Modeling interference in a cellular radiotelephone network

In a cellular radiotelephone network comprising cells served by respective base stations, the modeling of interference includes selecting a first frequency in the frequency spectrum allocated to the network, selecting a point of the network at which radio signals emitted at least at the first frequency of the spectrum from the base stations are received in accordance with a propagation model, assigning respective coefficients to the received radio signals, a coefficient being equal to 1 if the selected frequency is allocated to a base station emitting one of the received radio signals, and equal to 0 otherwise, and multiplying the radio signals by the respective coefficients to derive products that are summed to yield an interference model.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to cellular radiotelephone networks, and in 
particular the allocation of frequencies within a frequency band allocated 
to a cellular radiotelephone network to the cells of the radiotelephone 
network. 
2. Description of the Prior Art 
A given frequency band is conventionally allocated to a cellular 
radiotelephone network. Because of the restricted number of frequencies 
available, the same frequency must be allocated to plural cells of the 
network, i.e. used simultaneously by the respective base stations of the 
cells to emit radiotelephone signals, which causes interference between 
signals sent on the same frequency or on similar frequencies by different 
base stations. Frequency allocation is a complex combinatorial problem 
that must satisfy contradictory criteria, in particular handling all of 
the telephone traffic whilst restricting interference. 
A known method models the interference by means of a compatibility matrix 
that indicates for the cells of the network considered in pairs the 
minimal frequency offset that must exist between the frequencies allocated 
to the two cells for interference between the two cells to remain below a 
threshold. 
This method takes account of only the interference due to the cells 
considered in pairs, whereas in reality the interference due to all of the 
cells is cumulative. 
Moreover, the compatibility matrix supplies only a binary indication, 
namely that either the compatibility or the incompatibility of the 
frequencies allocated to a given two cells of the network, and give no 
information as to the exact level of interference. Modeling of 
interference by means of a compatibility matrix is usable when the problem 
is allocation of frequencies subject to the criterion of minimizing the 
number of frequencies used in the cellular radiotelephone network, which 
is a situation of little practical use. 
OBJECTS OF THE INVENTION 
The main object of the invention is to remedy the previously mentioned 
drawbacks. 
Another object of the invention is to provide a method of modeling 
interference that allows for multiple sources of interference whilst 
providing a simple formula for frequency allocation which can then be 
resolved in accordance with a selected criterion, for example maximizing 
radiotelephone traffic or minimizing interference or maximizing spectral 
efficiency or minimizing the number of used frequencies. 
SUMMARY OF THE INVENTION 
Accordingly, the invention is directed to a method of modeling interference 
in a cellular radiotelephone network comprising cells served by respective 
base stations, wherein a frequency spectrum comprising a finite number of 
frequencies is allocated to the network and a propagation model indicates 
radio signals respectively emitted at each frequency of the spectrum from 
the base stations of the network and received at a point of the network. 
According to a first embodiment, the method comprises: 
selecting a selected frequency in the spectrum allocated to the cellular 
radiotelephone network, 
selecting in the network a selected point for which the propagation model 
is determined, 
assigning respective coefficients to the radio signals at the selected 
frequency received at the selected point, one of the coefficients being 
equal to 1 if the selected frequency is allocated to a base station 
emitting a respective one of the radio signals, and equal to 0 otherwise, 
multiplying the radio signals at the selected frequency received at the 
selected point by the respective coefficients into respective products, 
and 
summing the respective products to yield an interference model. 
The invention is not directed to a calculation of interference, but takes 
into account of interference to allocate frequencies in a cellular 
radiotelephone network in an optional way. The sum of interference at the 
selected point depends upon of the coefficients of a frequency allocation 
plan thereby optimizing allocation of frequencies to the base stations in 
the network as a function of a selected criterion. 
Preferably, the method further comprises dividing the first interference 
model by the signal emitted at the selected frequency from the base 
station serving the point of the network. This first embodiment takes into 
account of co-channel interference. 
