WO2017060619A1

WO2017060619A1 - Method for controlling power distributed between k emitters and corresponding system

Info

Publication number: WO2017060619A1
Application number: PCT/FR2016/052558
Authority: WO
Inventors: Samson Lasaulce; Raphaël Visoz
Original assignee: Orange
Priority date: 2015-10-05
Filing date: 2016-10-05
Publication date: 2017-04-13
Also published as: FR3042086A1

Abstract

The present invention relates to a method for controlling power distributed between K emitters each having T_k emission antennas intended for communicating respectively with K receivers via communication links described between the emitter j and the receiver i by a set of MIMO channel gains G_ji , the covariance matrix with dimensions T_k x T_k of the signal emitted by the emitter k being determined by a conditional probability distribution Q_k(P_kΙY_k ) representing the power control knowing the observation Y_k available to the emitter k of the channel gains, k ∈ {1,..., K}, each emitter knowing a global metric W(Q ₁,..., Q_K ). The method: initialises the conditional probability distribution, noted Q_k ⁽⁰⁾, and in an iterative manner, with i being an iteration index, i = 0 to N — 1: and so on for each emitter k = 1 to K; determines the conditional probability distribution Q_k ⁽ⁱ⁺¹⁾ representing the power control of the emitter k as being that which maximises the mean global metric by considering the conditional probability distributions Q ₁ ⁽ⁱ⁺¹⁾,..., Q_K _-1 ⁽ⁱ⁺¹⁾, Q_K ₊₁ ⁽ⁱ⁾,... Q_K ⁽ⁱ⁾ that represent the power control of the other emitters previously obtained as fixed. The power emitted at a time t by the emitter k is given by the conditional probability distribution, determined at the end of the iterative process, knowing the performance of the observations Y_K at that time t.

Description

Distributed power control method between transmitters and corresponding system Field of the invention

The present invention relates to the field of telecommunications. Within this field, the invention relates to power control techniques emitted by a transmitter in a context where this transmitter can be impacted by transmitters of the same technology or different technologies that use common radio resources on a network. the same geographical area, that is to say on an area where the communications of one disturb the communications of another, it is said that there is an interference phenomenon.

The invention is placed in the context of a telecommunication system with K transmitters each having T _k transmit antennas and K receivers which communicate respectively with the K transmitters via links or communication channels, K> 1. The links are described between the transmitter j and the receiver i by a set of gains G ^ of multiple input and output channels (MIMO), i G {1, ..., K], i {1, ... , K}. The links are direct when j = i and the links are interfering when j ≠ i. More precisely, the links G _j i with j G {1,..., I-1, i + 1,..., K] interfere with the link of the useful signal G _a at the receiver i. A transmitter may as well be a base station as an access point of an access network or a terminal.

The power control consists in adapting the power p _k of the transmitter ke {l, ..., K} to the knowledge that the latter has transmission conditions while attempting to optimize the performance of the system. To evaluate the impact of the transmitted power on the performance of the interference system, it is common practice to evaluate the performances by means of a rate-sum metric given by the sum of the individual K rates and which corresponds to a defined function w. as following :

w (0u, ..., 9KK, PI- - - PK)

1 g (1 + RSIB _fc (0 _lfc> ..., g _Kk , p _t , ..., p _K )) (1)

The function w determines a sum rate on the system at K transmitters and K receivers.

The term k of the sum flow w corresponds to the individual flow rate of the user k and depends only on its RSIB (signal ratio to interference plus noise or SINR according to English terminology). The value of the RSIB generally depends on the transmitted power levels of all the transmitters p _{1 (...} , p _K and the various attenuations of the incident links for the receiver k, these attenuations being given by the positive scalar quantities g _lk,. .., g _Kk The quantity g _lk, for example, represents the attenuation that separates the link between the transmitter 1 and the receiver K. The RSIB of the user k is typically expressed as follows:

RSIB _fe G7 _lfe g _{Kkl V} i PK) = ° ^KKV _A ^K _V

^{Σ +} Zj ≠ ky jkPj (2) with σ ² the variance of the communication noise other than the interference (including in particular the thermal noise of the receiver).

Prior art The power control method amounts to determining a function p _k ( _gkk ) ¾ ^u ift correspond a power to the knowledge that the transmitter k of the gain g _kk of the direct link.

[KLGS2015] propose a threshold power control function defined as follows:

where At _k ≥ 0 is a determined threshold and P _max is the maximum transmission power, assumed to be identical for all transmitters. [KLGS2015] also proposes an iterative method, specific to the considered scenario, for setting the thresholds λ _χ ,. . . , λ _κ .

The function of power control p g _k _kk) ^is chosen empirically or ad hoc for the performance criterion considered: the decision rule adopted by the authors is to transmit at maximum power if the quality of the communication link kk ( between the transmitter k and the receiver k) is good enough and not to emit otherwise.

