrix is described by , in each time slot, where is the channel matrix in the previous timeslot, and is also a channel matrix formed by mutually independent zero mean complex Gaussian random coefficients (with timeuncorrelated channels,
). The signaltonoise ratio (SNR) given by
ranges from 0 to 10 dB, where is the energy transmitted from each SV or the RV(s) and . The protocols were tested for packets, each containing symbols.Fig. 2 illustrates the theoretical PEP worst case performance (calculated by the algorithm based on the chosen channel matrix , in each time slot) of CHDBestLink, for BPSK, , , , , , , perfect CSI, , 0.2, 0.4 and 0.8, (timecorrelated channels). Note that the lower the value the better the PEP worst case performance and the higher the MMD computation rate (higher cost). Thus, a tradeoff between PEP worst case and MMD computation rate is shown.
Fig. 3 depicts the BER and MMD Computation Rate of the CHDBestLink, MWCBestUserLink and MWMaxLink protocols, for , , in MWMaxLink and in CHDBestLink and MWCBestUserLink, , , BPSK, , perfect CSI, , 0.2 and 0.4 and and . The BER of CHDBestLink is quite superior to that of MWMaxLink for all SNR values tested. Remark that the BER performance of CHDbestLink, with , achieves a gain of approximately 3dB in SNR for the same BER as compared to that of MWMaxLink. Besides, the BER performance of CHDBestLink, for and is close to that of MWCBestUserLink for , but with the MMD computation rate approximately of 0.2 (considerably reduced cost). Furthermore, CHDBestLink has the same performance of MWCBestUserLink [15, 16], when or , as the MMD metrics are computed in each time slot and, consequently, the MMD computation rate is equal to 1 (100%). The full and dashed curves represent the uplink and downlink MMD computation rate, repectively, which show a tradeoff between BER performance and MMD computation rate.
Fig. 4 depicts the BER and the average delay performances of CHDBestLink and MWMaxLink, for BPSK, , , in MWMaxLink, and in CHDBestLink, , , , 5 and (where ), imperfect CSI ( and ), and and 0.95. The average delay performance of CHDBestLink is quite supeior to that of MWMaxLink, as CHDBestLink has a single group of clusterhead buffers. When the value of is reduced to 0 in CHDBestLink, the average delay achieves time slot, still keeping a superior BER performance to that of MWMaxLink.
Vi Conclusions
A new CRAN type structure with a UAV clusterhead as a central node and a recursive relay selection strategy that exploits timecorrelated channels often found in UAV communications has been introduced and studied as an appropriate relay selection technique for multiway UAV relaying schemes in FANETs. The simulation results, considering the worst case scenario (UAVs flying at ultralow altitude) without the presence of the LoS component, show an outstanding performance of the proposed CHDBestLink protocol as compared to those of other existing protocols in the literature. The performance of CHDBestLink is considerably better than that of MWMaxLink [13], in terms of BER, average delay and MMD computational rate (reduced complexity), and also is better than that of MWCBestUserLink [15], in terms of MMD computational rate. The Monte Carlo simulation method is adopted in this work, but practical experiments considering different scenarios may be performed in future studies.
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