I Introduction
In wireless networks, the use of cooperative diversity [1] can mitigate the signal fading caused by multipath propagation. The MultiWay Relay Channel (mRC) [2] includes both a full data exchange model, in which each user receives data from all other users, and the pairwise data exchange model, which is composed by multiple twoway relay channels. The incorporation of mRC with multiple relays in a system can significantly improve its performance. Considering 5G requirements [3], high spectrum efficiency relaying strategies are key due to their excellent performance. The use of a cloud as a central node can leverage the performance of relay techniques as network operations and services have recently adopted cloudenabled solutions in communication networks [4]. The ability to costeffectively manage interference is one of the main advantages of adopting the cloud network framework [4]. In the Cloud Radio Access Network (CRAN) architecture, the baseband processing, usually performed locally at each basestation (BS), is aggregated and performed centrally at a cloud processor. This is enabled by highspeed connections, denoted as fronthaul links, between the BSs and the cloud [4]. This centralized signal processing enables the interference mitigation across all the users in the uplink and downlink. The BSs in the CRAN are also referred to remote radio heads (RRHs) as their functionality is often limited to transmission and reception of radio signals [4].
The mRC has multiple clusters of users in which each user aims to multicast a single message to all the other users in the same cluster [2]. Processing users in a cluster corresponds to an way information exchange among the users in the same cluster. A group of relays facilitates this exchange, by helping all the users in the system. In particular, the mRC pairwise data exchange model () is formed by multiple twoway relay channels. In TwoWay MultipleAccess Broadcast Channel (MABC) schemes, based on the decodeandforward (DF) protocol [5], the transmission is organized in two successive phases: 1) MA phase  a relay is selected for receiving and decoding the messages simultaneously transmitted from two users (sources and ) and physicallayer network coding (PLNC) is performed on the decoded messages; 2) BC phase  the same selected relay broadcasts the decoded messages to the two sources. The TwoWay MaxMin (TWMaxMin) relay selection protocol [5] has a high performance, when all the channels are reciprocal and fixed during two consecutive time slots (MA and BC phases). Otherwise, with non reciprocal channels, the performance of relaying strategies can be enhanced by adopting bufferaided protocols, in which the relays are able to accumulate data in their buffers [6, 8], before sending data to the destination, as in the MultiWay MaxLink (MWMaxLink) [9] protocol for cooperative multiinput multioutput (MIMO) systems, which selects the best links among pairs of sources (diversity gain equals ), using the extended Maximum Minimum Distance (MMD) relay selection criterion [10, 11]. Furthermore, in [12], the TwoWay MaxLink (TWMaxLink) protocol (a special case of MWMaxLink, for a single twoway relay channel ()), also using the extended MMD criterion, was presented. However, cloudaided multiway protocols using the maximum minimum distance relay selection criterion, for multipleantenna systems, in which each cluster has a particular buffer, have not been previously investigated.
In this work, we develop a cloudaided framework and a MultiWay BestUserLink (MWCBestUserLink) protocol for cooperative MIMO systems, with non reciprocal channels, which selects the best links among pairs of sources (clusters) and relay nodes. In order to perform signal detection at the cloud and the nodes, we present maximum likelihood (ML) detectors. We then consider the maximum minimum distance criterion and devise a relay selection algorithm for MWCBestUserLink. Simulations illustrate the excellent performance of the proposed framework, the proposed MWCBestUserLink protocol and the relay selection algorithm as compared to previously reported approaches.
This paper is structured as follows. Section II describes the system model and the main assumptions. Section III presents the proposed MWCBestUserLink protocol, the relay selection criterion and algorithm, and analyzes MWCBestUserLink, in terms of pairwise error probability (PEP) and sumrate. Section IV illustrates and discusses the simulation results whereas Section V gives the concluding remarks.
