OMAMRC transmission method and system with slow link adaptation under BLER constraint

Abstract

A method for transmitting consecutive messages forming a frame for a telecommunication system. The system has M sources, optionally L relays, and a destination, M≥2, L≥0. An orthogonal multiple-access multiple-relay channel scheme is used between the M sources and the L relays with a maximum number of M+T max time intervals per transmitted frame, including M intervals allocated during a first phase to the consecutive transmission of the M sources and T used intervals for at least one cooperative transmission allocated during a second phase to at least one node selected according to a selection strategy. T used≤Tmax. The link adaptation implemented by the destination is slow and maximizes average utility metrics under constraint of an average individual BLER for each source. The utility metrics include average spectral efficiency tied to the strategy for selecting the nodes intervening during the second phase.

Claims

1. A transmission method for transmitting successive messages forming a frame for a telecommunications system with M sources, possibly L relays and a destination, M≥2, L≥0 according to an orthogonal multiple access scheme of a transmission channel between nodes taken from among the M sources and the L relays with a maximum number of M+T.sub.max time slots per transmitted frame including M slots allocated, during a first phase, to the successive transmission of the M sources, and T.sub.used slots for one or more cooperative transmissions allocated, during a second phase, to one or more nodes selected according to a selection strategy, T.sub.used≤T.sub.max, wherein the method comprises: performing, by the destination, an initial link adaptation phase including determining an initial rate for each source on the basis of the destination's knowledge of an average quality of each of the links in the system and with transmission of information about this initial rate by the destination to each source; and successively transmitting, by the M sources, for each frame from among a plurality of frames, messages during the M slots of the first phase with, respectively, modulation and coding schemes determined from the information about the initial rates, wherein the link adaptation implemented by the destination comprises maximizing an average utility metric under constraint of an average individual block error rate (BLER) for each source, the utility metric being an average spectral efficiency conditional upon the node selection strategy used in the second phase.

2. The transmission method as claimed in claim 1, wherein the method furthermore comprises iteratively calculating the initial rates by the destination.

3. The transmission method as claimed in claim 2, wherein the node selection strategy used during the second phase follows a sequence known in advance by all of the nodes.

4. The transmission method as claimed in claim 2, wherein the iteratively calculating the initial rates takes into account the node selection strategy.

5. The transmission method as claimed in claim 2, wherein the node selection strategy used during the second phase takes into account information coming from the nodes and indicating their set of correctly decoded sources.

6. The transmission method as claimed in claim 2, wherein the node selection strategy used during the second phase corresponds, at each slot, to the selection of the node from among the nodes that have correctly decoded at least one source that the destination has not correctly decoded at the end of the previous time slot, called eligible nodes, that has the best instantaneous quality from among the instantaneous qualities of all of the links between these eligible nodes and the destination.

7. A system comprising: M sources, L relays and a destination, M≥2, L≥0, for transmitting successive messages forming a frame according to an orthogonal multiple access scheme of a transmission channel between nodes taken from among the M sources and the L relays with a maximum number of M+T.sub.max time slots per transmitted frame including M slots allocated, during a first phase, to the successive transmission of the M sources, and T.sub.used slots for one or more cooperative transmissions allocated, during a second phase, to one or more nodes selected according to a selection strategy, T.sub.used≤T.sub.max, wherein: the destination comprises a first processor and a first non-transitory computer-readable medium comprising instructions stored thereon which when executed by the first processor configure the destination to: perform an initial link adaptation phase including determining an initial rate for each source on the basis of the destination's knowledge of an average quality of each of the links in the system and with transmission of information about this initial rate by the destination to each source, wherein the link adaptation implemented by the destination comprises maximizing an average utility metric under constraint of an average individual block error rate (BLER) for each source, the utility metric being an average spectral efficiency conditional upon the node selection strategy used in the second phase; and each of the M sources comprises a second processor and a second non-transitory computer-readable medium comprising instructions stored thereon which when executed by the second processor configure the M sources to: for each frame from among a plurality of frames, successively transmit messages during the M slots of the first phase with, respectively, modulation and coding schemes determined from the information about the initial rates.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Other features and advantages of the invention will become more clearly apparent upon reading the following description of embodiments, given by way of simple illustrative and non-limiting examples, and the appended drawings, in which:

(2) FIG. 1 is a diagram of an example of what is called a cooperative OMAMRC (Orthogonal Multiple Access Multiple Relays Channel) system according to the invention,

(3) FIG. 2 is a diagram of a transmission cycle of a frame, which may be preceded by an initialization step according to the invention,

(4) FIG. 3 is a diagram of the OMAMRC system of FIG. 1 for which all of the sources except for the source s.sub.1 are considered to be correctly decoded.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

(5) Channel use is the smallest granularity in terms of time-frequency resources defined by the system that allows transmission of a modulated symbol. The number of channel uses is linked to the available frequency band and to the transmission duration.