The relevance of the choice of the function is measured by a performance evaluation by considering T temporal realizations for all the attenuations _\ ι, - - -, κκ of the links of the system. Typically these embodiments are selected as T observations of attenuations over time. These T realizations make it possible to evaluate the performance of the telecommunication system over T communication periods, each period being characterized by a state in terms of quality of links represented by the realization of the quantities g _l ,. . . , g _KK . The performance evaluation consists in evaluating the average value of a performance criterion typically given by equation (1). This average W _{T is} expressed in the form:

WT = Σt = i w (tfiiCO 0mr (O.Pi (0i (O) Ρκ (κκ ())) (4)

where £ is the block index or communication period and T is the number of blocks considered. For example, <7n (£) is the attenuation value of the link between the transmitter 1 and the receiver 1 for the communication period t; the function w represents the performance criterion considered (for example w is the sum flow function defined by equation (1)).

A disadvantage of this method is that an ad-hoc choice of the power control function generally leads, for a given performance criterion, to a sub-optimality in terms of average performance that is to say measured by the criterion of equation (4).

A telecommunication network operator generally gives more importance or more speed to a given user based on, for example, the QoS that is guaranteed. Noting <¾ the weight that the operator gives to the user k, the weighted version of (1) is given by the equation: w (0n, ..., 9κκ · Pi- -, VK) = Σfc = i ^a k log (l + RSIB _fc (0i _fc> ..., g _Kk , p _lt ..., p _K )) (5) with a _k ≥ 0. When the weighting weight a _k is large, the user k receives more importance and the power control tends to favor his individual flow. Equation (1) is a special case of (5) when the weights a _k are taken as being all equal to 1. The threshold functions given by (3) for the performance criterion (5) can induce a significant loss of performance. Thus, if the chosen performance criterion allows fairness between users, the threshold method can be very suboptimal.

[LT2011] defines energy efficiency as a ratio of profit (net transmission rate) to cost (transmission power):

w (fu, ..., g _KK , Pi, ..., PK) = Σfe = i (6)

pk

where 0 </ (x) <1 is an increasing function typically representing the probability of packet success rate ("packet success rate"). The quantity R _k is fixed and represents the individual raw flow rate of the user k. This rate is in bits per second and depends on the choice of modulation and coding scheme (MCS). The quantity R _k f (RSlB _k (g _lk , ..., g _Kk , p, ..., p _K )) represents the benefit of the communication, this benefit being all the greater as the RSIB is large ( but saturates with the value R _k ). The power p _k represents the cost of communication and is expressed in Joule per second (Watt). The physical unit of w is therefore the bit by Joule, a unit that measures the energy efficiency. The threshold functions of type (3) are very sub-optimal for the energy performance criterion (6).

Presentation of the invention

The invention proposes a power control technique making it possible to improve the overall performance of a telecommunication system with K transmitters and K receivers compared with known methods.

Thus, the subject of the invention is a power control method distributed between K transmitters each having T _k transmitting antennas intended to communicate respectively with K receivers via communication links described between the transmitter j and the receiver i by a set of gains G _j i of multiple input and output channels (MIMO) of direct links when j = i and interfering links when j ≠ i, i G {1, ..., K], j G {1,. .., K], K> 1. More precisely, the links G ^ with j G {1, - + 1, ..., K) interfere with the link of the useful signal G _a at the receiver i. The covariance matrix of dimension T _k × T _k of the signal emitted by a transmitter k is determined by a conditional probability distribution Qk (Pk

representative of the power control knowing the observation Y _k available to the transmitter k channel gains, k G {1, ..., K). A global metric W (Q _lt Q _K ) is expressed as:. . , G _KK) Y (Y _t,..., _Υ κ _lt GI, G _KK) GKK, P * PI)

The global metric is therefore expressed as a sum over all possible values of the direct and interfering channel gains, over all possible power values, and over all possible values of the observations available to the transmitters of the channel gains. The number of possible discrete levels determines the complexity of the proposed power control algorithm at first order. However, it has been shown that the process remains very robust for prior quantifications of links, powers and coarse observations. w (G _{11 (...} , G ^, P _{1 (...} , _PK ) is an instantaneous metric function that responds to a global quality of service for the K transmitters, p (G _{11 (...} , G ^) is a statistic of the set of channel gains and / (Y _i , ..., Y _jf | G _{11 (...} , G _KK ) is a statistic of the set of estimates Y _k of conditioned gains To the knowledge of all links, each issuer has:

of the statistical knowledge γ (Κ _{1 (} ..., Υκ \ (* ιι _> - _> GRK) of the set of observations conditioned on the knowledge of all the links,

of the statistical knowledge p (G _{11 (...} , G ^) of the set of channel gains, of the instantaneous metric function w (G _{11 (...} , G ^, P _{1 (} . · Ρ ^).

The process according to the invention

initializes for k = 1 to K, the conditional probability distribution representative of the power control of the transmitter k, initialized function noted and

iteratively, with i an iteration index, i = 0 to N-1:

and successively for each transmitter k = 1 to K:

- determines the conditional probability distribution representative of the power control of the transmitter k as being that which maximizes the average global metric considering the conditional probability distributions

Q [ ^{Î + 1} "·, Qk-ι Qk + v"'QK ^ representative of the power control of the other transmitters previously obtained as fixed.

According to the method, the power emitted at a time t by the transmitter k is given by the conditional probability distribution, determined at the end of the iterative process, knowing a realization of the observations Y _fe at this instant t.

There are known techniques allowing a transmitter j to know the estimate of the direct channel gain G _Û and channel gains interfering Gj _j its receiver i, j ≠ i. For example, the transmitters exchange their estimated channel gains during an initialization phase.

