Method for distributing a load in a multi radio access technology heterogeneous network

Abstract

A method for distributing the traffic load in a multi radio access technology heterogeneous network, the network including macrocells operating in a first sub-6 GHz band, and minicells that can operate in the sub-6 GHz band and in a millimeter band. The distribution of the traffic is carried out with an association strategy that calls upon, on the first hand, a first bias (QT) in order to favour the association with the base stations of the minicells/macrocells and a second bias (QR) in order to favour the use of the millimeter/sub-6 GHz band when the terminal is associated with a base station SBS of a minicell.

Description

TECHNICAL FIELD

This invention generally relates to the field of multi radio access technology heterogeneous cellular networks, and more particularly a method for distributing the traffic load in these networks.

PRIOR ART

Heterogeneous cellular telecommunication networks or HetNets represent one of the most promising solutions for the development of the next generation of mobile telephones (5G). Generally, a heterogeneous cellular network is comprised of several tiers of cells: macrocells and small cells such as femtocells and picocells. A multi technology or multi-RAT cellular network (multi Radio Access Technology) is comprised of networks using different radio access technologies, for example Wi-Fi and 3G, with these networks able to use different frequency bands.

We shall consider in what follows multi radio access technology heterogeneous cellular networks (multi-RAT HetNets). A representative example of such a network is comprised of two layers of cells: a first layer of cells comprises macro-cells operating in the hyperfrequency range below 6 GHz (band referred to hereinafter as sub-6 GHz). The macro-cells are served by base stations, designated by MBSs (Macro Base Stations). To this first layer of cells is added a second layer comprised of small cells operating both in the sub-6 GHz range and in the millimeter range (25 GHz-300 GHz). The small cells are served by base stations designated by multi-RAT SBSs (multi Radio Access Technology Small Base Stations).

Although base stations MBSs of the conventional network provide a continuous coverage to users, the multi-RAT base stations SBSs make it possible to provide high speeds by jointly exploiting the sub-6 GHz and millimeter bands.

In the conventional HetNets networks (i.e. single technology), use is made of offloading mechanisms from the base stations MBSs of the macrocells to the base stations SBSs of small cells. Such an offloading mechanism, known under the acronym of CRE (Cell Range Expansion), consists in adding a positive bias to the power of the signal received from the base station SBS before comparing it with the power of the signal received by the base station MBS. Thus, for an equal receiving power, the mobile terminal is associated with a base station SBS rather than with a base station MBS. It has been able to be shown that, in the conventional HetNets networks, the aforementioned mechanism leads on the average to a degradation of the signal to noise and interference ratio or SNIR (Signal to Noise and Interference Ratio) at the terminal side.

In the multi-RAT HetNets networks, the strategy of distributing the traffic load between MBSs and SBSs is more complex. As such for example, when the stations SBSs operate in a band of the sub-6 GHz range and in the millimeter band, it is necessary to take account of the path loss and of the sensitivity to the situations of blockage in the millimeter band. In certain cases it has been able to be shown that the offloading mechanism made it possible to improve the SINR, since the high path loss and the directivity of the antennas of the stations SBSs reduce the level of interference received by the terminal.

The purpose of this invention is to propose a method for distributing loads in a multi radio access technology heterogeneous cellular network, in particular a network in which the base stations (SBSs) of the small cells operate both in a band of the sub-6 GHz range and in the millimeter band, said method making it possible to select the level of association (MBS or SBS) and the radio access technology (sub-6 GHz band from 0.7 to 6 GHz or millimeter band from 25 to 300 GHz) in such a way as to maximise the level of SINR on the terminals.

DISCLOSURE OF THE INVENTION

This invention is defined by a method for distributing traffic loads in a multi radio access technology heterogeneous network, said network comprising macrocells served by base stations of a first tier of the network, referred to as MBSs, operating in a first frequency band, and minicells served by second base stations of a second tier of the network, referred to as SBS, suitable for operating in said first frequency band and in a second frequency band, separate from the first frequency band, wherein

• • the coverage parameters of said network are acquired or measured;
  • from the coverage parameters of said network, an optimum pair of bias values (Q_T^opt,Q_R^opt) is determined that maximises the coverage probability, P_c(γ), defined as the probability that the signal to noise and interference ratio on a terminal is on the average greater than a predetermined threshold (γ) in the deployment zone of said network;
  • a base station MBS is associated with the terminal, if the strongest power received from a base station MBS in the first frequency band is greater, than the strongest power received from a station SBS in this same frequency band, corrected by the first bias value (Q_T^opt), the association then being carried out in the first frequency band; and otherwise,
  • the base station SBS with the strongest power received by the terminal in the first frequency band is associated with the terminal, the association being carried out in the first frequency band if this power is greater than the power received by the terminal in the second frequency band, corrected by the second bias value, and the association being carried out in the second frequency band in the opposite case.

For example, the first frequency band is a sub-6 GHz band from 0.7 to 6 GHz and the second frequency band is a millimeter band from 25 GHz to 300 GHz.

Advantageously, the pair of the coverage probability, P_c(γ), is calculated from

$P_c\left(\gamma \right)=\sum _{\underset{\underset{r\in \left\{\mu ,m\right\},t=S}{v\in \left\{L,N\right\}}}{t\in \left\{M,S\right\}}}P\left(\mathrm{SINR}>\gamma |t,v,r\right)P_{\mathrm{tvr}}$ where P_tvr is the probability of association of the terminal with a base station of tier t, in conditions of visibility v and in frequency band r, and where P(SINR>γ|t,v,r) is the conditional probability that the signal to noise and interference ratio on the terminal exceeds said predetermined threshold, γ.

According to a first alternative, the probability of association of the terminal with a base station of tier t, in conditions of visibility v and in frequency band r is calculated by means of P_tvr=P_tvP_vr where P_tv is the probability of association of the terminal with a base station of tier t, in conditions of visibility v and P_vr is the probability of association of the terminal with a station SBS of visibility P_vr in the frequency band r.