(6) In the “slow fading” case favored in the description, the fading gains are constant during the M+T.sub.max time slots, where M+T.sub.max is the maximum number of time slots to complete a transmission cycle.

(7) One embodiment of the invention is described in the context of an OMAMRC system illustrated in FIG. 1 and referring to the diagram of FIG. 2, which illustrates a transmission cycle of a frame.

(8) This system comprises M sources that belong to the set of sources ={s.sub.1, . . . , s.sub.M}, L relays that belong to the set of relays ={r.sub.1, . . . , r.sub.L} and a destination d. Each source of the set communicates with the single destination using the other sources (user cooperation) and cooperating relays.

(9) For the sake of simplifying the description, the following assumptions are made hereinafter on the OMAMRC system: the sources and the relays are equipped with a single transmission antenna; the sources, the relays and the destination are equipped with a single reception antenna; the sources, the relays and the destination are perfectly synchronized; the sources are statistically independent (there is no correlation between them); all of the nodes transmit with one and the same power; use is made of a CRC code assumed to be included in the K.sub.s bits of information from each source s in order to determine whether or not a message is correctly decoded; the links between the various nodes suffer from additive noise and fading. The fading gains are fixed during the transmission of a frame carried out for a maximum duration of M+T.sub.max time slots, but may change independently from one frame to another. T.sub.max≥2 is a parameter of the system; the instantaneous quality of the channel/direct link at reception (CSIR Channel State Information at Receiver) is available at the destination, at the sources and at the relays; the feedback is error-free (no error on the control signals); the duration of the time slots is variable.

(10) The nodes comprise the relays and the sources, which may behave like a relay when they are not transmitting their own message.

(11) The nodes, M sources and L relays, access the transmission channel according to an orthogonal multiple access scheme that allows them to listen to the transmissions from the other nodes without interference. The nodes operate in a half-duplex mode.

(12) The following notations are used: x.sub.a,k∈ is the coded modulated symbol for the use of the channel k transmitted by the node a ∈∪, y.sub.a,b,k is the signal received at the node b∈∪∪{d}\{a} corresponding to a signal transmitted by the node a ∈∪, γ.sub.a,b is the average signal-to-noise ratio (SNR), which takes into account the effects of channel attenuation (path-loss) and of masking (shadowing), h.sub.a,b is the channel attenuation gain (fading), which follows a complex circular-symmetry Gaussian distribution with an average of zero and a variance of γ.sub.a,b, and the gains are independent of one another, n.sub.a,b,k are samples of a white Gaussian noise (AWGN) distributed identically and independently and that follow a complex circular-symmetry Gaussian distribution with an average of zero and unitary variance.

(13) The signal received at the node b∈∪∪{d}\{a} corresponding to the signal transmitted by the node a ∈∪ may be written:
y.sub.a,b,k=h.sub.a,bx.sub.a,k+n.sub.a,b,k  (1)

(14) During the first phase of M time slots, each source transmits its code words during N.sub.1 channel uses, k∈{1, . . . , N.sub.1}. During the second phase of T.sub.max time slots, each selected node transmits information representative of the messages from the sources decoded without an error by this node during N.sub.2 channel uses, k∈{1, . . . , N.sub.2}.

(15) By using reference signals (pilot symbols, SRS signals from 3GPP LTE, etc.), the destination is able to determine the gains (CSI Channel State Information) of the direct links h.sub.dir={h.sub.s.sub.1.sub.d, . . . , h.sub.S.sub.M.sub.,d, h.sub.r.sub.1.sub.d, . . . , h.sub.r.sub.L.sub.,d}, that is to say of the source to destination and relay to destination links, and is therefore able to deduce the average SNRs of these links therefrom.

