Efficient Cooperative HARQ for Multi-Source Multi-Relay Wireless Networks
aa r X i v : . [ ee ss . SP ] A ug Efficient Cooperative HARQ for Multi-SourceMulti-Relay Wireless Networks st Stefan Cerovi´c
Orange Labs
Chˆatillon, [email protected] nd Rapha¨el Visoz
Orange Labs
Chˆatillon, [email protected] rd Louis Madier
Nokia
Nozay, [email protected]
Abstract —In this paper, we compare the performance of threedifferent cooperative Hybrid Automatic Repeat reQuest (HARQ)protocols for slow-fading half-duplex orthogonal multiple accessmultiple relay channel. Channel State Information (CSI) isavailable at the receiving side of each link only. Time DivisionMultiplexing is assumed, where each orthogonal transmissionoccurs during a time-slot. Sources transmit in turns in consecutivetime slots during the first transmission phase. During the secondphase, the destination schedules in each time-slot one node(source or relay) to transmit redundancies based on its correctlydecoded source messages (its decoding set) with the goal tomaximize the average spectral efficiency. Bidirectional limitedcontrol channels are available from sources and relays towardsthe destination to implement the necessary control signaling ofthe HARQ protocols. Among the three proposed HARQ, twofollow the Incremental Redundancy (IR) approach. One consistsin sending incremental redundancies on all the messages fromthe scheduled node decoding set (Multi-User encoding) whilethe other one helps a single source (Single User encoding)chosen randomly. The third one is of the Chase Combining(CC) type, where the selected node repeats the transmission(including modulation and coding scheme) of one source chosenrandomly from its decoding set. Monte-Carlo simulations confirmthat the IR-type of HARQ with Multi-User encoding offers thebest performance, followed by IR-type of HARQ with SingleUser encoding and CC-type of HARQ. We conclude that IR-type of HARQ with Single User encoding offers the best trade-off between performance and complexity for a small number ofsources in our setting.
Index Terms —chase combining, incremental redundancy,HARQ, multi-source multi-relay wireless network, spectral ef-ficiency
I. I
NTRODUCTION
Cooperative diversity by using relays in wireless networksallows increasing the total throughput of the network while(possibly) relying on single antenna nodes. Fundamental prin-ciples and the main idea of cooperative communications can befound in [1], where a three-terminal Relay Channel is studied.If a limited feedback control channel is available from the des-tination to the relaying nodes, the throughput can be increasedby using a cooperative version of Hybrid Automatic RepeatreQuest (HARQ) protocol [2]. We investigate the performanceof different flavors of cooperative HARQ protocols for theMultiple Access Multiple Relay Channel (MAMRC), denotedby ( M , L , )-MAMRC where M is the number of sources, L the number of relays. User cooperation is included in our model which means that the number of relays that can help agiven source is L + M − . Each source listens to the other nodetransmissions with the final goal to maximize its number ofcorrectly decoded source messages. The performance metric isthe average spectral efficiency. Transmissions are orthogonalin time. During the first phase, each source transmits in turnits message in consecutive time slots. During the second phase(retransmission phase) the destination schedules a relay ora source to transmit for each time slot. All nodes are half-duplex, i.e., they can not transmit and receive at the same time.All the links are subject to slow-fading and Additive WhiteGaussian Noise (AWGN). For that reason, we use the outageinformation-theory tool to analyze the performance of the dif-ferent protocols. Each node can cooperate with its successfullydecoded source messages or decoding set. Indeed, contraryto the classical Decode and Forward (DF) approach where arelay need to wait until it decodes all the source messagescorrectly, here, a node can cooperate as soon as its decodingset is not empty. This relaying behavior is called SelectiveDecode-and-Forward (SDF) relaying function. By receiving aChannel Distribution Information (CDI) from all sources andrelays (average SNR of all links), the destination can performslow-link adaptation. It consists in allocating a rate among adiscrete Modulation and Coding Scheme (MCS) family to