According to a second alternative, the probability P_tv is calculated by means of:P_ML=W₁exp(−πλ_Md_M²)exp(−πλ_Sd_S²)+exp(−πλ_Md_M²)(1−exp(−πλ_Sd_S²))for an association with a base station MBS in a state of visibility LOS,P_MN=W₂(1−exp(−πλ_Md_M²))(1−exp(−πλ_Sd_S²))for an association with a base station MBS in a state of visibility NLOS,P_SL=(1−W₁)exp(−πλ_Md_M²)exp(−πλ_Sd_S²)+exp(−πλ_Sd_S²)(1−exp(−πλ_Md_M²))for an association with a base station SBS in a state of visibility LOS, andP_SN=(1−W₂)(1−exp(−πλ_Md_M²))(1−exp(−πλ_Sd_S²))for an association with a base station SBS in a state of visibility NLOS, d_M is a characteristic distance beyond which a base station MBS is in a state of visibility LOS and beyond which it is in a state of visibility NLOS, d_S is a characteristic distance beyond which a base station SBS is in a state of visibility LOS and beyond which it is in a state of visibility NLOS, λ_M and λ_S are intensities of Poisson distributions giving respectively the spatial distribution of base stations MBS and that of base stations SBS, W₁ and W₂ are coefficients that depend on the transmitting powers of the base stations MBS and SBS as well as a first bias value Q_T used for the selection of the tier t of the base station.

According to a third alternative, the probability P_vr is calculated by

$P_{v\mu }=\exp \left(-{{\mathrm{\pi \lambda }}_S\left(\frac{K_{\mathrm{Svm}}{G}_0{Q}_R}{K_{\mathrm{Sv}\mu }}\right)}^{\frac{2}{{\alpha }_{\mathrm{Svm}}-{\alpha }_{\mathrm{Sv}\mu }}}\right)$ for an association with a base station SBS in the sub-6 GHz band and P_vm=1−P_vμ for an association with a station SBS in the millimeter band, where K_Svm and K_Svμ are respectively the respective path loss constants for the millimeter band and the sub-6 GHz band in a state of visibility v, α_Svm and α_Svμ are the respective path loss exponents for the millimeter band and the sub-6 GHz band in a state of visibility v, G₀ is the antenna gain, λ_S is the intensity of a Poisson distribution giving the spatial distribution of the base stations SBS, and Q_R is a second bias value used for the selection of the frequency band in the association of the terminal with a base station SBS.

In any case, the conditional probability P(SINR>γ|t,v,μ) that the signal to noise and interference ratio on the terminal exceeds said predetermined threshold, knowing that the terminal is associated with a base station of tier t, of state of visibility v, operating in the sub-6 GHz band, can be obtained from the probability density of the base station of tier t, of state of visibility v and of the strongest power received, as well as the measurement of the power received from this base station.

Alternatively, the conditional probability P(SINR>γ|S,v,m) that the signal to noise and interference ratio on the terminal exceeds said predetermined threshold, knowing that the terminal is associated with a base station SBS, of state of visibility v, operating in the millimeter band, can be obtained from the probability density of the base station SBS of the strongest power, of the power received from this base station, antenna gains of the terminal and of this base station as well as angular widths of the main lobes of radiation of the terminal and of the base station.

The coverage probability is advantageously calculated as a function P_c(γ)=F(G₀,Q_T,Q_R) where G₀ is the antenna gain, product of the receiving antenna gain of the terminal and of the transmitting antenna gain of a station SBS, and Q_T,Q_R are said first and second bias values.

The optimum pair of bias values (Q_T^opt,Q_R^opt) can be obtained by systematically sweeping the Cartesian product S_QT×S_QR where S_QT is a set of first possible bias values and S_QR is a set of second possible bias values and by searching for the pair of first and second bias values that maximises the function F(G₀,Q_T,Q_R).

Alternatively, the optimum pair of bias values (Q_T^opt,Q_R^opt) can be obtained by calculating

$Q_R^{\mathrm{opt}}=\frac{E\left[\frac{S_m}{I_m+{\sigma }_{N,m}^2}\right]}{E\left[\frac{S_{\mu }}{I_{\mu }+{\sigma }_{N,\mu }^2}\right]}\mathrm{where}\frac{S_m}{I_m+{\sigma }_{N,m}^2}$ is the signal to noise ratio on the terminal in the millimeter band,

$\frac{S_{\mu }}{I_{\mu }+{\sigma }_{N,\mu }^2}$ is the signal to noise ratio on the terminal in the sub-6 GHz band and E[.] is the mathematical expectation taken over all of the possible positions of the terminal with respect to the base stations of the network.

Alternatively encore, if the base stations SBS operate only in the millimeter band, the optimum pair of bias values (Q_T^opt,Q_R^opt) can be obtained by the gradient method.

In any case, in order to transfer a terminal associated with a base station SBS, from the sub-6 GHz band to the millimeter band, the antenna gain of the terminal, G_RX,m^UE, in the millimeter band, can be increased in such a way that

$G_{\mathrm{RX},m}^{\mathrm{UE}}=\frac{G_{\mathrm{RX},\mu }^{\mathrm{UE}}{G}_{\mathrm{TX},\mu }^{\mathrm{SBS}}}{G_{\mathrm{TX},m}^{\mathrm{SBS}}}\left(\frac{K_{\mathrm{SL}\mu }·P_{\mathrm{SL}\mu }}{K_{\mathrm{SLm}}·P_{\mathrm{SLm}}}\right)d^{\left({\alpha }_{\mathrm{SLm}}-{\alpha }_{\mathrm{SL}\mu }\right)}$ where G_RX,μ^UEis the antenna gain of the terminal in the sub-6 GHz band, G_TX,μ^SBS and G_TX,m ^SBS are the antenna gains of the base station SBS associated with the terminal, respectively in the sub-6 GHz band and in the millimeter band, K_SLμ and K_SLm are respectively the path loss constants in the sub-6 GHz band and in the millimeter band, P_SLμ and P_SLm are respectively the powers transmitted by the base station SBS in the sub-6 GHz band and in the millimeter band, α_SLμ and α_SLm are respectively the path loss exponents in the sub-6 GHz band and in the millimeter band, for the direct propagation path between the base station SBS associated with the terminal, and d is the distance between this base station and the terminal.