(16) On the other hand, the gains of the links between sources, of the links between relays and of the links between sources and relays are not known to the destination. Only the sources and the relays are able to estimate a metric of these links by using reference signals in a manner similar to that used for the direct links Given that the channel statistics are assumed to be constant between two initialization phases, the transmission of the metrics to the destination by the sources and the relays is able to be performed only at the same frequency as the initialization phase. The channel statistics for each link are assumed to follow a centered circular complex Gaussian distribution and the statistics are independent between the links. It is therefore enough to consider only the average SNR as a measure of the statistics of a link.

(17) The sources and the relays therefore feed back metrics representative of the average SNRs of the links that they are able to observe to the destination.

(18) The destination thus knows the average SNR of each of the links.

(19) During an initial link adaptation phase that precedes the transmission of a plurality of frames, the destination feeds back a value (index, MCS, rate, etc.) representative of an initial rate for each source. Each of the initial rates unambiguously determines an initial modulation and coding scheme (MCS) or, vice versa, each initial MCS determines an initial rate.

(20) These initial rates are determined by the destination so as to maximize an average spectral efficiency conditional upon the node selection strategy used during the second phase and under the constraint of an average individual BLER for each source. The initial rates are fed back via very low-rate control channels. The maximization is typically performed under the constraint of the average SNRs of the links in the system.

(21) Each source transmits its framed data to the destination using the other sources and the relays.

(22) A frame occupies time slots during the transmission of the M messages from the respectively M sources. The transmission of a frame (which defines a transmission cycle) takes place during M+T.sub.max time slots: M slots for the 1.sup.st phase, T.sub.max slots for the 2.sup.nd phase.

(23) During the first phase, each source s∈={s.sub.1, . . . , s.sub.M} transmits, after coding, a message u.sub.s containing K.sub.s bits of information u.sub.s ∈.sub.2.sup.K.sup.s, .sub.2 being the two-element Galois body. The message u.sub.s comprises a code of CRC type that makes it possible to verify the integrity of the message u.sub.s. The message u.sub.s is coded according to the initial MCS. Given that the initial MCSs may be different between the sources, the lengths of the coded messages may be different between the sources. The coding uses an incremental redundancy code. The code word that is obtained is divided into redundancy blocks. The incremental redundancy code may be systematic, and the bits of information are then included in the first block. Whether the incremental redundancy code is systematic or not, it is such that the first block is able to be decoded independently of the other blocks. The incremental redundancy code may be created for example by way of a finite family of punctured linear codes with compatible rates or of codes with no rate that are modified so as to operate with finite lengths: raptor code (RC), rate compatible punctured turbo code (RCPTC), rate compatible punctured convolutional code (RCPCC), rate compatible low density parity check code LDPC (RCLDPC).

(24) In the first phase, the M sources successively transmit their message during the M slots with, respectively, modulation and coding schemes determined from the initial rates. Each time slot comprises N.sub.1 channel uses such that the time resource is shared equally between the sources.

(25) With each transmitted message corresponding to a source s.sub.1, . . . , s.sub.M, a correctly decoded message is assimilated to the corresponding source for the purposes of notation.

(26) When a source transmits, the other sources and the relays listen and try to decode the messages received at the end of each time slot. The success of the decoding is decided using the CRC.

(27) In the second phase, the selected node, source or relay, acts as a relay by cooperating with the sources in order to help the destination to correctly decode the messages from all of the sources. The selected node transmits, that is to say it cooperates by transmitting the words or some of the words that it has correctly decoded. The second phase comprises at most T.sub.max time slots, called rounds. Each round t∈{1, . . . , T.sub.max} has a duration of N.sub.2 channel uses.

(28) During this phase, the destination follows a certain strategy in order to decide which node transmits at each time slot (round). The destination informs the nodes by using a low-rate control channel (limited feedback) in order to transmit a feedback message. This feedback message is based on its result of decoding the received frames. The destination thus supervises the transmission of the nodes by using these feedback messages, thereby making it possible to improve spectral efficiency and reliability by increasing the probability of the destination decoding all of the sources.

(29) If the decoding of all of the sources is correct, the feedback is a message of type ACK. In this case, a transmission cycle of a new frame begins with the erasure of the memories of the relays and of the destination and with the transmission of new messages by the sources.

(30) If the decoding of at least one source is incorrect, the feedback message is typically a NACK. Each node a ∈∪ transmits its set of correctly decoded sources at the end of the previous time slot (round) denoted .sub.a,t−1. By convention, .sub.b,t.Math. denotes the set of messages (or sources) correctly decoded by the node b∈∪∪{d} at the end of the time slot t (round t), t∈{0, . . . , T.sub.max}. The end of the time slot (round) t=0 corresponds to the end of the first phase. The number of time slots used during the second phase t.sub.used={1, . . . , T.sub.max} depends on the success of decoding at the destination.