eachsource in order to maximize the average spectral efficiency.For each possible M -tuple of source rates, the optimal slowlink adaption algorithm exhaustively check which one achievesthe best metric by performing Monte-Carlo simulations over asufficient number of channel outcomes. The rate allocation isconveyed by a slow limited control channel from destinationto sources prior to the HARQ protocol. Note that the optimalalgorithm based on exhaustive search for finding the M -tupleof rates is quickly becoming intractable for either a large MCSfamily and/or an increasing number of sources. We designeda low complexity search algorithm for these cases whoseperformance gets very close to the optimal one. Its detailedpresentation is out of the scope of this paper. In the following,we always assume that a slow link adaption rate allocationtakes place before any source transmission. Since the CDIvariations are much slower than the channel variations, theslow link adaptation keeps valid for many channel outcomes(actually our simulation are performed for a fixed CDI). Thereexist a limited feedback broadcast control channel from the estination towards sources and relays (e.g., to carry thescheduling decision of the destination) and multiple unicastforward coordination control channels from sources and relaystowards the destination (to help the destination to take itsscheduling decision). Particular care is paid to minimize thecontrol overhead in this paper. Among the three proposedHARQ protocols, one consists in sending incremental redun-dancies on all the messages from the scheduled node decodingset (Multi-User encoding) while the other one helps a singlesource (Single User encoding) chosen randomly. The latter isparticularly attractive since its implementation can reuse state-of-art rate compatible punctured codes such as low densityparity check codes or turbo codes. The third one is of thechase combining (CC) type, where the selected node repeatsthe transmission (including modulation and coding scheme) ofone source chosen randomly from its decoding set. It allowsMaximal Ratio Combining (MRC) at the destination of all thetransmissions related to a given source. We can expect thatsuch a protocol behaves poorly in general compared to theIR-type of HARQ.In [3] and [4], the performance of different HARQ protocolsis investigated for the single source, single relay and singledestination case. Both CC and IR types of HARQ protocolwere analyzed. In [4], it is shown that IR-type of HARQperforms better than CC-type of HARQ in terms of systemoutage probability, average number of retransmissions andaverage transmission rates. The advantage of using relay selec-tion (with limited feedback) over distributed space-time blockcoded transmissions in multiple relay networks is shown in [5].User co-operation is included as in our paper. In [6], Multi-User relay channel consisting of two sources, one relay and adestination is shown to take benefit from Multi-User encoding(network coding). In this work, a feedback channel is assumedto be available from both the relay and the destination towardsthe sources. For the multiple-source multiple-relay channel, arelay ordering algorithm based on finite field network codinghas been proposed in [7]. An outage analysis has been donefor that protocol, where Separate Network Channel Coding(SNCC) is used in combination with the DF relaying protocol.In [8], the relay selection strategies that aim to maximize thelong-term aggregate throughput are studied for slow-fadingMAMRC, where SDF relaying protocol is applied under theJNCC/JNCD framework (Multi-User encoding at the relayswith Multi-User iterative joint decoding at the destination). Aproper comparison between the two IR-type of HARQ and theCC-type of HARQ has not been performed by the previouslymentioned works. Our goal in this paper is to identify themost efficient cooperative HARQ protocol, i.e., the one thatachieves the best complexity-performance tradeoff keeping inmind that Single User encoding and decoding is well masteredin terms of code construction and, clearly, less complex thanMulti-User encoding and iterative joint decoding. On the otherhand, the Chase Combining approach can be considered ashaving a similar complexity to Single User IR-HARQ. Asa result, the HARQ protocol comparison comes down toa performance comparison where information theory outage Fig. 1. Cooperative Orthogonal Multiple Access Multiple Relay Channel(OMAMRC) with feedback. analysis is particularly relevant.The remainder of the paper is organized as follows. Thesystem model is detailed in section II. In section III theperformance metric, the outage event definitions, as well asthe three different HARQ protocols together with the proposednode selection strategy are described. Numerical results arepresented in section IV. Finally, we conclude the paper insection V. II. S