In other words, the interference-to-useful-signal ratio, and not the known 
signal-to-interference ratio, is derived to obtain a linear formulation of 
the single and multipath interference on each radio channel as a function 
of the coefficient of a frequency allocation plane. 
According to a second embodiment, the method comprises: 
(a) selecting a first selected frequency and second selected frequencies in 
the spectrum allocated to the cellular radiotelephone network, 
(b) selecting in the network a selected point for which the propagation 
model is determined, 
(c) for each of the first selected frequency and second selected 
frequencies: 
assigning coefficients respectively to the radio signals at the each 
selected frequency received at the selected point, each the respective 
coefficient being equal to 1 if the each selected frequency is allocated 
to a base station emitting a respective one of the radio signals, and 
equal to 0 otherwise, 
multiplying the radio signals at the each selected frequency received at 
the selected point by the respective coefficients into respective 
products, and 
summing the respective products to derive a first interference model, 
(d) assigning interference ratios respectively to the first interference 
models respectively derived for the first and second selected frequencies, 
the interference ratio relative to a respective first interference model 
being a function of the difference between the first selected frequency 
and the respective second selected frequency, except for the interference 
ratio relative to said first selected frequency which is equal to 1, 
(e) multiplying the first interference models respectively by the 
interference ratios into model products, and 
(f) summing the model products to yield a second interference model. 
This second embodiment includes co-channel interferences and 
adjacent-channel interferences. 
According to a third embodiment, the method comprises: 
(a) selecting a selected frequency in the spectrum allocated to the 
cellular radiotelephone network, 
(b) selecting plural selected points in the network situated in the same 
cell, propagation models being respectively determined for the selected 
points, 
(c) for each the selected point: 
assigning respective coefficients to the radio signals at the selected 
frequency received at the selected point, one of the coefficients being 
equal to 1 if the selected frequency is allocated to a base station 
emitting a respective one of the radio signals, and equal to 0 otherwise, 
multiplying the radio signals at the selected frequency received at the 
selected point by the respective coefficients into respective products, 
and 
summing the respective products to derive a first interference model, 
(d) averaging the first interference models respectively derived for the 
selected points to yield a second interference model. 
This third embodiment reduces the number of interference constraints, 
typically from a few hundred points per cell to a few points per cell. 
Furthermore, some propagation models do not give the radio signals 
received at points of the network, but only averages which can then be 
used in this embodiment.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Referring to FIG. 1, a cellular radiotelephone network RES comprises a set 
of cells {C.sub.j, 1.ltoreq.j.ltoreq.J} where J is a positive integer. The 
network RES is the GSM ("Global System for Mobile communications") 
pan-european digital cellular network, for example. 
The cells C.sub.1 through C.sub.J are associated with respective base 
stations SB.sub.1 through SB.sub.J. A cell C.sub.j, with j between 1 and 
J, comprises a base station SB.sub.j through which a mobile station sets 
up and receives radiotelephone calls. The remainder of the description is 
more particularly concerned with the radiotelephone signals emitted by the 
base stations SB.sub.1 through SB.sub.J. 
By way of example, FIG. 1 shows cells C.sub.a, C.sub.b, C.sub.d, C.sub.e 
and C.sub.j associated respectively with base stations SB.sub.a, SB.sub.b, 
SB.sub.d, SB.sub.e, and SB.sub.j where a, b, d, e and j are integers lying 
between 1 and J. 
A frequency spectrum {F.sub.k, 1.ltoreq.k.ltoreq.K} is allocated to the 
cellular radiotelephone network RES, where K is a positive integer. The 
frequency spectrum is a series of discrete values uniformly distributed 
within a given frequency band. Prior to commissioning the cellular 
radiotelephone network RES, or at the time of periodic reorganization 
thereof, it is necessary to allocate one or more frequencies selected in 
the spectrum to each of the base stations of the network. In practice, 
between one and seven frequencies are allocated to each cell in the GSM 
network. If the frequency F.sub.k, where k is an integer lying between 1 
and K, is allocated to the cell C.sub.j, the combination (C.sub.j, 
F.sub.k) forms one radiotelephone channel. 