The coefficients G _Û, Gj _j can model both the attenuation associated with the spread coefficients (path loss) as the coefficients of weakness associated with slow fading (shadowing) or fast (fast fading). There are also known techniques for determining joint probabilities. In particular, the method described in [LVV2013] makes it possible to estimate the joint probabilities from realizations of the gains of direct and interfering channels. Indeed, it is much easier (robust and efficient) to go back to the joint probabilities of the radio link coefficients than to know the overall state of the channel at a time t.

According to one embodiment, the power emitted by the transmitter k depends on a coordination key U, the global metric WQ, Q _K ) is then expressed as:

with Qy (U) the probability distribution used to generate the key U.

According to one embodiment, the instantaneous metric function w (G _{11 (...} , G ₁ , P _{1 (} .., Ρ ·)) is the sum on the K transmitters of the ratio between a net transmission rate on an emitted power.

This metric makes it possible to measure an energy efficiency of the system with K transmitters and K receivers.

According to one embodiment, the observation Y _FE for the transmitter k is equal to an estimate G _kk of the direct link.

In one embodiment, the channel gains follow an exponential distribution.

The invention further relates to a telecommunication system comprising K transmitters and K receivers. Each transmitter participating in the implementation of the power control method according to the invention. The K transmitters each have T _k transmit antennas and are respectively in communication with the K receivers via communication links described between the transmitter j and the receiver i by a set of gains of channels with multiple inputs and outputs (MIMO). direct links when j = i and interfering bonds when j ≠ i, i G {1, ..., K], j G {1, ..., K], K> 1. The size covariance matrix T _k × T _k of the signal emitted by the transmitter k is determined by a conditional probability distribution Q _k (P _k \ Y _k ) representative of the power control knowing the observation Y _k available at the time. emitter k channel gains, k G {1, ..., K). The observation Y _k , as the use of the bold character indicates, can gather a discrete set of scalar, vectorial or matrix observations.

The transmitters have the knowledge of a global metric WQ,. . . , Q _K ) expressed as:

Qk (.Pk \ Yk)) w (Gii Gra. Pi P "either as a sum over all possible values of direct and interfering channel gains, on all possible power values and on all possible values observations available to the transmitters of the channel gains with w (G _{11 (...} , G ₁ , P _{1 (...} , P _K ) an instantaneous metric function responding to a global quality of service for the K transmitters, with p (G _L,..., G _KK) a statistics of all the channel gains and Y (Y _{1 I...,} _K Y \ CI _{11 I...} _I CI _KK) a statistical of set of Y _K estimates of the gains conditioned to the knowledge of the set of links Each issuer has:

of the statistical knowledge (Y _lt ..., Y _K \ G _llt ..., G _KK ) of all the observations conditioned to the knowledge of all the links,

- the statistical knowledge p (G _{11 (...} , G ^) of the set of channel gains,

the instant metric function w (G _{11 (...} , G ^, P _{1 (...} , Ρ ^ ·).

Each transmitter includes a processor and an amplifier such as:

the processor initializes for k = 1 to K, the conditional probability distribution representative of the power control of the transmitter k, initialized function noted and iteratively, with i an iteration index, i = 0 to N-1:

and successively for k = 1 to K:

the processor determines the conditional probability distribution Q ^ ⁺¹ ^ representative of the power control as being that which maximizes the average overall metric by

Qk + v "'· Qt representative of the power control of other transmitters previously obtained as fixed.

The transmitter amplifier k emits at a time t a signal at the power p _k given by the conditional probability distribution determined at the end of the iterative process, knowing a realization of the observations Y _fe at this instant t.

According to a preferred implementation, the steps of the method according to the invention of power control implemented by an emitter are determined by the instructions of a program incorporated in an electronic circuit such as a chip. The transmitter is part of a communication entity (base station, access point, etc.). The power control method according to the invention can just as easily be implemented when this program is loaded into a calculation such a processor or equivalent whose operation is then controlled by the execution of the program.

Accordingly, the invention also applies to a computer program, including a computer program on or in an information carrier, adapted to implement the invention. This program can use any programming language, and be in the form of source code, object code, or intermediate code between source code and object code such as in a partially compiled form, or in any other form desirable to implement a method according to the invention. The program according to the invention can in particular be downloaded to an Internet-type network and transmitted in the form of a succession of binary data.

The information carrier may be any device capable of storing the program.

For example, the medium may comprise storage means, such as a ROM, for example a CD ROM, a USB key or a microelectronic circuit ROM, or a magnetic recording means, by a hard disk.

Alternatively, the information carrier may be an integrated circuit in which the program is incorporated, the circuit being adapted to execute or to be used in the execution of the method in question.

List of Figures

Other features and advantages of the invention will become apparent from the following description of particular examples made with reference to appended figures given by way of non-limiting examples.

FIG. 1 is a schematic representation of the communication links between K transmitters and K receivers, these links being described by gains of direct transmission channels when j = i and gains μ of interfering transmission channels when j ≠ i between the emitter j and the receiver i, ie [i K], I [i K] -,

FIG. 2 is a diagram of the simplified structure of a transmitter intended for a system implementing a method according to the invention.

Figure 3 illustrates results from simulations for a system with K = 2.