(31) The selected node transmits parities determined from the messages in its set of correctly decoded sources using joint network coding and channel coding (Joint Network Channel Coding). This transmission takes place during a time slot of N.sub.2 channel uses. The other nodes and the destination may improve their own decoding by using the transmission of the selected node and update their set of correctly decoded sources accordingly.

(32) The initial transmission rate of a source s is R.sub.s=K.sub.s/N.sub.1 in bits per complex dimension (b.c.u.). The long-term rate R.sub.s of a source is defined as the number of bits transmitted compared to the total number of channel uses for a number of frames transmitted, which tends towards infinity:

(33) $\begin{array}{cc}{\overline{R}}_s=\frac{R_s}{M+\alpha 𝔼\left(T\right)}& \left(2\right)\end{array}$

(34) where (T)=Σ.sub.t=1.sup.T.sup.maxtPr{T=t} is the average number of retransmission time slots (rounds) used during the second phase, and where α=N.sub.2/N.sub.1.

(35) Spectral efficiency may be defined as the sum of individual spectral efficiencies:
η=Σ.sub.i=1.sup.MR.sub.s.sub.i(1−Pr{.sub.s.sub.i.sub.,T.sub.max})  (3)
where .sub.s,T.sub.max is the event that the source s is not correctly decoded by the destination at the end of the time slot (round) T.sub.max, hereinafter called individual outage event of the source s at the end of the time slot (round) T.sub.max.

(36) In general, the individual outage event of the source s at the end of the time slot (round) t, .sub.s,t(a.sub.t, .sub.a.sub.t.sub.,t−1|h.sub.dir,.sub.t−1) depends on the selected node a.sub.t∈=∪ and on the associated set of decoded sources .sub.a.sub.t.sub.,t−1. This is the case conditionally on the knowledge of the gains of the direct channels h.sub.dir and of .sub.t−1. .sub.t−1 is the set comprising all of the nodes â.sub.l that were selected at the time slots (rounds) l∈{1, . . . t−1} preceding the time slot (round) t and their associated decoding set .sub.â.sub.l.sub.,l−1 and the decoding set of the destination .sub.d,t−1.

(37) The common outage event at the end of the time slot (round) t, .sub.t(a.sub.t,.sub.a.sub.t.sub.,t−1|h.sub.dir,.sub.t−1), is defined as being the event that at least one source is not correctly decoded by the destination at the end of the time slot (round) t.

(38) The probability of the individual outage event of the source s at the end of the time slot (round) t for a candidate node a.sub.t may be expressed in the form: () where (.Math.) is the expectation operator and such that takes the value 1 if the event is true and the value 0 if not.

(39) The probability of the common outage event may be defined in the same way. Hereinafter, the dependency on the knowledge of h.sub.dir and of .sub.t−1 is omitted for the sake of simplifying the notations.

(40) The common outage event of a set of sources occurs when the vector of their rate is outside the corresponding MAC capacity region.

(41) For some subsets of sources .Math..sub.d,t−1 where .sub.d,t−1=\.sub.d,t−1 is the set of sources that are not correctly decoded by the destination at the end of the time slot (round) t−1, the common outage event may be expressed in the form:
(a.sub.t,.sub.a.sub.t.sub.,t−1)=  (4)
such that the sources that belong to =.sub.d,t−1\ are considered to be interference.

(42) reflects non-compliance with the MAC inequality associated with the sum rate of the sources contained in :
={R.sub.s>I.sub.s,d+Σ.sub.l=1.sup.t−1αI.sub.â.sub.l.sub.,d+αI.sub.a.sub.t.sub.,d}  (5)
where
.sub.â.sub.l.sub.,s={{s∈.sub.â.sub.l.sub.,l−1∩}∧{.sub.â.sub.l.sub.,l−1∩=ø}},.sub.a.sub.t.sub.,s={{s∈.sub.a.sub.t.sub.,t−1∩}∧{.sub.a.sub.t.sub.,t−1∩=ø}}
where ∧ which represents the logical operator,
I.sub.a,b denotes the mutual information between the nodes a and b, â.sub.l, l=1àt−1 denotes an already selected node.