The allocation of frequencies to the cells must satisfy two contradictory 
criteria. Sufficient frequencies must be allocated to handle the traffic 
but the interference between the signals emitted must be limited. 
At any point M in the network, within the cell C.sub.j, for example, a 
receiver of a mobile station receives a sum of signals emitted by the J 
base stations SB.sub.1 through SB.sub.J of the network. 
A predetermined propagation model supplies signals P.sub.1,k through 
P.sub.J,k received at the point M and emitted at the frequency F.sub.k 
from the base stations SB.sub.1 through SB.sub.J of the network. All of 
the signals are expressed in power terms. 
The propagation signals are obtained by calculation or by measurement. 
The sum of the signals emitted at the frequency F.sub.k and received at the 
point M at the same frequency F.sub.k is expressed in the form: 
##EQU1## 
where x.sub.i,k has the value 1 if the frequency F.sub.k is allocated to 
the base station SB.sub.i and X.sub.i,k has the value 0 if the frequency 
F.sub.k is not allocated to the base station SB.sub.i. The set of the 
coefficients X.sub.i,k for 1.ltoreq.i.ltoreq.J and 1.ltoreq.k.ltoreq.K 
defines a frequency allocation plan for the network. The frequency 
allocation plan for the network is the solution to the problem of 
allocating frequencies and indicates the frequency or frequencies 
allocated to each of the base stations of the network. 
On the other hand, the sum of the signals at the frequency F.sub.k received 
at the point M may be expressed in the following manner: 
EQU SU.sub.j,k +I.sub.k 
where SU.sub.j,k is a useful signal emitted at the frequency F.sub.k from 
the base station SB.sub.j and received at the point M in the cell C.sub.j, 
with SU.sub.j,k =P.sub.j,k and 
I.sub.k is a sum of interference signals emitted at the frequency F.sub.k 
from the other base stations of the network and received at the point M in 
the cell C.sub.j. 
The sum of the signals at the frequency F.sub.k received at point M is 
then: 
##EQU2## 
If the frequency F.sub.k is allocated to the cell C.sub.j, the useful 
signal SU.sub.j,k is not null. 
Equation (1) is then written: 
##EQU3## 
Thus, at the point M, the ratio of the sum of the interference due to the 
signals emitted at the frequency F.sub.k and the useful signal at the 
frequency F.sub.k is expressed in the form of a linear function of 
variables x.sub.i,k with 1.ltoreq.i.ltoreq.J. 
For example, if the frequency F.sub.k is allocated to the cells C.sub.a, 
C.sub.b and C.sub.j, as shown in FIG. 1, the following equality is 
verified at point M: 
##EQU4## 
The terms P.sub.a,k, P.sub.b,k and P.sub.j,k =SU.sub.j,k are supplied by 
the propagation model at the point M. 
Referring to FIG. 2 and according to a first embodiment of the invention, 
an algorithm for modeling interference due to the signals emitted at the 
frequency F.sub.k by the base stations SB.sub.1 through SB.sub.J of the 
network RES and received at the point M comprises five steps E1 through 
E5. 
Step E1 is the selection of the frequency F.sub.k from the frequencies 
F.sub.1 through F.sub.K. 
In step E2 the point M in the cell C.sub.j is selected. The propagation 
model is known at the point M and provides the signals P.sub.1,k through 
P.sub.J,k. 
Step E3 assigns the coefficients x.sub.1,k through x.sub.J,k to the signals 
P.sub.1,k through P.sub.J,k In other words, the frequency F.sub.k is 
allocated to predetermined cells of the network RES. 
In step E4 the signals P.sub.1,k through P.sub.J,k are multiplied by 
respective coefficients x.sub.1,k through x.sub.J,k and the sum of the 
products obtained in this way is calculated. 