Description of an embodiment of the invention

The system can be shown schematically in FIG. 1. In the downstream direction, the K transmitters are for example those of K access points API, AP2 and APK and the K receivers are those of K stations STA1, STA2 and STAK. In ascending order, the situation is reversed. The communication links are symbolized by lines between transmitters and receivers, they are supposed to be independent of each other. Each transmitter and receiver can be equipped with one or more antennas. In a MIMO system, each transmitter has T _k transmit antennas and each transmitter has R _k receiving antennas. The gain of the link kk is therefore a matrix G _kk . Thus, the links are described between the transmitter j and the receiver i by a set of gains G _j i channels with multiple inputs and outputs. The links are called direct when j = i and the links are said to be interfering when j ≠ i, i G {1, ..., K], j G {1, ..., K], K> 1. P _fe represents the covariance matrix of the signal emitted by the transmitter k: P _fe = E (x _¾ x ^). The proposed invention thus covers the case of multiple input multiple output (MIMO) links as well as the multi-band MIMO case which corresponds to the case where P _fe is diagonal block, each block being of dimension T _k T _k . Each block, for a given band, expresses the pre-coding V _k which will link the T _k antennas and the T _k power levels (P _x , ..., P _r ) of the spatially multiplexed data streams at its input and can be written V _fe diag (P ₁ , ..., P _T ) V ^* _k where the operator ^* is the conjugated transpose. In practice the pre-coding matrices belong to a discrete dictionary (codebook in the English terminology) and the power values to a finite set of possible values (including the null value), it follows that the matrices P _fe belong to a finite discrete set of matrices (or live in a discrete set). The single-band and mono-antenna case (T _k = 1) corresponds to the particular case where P _fe is reduced to a scalar.

For any k, each transmitter APk has the observation Y _k gains G _jk channels, k G {1, ..., K). The acquisition by the transmitter APk of the observation of the channel gains for all j G {1, ..., K] is performed according to known methods for estimating channel gains.

The size covariance matrix T _k × T _k of the signal transmitted by a transmitter k is determined by a conditional probability distribution Q _k (P _k \ Y _k ) representative of the power control knowing the observation Y _k .

The invention is based on a function w which represents a performance criterion to be maximized on each block of data to be transmitted by an issuer. The value of w depends on the realizations of the gains or qualities of the links g _jk and the transmission power levels, which structures w as follows in the particular case of a system with two transmitters and two receivers:

^{W '} (01 022. Pl.P2) ^→ W (9ll.012.021.022.Pl.Vz)

where Q _jk (respectively T _k ) is the set in which lives g _jk (respectively p _k ). The invention considers discrete and finite sets. Optionally, the method includes an initial quantization procedure. The size of these sets is chosen so as to limit the computation complexity of the proposed method and to obtain a certain robustness in the face of estimation or measurement errors.

The average performance criterion taken into account by the process is given by the following formula:

W _T = iΣ [ _{= 1} w (G _n (t) G _KK (t), PiCYiC) P * (Y * (0)) (

The notation P _fe (Y _fe (t)) means that the transmitter k chooses on each time slot indexed by t its power matrix P _fe as a function of the observation M _k (t) available for this interval. P _k (Y _k (t)) can also be written P _fe = f _k ( _k (t)), where f _k is the power function to be determined. Function : (G (£) G _KK (t), PiCYi Ct)) P * (Y _K (£)) (8) is an instantaneous metric function corresponding to an overall quality of service for the K transmitters.

The method according to the invention considers an asymptotic W approximation of the criterion W _T given by the average performance relation (7) based on the properties of ergodicity and stationarity of the joint probabilities. This performance criterion W is a statistical average of the instant metric function w given by the expression (8). The expression of this global metric W (Q _lt Q _K ) is the following:

This known global metric of each transmitter is a sum on all possible values of the direct and interfering channel gains, on all the possible power values and on all the possible values of the observations available to the transmitters of the channel gains. The relation (9) is such that:

Y (Y ₁ , ..., Y _K \ G ₁₁ , ..., G _KK ) is a statistic of the set of estimates Y _K of the gains conditioned to the knowledge of all the links. This statistic expresses the degree of imperfection or partiality of knowledge of the transmitter k.

Qk (Pk \ Yk) represents the power control function at the transmitter k, it is the conditional probability that the transmitter k uses the power matrix P _k knowing its observation Y _k . For example, Q _k is the probability that the power level p _k is selected knowing that the quality of the link kk has the value g _kk . The conditional probability Q _k includes all the functions of Q _kk in T _k as special cases, that is, any power function of the form y = g (x). Or expressed otherwise, the conditional probability distribution Q _k (p _k \ y _k) can be written as Qk IPK lk ⁼ O (Pk ~ giykî) which ^is ^a probability distribution that takes the value 1 for p _k = g ( y _k ) and 0 everywhere else.

The advantage of this technical choice is twofold: to offer a potential gain in performance compared to the state of the art which exploits only power control functions and to simplify the numerical optimization procedures by considering variables that belong to compact and convex sets.

p (G _L , ..., G _KK ) is the joint probability density, it is a CDI Channel Distribution Information known for all channel gains. Independence (this independence can be used as a simplifying assumption in the absence of correlation data) between the links allows to determine the joint distribution (or joint probabilities) from the statistics of all channel gains : κ κ

piG ^, ..., G _KK ) = [[pij (Gij)

i = 1; = 1

According to the method, each transmitter k initializes the conditional probability distribution representative of its power control:

can be arbitrary or one of the best known power control functions. The initial functions are denoted k = 1 to K.