(43) The factor α makes it possible to normalize, before addition, the two terms associated respectively with the two phases for which the time slots have respective durations of N.sub.1 and N.sub.2 channel uses.

(44) The individual outage event of the source s at the end of the time slot (round) t may be written:
.sub.s,t(a.sub.t,.sub.a.sub.t.sub.,t−1)={R.sub.s>I.sub.s,d+Σ.sub.l=1.sup.t−1αI.sub.â.sub.l.sub.,d+αI.sub.a.sub.l.sub.,d}  (6)
where =.sub.d,t−1 and .sub.â.sub.l.sub.,s and .sub.a.sub.t.sub.,s have the same expression as for (5).

(45) The destination implements, according to the invention, a slow link adaptation. This adaptation consists in maximizing an average utility metric after a number X≤T.sub.max of retransmissions (cooperative transmissions) taking place during the second phase under the constraint of an average individual BLER for each source. The utility metric is an average spectral efficiency conditional upon the node selection strategy used during this second phase.

(46) According to a first class of strategies, the selection of the nodes taken from among the sources and the relays depends on the sets of sources correctly decoded by the nodes. One example under consideration, called preferred strategy, is based on an IR-HARQ type selection that aims to maximize spectral efficiency. According to this preferred strategy, at the time slot (round) t of the second phase, the destination chooses the node with the best instantaneous quality of the link between itself and this node (for example the greatest mutual information between itself and this node) taken from among all of the nodes that were able to correctly decode at least one source of the set .sub.d,t−1, these nodes being said to be eligible. This strategy makes it possible to achieve a good compromise between computation complexity and performance, but at the expense of a large number of control signals.

(47) According to a second class of strategies, the selection of the nodes taken from among the sources and the relays does not depend on the sets of the sources correctly decoded by the nodes. According to this class, the selection is determined and known to all the nodes. One example under consideration is such that the selection sequence is cyclical and such that the selected node is selected only from among the relays. According to this example, each relay benefits from at least one dedicated time slot (round) during the second phase to transmit. In order not to favor one relay over another, the sequence changes with each frame. According to this example, only one feedback bit from the destination is enough to feed back a common ACK/NACK message.

(48) In the first phase, each source s transmits with the initial rate R.sub.s.

(49) Let BLER.sub.s,X(R.sub.s) be the average probability of having the message from the source s not correctly decoded after X time slots (rounds) of the second phase.

(50) In a point-to-point transmission, the individual throughput of the source is given by:
R.sub.s(1−BLER.sub.s,X(R.sub.s))

(51) And to optimize this throughput, the usual method consists in finding the optimum pair (R.sub.s, BLER.sub.s,X(R.sub.s)).

(52) Such a usual method is not able to be used for a system with M sources, possibly L relays, and a destination with an orthogonal multiple access scheme of the transmission channel, since the BLER.sub.s,X is dependent on all of the rates (R.sub.1, . . . , R.sub.M). This is because the decoding set of the node selected at the current time slot (round) depends on all of the rates, and these influence the probability of incorrect decoding of the message from the source s.

(53) In order not to overload the notations, R.sub.s.sub.i is used to distinguish the rate of the source s.sub.i after optimization from R.sub.i, which is a possible value of R.sub.s.sub.i from the whole set of possible rates {R.sub.1, . . . , R.sub.n.sub.MCS}. n.sub.MCS is the number of different MCSs. The method according to the invention is a solution to the following optimization problem:

(54) $\begin{array}{cc}\left(R_{s_1},\mathrm{.Math.},R_{s_M}\right)=\underset{\left(R_1,\mathrm{.Math.},R_M\right)\in {\left\{{\stackrel{\_}{R}}_1,\mathrm{.Math.},{\stackrel{\_}{R}}_{n_{\mathrm{MCS}}}\right\}}^M}{\arg \max }\underset{i=1}{\overset{M}{.Math.}}\frac{R_i}{M+\alpha 𝔼\left(X_{\mathrm{used}}\right)}\left(1-\mathrm{Pr}\left\{{𝒪}_{s_i,X}\right\}\right)& \left(7\right)\end{array}$

(55) under the constraint that Pr{.sub.s,X}≤QoS.sub.s, ∀s∈.