YSTEM M ODEL
In this paper, we investigate OMAMRC under slow-fading assumption. M sources, belonging to the set S = { s , . . . , s M } , transmit independent messages u s ∈ F K s of K s information bits towards a common destination. The lengthof a source message depends on the selected MCS by thedestination, where the decision about the selection is conveyedover the error-less limited feedback broadcast control channel. L relays, that operate in half-duplex mode and that belong tothe set R = { r , . . . , r L } , help the destination in decoding thesources’ messages. They overhear the messages from sourcesdue to the broadcast property of wireless medium, and applySDF relaying protocol. Relays do not have their own messagesto transmit. Additionally, user-cooperation is performed, i.e.when not transmitting, sources listen to other sources andrelays transmissions and help the decoding at the destinationby applying the SDF relaying protocol (see Fig. 1). Moreover,HARQ protocol is used, which is either of type IncrementalRedundancy, or Chase Combining. In the case of IR-typeof HARQ protocol, two types of encoding are considered:Single User encoding and Multi-User encoding, depending onthe number of sources that the node performing the relayingfunctions will help during its transmission. We define the setof all source and relay nodes as N = S ∪ R .CSI is available only at the receiver side of each linkand is assumed perfect. Hence, the destination only has theperfect knowledge of CSI of source-to-destination (S-D) links, h S,D = [ h s ,d , . . . , h s M ,d ] , and of relay-to-destination (R-D)links h R,D = [ h r ,d , . . . , h r L ,d ] . On the other hand, the CSIof source-to-source (S-S), source-to-relay (S-R) and relay-to-relay (R-R) links are unknown to it.Transmission of source messages is split into frames, duringwhich exactly one message from each source is sent, as well ig. 2. Transmission of a frame: initial, first and second phase. as the retransmissions related to those messages. Slow (block)fading is assumed, where within one frame the radio-linksbetween the different nodes are considered to be fixed, whilethey change independently from frame to frame. Furthermore,we consider that during a certain number of frames N f >> ,the probability distribution of the quality of each link remainsconstant. That means that the quality of the given link inthe given frame represents one realization of the associatedprobability distribution. The choice of the MCS for eachsource by the destination takes place in the “initial phase”by applying the slow-link adaptation algorithm. That phaseoccurs before any transmission, and is repeated whenever theprobability distributions of different channels change (see Fig.2). CDI of each link in the network is needed as an inputto the slow-link adaptation algorithm. For S-S, S-R and R-Rlinks, sources and relays convey the information about CDIto the destination over forward coordination control channelsthat are assumed to be errorless. The destination can track theCDI of S-D and R-D links by itself. The information about theselected MCSs is conveyed from the destination to all nodesover limited feedback control channel. The source rates arekept fixed between two occurrences of the initial phase.Transmission frame is split into two phases. The first phaseconsists of M time-slots made of N channel uses each, whereeach one of the M sources transmits in turn. User co-operationbeing used, when one source transmits a message, both relaysand non-transmitting sources listen and try to decode thatmessage relying on a Cyclic Redundancy Check (CRC) codefor error detection. The second phase consists of maximumof T time-slots of duration of N channel uses each, calledalso “retransmission rounds” in the following. T is a systemdesign parameter chosen by the destination, which dependson the latency requirements. In each retransmission round thedestination selects one