N is a parameter.

Iteratively, with i an iteration index, i = 0 to N-1 and, at each iteration successively for each transmitter k = 1 to K, the method determines the conditional probability distribution representative of the power control of the emitter k as the one that maximizes the mean global metric by considering the conditional probability distributions

Q [ ^{Î + 1} "·, Qk- 'Qk + v"' QK ^ representative of the power control of the other transmitters previously obtained as fixed.

The power emitted at a moment by the emitter k is then given by the conditional probability distribution, determined at the end of the iterative process, knowing a realization of the observations Y _fe at this instant t.

According to one embodiment, each transmitter has knowledge of a sequence of matrices called a coordination key. This key is a sequence · · ·, U (T) of realizations of a random matrix U exchanged during an initialization phase. An example of a sequence U (1),. , U (7 ") is as follows: According to an illustrative example, the system comprises two transmitter-receiver pairs During an initialization phase, T draws of a binary random variable are carried out: (U (1), U (T)) = (0010111001 ... 0010101) and this sequence or key is revealed to the transmitters During the process according to the invention, the transmitter 1 transmits if U (t) is equal to one and the transmitter 2 emits if U (t) is zero, in this case the sequence (U (1), U (T)) represents a time-sharing policy between transmitters, when T becomes large, the number one of the sequence tends to the exact probability that the random variable is 1. In this case, the emitters have a priori knowledge of Qi (Pi | Yi, U = 0) = δ (Ρ ₁ - 0) and Q ₂ (P2 | Y2 _" U = 1) = δ (Ρ ₂ - 0) Moreover, Qu (l) and Qu (0) respectively represent the percentages of occurrence of a and of zero of the sequence (U (1), U (T)) = (0010111001 ... 0010101).

Relationship (7) is replaced by:

W _T = ± Σ [ _{= 1} w (G _n (t) G ^ C, Pi CYi C, UC) Ptf (Y * (.U (t))) (7a)

The notation P _fe (Y _fe (t), U (t)) means that the transmitter k chooses on each time interval (time slot) indexed by t its power matrix P _fe according to what it knows: the observation Y _fe (t) available for this interval and the value U (t) of coordination key for this interval. P _FE (Y _fe (t), U (t)) can also be written P _fe = f _k ( _k (t), U (t)), where f _k is the power function to be determined. Relationship (8) is replaced by:

w (G (£) G _KK (t), P ₁ (Y ₁ (_t) U _s (t)) P _K _(K Y (t), U (t))) (8a)

Relationship (9) is replaced by:

ΣG ₁₁ , ..., G _KK , P ₁ , ..., P _K , V, Y ₁ , ..., Y _k Qu (U) p (G _lt , G _KK ) Y (Y _t , YK - | G _{11 (...} , G ^) (9bis)

G ^ _f , Pi, ■■■, Pi _f )

Qy (U) is the statistical distribution of the coordination key.

Q _fe (P _fe | F _fe , U) = (V _k - P _FE (Y _fe , U)) is the conditional probability that the transmitter k uses a certain power matrix knowing its observation Y _k and knowing the key U .

The method is detailed below in the case of a system with K = 3. In addition, the links are supposed to follow a Rayleigh statistic. The quality of each link is then given by its module squared. Transmitters and receivers are for example equipped each with a single antenna. is then a noted scalar and gij = 1.1 ² . Gains following according to Example an exponential distribution of the form Pjk igjk) ⁼ _E _^, ^ ^ex P ^(~ Ε (^ ^¾)) ^ f ° ^has ^nct i ⁿ ° Pjk ^is ^a probability density gj _k and the notation E indicates the statistical expectation operator. This distribution depends on a single parameter that is sufficient to estimate to go back to the distribution function. E (<7 _; - _fe ) is the average power of the link that can be measured from the system reference signals that occur especially when selecting a cell ("handover").

The metric to be optimized is, for example, the energy efficiency: w (g11, gl2, gl3-g21-g22, g23-g31-g32, g33-P1-Vl, Ps)

(RSIB ₁ (g ₁₁ , g ₂₁ , g ₃₁ , p _{1 (} p ₂ , p ₃ )) (RSIB ₂ (g ₁₂ , g ₂₂ , g ₃₂ , p _{1 (} p ₂ , p ₃ ))

pi

(RSIB ₃ (g ₁₃ , g ₂₃ , g ₃₃ , p _{1 (} p ₂ , p ₃ ))

+

Ps

where 0 <f (x) <1 is a function that typically represents the probability of packet success rate. Subsequently, the function considered is of type f (x) = exp ^ with c> 0.

Thus when K = 3, the respective initial functions of the emitters are Q ^ ° and Q ^. The method then proceeds iteratively, with i an iteration index, i = 0 to N-1. For each iteration, and successively for each transmitter k = 1 to K, the method determines the conditional probability distribution Q _k ⁺¹ ^ representative of the power control of the emitter k as the one that maximizes the mean global metric by considering the conditional probability distributions

representative of the power control of other transmitters previously obtained as fixed.