(56) In relationship (7), X.sub.used is a random variable that represents the number of time slots (rounds) used during the second phase X.sub.used≤X. The distribution of X.sub.used depends on (R.sub.1, . . . , R.sub.M) and on Pr{.sub.s.sub.i.sub.X}, thereby making optimization (7) multidimensional of cardinality n.sub.MCS.sup.M, that is to say 3375 possible M-tuples (R.sub.1, . . . , R.sub.M) for a family of fifteen MCSs and three sources. An exhaustive search very quickly becomes impossible when the number of sources increases.

(57) What is called the “Genie Aided” approach consists in assuming, in the initialization step, that all of the sources s except for the source s.sub.i whose rate it is desired to initialize are considered to be correctly decoded, s ∈\s.sub.i={s.sub.1, s.sub.2, . . . , s.sub.i−1, s.sub.i+1, . . . , s.sub.M}. All of the sources {s.sub.1, s.sub.2, . . . , s.sub.i−1, s.sub.i+1, . . . , s.sub.M} other than s.sub.i act as relays, denoted {r.sub.L+1, . . . , r.sub.L+M−1}. For the source s.sub.i under consideration, the network is a multiple relay network denoted (1, L+M−1,1) and no longer a multiple relay and multiple user network. The corresponding system is illustrated by the diagram in FIG. 3 when s.sub.i=s.sub.1.

(58) According to the invention, this approach is supplemented by taking into account the quality of all of the links that are able to assist the transmission of the source s.sub.i. This method gives a more precise solution in particular in the case of a priori knowledge of the node selection sequence used in the second step.

(59) Given the simplification of the network (1, L+M−1,1), finding the maximum rate R.sub.s.sub.i for the source s.sub.i under the “Genie Aided” scenario may be written in the form:

(60) $\begin{array}{cc}{R}_{s_i}=\underset{R_i\in \left\{{\stackrel{\_}{R}}_1,\mathrm{.Math.},{\stackrel{\_}{R}}_{n_{\mathrm{MCS}}}\right\}}{\arg \max }\left\{\frac{R_i}{M+\alpha 𝔼\left(X_{\mathrm{used},R_i}\right)}\left(1-\int \left[R_i>I_{s_i,d}+\underset{l=1}{\overset{X}{.Math.}}\alpha I_{{\hat{a}}_l,d}{1}_{\left\{s_i\in {𝒮}_{{\hat{a}}_l,l-1}\right\}}\right]P\left(H\right)dH\right)\right\}& \left(8\right)\end{array}$
such that Pr{.sub.s.sub.i.sub.,X}≤QoS.sub.s.sub.i

(61) It is clearly apparent from equation (8) that the rate R.sub.s.sub.i under the “Genie Aided” scenario depends on the selected node â.sub.l at the time slot (round) l. In order to determine an upper bound on the rate R.sub.s.sub.i under the “Genie Aided” scenario for the source s.sub.i, it is enough to choose the optimum node selection strategy under the “Genie Aided” scenario for this same source s.sub.i. This is described by algorithm 3 in appendix A.

(62) Furthermore, calculation of optimization (8) is given by algorithm 1 in appendix A. Each rate value of the set of possible rates {R.sub.1, . . . , R.sub.n.sub.MCS} is considered one after the other in a first loop on j. n.sub.MCS is the number of modulation and coding schemes. A second loop on cnt makes it possible to average the individual BLER or Pr{.sub.s,X} on Nb_MC channel draws according to the statistics given by the average SNRs of all of the links Inside the loop cnt, all of the channels are thus known resulting from a random draw. It is thereafter enough to calculate equation (8) using a Monte-Carlo approach where the integral is replaced by a sum:

(63) $\int \left[R_i>I_{s_i,d}+\underset{i=1}{\overset{X}{.Math.}}\alpha I_{{\hat{a}}_l,d}{1}_{\left\{s_i\in {𝒮}_{{\hat{a}}_l,l-1}\right\}}\right]P\left(H\right)\mathrm{dH}=\frac{1}{N{b}_{-}MC}\underset{cnt=1}{\overset{N{b}_{-}MC}{.Math.}}\left[R_i>I_{s_i,d}\left(H_{cnt}\right)+\underset{l=1}{\overset{X}{.Math.}}\alpha I_{{\hat{a}}_l,d}\left(H_{cnt}\right)1_{\left\{s_i\in {𝒮}_{{\hat{a}}_l,l-1}\right\}}\right]$
and where the variable out corresponds to:

(64) $\mathrm{out}=\underset{cnt=1}{\overset{N{b}_{-}MC}{.Math.}}\left[R_i>I_{s_i,d}\left(H_{cnt}\right)+\underset{l=1}{\overset{X}{.Math.}}\alpha I_{{\hat{a}}_l,d}\left(H_{cnt}\right)1_{\left\{s_i\in {𝒮}_{{\hat{a}}_l,l-1}\right\}}\right]$

(65) In order to determine an average approximation of the rate that the source s.sub.i is able to use under the “Genie Aided” scenario, a strategy of random selection of the node â.sub.l (from among all of the relay nodes and for each time slot (round) l) is adopted. This is undertaken during step 11 of algorithm 1 in Appendix A and consists in randomly selecting the node â.sub.x from among all of the possible relay nodes.