relay or a source to transmit, where asource can either retransmit its own message or act as a relayfor other sources. In [8], the scheduling strategy that consistsin selecting the node whose link to the destination has thebest quality among the nodes that can help the destination(their decoding sets contain at least one message that thedestination has not been able to decode at the end of theprevious round) is shown to achieve a performance close tothe optimal (exhaustive) one. Taking into account the teachingof [8], we propose a low overhead control signaling exchangesbetween the destination and the other nodes as follows: • The destination broadcasts M bits that indicate its decod-ing set S d,t − after round t − over the control channel. • If the decoding set of the destination consists of all source messages, a new frame begins and the sources transmitnew messages while the relays and destination emptytheir memory buffers. Otherwise, each cooperating sourceand each relay which was able to decode at least onesource message that is not included in the decoding setof the destination sends a signal on a dedicated unicastcontrol channel. Each cooperating source or relay whichdid not decode any message needed by the destination,i.e., any message that is not included in the decoding setof the destination after round t − , remains silent (ON-OFF modulation). • Using the adopted node selection strategy, the destinationcan make the scheduling decision about the node toselect for transmission. Its decision is broadcasted usinga control channel. • Selected node transmits applying the appropriate type ofHARQ protocol.Note that the end of the first phase is considered as theend of the round zero. The non-selected nodes in a givenretransmission round can benefit from the transmission ofthe scheduled node as well, and update their decoding setsaccordingly. The number of retransmission rounds used in thesecond phase T used ∈ { , . . . , T } depends on the success ofthe decoding process at the destination. Each node in thenetwork is equipped with one antenna only and transmitswith the same power. In the rest of the paper, the followingnotations are used: • x a,k ∈ C is the coded modulated symbol whose poweris normalized to unity for channel use k , sent from node a ∈ S ∪ R . • y a,b,k is a received signal at node b ∈ S ∪ R ∪ { d } \ { a } ,originating from node a . • γ a,b is the average signal-to-noise ratio (SNR) that cap-tures both path-loss and shadowing effects. • h a,b are the channel fading gains, which are independentand follow a zero-mean circularly symmetric complexGaussian distribution with variance γ a,b . • n a,b,k are independent and identically distributed AWGNsamples, which follow a zero-mean circularly-symmetriccomplex Gaussian distribution with unit variance.Using the previous notation, we can represent the receivedsignal at node b ∈ S ∪ R ∪ { d } \ { a } which originates fromnode a ∈ S ∪ R as: y a,b,k = h a,b x a,k + n a,b,k , (1)where k denotes a current channel use, taking a value k ∈{ , . . . , N } during the first phase, and k ∈ { , . . . , N } during the second phase.III. C OOPERATIVE
HARQ
PROTOCOLS
A. Performance metric and outage events
Let us denote with R s = K s /N the initial transmissionrate of a source s in bit per complex dimension or bit perchannel use [b.c.u]. We can define a long-term transmissionrate ¯ R s per source as the fraction of the number of transmittednformation bits over the total number of channel uses spent,for a number of frames that tends to infinity: ¯ R s = R s M + α E ( T used ) , (2)where E ( T used ) = P Tt =1 t Pr { T used = t } is the average numberof retransmission rounds used in the second phase, and α = N /N .A performance metric that we use throughout the paper isthe average spectral efficiency, which can be defined as: η = M X i =1 ¯ R s i (1 − Pr {O s i ,T } ) , (3)where O s,T is the “individual outage event of source s afterround T ”, which is the event that source s is not decodedcorrectly at the destination after round T .Before defining it analytically for different HARQ pro-tocols in the following subsections, we should emphasizethat the individual outage event of source s after round t , O s,t ( a t , S a t ,t − | h S,D , h R,D , P t − ) , directly depends on thechoice of a transmitting node a t ∈ N in round t and itsassociated decoding set S a t ,t − . Furthermore, it is conditionalon