Thus, when K = 3, the l ^st iteration, i = 0, the method sequentially determines the conditional probability distributions Qi, Q ₂ ^and Q ₃ ■

The conditional probability distribution Q _i (1) ^is determined by considering the conditional probability distributions representative of the power controls of the two other emitters previously obtained as fixed, these values are the initial functions Q ₂ ° Q ^ - The relation (9) then becomes:

WQQ Q? Q∞) =

Σ5ll Pi

^X Σgl2, gl3, g21, g22,, g23, g31, g32,, g33, P2, P3 P (§11 '"""'33) ^X (10)

The links being independent:

P (gll .-- -. G33) =

Pll (gll) Pl2 (gl2) Pl3 (GL3) P2L (G2L) P22 (g22) P23 (g23) P3l (G3L) P32 (g3 ₂₎ P33 (g33)

The performance criterion function w (g ₁₂ , g ₁₃ , g ₂₁ , g _22i , g ₂₃ , g ₃₁ , g _32i , g ₃₃ , p ₂ , p ₃ ) is known either from the knowledge of its expression, by example the relation (4), or by the knowledge of an abacus (look-up table) which gives the values of the function.

Thus, the expression:

. Σgl2.gl3.g21.g22 g23.g31.g32, .g33.P2.P3 fell '"-'33) ^X

1 (gii-Pi) = _{n (0} ), ()

Qi (P2

is known.

The sum to be maximized is written:

The maximization of W (Q ^ Q ₂ ° amounts to maximizing for each coefficient g _l the relation:

OrΣ _Pl Q \ (ilfif) = 1 by definition.

so born

Ά ^ ι ^{, ρ} Γ) with ρ ^αχ e argmax _Pi w ¹ (g ₁₁ , _Pl ), and argmax _Pi w ¹ (g ₁₁ ^,. ) designating the set of power values p- ^ that maximize the function w ¹ knowing g _l .

The maximization of W (Q ^ Q ₂ ° \ is obtained according to the method by choosing a conditional probability which is reduced to a function:

Qp'foltfu) = ₍₁₃₎

wire

Then, the conditional probability distribution Q is determined by considering the conditional probability distributions representative of the power control of the two other emitter wires previously obtained, these values being respectively fixed at the value Q obtained previously and at the initial function.

The relation (9) then becomes:

WÎQ∞ Q∞ Q∞) =

(1)

Σ5 ₂₂ , P ₂ ¾ (2ΐ # 22) ^X Σg ₁₁ g ₁₂ , g _l3 .g ₂₁ .g ₂₃ .g ₃₁ .g ₃₂ , .g ₃₃ .P _l .P ₃ P (gl 1 '"""'§33) ^X (14)

Ql ⁽¹⁾ (P1 # 1ΐ) (? 30 ⁾ (Ρ31033) w (gu, gl2-gl3-21, gl3> gsig2, - gS3-P1. Ps)

The expression:

y, Σgllgl2.gl3.g21.g23.g31.g32 g33.Pl.P3

^X ....

W (g ₂₂ , P ₂ ) = ₍₁₎ (15)

Q _l (Pl

is known.

The sum to be maximized is written:

WIQ .Q .QW) = Σ ₅₂₂ (Σ <# ^} (p ₂ | 0 ₂₂ ) w ² (g ₂₂ , p ₂ )) (16)

Maximization of

is to maximize for each coefficient c / ₂₂ the relation:

Σ _P2 Q ^ ⁾ (p ₂ | ^ ₂ ² (g ₂₂ , p ₂ )

OrΣ _P2

¹ P = ^y definition.

The relation (16) is therefore bounded since:

with ρ ^αχ e argmaXp ₂ w ² (g ₂₂ , p ₂ ), and argmax _p2 w ² (c / ₂₂ ,.) designating the set of power values p ₂ that maximize the function w ² knowing c / ₂₂ .

Maximization of

is obtained according to the method by choosing a conditional probability which is reduced to a function:

_/] (!) ₍ · "I" _ | lsip ₂ eargmax _p w ² (g ₂₂ , p ₂ ) _n

Q ₂ (P ₂ I ^ ₂₂ ) - 1 _Osin ^p _on ^1?) (1)

Then, the conditional probability distribution Q ₃ is determined by considering the conditional probability distributions representative of the power control of the two other emitters previously obtained, these values being respectively fixed at the values and Q ₂ previously obtained.

The relation (9) then becomes:

Σ533, P3

^X Σgngl2, gl3.g21.g22.g23.g31.g32.P l.P2 P (§11 '"""' §33) ^X (18)

(Pl lfi ^f ll) Q ₂ ¹⁾ (2 L022) w (gu, gi2, gl3- g21- G22 g23- gsi- GS2 -. Pl P2)

The expression:

is known.

to maximize is written: 3)) (20)

t to maximize for each coefficient g ₃₃ the relation:

Σp ₃ Q3 ¹⁾ (P3 lfi ^f 3 ³ (g ₃ 3, p ₃ )

OrΣ _P3

¹ P = ^y definition.