In step E5 the sum obtained in step E4 is put into the form previously 
indicated: 
##EQU5## 
in order to subtract from it a predetermined threshold S1.sub.k. If the 
sum 
##EQU6## 
is less than or equal to the threshold S1.sub.k, the coefficients 
x.sub.1,k through x.sub.J,k assigned in step E3 correspond to interference 
that is compatible with correct operation of the network. 
If the sum 
##EQU7## 
is greater than the predetermined threshold S1.sub.k, this means that the 
coefficients x.sub.1,k through x.sub.J,k assigned in step E3 are badly 
chosen. 
Division by the signal SU.sub.j,k in step E5 has the advantage that the 
sums and therefore the threshold S1.sub.k are dimensionless quantities. 
Division by the signal SU.sub.j,k is optional, however. 
In one variant of the first embodiment, the step E5 includes the 
calculation of the difference: 
##EQU8## 
The difference D.sub.j,k is to be minimized. 
A function f(D.sub.j,k) is selected, for example equal to: 
EQU F(D.sub.j,k)=e.sup.a.multidot.Dj,k 
where a is a positive real number. 
The function to be minimized to optimize the frequency allocation plan for 
the network is: 
##EQU9## 
In a second embodiment, the interference taken into account is not only the 
interference due to the signals emitted at the frequency F.sub.k, called 
co-channel interference, but also the interference due to signals 
transmitted at all the frequencies F.sub.1 through F.sub.K of the 
spectrum, which are summed to produce a sum I1.sub.k. 
For the second embodiment, equation (1) becomes: 
##EQU10## 
In this equation, R.sub.k,n is a ratio of interference between the 
frequencies F.sub.k and F.sub.n. The ratio R.sub.k,n depends on the 
difference between the frequencies F.sub.k and F.sub.n. To give a first 
example, 
R.sub.k,n =1 if n=k, 
R.sub.k,n =0.01 if n=k-1 or n=k+1, and 
R.sub.k,n =0 if n.noteq.k, n.noteq.k-1 and n.noteq.k+1. 
To give a second example, for the GSM network, 
R.sub.k,n =1 if n=k, 
R.sub.k,n =10.sup.-1.8 if n=k-1 or n=k+1, 
R.sub.k,n =10.sup.-5 if n=k-2 or n=k+2, 
R.sub.k,n =10.sup.-20 if n=k-3 or n=k+3, and 
R.sub.k,n =0 in all other cases. 
On dividing by the useful signal SU.sub.j,k, as previously, the above 
equation becomes: 
##EQU11## 
At point M the ratio of the sum of the interference due to the signals 
transmitted at all the frequencies in the spectrum allocated to the 
network RES and the useful signal at frequency F.sub.k is expressed in the 
form of a linear function of variables x.sub.i,k, with 1.ltoreq.i.ltoreq.J 
and 1.ltoreq.k.ltoreq.K. 
Referring to FIG. 3, and by way of example, the frequency F.sub.k is 
allocated to the cells C.sub.a, C.sub.b and C.sub.j, the frequency 
F.sub.k-1 is allocated to the cell C.sub.e and the frequency F.sub.k+1 is 
allocated to the cell C.sub.d. 
The following equation is then satisfied for the first example: 
EQU SU.sub.j,j +I1.sub.k =P.sub.a,k +P.sub.b,k +P.sub.j,k 
+0,01.multidot.P.sub.e,k-1 +0,01.multidot.P.sub.d,k+1. 
Referring to FIG. 4, an interference modeling algorithm for the second 
embodiment of the invention has five steps E11 through E15. 
Step E11 includes the selection of a first frequency F.sub.k in the 
spectrum and of a set of second frequencies {F.sub.n }. For example, the 
set of second frequencies comprises all the frequencies allocated to the 
radiotelephone network RES. 
Step E12 is the selection of a point M in the cell C.sub.j for which the 
propagation model supplies the signals P.sub.1,1 through P.sub.J,K 
transmitted at the selected first frequency F.sub.k and at selected second 
frequencies from all the base stations of the radiotelephone network. 
Step E13 assigns the coefficients x.sub.1,1 through x.sub.J,K to the 
signals supplied by the propagation model respectively. As previously, the 
variable x.sub.j,k has the value 0 or 1. 