the knowledge of h S,D , h R,D and P t − , the last onedenoting the set which collects the nodes ˆ a k selected inrounds k ∈ { , . . . , t − } prior to round t together with theirassociated decoding sets S ˆ a k ,k − , and the decoding set of thedestination S d,t − . The same holds for the “common outageevent after round t ” E t ( a t , S a t ,t − | h S,D , h R,D , P t − ) , which isthe event that at least one source is not decoded correctly at thedestination at the end of the round t . If E { . } is the expectationoperator, and {V} is the function having a value if the event V is true, and otherwise, we can define the probability ofthe individual outage event of source s after round t for acandidate node a t as E { {O s,t ( a t , S at,t − | h S,D , h R,D , P t − ) } } . Wecan define the probability of the common outage event in asimilar way. In order to simplify the notation in the rest ofthe paper, we will omit the condition on h S,D , h R,D and P t − when recalling the individual and common outage events. B. IR-type of HARQ protocol with Multi-User encoding
In this part, we assume that in given round t , the selectednode a t sends incremental redundancies on all the messagesin its decoding set. If the decoding set at the destinationafter round t − is given by S d,t − , we define the setof non-successfully decoded sources at the destination as ¯ S d,t − = S \ S d,t − . First, we want to analytically definethe common outage event E IR,MU t, B ( a t , S a t ,t − ) after round t for a candidate node a t of some subset B of the set ofnon-successfully decoded sources at the destination B ⊆ ¯ S d,t − . Since in a given round the transmitted incrementalredundancies potentially contain multiple source messages, thedestination has no choice but to decode the source messagesjointly, i.e., considering the received transmissions as part ofa joint codeword on all the source messages. As a result, weresort to Multiple Access Channel (MAC) framework, where the event E IR,MU t, B ( a t , S a t ,t − ) is true if the vector of rates ofsources contained in B lies outside of the corresponding MACcapacity region.We can express this event as: E IR,MU t, B ( a t , S a t ,t − ) = [ U⊆B n X s ∈U R s > X s ∈U I s,d + t − X l =1 αI ˆ a l ,d {C IR,MU ˆ al } + αI a t ,d {C IR,MU at } o , (4)where I a,b denotes the mutual information between the nodes a and b , the sources contained in the set I = ¯ S d,t − \ B are considered as interference and C IR,MU ˆ a l and C IR,MU a t have thefollowing definitions: C IR,MU ˆ a l = n {S ˆ a l ,l − ∩ U 6 = ∅} ∧ {S ˆ a l ,l − ∩ I = ∅} o , C IR,MU a t = n {S a t ,t − ∩ U 6 = ∅} ∧ {S a t ,t − ∩ I = ∅} o , (5)with ∧ standing for the logical and. Since IR-type of HARQis used, we basically compare the sum-rate of sources con-tained in each subset U ⊆ B with the accumulated mutualinformation at the destination that originates from: (1) thetransmissions during the first phase; (2) the transmissionsof previously activated nodes in rounds , . . . , t − ; and(3) the transmission of the candidate node a t . Node ˆ a k for k = { , . . . , T } is involved in the calculation only if it wasable to successfully decode at least one source from the set U while its decoding set does not contain any interference, i.e.,source message that is outside B . Multiplication by α servesas a normalization before adding two mutual informationoriginating from two different phases, where the transmissionuses N and N time slot channel uses in the first andsecond phase, respectively. If one or more MAC inequalitiesassociated to the sum-rate of sources in different sets U is notrespected, the common outage event of the set B is proclaimed.By similar reasoning, the individual outage event of thesource s after round t can be defined as: O IR,MU s,t ( a t , S a t ,t − ) = \ I⊂ ¯ S d,t − [ U⊆ ¯ I : s ∈U n X s ∈U R s > X s ∈U I s,d + t − X l =1 αI ˆ a l ,d {C ˆ al,s } + αI a t ,d {C at,s } o , (6)where ¯ I = ¯ S d,t − \ I , and C IR,MU ˆ a l ,s and C IR,MU a t ,s have thefollowing definitions: C IR,MU ˆ a l ,s = n { s ∈ S ˆ a l ,l − ∩ U} ∧ {S ˆ a l ,l − ∩ I = ∅} o , C IR,MU a t ,s = n { s ∈ S a t ,t − ∩ U} ∧ {S a t ,t − ∩ I = ∅} o , (7) C. IR-type of HARQ protocol with Single User encoding