BRIEF DESCRIPTION OF THE DRAWINGS

Other features and advantages of the invention shall appear when reading a preferred embodiment of the invention, given in reference to the accompanying figures among which:

FIG. 1 diagrammatically shows the flowchart of a method for distributing loads in a multi radio access technology heterogeneous cellular network, according to an embodiment of the invention;

FIG. 2 diagrammatically shows the flowchart of a method of calculating an optimum pair of bias values in a step of the FIG. 1;

FIG. 3 diagrammatically shows the flowchart of a first alternative for searching an optimum pair of bias values in a step of the FIG. 2;

FIG. 4 diagrammatically shows the flowchart of a second alternative for searching an optimum pair of bias values in a step of the FIG. 2.

DETAILED DESCRIPTION OF PARTICULAR EMBODIMENTS

It shall be considered in what follows a multi radio access technology heterogeneous cellular network. Without loss of generality, it shall be supposed that the network comprises two types of cells: macrocells (served by base stations MBSs) operating in the sub-6 GHz band (i.e. from 0.7 to 6 GHz) and minicells, also referred to as small cells, (served by base stations SBSs) operating both in this sub-6 GHz band (or in a band that is not separate from the latter) and in the millimeter band (25 to 300 GHz).

The principle at the base of the invention is to use a first bias value, Q_T, in order to select the cell tier (macrocell or minicell) that will serve the terminal and a second bias value, Q_R, in order to select the radio access technology in the case where the terminal is located in a coverage zone of a minicell.

More precisely, FIG. 1 diagrammatically shows the flowchart of a method for distributing loads in a multi technology heterogeneous cellular network, according to an embodiment of the invention.

In a first step, 110, the coverage parameters of the network are acquired or are measured. These parameters are for example the parameters of the statistical distribution of the base stations MBSs and SBSs in the zone covered by the network, the transmitting powers of the base stations MBSs and SBSs, the exponents and the coefficients of the laws of path losses LOS and NLOS, the bandwidths respectively used for the transmission in sub-6 GHz band and for the transmission in millimeter band, the respective noise densities in these two bands, the average propagation distances LOS in these two bands. Recall that a propagation LOS (Line Of Sight) corresponds to the case where the base station is in a direct line of sight and a propagation NLOS (Non Line Of Sight) otherwise.

In a second step, 120, an optimum pair of bias values Q_T and Q_R is determined according to the parameters of the network, as exposed further on. This step can be carried out once and for all or at each modification of the parameters of the cellular network. The optimum bias values, noted as Q_T^opt and Q_R^opt apply to the entire network.

We then pass to the phase of association itself, executed each time a terminal wants to access the network.

In the step 130, the terminal measures the power of the control signal of the base stations MBSs. In what follows, respectively P_Mμ1 denotes the highest signal power received from a base station MBS. Similarly, P_Sμ1 is respectively the measurement of the highest signal received from a base station SBS.

It is sought whether a base station (MBS) of a macrocell (choice of the first tier) can be associated with the terminal.

To do this, it is first tested in 140 if:P_Mμ1≥Q_T^optP_Sμ1  (1)

If the condition (1) is satisfied, in 145 the terminal is associated with the station MBS corresponding to the strongest signal received. In other terms, a station MBS is associated with the terminal, if there is at least one station MBS and if the strongest power received from such a station in the sub-6 GHz band is greater, by a factor Q_T^opt, than the highest power received from a station SBS in this same band. MBS_max (resp. SBS_max) denote the base station MBS (resp. SBS) corresponding to the strongest power received by the terminal in the sub-6 GHz band in question. Thus P_Mμ1 is the power received from MBS_max in the sub-6 GHz band and P_Sμ1 is the power received from SBS_max in this band.

If the condition (1) is not fulfilled, in 150 the signal power of the base station SBS_max is measured in the millimeter band, which is P_Sm1, then in 160 it is tested if:P_Sμ1≥Q_R^optP_Sm1  (2)

If the condition (2) is fulfilled, the terminal is associated with the station SBS_max in the sub-6 GHz band. Otherwise, if the condition (2) is not satisfied, the same station SBS_max is associated with the terminal but in the millimeter band, in 170.

FIG. 2 diagrammatically shows the flowchart of a method for calculating the optical pair of bias values in the step 120 of the FIG. 1.

This method of calculation calls upon the parameters of the network as detailed hereinafter. It aims to maximise the coverage probability, defined as the probability that the signal to noise and interference ratio on a terminal is, on the average, greater than a predetermined value γ. The average is taken over all of the possible relative positions of the terminal with respect to the base stations deployed in the zone.

More precisely if P_tvr denotes the probability of association of a terminal UE (User Equipment) with a base station of tier t (t=M for the macrocellular tier and t=S for the minicellular tier), in conditions of visibility v (v=L in conditions of LOS and v=N in conditions of NLOS) and with the radio access technology r(r=μ for the sub-6 GHz band and r=m for the millimeter band), the coverage probability P_c(γ) relative to a level of SINR greater than γ, can be expressed in the form:

$\begin{array}{cc}{P}_c\left(\gamma \right)=P\left(\mathrm{SINR}>\gamma \right)=\sum _{\underset{\underset{r\in \left\{\mu ,m\right\},t=S}{v\in \left\{L,N\right\}}}{t\in \left\{M,S\right\}}}P\left(\mathrm{SINR}>\gamma |t,v,r\right)P_{\mathrm{tvr}}& \left(3\right)\end{array}$ where P(SINR>γ|t,v,r) is the probability that the level of SINR on the terminal in an association configuration t,v,r is greater than γ. Note that all of the triplets whereon the summing (3) is carried out do not contain all of the triplets (t,v,r) since the choice of the radio access technology is possible only in the case of an association with an SBS.

In a first step, 210, the probabilities of association are calculated of a terminal with a base station MBS and a base station SBS in the states of visibility LOS and NLOS, is P_tv, t∈{M,S}, v∈{L,N}.