The relation (20) is therefore bounded since:

with ρ ^αχ e argmaXp ₃ w ³ (g ₃₃ , p ₃ ), and argmax _p3 w ³ (c / ₃₃ ,) denoting the set of power values p ₃ that maximize the function w ³ knowing c / ₃₃ .

fi) fi) fi)

The maximization of, ¾, Q ₃ ) is obtained according to the method by choosing a conditional probability which is reduced to a function:

in the ^era of the iteration, the method has determined the functions Q _i (Pi l <7ii)

and

The process proceeds to the next iteration and successively determines the distributions of

(2) (2) (2)

conditional probability, ¾ and Q ₃ in a manner similar to the determination of the distributions il) il) il) il)

of conditional probability Q _i> Q and Q ₃ made during the previous iteration. At the end of the last iteration, i = Nl, or if an iteration stop criterion is satisfied, then the method has determined the conditional probability distributions Q ₁ = or Q ^M Q ₂ = or and Q ₃ = or Q ^ ^M with M <N, i = M-1 being the index of iteration during which the stopping criterion is satisfied. These distributions are: Q _k (p _k

The power emitted p _k at a time t by the transmitter k is therefore given by the conditional probability distribution Q _k , determined at the end of the iterative process, knowing a realization g _kk of the observations g _kk at this instant t: p _k = f _k (g _kk ).

Figure 3 illustrates results from simulations for a system with K = 2. The simulation parameters are: σ ² = 1 for the variance of the reception noise; c = 1;

= 0.75, Ε (# ₁₂ ) = 0.20, E (fu ₂₁ ) = 0.20, E (g ₂₂ ) = 1.25; Q _jk = {0.1.0.22.0.34,. . . , 9.82,9.94} (arithmetic sequence of reason 0.12) for the four links present; the probabilities of each element of its alphabet follow a decreasing exponential law of type P _jk (g _jk ) = _E ^ ^ exp ^ ^k ; the power level alphabets as [dB] = T ₂ [dB] = {0.5,1,. . . , 30} U {-∞} .- ∞ amounts to considering a null power.

FIG. 3 successively represents the evolution of the power control functions

Ρι 0? Ιι) ^and P ₂ Q7 ₂₂₎ ^during iterations i = £ = 1 to 5. In comparison with the prior art which calls for channel inversion type power control functions i (<7n ) =, the invention produces non-trivial functions showing a threshold whose value is automatically adjusted during iterations and the decay is slower than-. This results in a reduction of energy consumed by a factor greater than 10.

The simplified structure of an emitter EM intended for a system implementing a power control method according to the invention is described in connection with FIG. 2. The emitter is a part of a WiFi access point denoted APk. , a base station of a cellular network, a femto cell, etc. of a SYS telecommunication system such as that shown in Figure 1. The transmitter is in communication with a STAk receiver of the system. The communication links are described by gains gji of direct transmission channels when j = i and interfering transmission channel gains when j ≠ i between the transmitter j and the receiver i.

Such an emitter EM comprises a memory 100 comprising a RAM buffer, a microprocessor μΡ 101 driven by the computer program 102 implementing the power control method according to the invention and an amplifier 103.

At initialization, the code instructions of the computer program 102 are for example loaded into the RAM before being executed by the microprocessor 101. The microprocessor 101 implements the steps of the power control method described. previously, according to the instructions of the computer program 102, for outputting the amplifier 103 a signal at the determined power. The microprocessor 101 uses the observation Y _K of the channel gains as input. The microprocessor 101 is aware of the global metric W (Q _LT Q _K ) and has:

- of the statistical knowledge y (Fi, ..., YK l ^. ..., G _KK ) of the set of observations conditioned to the knowledge of all the links,

When the microprocessor 101 executes the code instructions of the computer program 102, the microprocessor of the emitter EM:

initializes the conditional probability distribution representative of the power control, an initialized function noted for k = 1 to K, and

iteratively, with i an iteration index, i = 0 to N-1:

and successively for k = 1 to K:

Qi ⁺¹ ", Qk-i Qk + v"'QK ^ representative of the power control of other transmitters previously obtained as fixed.

The amplifier 103 emits at a time t the telecommunication signal at the power p _k given by the conditional probability distribution determined at the end of the iterative process, knowing a realization of the observations Y _k at this instant t.

References :

[KLGS2015]: P. de Kerret, S. Lasaulce, D. Gesbert., And U. Salim, "Best-Response Team Power Control for the Local CSI Interference Channel wifh," IEEE International Conference on Communications (ICC) 2015, London, UK

[LT2011]: S. Lasaulce and H. Tembine, "Game Theory and Learning for Wireless Networks: Fundamentals and Applications", Academy Press, Elsevier, page 186, definition 177, Oct. 2011, ISBN 978-0123846983.