In step E14 interference ratios R.sub.k,1 through R.sub.k,K are allocated 
to the signals supplied by the propagation model respectively. An 
interference ratio R.sub.k,n depends on the difference between the first 
frequency F.sub.k and one F.sub.n of the second frequencies. The 
interference ratio R.sub.k,n is assigned to the signal P.sub.i,n for 
1.ltoreq.i.ltoreq.J. 
Step E15 multiplies the signals P.sub.1,1 through P.sub.J,k supplied by the 
propagation model by the respective coefficients x.sub.1,1 through 
x.sub.J,K and by the respective interference ratios R.sub.k,1 through 
R.sub.k,K, followed by the addition of all the products obtained. A 
predetermined threshold S.sub.2k is subtracted from the sum obtained in 
this way to determine if the coefficients x.sub.1,1 through x.sub.J,K 
assigned in step E13 guarantee interference below the threshold S2.sub.k. 
As an alternative to this, step E15 further includes the division of the 
sum obtained by the useful signal SU.sub.j,k in the cell C.sub.j, as in 
step E5 previously described. 
In one variant of the second embodiment the step E15 includes calculation 
of the difference: 
##EQU12## 
A function f(D.sub.j,k) is selected such that: 
f(D.sub.j,k) is close to 0 for D.sub.j,k .ltoreq.0, and 
f(D.sub.j,k) increases rapidly when D.sub.j,k .gtoreq.0 
The function selected is, for example: f(D.sub.j,k)=e.sup.aDj,k where a is 
a strictly positive real number. 
To optimize the frequency allocation plan for the network: 
(i) the following function is minimized: 
##EQU13## 
to minimize the interference; (ii) the following function is maximized: 
##EQU14## 
to maximize the traffic. 
In a third embodiment, the sum of the signals received is averaged over a 
set of points M.sub.j,1 through M.sub.j,s situated in the cell C.sub.j, 
where S is a positive integer. 
At a point M.sub.j,s, where s is an integer lying between 1 and S, the 
useful signal emitted at the frequency F.sub.k by the base station 
SB.sub.j is denoted SU.sub.j,k,s. The sum of the interference signals at 
the point M.sub.j,s emitted at the frequency F.sub.k from the base 
stations other than the base station SB.sub.j is denoted I.sub.k,s. The 
propagation model at the point M.sub.j,s supplies signals P.sub.1,1,s 
through P.sub.J,K,s s received at the point M.sub.j,s and emitted at the 
frequencies F.sub.1 through F.sub.K by the base stations of the cells 
C.sub.1 through C.sub.J. 
The sum of the interference due to the signals emitted at the frequency 
F.sub.k and the useful signal at frequency F.sub.k, averaged over the 
points M.sub.j,1 through M.sub.j,S in the cell C.sub.j, is: 
##EQU15## 
At the points M.sub.j,1 through M.sub.j,S of the cell C.sub.j, the average 
of the ratio of the sum of the interference due to the signals emitted at 
the frequency F.sub.k and the useful signal at frequency F.sub.k is 
expressed in the form of a linear function of variables x.sub.i,k with 
1.ltoreq.i.ltoreq.J. 
Referring to FIG. 5, an interference modeling algorithm in the third 
embodiment has five steps E.sub.111 through E.sub.115. 
Step E111 is the selection of the points M.sub.j,1 through M.sub.j,S, for 
example, distributed in the cell C.sub.j for which the propagation model 
provides the received signals {P.sub.i,k,s, 1.ltoreq.i.ltoreq.J, 
1.ltoreq.k.ltoreq.K and 1.ltoreq.s.ltoreq.S} which are emitted from all 
the cells and at all the frequencies. 
The step E112 is similar to the step E1 previously described (FIG. 2). The 
frequency F.sub.k is selected. 
In step E113, coefficients {x.sub.i,k, 1.ltoreq.i.ltoreq.J} are assigned to 
the signals {P.sub.i,k,s, 1.ltoreq.i.ltoreq.J and 1.ltoreq.s.ltoreq.S}. 