As stated in the introduction, Single User encoding isparticularly attractive since its implementation can reuse state-of-art rate compatible punctured codes such as low densityparity check codes or turbo codes. Here, a selected noden retransmission round t of the second phase cooperateswith a single source from its decoding set, i.e., it transmitsincremental redundancies for a single source. The choice ofthe source that the selected node will help is random, butamong all sources which the destination has not successfullydecoded up until that round. That information is availableto each node in the network due to the control informationexchange mechanism described in section II.Let us denote with s ˆ a k a randomly chosen source by thenode ˆ a k in round k ∈ { , . . . , T } from its decoding set underthe previously described condition. In this case, since the se-lected nodes during the second phase do not apply Multi-Userencoding anymore and since the transmission is orthogonalin time, there is no need to use the MAC framework. Theindividual outage event of the source s after round t for theselected node a t which cooperates with the source s a t can besimply defined as: O IR,SU s,t ( a t , s a t ) = n R s > I s,d + t − X l =1 αI ˆ a l ,d { s = s ˆ al } + αI a t ,d { s = s at } o , (8)To find the common outage event of sources contained inthe set B ⊆ ¯ S d,t − after round t , for the selected node a t which cooperates with the source s a t , we simply check if theindividual outage event of any source s contained in B is true: E IR,SU t, B ( a t , s a t ) = [ s ∈B O IR,SU s,t ( a t , s a t ) . (9) D. CC-type of HARQ protocol
In this type of protocol, the selected node a t in round t in thesecond phase apply the exact same MCS as source s whosemessage is randomly selected from the decoding set of thedestination ¯ S d,t − . It implies the constraint that N = N or α = 1 . At the destination, Maximal Ratio Combining (MRC)(at symbol or coded bit level) is used after each round inorder to decode the message of a given source. By doing so,we obtain the highest achievable SNR, denoted γ MRC , for agiven source at the destination which is equal to the summationof individual SNRs from the previous rounds. This kind ofprotocol offers less complexity in decoding then the protocolbased on Multi-User encoding. The individual outage eventof the source s after round t for the selected node a t whichcooperates with the source s a t is defined in this case as: O CC s,t ( a t , s a t ) = n R s > I ( γ MRC ( a t , s a t )) o (10)where γ MRC ( a t , s a t ) = | h s,d | + t − X l =1 | h ˆ a l ,d | { s = s ˆ al } + | h a t ,d | { s = s at } (11)The common outage event of sources contained in the set B ⊆ ¯ S d,t − after round t , for the selected node a t which cooperates with the source s a t is, just as in the previous case,defined as: E CC t, B ( a t , s a t ) = [ s ∈B O CC s,t ( a t , s a t ) . (12) E. Node selection strategy used during the second phase
In [8], it is shown that the node selection strategy whichoffers the best trade-off between the performance and compu-tational complexity is the one where in a given round of thesecond phase the node with the highest mutual informationbetween itself and the destination is selected among all nodesthat were able to decode at least one source from the set ofnon-successfully decoded sources at the destination after round t − : ˆ a t = argmax a t ∈S∪R { I a t ,d { ¯ S d,t − ∩S at,t − = ∅} } . (13)Namely, it is demonstrated by performing Monte-Carlo simu-lations that such a strategy performs close to the upper-boundgiven by the strategy based on the exhaustive search for thebest activation sequence, which requires the knowledge of theCSI of each link in the network and is much more complex. Byobserving the expressions for the individual outage probability,it is clear that such a node selection strategy can be equallyapplied to the IR-type of HARQ with the Single User encodingand the CC-type of HARQ.IV. N UMERICAL R ESULTS