This probability of association depends, on the one hand, on the distance of the terminal to a base station and, on the other hand, of the state of visibility of the base station in question.

If the positions of the different base stations are known, it can be supposed that the position of the terminal obeys a uniform law of spatial distribution.

On the other hand, if the positions of the different base stations are not known, it can be supposed that the positions of the base stations MBS and SBS follow a one-off Poisson stochastic process in the zone involved. λ_M and λ_S respectively denote the two-dimensional distribution densities of the one-off Poisson process for the stations MBS and SBS.

Regarding the states of visibility LOS and NLOS, it is supposed that they follow an LOS ball model, such as described for example in the article by T. Bai at al. entitled “Coverage and rate analysis for millimeter-wave cellular networks”, IEEE Trans. Wireless Comm. vol. 13, no. 2, pp. 1100-1114, 2015. According to this model, if the terminal is located at a distance less than a characteristic distance d_M (resp. d_S) from a base station MBS (resp. SBS), the base station will be supposed as being in direct line of site (LOS) of the terminal. Otherwise, the state of visibility will be considered as being NLOS.

The probabilities of association with a base station MBS or SBS, in a state of visibility LOS or NLOS, noted as P_tv with t∈{M,S} and v∈{L,N}, are respectively given by:P_ML=W₁exp(−πλ_Md_M²)exp(−πλ_Sd_S²)+exp(−πλ_Md_M²)(1−exp(−πλ_Sd_S²))  (4-1)P_MN=W₂(1−exp(−πλ_Md_M²))(1−exp(−πλ_Sd_S²))  (4-2)P_SL=(1−W₁)exp(−πλ_Md_M²)exp(−πλ_Sd_S²)+exp(−πλ_Sd_S²)(1−exp(−πλ_Md_M²))  (4-3)P_SN=(1−W₂)(1−exp(−πλ_Md_M²))(1−exp(−πλ_Sd_S²))  (4-4)where W₁ is the probability that the terminal is associated with a station MBS in the case where a base station MBS and a base station SBS are in a state of visibility LOS with respect to the terminal, and where W₂ is the probability that the terminal is associated with a station MBS in the case where a base station MBS and a base station SBS are in a state of visibility NLOS with respect to the terminal. The analytical expressions of W₁ and W₂ are given in the appendix. They depend in particular on the respective transmitting powers, P_M and P_S of the base stations MBS and SBS, on the bias Q_T introduced for the selection of the tier, as well as on the characteristics of the propagation paths between the base station MBS and the terminal, on the one hand, and of the base station SBS and the terminal, on the other hand.

In a second step 220, the probability is calculated that, when a terminal is associated with a base station SBS, in the state of visibility LOS or NLOS, it is as such in the sub-6 GHz band or in the millimeter band.

More precisely, the probability P_vμ that the terminal is associated with the base station SBS in the state of visibility v via the sub-6 GHz band is given by:

$\begin{array}{cc}{P}_{v\mu }=\exp \left(-{{\mathrm{\pi \lambda }}_S\left(\frac{K_{\mathrm{Svm}}{G}_0{Q}_R}{K_{\mathrm{Sv}\mu }}\right)}^{\frac{2}{{\alpha }_{\mathrm{Svm}}-{\alpha }_{\mathrm{Sv}\mu }}}\right)& \left(5\text{-}1\right)\end{array}$ and, consequently, the probability P_vm that the terminal is associated with the base station SBS in the state of visibility v via the millimeter band is given by:P_vm=1−P_vμ  (5-2)where G₀ is the antenna gain in the millimeter band, i.e. the product of the transmitting antenna gain of the base station SBS and of the receiving antenna gain of the terminal UE in this band (the antenna gain is assumed to be equal to 1 in the sub-6 GHz band, the transmitting and receiving antennas in this band able to be considered as practically omnidirectional), K_Svm and K_Svμ are respectively the path loss constants for the millimeter band and for the sub-6 GHz band, α_Svm and α_Svμ are respectively the path loss exponents for the millimeter band and for the sub-6 GHz band. In a logarithmic path loss model, the path loss coefficients in these two bands are given by:η_Svm(dB)=K_Svm+10α_Svm log₁₀(d)  (6-1)η_Svμ(dB)=K_Svμ+10α_Svμ log₁₀(d)  (6-2)where d is the distance between the terminal UE and the base station SBS.

The probability P_tvr in the expression (4) is then given by:P_tvr=P_tvP_vr  (7)where P_tv is given by one of the expressions (4-1) to (4-4) and P_vr is given by one of the expressions (5-1) to (5-2).

In the step 230, by using the principles of stochastic geometry, such as presented in the article by H. ElSawy et al. entitled “Stochastic geometry for modeling, analysis and design of multi-tier and cognitive cellular wireless networks: a survey” published in IEEE Corn. Surveys & Tutorials, vol. 15, No. 3, 2013, pp. 996-1019, the conditional coverage probability P(SINR>γ|t,v,r) in the sub-6 GHz band (i.e. r=μ) is calculated:

$\begin{array}{cc}P\left(\mathrm{SINR}>\gamma |t,v,\mu \right)={\int }_0^{\infty }\exp \left(-{\mathrm{\gamma \sigma }}_{N,\mu }^{2}x-\sum _{t^{\prime },v^{\prime }}{A}_{t^{\prime }{v}^{\prime }}\left(\gamma ,x\right)\right){\hat{f}}_{\xi \mathrm{tv}\mathrm{\mu 1}}\left(x\right)\mathrm{dx}& \left(8\right)\end{array}$ where

$A_{t^{\prime }{v}^{\prime }}={\int }_{l_{t^{\prime }}}^{\infty }\frac{\gamma x}{y+\gamma x}{\Lambda }_{t^{\prime }{v}^{\prime }\mu }^{\prime }\left(y\right)\mathrm{dy}\forall t^{\prime }\in \left\{M,S\right\},v^{\prime }\in \left\{L,N\right\}$ with _t′=x/Q_T if t′=t; _t′=Q_Tx if t=M and t′=S; _t′=x/Q_T if t=S and t′=M, σ_N,μ² is the power of the noise in the sub-6 GHz band and where {circumflex over (ƒ)}_ζtvμ1(x) represents the probability density (pdf) of the distance of the base station of the strongest power received from tier t, of visibility v, in the sub-6 GHz band, and finally where Λ′_t′v′μ represents the number of points of the Poisson process linked to the base stations MBS (t′=M) resp. SBS (t′=S) in the sub-6 GHz band.