Ii System Description
We assume a MIMO multiway MABC relay network formed by clusters (pair of sources and ) and half duplex (HD) DF relays, ,…,. In a CRAN framework, the sources would represent mobile users and the relays would represent RRHs. The sources have antennas for transmission or reception and each relay antennas, where , all of them used for reception () and a part of them used for transmission (), where , forming a spatial multiplexing network, in which the channel matrices are square or formed by multiple square submatrices in the MA mode. Note that the reason for using multiples of antennas at the relays is because the relay selection algorithms explained in Section III use criteria that depend on these matrices to be square or to be formed by multiple square submatrices. Moreover, the computational complexity The selected relays access a number of cloud buffers for extracting or storing packets in each time slot. Each cluster has a particular cloud buffer that is established on demand, whose size is packets, as depicted in Fig.1. In the multipleaccess phase (uplink), a cluster is selected to send packets simultaneously to a selected relay for reception. Then, the data are decoded by the cloud processor, PLNC is employed on the decoded information and the resulting data are stored in their particular cloud buffers. In the broadcastchannel phase (downlink), two relays and are selected to broadcast packets from the particular cloud buffer to the selected cluster. Note that may be different from . In most of the situations the selection of only one relay in downlink is enough for a good performance [9, 10, 11, 12, 13]
. However, by selecting two relays, the possibility of combining the channels related to the selected relays increases the degrees of freedom of the system and, consequently, its performance is improved. The system could select more than two relays to further improve its performance, but the computational complexity would be considerably increased for a high number of relays. For the sake of simplicity, we adopt the mRC pairwise data exchange model, but the full data exchange model can be considered in future works.
Iia Assumptions
The energy transmitted from each source node to the selected relay for reception () or from the selected relay(s) for transmission to the sources (), in each time slot, is the same, i. e.,
. We consider mutually independent zero mean complex Gaussian random channel coefficients, which are fixed for the duration of one time slot and vary independently from one time slot to the following, and the transmission is organized in data packets. The order of the packets is included in the preamble and the original order is recovered at the destination. Signaling for network coordination and pilot symbols for estimation of the channel state information (CSI) are also contained in the preamble. The cloud is the central node and decides whether a cluster or the relay(s) must transmit in a given time slot
, through a feedback channel. An appropriate signalling provides global CSI at the cloud. Moreover, we assume that each relay only has information about its and links. The use of a cloud as a single central node and its buffers reduces the system complexity and the delay, since a unique central node decides which nodes transmit (rather than all destination nodes) and the packets associated with a cluster are stored in only its particular cloud buffer instead of being spread in the buffers of all relays. In this work, we focus on the ideal case where the fronthaul links have unconstrained capacities, and the relays can convey their exact received signals to the cloud processor. Practical systems, however, have capacityconstrained fronthaul links [4] and this limits the amount of information that the relays can retransmit. Although these unconstrained capacities in the fronthaul links simplify our analysis, it does not limit the advantages of the proposed protocol and relay selection algorithm, explained in the next section. Moreover, capacityconstrained fronthaul links can be considered elsewhere in future works and the performance achieved by the proposed protocol may be considered as a baseline or an upper bound.IiB System Model
For multiway HD DF MABC systems, in the MA phase, the signal sent by the selected cluster ( and ) and received at (the relay selected for reception) is organized in an vector given by
(1) 
where is an vector with symbols sent by () and (), is a matrix of and links and is the zero mean additive white complex Gaussian noise (AWGN) at . Note that is formed by square submatrices of dimensions as given by
(2) 
The Maximum Likelihood (ML) detector is the optimal detector from the point of view of minimizing the probability of error (assuming equiprobable ). However, the ML detector has high (exponential in ) complexity and is only suited to MIMO systems with a small number of antenna elements. Assuming perfect synchronization, we may adopt the ML receiver at the cloud processor:
(3) 
where is each of the possible vectors of sent symbols ( is the quantity of symbols in the constellation adopted). The ML receiver calculates an estimate of the vector of symbols sent by the sources . Other suboptimal detection techniques could be considered in future work [17, 18, 19, 20, 21, 22, 54, 24, 25, 26, 27, 28, 31, 32, 33].
By performing PLNC, only the XOR outputs (resulting packets) are stored with the information: ”the bit sent by is equal (or not) to the corresponding bit sent by ”. Therefore, we apply the bitwise XOR:
(4) 
and store the resulting data in the cloud buffer. Therefore, an advantage of applying PLNC is that we have to store only packets in the cloud buffer, instead of .