In this Section, we want to evaluate the performance ofthe three types of HARQ protocols described in SectionsIII-B, III-C, III-D in terms of the average spectral efficiencyby performing Monte-Carlo simulations. The node selectionstrategy described in subsection III-E is assumed to be usedin the second phase. Also, we assume the presence of theoptimal slow-link adaptation algorithm conditional on thechosen node selection strategy. A discrete MCS family whoserates belong to { , , , , , , } [b.c.u] is used for theinitial rates. Independent Gaussian distributed channel inputsare assumed (with zero mean and unit variance) where I a,b =log (1 + | h a,b | ) . There are some other formulas that could bealso used for the calculation of I a,b which take into account, forexample, discrete entries, finite length of the codewords, non-outage achieving Multi-User encoding/iterative joint decodingarchitectures etc. Although the calculation would be differentfor each type of HARQ protocol, the basic concept of the workwould stay the same.In the first part of the simulations, we consider ( , , )-OMAMRC with α IR = 0 . and T IR = 4 for IR-types ofHARQ protocol, and α CC = 1 and T CC = 2 for CC-typeof HARQ protocol. The asymmetric link configuration isassumed, where the average SNR of each link is in the range {− dB , . . . , dB } , where the source s is set on purposeto be in the best propagation condition, while the source s is in the worst one. Concretely, the network is configured asfollows: (1) the average SNR of the links between source s and each relay, as well as the link between source s and ABLE IA
VERAGE
SNR
OF THE LINKS BETWEEN ALL SOURCES γ x,y [ dB ] s s s s N.A. γ − dB γ − dB s γ − dB N.A. γ − dB s γ − dB γ − dB N.A. the destination, is set to γ ; (2) the average SNR of the linksbetween source s and each relay, as well as the link betweensource s and the destination, is set to γ − dB; (3) the averageSNR of the links between source s and each relay, as wellas the link between source s and the destination, is set to γ − dB; (4) the average SNR of the links between all relays,as well as the links between each relay and the destination isset to γ ; (5) the average SNR of the links between all sourcesare set according to the Tab. I.As a result, the initial rates associated to all sources areasymmetric. They are shown on Fig. 3 as a function of γ ,which is the average SNR of the link between source s andthe destination. On that figure, IR-type of HARQ protocol withMulti-User encoding is labeled as “IR-HARQ MU”, IR-type ofHARQ protocol with Single User encoding as “IR-HARQ SU”while CC-type of HARQ protocol is labeled as “CC-HARQ”.Fig. 4 shows the average spectral efficiency of the network asa function of γ . We observe that the IR-type of HARQ pro-tocol with Multi-User encoding provides the highest averagespectral efficiency. This result was expected since the selectednodes in the second phase may help the decoding of multiplesources at the same time. IR-type of HARQ protocol withSingle User encoding performance is not far behind, providingslightly lower average spectral efficiency. It can be explainedby the fact that “only” three sources are present in the network,so there is often a case where the selected node in the secondphase cooperates with exactly one source, even if Multi-Userencoding is employed. Naturally, CC-type of HARQ has anoticeably worse performance compared with two IR basedprotocols.Fig. 5 and Fig. 6 show the same comparison but for ( , , )-OMAMRC and ( , , )-OMAMRC, respectively. The averageSNR of the links between source s and each relay, as wellas the link between source s and the destination, is set to γ − dB, while the average SNR of the links between source s and each relay, as well as the link between source s andthe destination, is set to γ − dB. The average SNR of thelink between sources s and s is set to γ − . dB, while thesame parameter for the links between sources s and s andall other sources is set to γ reduced by a value from the set [0 dB , . . . , dB ] , following the similar logic as in the case of( , , )-OMAMRC. We observe that the performance orderingof the different protocols remains the same. But, as the numberof sources in the network grows, we notice that for IR-type ofHARQ the difference in performance between the Multi-Userand Single User encoding slowly grows. Indeed, a schedulednode has all the more chances to have more than one sourcein its decoding set as the number of sources increases. -5 0 5 10 15 200123 A ll o c a t ed r a t e -5 0 5 10 15 200123 A ll o c a t ed r a t e -5 0 5 10 15 20 γ [dB] A ll o c a t ed r a t e (3,3,1) IR-HARQ CC(3,3,1) IR-HARQ SU(3,3,1) IR-HARQ MU Fig. 3. Allocated rates to sources for different HARQ protocols for asym-metric link configuration in ( , , )-OMAMRC. -5 0 5 10 15 20 γ [dB] A v e r age s pe c t r a l e ff i c i en cy (3,3,1) IR-HARQ CC(3,3,1) IR-HARQ SU(3,3,1) IR-HARQ MU Fig. 4. Average spectral efficiency obtained by using different HARQprotocols