[LVV2013]: patent application WO2015 / 079174

Claims

A power control method (1) distributed between K transmitters each having T _k transmit antennas intended to communicate respectively with K receivers via communication links described between the transmitter j and the receiver i by a set of gains G _j i of multiple input and output channels (MIMO) of direct links when j = i and interfering links when j ≠ i, i G {1, ..., K], j £ {l, ..., K }, K> 1, the dimension covariance matrix T _k x T _k of the signal emitted by the transmitter k being determined by a conditional probability distribution Q _k (P _k \ Y _k ) representative of the power control knowing the observation Y _k available to the transmitter k channel gains, k G {1, ..., K], a global metric W (Q, ..., Q _K ) being expressed in the form:

either in the form of a sum over all possible values of the direct and interfering channel gains, on all possible power values and on all possible values of the observations available to the transmitters of the channel gains with w (G _{11 (} . ., G ^, P _{1 (...} , P _K ) an instant metric function responding to a global quality of service for the K transmitters, with p (G _{11 (...} , G ^) a statistic of set of channel gains and with Y (Y ₁ , ..., Y _K \ G ₁₁ , ..., G _KK ) a statistic of the set of estimates Y _K of the gains conditioned to the knowledge of the set links, each transmitter having:

of the statistical knowledge γ (Κ _{1 (} ..., Y _K \ G _l , ..., G _KK ) of the set of observations conditioned on the knowledge of all the links,

of the statistical knowledge p (G _{11 (...} , G ^) of the set of channel gains, of the instantaneous metric function w (G _{11 (...} , G ^, P _{1 (} . · Ρ ^)

characterized in that the method

iteratively, with i an iteration index, i = 0 to N-1:

and successively for each transmitter k = 1 to K:

determines the conditional probability distribution Q _k representative of the power control of the transmitter k as being that which maximizes the metric global average by considering conditional probability distributions

Q _i ⁺¹ "·, Qk-> Qk + v"'QK ^ representative of the power control of the other transmitters previously obtained as fixed,

the power emitted at a time t by the transmitter k being given by the conditional probability distribution, determined at the end of the iterative process, knowing a realization of the observations Y _FE at this instant t.

2. The power control method (1) according to claim 1, wherein the power emitted by the transmitter k depends on a coordination key U, the global metric W (Q ₁ , ..., Q _K ) s'. expressing in the form:

with Qu (U) the probability distribution used to generate the key U.

A power control method (1) according to claim 1, wherein the instantaneous metric function (w (G _{11 (...} , G ₁ , P _{1 (} .., Ρ)) is the sum on the K transmitters of the ratio between a net transmission rate on an emitted power.

4. The power control method (1) according to claim 1, wherein for the transmitter k the observation Y _FE comprises an estimate G _KK of the direct link.

5. The power control method (1) according to claim 1 wherein the transmitter k only knows the observation Y _FE which is equal to an estimated G _kk of the direct link, it comes

6. The power control method (1) according to claim 1, wherein for the transmitter k the observation Y _FE comprises the gain G _KK of the channel of the direct link.

7. The power control method (1) according to claim 1, wherein the transmitter k only knows the observation Y _FE which is equal to the gain G _KK of the channel of the direct link, there comes y (Yi Wu G) = I.

The power control method (1) of claim 1 wherein the channel gains follow an exponential distribution.

9. A system for implementing a power control method with K transmitters and K receivers, the K transmitters each having T _k transmit antennas and being in communication respectively with the K receivers via communication links described between the transmitter j and receiver i by a set of gains G _j i of multiple input and output channels (MIMO) of direct links when j = i and interfering links when j ≠ i, i G {1, ..., K ), G {1, ..., K), K> 1, the dimension covariance matrix T _k × T _k of the signal emitted by the transmitter k being determined by a conditional probability distribution Qk (Pk

representative of the power control knowing the observation Y _k available to the transmitter k channel gains, k G {1, ..., K), a global metric WQ, Q _K ) being expressed in the form:

I p (G, ..., G _KK ) Y (Y _T , ..., Υ _Κ IG _LT , G _KK ) G, Pj Pif)

either in the form of a sum over all possible values of the direct and interfering channel gains, on all possible power values and on all possible values of the observations available to the transmitters of the channel gains with w (G _{11 (} . ., G ^, P _{1 (} .., Ρ ^ ·) an instantaneous metric function responding to a global quality of service for the K transmitters, with p (G _{11 (...} , G ^) a statistic of the set of channel gains and with Y (Y ₁ , ..., Y _K \ G ₁₁ , ..., G _KK ) a statistic of the set of estimates Y _K of the gains conditioned to the knowledge of the set of links, each transmitter having:

- statistical knowledge (Y _lt ..., Υκ \ (* ιι _> - _> (* κκ of the set of observations conditioned on the knowledge of all the links,

of the statistical knowledge p (G _{11 (...} , G ^) of the set of channel gains, of the instantaneous metric function w (G _{11 (...} , G ^, P _{1 (} . Ρ _# ·),

characterized in that each transmitter comprises a processor and an amplifier such as:

the processor initializes for k = 1 to K, the conditional probability distribution representative of the power control of the transmitter k, the initialized function noted and iteratively, with i an iteration index, i = 0 to N-1 :

and successively for k = 1 to K:

the processor determines the conditional probability distribution Q _k representative of the power control as being that which maximizes the overall average metric by considering conditional probability distributions

Q _k + i '"' · · Q _t representative of the power control of the other transmitters previously obtained as fixed,

and the transmitter amplifier k emits at a time t a signal at the power p _k given by the conditional probability distribution determined at the end of the iterative process, knowing a realization of the observations Y _fe at this instant t.

10. Computer program on an information medium, said program comprising program instructions adapted to the implementation of a power control method of K transmitters according to any one of claims 1 to 9, when said program is loaded and executed in K transmitters for implementing the power control method.

An information carrier having program instructions adapted to implement a power control method according to any one of claims 1 to 9, when said program is loaded and executed in K transmitters for implementing the power control process.