(66) In order to determine the best initial rates that all of the sources are able to use, one embodiment of the method according to the invention according to which the determination of the initial rates by the destination comprises an iterative calculation step may follow the sequence given in Appendix A, algorithm 2. This algorithm takes the initial rates under the “Genie Aided” scenario and a particular selection strategy (for example random selection) as starting point. The upper bound is based on the selection strategy given by algorithm 3, which may be used to minimize the number of calculations (no rate higher than that given by the “Genie Aided” upper bound for a source s should be tested for this same source) or even as a starting point for algorithm 2.

(67) According to algorithm 2, all of the source rates are updated cyclically. The rate of a source s.sub.i depends on the rates of the sources having an index i′ less than i, i′<i, updated in the same iteration and rates updated for the last time in the previous iteration for the sources having an index i″ greater than i, i″>i. The update, at each iteration t of the rate of a source s.sub.i, i∈{1, . . . , M}, consists in verifying, from the rate calculated in the previous iteration, R.sub.s.sub.i(t−1), whether the spectral efficiency increases or decreases by increasing the value of the rate R.sub.s.sub.i(t) to the slightly higher value (the rate values being quantified).

(68) If the spectral efficiency increases, then the increase in the rate value is continued until the spectral efficiency decreases. The selected rate value R.sub.s.sub.i(t) is the one just before the spectral efficiency decreases.

(69) If the spectral efficiency decreases when the rate R.sub.s.sub.i(t) is increased for the first time, then the value of the rate is decreased until the spectral efficiency decreases. The selected rate value R.sub.s.sub.i(t) is the one just before the spectral efficiency decreases.

(70) Any decrease or increase in the rate is bounded by the upper bound as determined by algorithm 3.

REFERENCES

(71) [1] A. Mohamad, R. Visoz and A. O. Berthet, “Cooperative Incremental Redundancy Hybrid Automatic Repeat Request Strategies for Multi-Source Multi-Relay Wireless Networks,” IEEE Commun. Lett., vol. 20, no. 9, pp. 1808-1811, September 2016.