Similarly, the conditional coverage probability P(SINR>γ|t,v,r) is calculated in the millimeter band (t=S,r=M) by means of:

$\begin{array}{cc}P\left(\mathrm{SINR}>\gamma |S,v,m\right)={\int }_0^{\infty }\exp \left(-\frac{{\mathrm{\gamma \sigma }}_{N,m}^{2}x}{G_0}-B_1\left(\gamma ,x\right)-B_2\left(\gamma ,x\right)\right){\hat{f}}_{\xi \mathrm{Svm}1}\left(x\right)\mathrm{dx}& \left(9\right)\end{array}$ with

$B_1\left(\gamma ,x\right)=\sum _{k=1}^4\left(-b_k{\int }_x^{\infty }\frac{a_k\gamma x}{y+a_k\gamma x}{\Lambda }_{\mathrm{Svm}}^{\prime }\left(y\right)\mathrm{dy}\right)\mathrm{and}$ $B_2\left(\gamma ,x\right)=\sum _{k=1}^4\left(-b_k{\int }_x^{\infty }\frac{a_k\gamma x}{y+a_k\gamma x}{\Lambda }_{{\mathrm{Sv}}^{\prime }m}^{\prime }\left(y\right)\mathrm{dy}\right)$ where σ_N,m ² is the power of the noise in the millimeter band, {circumflex over (ƒ)}_ζSvm1(x) represents the probability density (pdf) of the distance of the base station SBS of the strongest power (t=S), with a visibility v, in the millimeter band, and finally where Λ′_Svm represents the number of points of the Poisson process linked to the base stations SBS in the millimeter band.

The antennas of the base stations SBS in the millimeter band are assumed to be directional (for example by means of a formation of a beam) with a main lobe corresponding to a gain G_h^SBS and an angular width band θ_h^SBS and secondary lobes corresponding to a gain and an angular width =2π−θ_h^SBS. A detailed description of the model of the antennas can be found in the aforementioned article by T. Bai et al. Likewise, the antenna of the terminal UE in the millimeter band is assumed to be directional, with a main lobe of gain G_h^UE and of angular width θ_h^UE and secondary lobes corresponding to a gain and an angular width =2π−θ_h^UE.

The summing on k=1, . . . , 4 corresponds to the four overlapping configurations of lobes between the base station SBS assumed to be associated with the terminal UE and the terminal UE itself. The coefficients a_k and b_k are given by the table:

k	1	2	3	4
ak	GhUEGhSBS	GhUEGlSBS	GlUEGhSBS	GlUEGlSBS
bk	$\frac{{\theta }_h^{\mathrm{UE}}}{2\pi }·\frac{{\theta }_h^{\mathrm{SBS}}}{2\pi }$	$\frac{{\theta }_h^{\mathrm{UE}}}{2\pi }·\frac{{\theta }_l^{\mathrm{SBS}}}{2\pi }$	$\frac{{\theta }_l^{\mathrm{UE}}}{2\pi }·\frac{{\theta }_h^{\mathrm{SBS}}}{2\pi }$	$\frac{{\theta }_l^{\mathrm{UE}}}{2\pi }·\frac{{\theta }_l^{\mathrm{SBS}}}{2\pi }$

In order to simplify the calculations, the interfering base stations SBS (i.e. separate from the associated base station SBS) are assumed to have a main lobe with an arbitrary orientation with respect to the main lobe of the terminal.

In the step 240 the coverage probability is calculated by means of the expression (3), in other words:

$\begin{array}{cc}{P}_c\left(\gamma \right)=\sum _{\underset{v\in \left\{L,N\right\}}{t\in \left\{M,S\right\}}}P\left(\mathrm{SINR}>\gamma |t,v,\mu \right)P_{\mathrm{tv}}{P}_{v\mu }+\sum _{v\in \left\{L,N\right\}}P\left(\mathrm{SINR}>\gamma |S,v,m\right)P_{\mathrm{Sv}}{P}_{\mathrm{vm}}& \left(10\right)\end{array}$ where the conditional probabilities of SINR P(SINR>γ|t,v,μ) and P (SINR>γ|S,v,m) were respectively calculated in the step 230.

It will be understood that the coverage probability P_c(γ) depends on the parameters of the network, such as the deployment density of the macrocells and of the microcells, the transmitting powers of the stations MBSs and SBSs, the antenna gain G₀, the bias values Q_T and Q_R. With all of the parameters of the network being equal, the coverage probability can be considered as a function of G₀, Q_T and Q_R:P_c(γ)=F(G₀,Q_T,Q_R)  (11)

In the step 250, for a given antenna gain G₀, i.e. in practice for a given antenna gain of the terminal UE in the millimeter band (with the antenna gain of the station SBS assumed to be fixed), the pair of bias values (Q_T^opt,Q_R^opt) that maximises the coverage probability is sought, i.e.:

$\begin{array}{cc}\left(Q_T^{\mathrm{opt}},Q_R^{\mathrm{opt}}\right)=\underset{\underset{Q_R\in S_{\mathrm{QR}}}{Q_T\in S_{\mathrm{QT}}}}{\mathrm{argmax}}\left(F\left(G_0,Q_T,Q_R\right)\right)& \left(12\right)\end{array}$ where S_QT and S_QR are respectively the possible sets of bias values Q_T and Q_R. In what follows F*(G₀)=F(G₀,Q_T^opt,Q_R^opt) shall denote the coverage probability obtained for the optimal bias pair (Q_T^opt,Q_R^opt).

The searching in 250 of the optimum pair (Q_T^opt,Q_R^opt) on S_QT×S_QR can be carried out according to different alternatives as explained hereinafter.