for asymmetric link configuration in ( , , )-OMAMRC. As a general conclusion, we can argument that for theOMAMRC with relatively small number of sources the IR-type of HARQ with Single User encoding offers the bestcompromise between performance and complexity.It is also interesting to observe that the average spectralefficiency decreases for all three types of the HARQ protocolwhen the number of sources increases. There are two reasonsfrom our understandings. The first one is that by adding moresources that are progressively in worse conditions than theprevious ones, the probability that the added source will besuccessfully decoded decreases. The other reason is that thenumber of retransmission rounds in the second phase is fixedto T IR = 4 and T CC = 2 , so by adding more sources, even ifthey are all in the same conditions in average, it may happensthat there are not enough available retransmissions for helpingthem all efficiently.For that reason, in the last part of simulations, we considerthe symmetric link configuration where the average SNR of γ [dB] A v e r age s pe c t r a l e ff i c i en cy (4,3,1) IR-HARQ CC(4,3,1) IR-HARQ SU(4,3,1) IR-HARQ MU Fig. 5. Average spectral efficiency obtained by using different HARQprotocols for asymmetric link configuration in ( , , )-OMAMRC. -5 0 5 10 15 20 γ [dB] A v e r age s pe c t r a l e ff i c i en cy (5,3,1) IR-HARQ CC(5,3,1) IR-HARQ SU(5,3,1) IR-HARQ MU Fig. 6. Average spectral efficiency obtained by using different HARQprotocols for asymmetric link configuration in ( , , )-OMAMRC. each link is equal to γ , and where the number of possibleretransmission rounds in the second phase varies with thenumber of sources. Namely, we try to keep a constant ratiobetween the number of time-slots in the first phase and thenumber of possible retransmissions in the second phase. Let M = 3 be the number of sources in ( , , )-OMAMRC, with T IR = 4 the number of retransmissions in the second phasefor IR-type of HARQ, and with T CC = 2 the same number,but for CC-type of HARQ. In ( , , )-OMAMRC, M = 4 , T IR = ⌈ T M M ⌉ = 6 , and T CC = T IR = 3 . In the case of( , , )-OMAMRC, by similar reasoning and forcing the T CC to be the round number, we choose T IR = 8 and T CC = 4 .Fig. 7 shows the comparison of the average spectral efficiencyfor all M , M and M where we see that in this case themore sources there are in the network, the higher the averagespectral efficiency is. For the clarity of the figure only therange γ ∈ { dB , . . . , dB } is shown. γ [dB] A v e r age s pe c t r a l e ff i c i en cy (3,3,1) IR-HARQ CC(3,3,1) IR-HARQ SU(3,3,1) IR-HARQ MU(4,3,1) IR-HARQ CC(4,3,1) IR-HARQ SU(4,3,1) IR-HARQ MU(5,3,1) IR-HARQ CC(5,3,1) IR-HARQ SU(5,3,1) IR-HARQ MU Fig. 7. Average spectral efficiency obtained by using different HARQprotocols for symmetric link configuration and different OMAMRC.
V. C
ONCLUSION
In this paper, we investigate the performance of three dif-ferent cooperative HARQ protocols for slow-fading MAMRC.Among the three proposed HARQ protocols, two followthe Incremental Redundancy (IR) approach. One consists insending incremental redundancies on all the source messagesdecoded correctly by the scheduled node (Multi-User encod-ing) while the other one helps a single source (Single Userencoding) chosen randomly. The third one is of the ChaseCombining (CC) type, where the selected node repeats thetransmission (including modulation and coding scheme) ofone source chosen randomly in its correctly decoded sourcemessage set (its decoding set). It allows Maximal RatioCombining (MRC) at the destination of all the transmissionsrelated to a given source. Single User encoding and decodingis well mastered in terms of code construction (state of the artrate compatible punctured codes) and, clearly, less complexthan Multi-User encoding and iterative joint decoding. On theother hand, the Chase Combining approach can be consideredas having a similar complexity to Single User IR-HARQ. Toidentify the most efficient cooperative HARQ protocol, i.e., theone that achieves the best complexity-performance tradeoff,we resort to information theory outage based average spectralefficiency performance comparison. We conclude that IR-typeof HARQ with Single User encoding offers the best trade-offbetween performance and complexity for a small number ofsources in our setting. R
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