(72) TABLE-US-00001 APPENDIX A Alg. 1 - Monte-Carlo simulation to determine rates under the “Genie Aided” scenario:  1.  1.sup.st loop: sequentially select the possible candidate rate R.sub.j that has not yet been considered in  the set {R.sub.1, . . . , R.sub.n.sub.MCS}. If all of the rates have been considered, go to end 1.sup.st loop.  2. Initialize the counter out of the Monte-Carlo implementations (of channel matrix H) that lead to  an outage: out = 0, the counter X.sub.used of the number of cumulative time slots (rounds) used  during the second phase: X.sub.used = 0, the set .sub.d,0 = \s.sub.i according to the “Genie Aided”  scenario.  3. 2.sup.nd loop: sequentially select the counter cnt of the current implementation of a Monte- Carlo simulation: 1 ≤ cnt ≤ Nb_MC where Nb_MC is the maximum number of Monte-Carlo implementations, for example Nb_MC = 1000. If the counter has reached the maximum number cnt > Nb_MC, go to end 2.sup.nd loop.  4.  determine H.sub.cnt based on P(H) the joint probability of implementing the channels of  all of the links h.sub.a,b.  5.  calculate I.sub.a,b(H.sub.cnt) for all of the links  6.  if R.sub.j ≤ I.sub.s.sub.i.sub.,d then  7.    .sub.d,0 = .sub.d,0 ∪ {s.sub.i},  8.   continue, (no change in the values of counters out and X.sub.used).  9.  end if 10.  3.sup.rd loop: for each time slot (round), x = 1 à X 11.    selection of the node â.sub.x by the destination by applying a selection strategy (for    example Alg. 3 for an upper bound or random selection) 12.    calculate C.sub.2 = I.sub.s.sub.i.sub.,d + Σ.sub.k=1.sup.x  13.    if R.sub.j ≤ C.sub.2 then 14.   X.sub.used = x .Math. (the number of time slots (rounds) used in the current implementation of the Monte-Carlo simulation) 15.     break, (no change in the value of the counter out) 16.    end if 17.    if x = X then 18.     out = out + 1 19.     X.sub.used = X. 20.    end if 21.   end of the 3.sup.rd loop 22.   X.sub.used = X.sub.used + X.sub.used 23.  end of the 2.sup.nd loop 24.  $\mathrm{determine}\mathrm{the}\mathrm{average}\mathrm{outage}\mathrm{probability}\mathrm{of}\mathrm{the}\mathrm{source}{s}_i\mathrm{for}\mathrm{the}\mathrm{rate}{R}_j\text{:}{P}_{s_i,R_j}^{\mathrm{out}}=\frac{\mathrm{out}}{\mathrm{Nb\_MC}}$ 25.  determine the average number of time slots (rounds) used during the second phase:    $𝔼\left(X_{\mathrm{used},R_j}\right)=\frac{{\overline{X}}_{\mathrm{used}}}{\mathrm{Nb\_MC}}$ 26.  end of the 1.sup.st loop 27.  choose the maximum rate R.sub.s.sub.i that the source s.sub.i is able to use:         $R_{s_i}=\underset{R_j\in \left\{{\stackrel{\_}{R}}_1,\mathrm{.Math.},{\stackrel{\_}{R}}_{n_{MCS}}\right\}}{\arg \max }\left\{\frac{R_j}{M+\mathrm{\alpha 𝔼}\left(X_{\mathrm{used},R_j}\right)}\left(1-P_{s_i,R_j}^{\mathrm{out}}\right)\right\}$   such that P.sub.s.sub.i.sub.,R.sub.j.sup.out ≤ QoS.sub.s.sub.i.

(73) TABLE-US-00002 Alg.2-Iterative procedure for correcting “Genie Aided” rates: 1. initialization of the iteration counter: t = 0, 2. initialization of the rates of the sources using what is called a “Genie Aided” approach conditional upon a random selection of nodes, 3. as long as (|R.sub.s.sub.i(t) − R.sub.s.sub.i(t − 1)| > 0, ∀i ∈ {1, . . . , M}) do 4.  increment the iteration counter: t = t + 1 5.  for each source s.sub.i, i ∈ {1, . . . , M} do 6.   considering the already determined rates of the sources:    (R.sub.s.sub.1(t), . . . , R.sub.s.sub.i−1(t), R.sub.s.sub.i+1 (t − 1), . . . , R.sub.s.sub.M (t − 1)), update the rate value R.sub.s.sub.i (t) of   the source s.sub.i such that BLERs.sub.i ≤ QoS.sub.s.sub.i. Rem1. The value of R.sub.s.sub.i (t) is different from   R.sub.s.sub.i (t − 1) if and only if BLER.sub.s.sub.i ≤ QoS.sub.s.sub.i and the average spectral efficiency has   increased. Rem 2: the calculation of the average individual BLERs and the spectral   efficiency follows a Monte-Carlo approach without a “Genie Aided” scenario. 7.  end for 8. end as long as

(74) TABLE-US-00003 Alg. 3 - Optimal selection strategy under the “Genie Aided” scenario: 1. Loop: determine the decoding set of each candidate node a.sub.x ∈   ∪   at the end of the time slot (round) x − 1. 2.  “Genie Aided ” initialization: .sub.a.sub.x.sub.,x−1 =  \s.sub.i. 3.   calculate C.sub.1 = I.sub.s.sub.i.sub.,a.sub.x + Σ.sub.k=1.sup.x−1  4.   if R.sub.j ≤ C.sub.1 then 5.     .sub.a.sub.x.sub.,x−1 = .sub.a.sub.x.sub.,x−1 ∪{s.sub.i}. 6.   end if 7. end of the loop 8. selection of the node â.sub.x by the destination: ${\hat{a}}_x=\underset{a_x\in .Math.}{\arg \max }\left\{I_{a_x,d}{1}_{\left\{s_i\in {a_x,x-1}_{}\right\}}\right\}$

(75) Although the present disclosure has been described with reference to one or more examples, workers skilled in the art will recognize that changes may be made in form and detail without departing from the scope of the disclosure and/or the appended claims.