For a given cell C.sub.i the same coefficient x.sub.i,k with the value "0" 
or "1" is therefore assigned to S signals P.sub.i,k,s. Alternatively, a 
coefficient is assigned to each signal P.sub.i,k,s. 
Step E114 calculates the sum: 
##EQU16## 
Step E115 is a calculation of the arithmetical mean of the above sum, from 
which a predetermined threshold S3.sub.k is subtracted. This verifies if 
the assignment of the coefficients {X.sub.i,k } in step E113 limits 
interference to a value below the threshold S3.sub.k. 
The difference D.sub.j,k obtained contributes to establishing the 
optimization criterion as in the first and second embodiments. 
In the above third embodiment, the mean calculated is an arithmetical mean. 
As an alternative to this, the mean calculated is a mean for the 
coefficient p, where p is a positive real number: 
##EQU17## 
In particular, if 
##EQU18## 
is a quadratic mean, and if 
##EQU19## 
is equal to the maximal value of interference at the points M.sub.1 
through MS of the cell C.sub.j : 
##EQU20## 
As an alternative, the interference taken into account is not only the 
interference due to the signals at frequency F.sub.k. The interference due 
to all the frequencies F.sub.1 through F.sub.k of the spectrum allocated 
to the radiotelephone network RES is also considered. 
The mean of the ratio of the sum of the interference due to the frequencies 
F.sub.1 through F.sub.k and the useful signal at the frequency F.sub.k is: 
##EQU21## 
In other embodiments the interference is averaged over a set of points that 
are distributed across a plurality of adjacent cells to obtain a mean 
interference for these adjacent cells, or the interference is averaged 
over all of the cells of the network. 
In practice the frequency allocation problem is directed to a target to be 
achieved dependent on a "cost" function that combines interference 
constraints and traffic requirements in the cells that must be complied 
with. The solution of the problem is the allocation plan expressed in the 
form of the set {X.sub.j,k, 1.ltoreq.J, 1.ltoreq.k.ltoreq.K}. 
The target is chosen from, for example: 
maximizing total effective traffic TTE in a cellular radiotelephone 
network, 
minimizing interference, 
minimizing a number NFU of frequencies used in the network, or 
maximizing a spectral efficiency ES. 
For example, the total effective traffic TTE is: 
##EQU22## 
where r.sub.j,k is a function of a difference D.sub.j,k between the 
interference at the frequency F.sub.k for the cell C.sub.j and a 
predetermined threshold. 
The function r.sub.j,k varies as a function of D.sub.j,k between 0 and 1, 
tends towards 1 when the variable D.sub.j,k tends towards -.infin., i.e. 
when the interference at the frequency F.sub.k for the cell C.sub.j is 
very low, and towards 0 when the variable D.sub.j,k tends towards 
+.infin., i.e. when the interference at the frequency F.sub.k for the cell 
C.sub.j is very high. 
The function r.sub.j,k shown in FIG. 6 is, for example: 
##EQU23## 
in which tanh denotes the hyperbolic tangent. 
The process of interference minimization is effected, for example, on a 
mean interference calculated for all the cells C.sub.j and for all the 
frequencies F.sub.k such that the associated coefficient x.sub.j,k is 
equal to 1. 
The spectral efficiency ES is: 
##EQU24## 
The constraints to be complied with are: 
minimizing interference, for example the mean power level received per 
cell, for all the cells C.sub.1 through C.sub.j of the network and all the 
frequencies F.sub.1 through F.sub.k of the spectrum; 
assigning sufficient frequencies per cell to handle all the traffic: 
##EQU25## 
where NFC.sub.j is an integer equal to the minimum number of frequencies 
to be allocated to the cell C.sub.j ; 
choosing the variables x.sub.j,k such that: 
EQU X.sub.j,k .epsilon.{0,1} for 1.ltoreq.j.ltoreq.J and 1.ltoreq.k.ltoreq.K.