In the BC phase, the signal sent by the relays selected for transmission ( and ) and received at and is structured in an vector given by
(5) 
where is a vector with symbols, represents the matrix of and links, and is the AWGN at or . Note that is formed by summing matrices of dimension as given by
(6) 
We may also adopt the ML receiver at the selected cluster, which yields
(7) 
where is each of the possible vectors with symbols.
Therefore, at we calculate the vector of symbols sent by by performing PLNC:
(8) 
It is also applied at to calculate the vector of symbols sent by :
(9) 
The estimated channel matrix is considered instead of in (3) and (7), when performing the ML receiver, by assuming imperfect CSI. Note that is computed as =+
, where the variance of the mutually independent zero mean complex Gaussian
coefficients is given by ( and ) [14], in which , in the MA phase, and , in the BC phase. Channel and parameter estimation [42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55] techniques could be considered in future work in order to develop algorithms for this particular setting.Iii Proposed MWCBestUserLink Protocol and Relay Selection Algorithm
The system of Fig. 1 is equiped with the novel MWCBestUserLink protocol, which in each time slot may operate in two possible modes: MA or BC. The relay selection algorithm of the proposed MWCBestUserLink protocol may operate using the extended MMD [10] criterion. The MMDbased relay selection algorithm minimizes the error in the ML receiver and can be used for MIMO systems with a small number of antenna elements due to its reduced complexity in this case.
The MMDbased relay selection algorithm, in the MA mode, chooses the relay and the associated channel matrix with the largest minimum distance as given by
(10) 
where , , and represent each possible vector formed by symbols and . The metric is calculated for each of the (combination of in ) possibilities, for each submatrix , and is the smallest of these values. Thus the selected matrix has the largest value. Moreover, the MMDbased relay selection algorithm, in the BC mode, chooses the relay and the associated channel matrix with the largest minimum distance as given by
(11) 
where , and represent each possible vector formed by symbols and . The metric is calculated for each of the possibilities, for each matrix , and is the smallest of these values. Thus, the selected matrix has the largest value. The following subsections explain how this protocol works.
Iiia Relay selection metric for MA and BC modes
For each cluster (formed by and ), in the first step, we calculate the metric
related to the links of each square submatrix associated with the relay , in the MA mode:
(12) 
where and . In the second step, we compute the ordering on and find the smallest metric, for being critical:
(13) 
In the third step, we compute the ordering on and find the largest metric:
(14) 
where . After finding for each cluster , we compute the ordering and find the largest metric:
(15) 
Therefore, we choose the cluster and the relay that fulfil (15) to receive packets from the selected cluster. For each cluster, in the fourth step, we calculate the metrics
related to the links of each matrix associated with each pair of relays and , for BC mode:
(16) 
where , and . In the fifth step, this reasoning is also applied to calculate the metric . In the sixth step, we compare the metrics and and store the smallest one:
(17) 
In the seventh step, after finding for each pair of relays, we compute the ordering and find the largest metric:
(18) 
where . After finding for each cluster , we compute the ordering and find the largest metric:
(19) 
Therefore, we select the cluster and the relays and that fulfil (19) to send simultaneously packets stored in the particular cloud buffer to the selected cluster. The estimated channel matrix is considered in (12) and (16), instead of , if we consider imperfect CSI. Alternatively, a designer can consider precoding techniques [34, 35, 36, 37, 38, 39, 40, 41, 47, 48] to help mitigate interference rather than open loop transmission.
IiiB Choice of the transmission mode
After calculating the metrics related to the SR and RS
links and finding and , these metrics are compared and we select the transmission mode:
where , is the total number of packets stored in the cloud buffers, is a parameter that when reduced increases the probability of the protocol to operate in BC mode and, consequently, achieve a reduced average delay (low latency).