FIG. 3 diagrammatically shows the flowchart of a first alternative for searching the optimum pair (Q_T^opt,Q_R^opt).

This first alternative consists in a brute force search in the Cartesian product S_QT×S_QR, in other words this search is carried out by means of a double iteration loop on the elements Q_T and Q_R of S_QT and S_QR. The sets S_QT and S_QR are in practice intervals of discrete values.

The coverage probability P_c(γ)=F(G₀,Q_T,Q_R) is calculated in 320 and it is compared with the maximum value valmax(F) in 330, with the latter initialised beforehand to 0 in the step 310. If the coverage probability calculated as such satisfies P_c(γ)>valmax(F) in 330, the maximum value is updated with this probability in 335. In any case, the search is continued until a full sweep of S_QT×S_QR (340, 350) by checking if there are still pairs of elements (Q_T,Q_R) to be tested. In the affirmative, we move to the following threshold value of Q_T (355) or of Q_R (345), according to the case. In the negative, this is terminated in 360, by recovering the optimum thresholds values (Q_T^opt, Q_R^opt) corresponding to the maximum of F(G₀,Q_T,Q_R).

The FIG. 4 diagrammatically shows the flowchart of a second alternative for searching the optimum pair (Q_T^opt,Q_R^opt).

This second alternative can be used if the brute force search is too complex, for example if the cardinal of the set S_QT×S_QR is too high.

In this case, in a first step, in the step 410, an optimum value of the bias calculated, according to the following heuristic formula:

$\begin{array}{cc}{Q}_R^{\mathrm{opt}}=\frac{E\left[\frac{S_m}{I_m+{\sigma }_{N,m}^2}\right]}{E\left[\frac{S_{\mu }}{I_{\mu }+{\sigma }_{N,\mu }^2}\right]}& \left(13\right)\end{array}$ where E[.] represents the mathematical expectation taken on all of the possible relative positions of the terminal with respect to the base stations of the network,

$\frac{S_m}{I_m+{\sigma }_{N,m}^2}$ represents the SINR on the terminal in the millimeter band and

$\frac{S_{\mu }}{I_{\mu }+{\sigma }_{N,\mu }^2}$ the SINR on the terminal in the sub-6 GHz band. I_m represents the sum of the interferences generated in the millimeter band by the base stations SBSs (in LOS and NLOS). Likewise, I_μ represents the sum of the interferences generated in the sub-6 GHz band by the base stations MBSs and SBSs (in LOS and NLOS).

As soon as the optimum value Q_R^opt is obtained, a search for the optimum value Q_T^opt can be carried out, via brute force, according to a single dimension:

$\begin{array}{cc}{Q}_T^{\mathrm{opt}}=\underset{Q_T\in S_{\mathrm{QT}}}{\mathrm{argmax}}\left(F\left(G_0,Q_T,Q_R^{\mathrm{opt}}\right)\right)& \left(14\right)\end{array}$

To do this, in 420, a value valmax(F) is initialised to zero and we enter an iteration loop where an element of S_QT is selected. At each iteration, in 430 the coverage probability P_c(γ)=F(G₀,Q_T,Q_R^opt) is calculated and it is compared with the current value valmax(F) in 440. If the coverage probability thus calculated is such that P_c(γ)>valmax(F), the maximum value is updated with this probability in 445. In any case, it is checked in 450 if there are other values of Q_T to be tested. In the affirmative, we return to the step 455. Otherwise, the search is terminated in 460 by recovering the optimum threshold values Q_T^opt corresponding to the maximum of F(G₀,Q_T,Q_R^opt).

A third alternative (not shown) for searching for the optimum bias pair consists in a simplification of the second alternative in the particular case where the base stations SBSs transmit only in the millimeter band. In this case, it can be shown that the coverage probability F(G₀,Q_T,Q_R) and in particular F(G₀,Q_T,Q_R^opt) is convex in relation to Q_T. The value Q_T^opt can then be obtained by the method of the gradient.

The method for distributing the load in a heterogeneous network with multi radio access technology such as described hereinabove makes it possible to obtain an optimum distribution of the load in terms of SINR, on the average for the different terminals UEs of the network. However, the operator can wish that certain terminals UEs be handled by the stations SBSs in the millimeter band in order to relieve the sub-6 GHz band, without however derogating from the criterion of optimality in terms of SINR for the association of the terminals in question.

According to a second embodiment of the invention, optionally, after the distribution of the load according to the first embodiment, a modification is carried out in this distribution in favour of the millimeter band.

To do this, a critical distance, d_CL, is introduced from the terminal UE that is sought to have handled by a base station SBS in the millimeter band. This critical distance defines a disc around the terminal in question. If there is a base station SBS and only one in this disc, the user will be associated with this base station in the millimeter band.

This critical distance is given by:

$\begin{array}{cc}{d}_{\mathrm{CL}}={\left(\frac{K_{\mathrm{SLm}}·P_{\mathrm{SLm}}}{K_{\mathrm{SL}\mu }·P_{\mathrm{SL}\mu }}{G}_0\right)}^{\frac{1}{{\alpha }_{\mathrm{SLm}}-{\alpha }_{\mathrm{SL}\mu }}}& \left(15\right)\end{array}$

where K_SLm and K_SLμ are respectively the path loss constants for the millimeter band and for the sub-6 GHz band in the case of a direct line propagation path (LOS), P_SLm and P_SLμ are the powers transmitted by the SBS respectively in the millimeter band and in the sub-6 GHz band and α_SLm and α_SLμ are respectively the path loss exponents for the millimeter band and for the sub-6 GHz band on this path.

It is understood that, if a base station SBS is located in a disc of radius d_CL around the terminal UE, the power of the signal received in the millimeter band is greater than that of the signal received in the sub-6 GHz band. Furthermore, in that the other stations SBS are outside of this zone, the level of interference in the sub-6 GHz band (coming from the other stations SBSs or from stations MBSs) is higher than in the millimeter band. This results in that the level of SINR in the millimeter band is necessarily higher than in the sub-6 GHz band and, consequently, than the terminal will be associated with the base station SBS in the millimeter band.