IiiC Pairwise Error Probability
The PEP assumes an error event when is sent and the detector calculates an incorrect (where ), based on the received symbol [9, 10, 11]. Considering , in MA mode, and , in BC mode, the worst value of the PEP (PEP worst case) that occurs for the smallest value of () is given by
(20) 
where , in the MA mode, and , in the BC mode. By considering that the probability of having no error in the two phases of the system is approximately given by the square of , an expression for calculating the worst case of the PEP for cooperative transmissions (CT), in each time slot is given by
(21) 
Note that this expression may be used for calculating the worst case of the PEP, for both symmetric and asymmetric channels. The proposed MWCBestUserLink, using the MMD relay selection criterion, selects the channel matrix , minimizing the PEP worst case, as shown by
(22) 
Consequently, the MMD relay selection criterion, by maximizing the minimum Euclidian distance between different vectors of transmitted symbols, minimizes the error in the ML receiver. This reasoning may be applied also for each of the square submatrices in a non square matrix (formed by multiple square submatrices). In a future journal version of this paper we develop a proof that shows that the MMD relay selection criterion minimizes the PEP worst case and, consequently, the error in the proposed MWCBestUserLink protocol, with ML receiver.
IiiD SumRate
In [9], a framework is proposed to analyze the sumrate of the MWMaxLink. In the following, we use this framework to compute the sumrate of the proposed MWCBestUserLink. In the case of a time slot selected for MA mode, the sumrate is given by
(23) 
where . Furthermore, in the case of a time slot selected for BC mode, the sumrate is given by
(24) 
where . So, the average sumrate () of the MWCBestUserLink scheme can be approximated by
(25) 
where and are the number of time slots selected for SR and RS transmissions, respectively.
Iv Simulation Results
We assess via simulations the proposed MWCBestUserLink and the existing MWMaxLink [9], using the MMDbased relay selection algorithm, with the ML receiver. We employ BPSK signals and note that other constellations as QPSK and 16QAM were not included but can be examined elsewhere. The average delay is calculated by considering the time a packet needs to reach the destination once it has left the source (no delay is measured when the packet resides at the source [15]). So, the delay is the number of time slots the packet stays in the cloud buffer. The performance of MWCBestUserLink and MWMaxLink protocols was assessed for a set of values. Then, we found that sets of packets is sufficient to ensure a good performance. We consider perfect and imperfect CSI and symmetric unit power channels (
). The signaltonoise ratio (SNR) given by
ranges from 0 to 10 dB, where is the energy transmitted from each source or the relay(s) and we consider . The transmission protocols were simulated for packets, each with symbols. We assumed perfect signaling between the cloud and the network, but imperfect signaling can be considered in future works.Fig. 2 depicts the BER and sumrate performances of the MWCBestUserLink (MMD) and MWMaxLink (MMD) protocols, for , , in MWMaxLink and and in MWCBestUserLink, , , BPSK, , perfect and imperfect CSI ( and ). For both perfect and imperfect CSI (full and dashed curves, respectively), the BER performance of MWCBestUserLink is considerably better than that of MWMaxLink for all the range of SNR values simulated. Note that the BER performance of MWCBestUserLink, with , obtains a gain of almost 3dB in SNR for the same BER as compared to that of MWMaxLink. Moreover, the sumrate performances of MWCBestUserLink are also considerably better than that of MWMaxLink.
Fig. 3 illustrates the BER and the average delay performances of MWCBestUserLink (MMD) and MWMaxLink (MMD), for BPSK, , , in MWMaxLink, and in MWCBestUserLink, , , , 1, 5 and and perfect CSI. The average delay performance of MWCBestUserLink is considerably better than that of MWMaxLink, as MWCBestUserLink has a unique set of cloud buffers. When we reduce the value of to 0 in the MWCBestUserLink protocol, the average delay is reduced to time slot, still keeping a considerably better BER performance than that of MWMaxLink.
V Conclusions
A novel framework configured by a cloud as a central node with buffers has been introduced and investigated as a favorable relay selection strategy for multiway protocols. We have examined relayselection techniques for multiway cooperative MIMO systems that are aided by a cloud central node, where a cluster with two sources is selected to simultaneously transmit to each other aided by relays. Simulations illustrate the excellent performance of the proposed MWCBestUserLink protocol, that by using the MMDbased relay selection algorithm, outperformed the existing MWMaxLink scheme in terms of BER, sumrate and average delay. In particular, this novel protocol has a considerably reduced average delay, keeping the high diversity gain.
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