If d denotes the distance of the terminal UE with the base station which serves it in the sub-6 GHz band, it is sufficient then for the operator to request that the terminal modify its receiving antenna gain (for example by modifying the formation of the beam by the antenna network of the terminal) in such a way that d_CL=d, i.e.:

$\begin{array}{cc}{G}_0^{\mathrm{offload}}={\left(\frac{K_{\mathrm{SL}\mu }·P_{\mathrm{SL}\mu }}{K_{\mathrm{SLm}}·P_{\mathrm{SLm}}}\right)}^{d^{\left({\alpha }_{\mathrm{SLm}}-{\alpha }_{\mathrm{SL}\mu }\right)}}& \left(16\right)\end{array}$ or, if it is recalled that the gain G₀ is the product of the receiving antenna gain of the terminal G_RX,m^UE in the millimeter band and of the transmitting antenna gain of the base station SBS in this band, G_TX,m^SBS:

$\begin{array}{cc}{G}_{\mathrm{RX},m}^{\mathrm{UE}}=\frac{1}{G_{\mathrm{TX},m}^{\mathrm{SBS}}}{\left(\frac{K_{\mathrm{SL}\mu }·P_{\mathrm{SL}\mu }}{K_{\mathrm{SLm}}·P_{\mathrm{SLm}}}\right)}^{d^{\left({\alpha }_{\mathrm{SLm}}-{\alpha }_{\mathrm{SL}\mu }\right)}}& \left(17\right)\end{array}$

The expression (17) is valid only in the hypothesis supra where the transmitting antennas (of the base station SBS) and of receiving (of the terminal UE) are omnidirectional in the sub-6 GHz band (antenna gain equal to 1 in this band). If this hypothesis does not apply and if we note respectively G_RX,μ^UE and G_TX,μ^SBS the receiving antenna gains of the terminal UE and of the transmitting antenna of the base station SBS in the sub-6 GHz band, the expression (17) becomes:

$\begin{array}{cc}{G}_{\mathrm{RX},m}^{\mathrm{UE}}=\frac{G_{\mathrm{RX},\mu }^{\mathrm{UE}}{G}_{\mathrm{TX},\mu }^{\mathrm{SBS}}}{G_{\mathrm{TX},m}^{\mathrm{SBS}}}\left(\frac{K_{\mathrm{SL}\mu }·P_{\mathrm{SL}\mu }}{K_{\mathrm{SLm}}·P_{\mathrm{SLm}}}\right)d^{\left({\alpha }_{\mathrm{SLm}}-{\alpha }_{\mathrm{SL}\mu }\right)}& \left(18\right)\end{array}$ in which case it will be possible for the operator to request that the terminal UE modify G_RX,m^UE and/or G_RX,μ^UE in such a way that the condition (18) is met.

APPENDIX

$W_1=\frac{1-e^{-\left(K_1+1\right)t_1}}{1+K_1}+\exp \left(-\pi {\lambda }_S{d}_S^2\right)\left[\exp \left(-{\Lambda }_{\mathrm{ML}\mu }^{\prime }\left(0,\frac{d_S^{{\alpha }_{\mathrm{SL}\mu }}}{Q_T{K}_{\mathrm{SL}\mu }{P}_S}\right)\right)-\exp \left(-\pi {\lambda }_M{d}_M^2\right)\right]$ $W_2=\exp \left(-\pi {\lambda }_S{d}_S^2\right)\frac{e^{-\left(K_2+1\right)t_2}}{1+K_2}\mathrm{with}$ ${\Lambda }_{\mathrm{ML}\mu }^{\prime }\left(0,\frac{d_S^{{\alpha }_{\mathrm{SL}\mu }}}{Q_T{K}_{\mathrm{SL}\mu }{P}_S}\right)=\{\begin{array}{cc}\pi {{\lambda }_M\left(K_{\mathrm{ML}\mu }{P}_M\right)}^{\frac{2}{{\alpha }_{\mathrm{ML}\mu }}}{\left(\frac{d_S^{{\alpha }_{\mathrm{SL}\mu }}}{Q_T{K}_{\mathrm{SL}\mu }{P}_S}\right)}^{\frac{2}{{\alpha }_{\mathrm{ML}\mu }}},& \mathrm{if}\frac{d_S^{{\alpha }_{\mathrm{SL}\mu }}}{Q_T{K}_{\mathrm{SL}\mu }{P}_S}<\frac{d_M^{{\alpha }_{\mathrm{ML}\mu }}}{K_{\mathrm{ML}\mu }{P}_M}\\ \pi {\lambda }_M{d}_M^2,& \mathrm{if}\frac{d_S^{{\alpha }_{\mathrm{SL}\mu }}}{Q_T{K}_{\mathrm{SL}\mu }{P}_S}>\frac{d_M^{{\alpha }_{\mathrm{ML}\mu }}}{K_{\mathrm{ML}\mu }{P}_M}\end{array}{K}_1=\pi {{\lambda }_S\left(\frac{K_{\mathrm{SL}\mu }{P}_S{Q}_T}{K_{\mathrm{ML}\mu }{P}_M}\right)}^{\frac{2}{{\alpha }_{\mathrm{SL}\mu }}}{\left(\pi {\lambda }_M\right)}^{-\frac{{\alpha }_{\mathrm{ML}\mu }}{{\alpha }_{\mathrm{SL}\mu }}}\mathrm{and}{t}_1=\pi {{\lambda }_M\left(K_{\mathrm{ML}\mu }{P}_M\right)}^{\frac{2}{{\alpha }_{\mathrm{ML}\mu }}}{\left(\frac{d_S^{{\alpha }_{\mathrm{SL}\mu }}}{Q_T{K}_{\mathrm{SL}\mu }{P}_S}\right)}^{\frac{2}{{\alpha }_{\mathrm{ML}\mu }}}{K}_2=\pi {{\lambda }_S\left(\frac{K_{\mathrm{SN}\mu }{P}_S{Q}_T}{K_{\mathrm{MN}\mu }{P}_M}\right)}^{\frac{2}{{\alpha }_{\mathrm{SN}\mu }}}{\left(\pi {\lambda }_M\right)}^{-\frac{{\alpha }_{\mathrm{MN}\mu }}{{\alpha }_{\mathrm{SN}\mu }}}\mathrm{and}{t}_2=\pi {\lambda }_M{d_M^2\left(K_{\mathrm{MN}\mu }{P}_M\right)}^{\frac{2}{{\alpha }_{\mathrm{ML}\mu }}}$

Claims

1. A method for distributing traffic load in a multi radio access technology heterogeneous network, the network comprising macrocells served by first base stations of a first tier of the network, each being referred to as a MBS, operating in a first frequency band, and minicells served by second base stations of a second tier of the network, each being referred to as a SBS, configured to operate in the first frequency band and in a second frequency band, separate from the first frequency band, wherein: coverage parameters of the network are acquired or measured,using the coverage parameters of the network, an optimum pair of bias values (QTopt, QRopt) is determined that maximises a coverage probability, Pc (γ), defined as a probability that a signal to noise and interference ratio on a terminal is on average greater than a predetermined threshold (γ) in a deployment zone of the network,a first base station MBS is associated with the terminal, if a strongest power received from the first base station MBS in the first frequency band is greater than a strongest power received from a second base station SBS in the same frequency band, corrected by a first bias value (QTopt) of the optimum pair of bias values (QTopt, QRopt), the association then being carried out in the first frequency band, and otherwise,the second base station SBS of the strongest power received by the terminal in the first frequency band is associated with the terminal, the association being carried out in the first frequency band if the strongest power is greater than a power received by the terminal in the second frequency band, corrected by a second bias value (QRopt) of the optimum pair of bias values (QTopt, QRopt), and the association being carried out in the second frequency band in the opposite case.

2. The method for distributing traffic load according to claim 1, wherein the first frequency band is a sub-6 GHz band from 0.7 GHz to 6 GHz, and the second frequency band is a millimeter band from 25 GHz to 300 GHz.

3. The method for distributing traffic load according to claim 2, wherein the coverage probability, Pc(γ), is calculated from

4. The method for distributing traffic load according to claim 3, wherein the probability Ptvr, of association of the terminal with the given base station of tier t ∈{M,S}, in conditions of visibility v ∈{L, N} and in frequency band r ∈{μ,m} is calculated with Ptvr=PtvPvr, where Ptv is a probability of association of the terminal with the given base station of tier t ∈{M,S}, in conditions of visibility v ∈{L,N} and Pvris a probability of association of the terminal with a second base station SBS of visibility Pvr in the frequency band r.

5. The method for distributing traffic load according to claim 4, wherein the probability Ptv is calculated with: PML=W1exp(−πλMdM2)exp(−πλSdS2)+exp(−πλMdM2)(1−exp(−πλSdS2))for an association with a first base station MBS in a state of visibility LOS, PMN=W2(1−exp(−πλMdM2))(1−exp(−πλSdS2))for an association with a first base station MBS in a state of visibility NLOS, PSL=(1−W1)exp(−πλMdM2)exp(−πλSdS2)+exp(−πλSdS2)(1−exp(−πλMdM2))for an association with a second base station SBS in a state of visibility LOS, and PSN=(1−W2)(1−exp(−πλMdM2))(1−exp(−πλSdS2))for an association with a second base station SBS in a state of visibility NLOS, dM is a characteristic distance beyond which a first base station MBS is in a state of visibility LOS and beyond which it is in a state of visibility NLOS, ds is a characteristic distance beyond which a second base station SBS is in a state of visibility LOS and beyond which it is in a state of visibility NLOS, λM and λS are intensities of Poisson distributions giving respectively a spatial distribution of the first base stations MBS and that of the second base stations SBS, W1 and W2, are coefficients that depend on transmitting powers of the first base stations MBS and the second base stations SBS as well as a first bias value QT, used for selection of the tier t of the given base station.

6. The method for distributing traffic load according to claim 4, wherein the probability Pvr is calculated by

7. The method for distributing traffic load according to claim 3, wherein the conditional probability P(SINR>γ|t, v, μ) that the signal to noise and interference ratio on the terminal exceeds the predetermined threshold, knowing that the terminal is associated with the given base station of tier t, of state of visibility v, operating in the sub-6 GHz band, is obtained from the probability density of the given base station of tier t, of state of visibility v and of the strongest power received, as well as a measurement of power received from the given base station.

8. The method for distributing traffic load according to claim 3, wherein the conditional probability P (SINR>λ|S, v, m) that the signal to noise and interference ratio on the terminal exceeds the predetermined threshold, knowing that the terminal is associated with a second base station SBS, of state of visibility v, operating in the millimeter band, is obtained from the probability density of the second base station SBS of the strongest power received from the second base station SBS, from antenna gains of the terminal and from the second base station SBS as well as from angular widths of main lobes of radiation of the terminal and of the second base station SBS.

9. The method for distributing traffic load according to claim 3, wherein the coverage probability is calculated as a function Pc (γ)=F (G0, QT, QR), where G0 is the antenna gain, a product of the receiving antenna gain of the terminal and of a transmitting antenna gain of a second station SBS, and QT, QR are the first and the second bias values.

10. The method for distributing traffic load according to claim 9, wherein the optimum pair of bias values (QTopt, QRopt) is obtained by systematically sweeping a Cartesian product SQT×SQR where SQT is a set of first possible bias values and SQR is a set of second possible bias values, and by searching for a pair of first and second bias values that maximises the function F (G0,QT, QR).

11. The method for distributing traffic load according to claim 9, wherein the optimum pair of bias values (QTopt, QRopt) is obtained by calculating

12. The method for distributing traffic load according to claim 9, wherein the second base stations SBS operate only in the millimeter band, and the optimum pair of bias values (QTopt, QRopt) is obtained by applying a gradient descent to the function F (G0,QT,QR).

13. The method for distributing traffic load according to claim 1, wherein, in order to transfer a terminal associated with a second base station SBS, from the sub-6 GHz band to the millimeter band, an antenna gain of the terminal is increased, GRX,mUE, in the millimeter band, such that