Antenna beam coverage reconfiguration

A earth station calling another station sends a link setting-up a request to a control station. The control station memorizes in a transformed reference system the contour of a global geographical coverage including all the earth stations together with the earth positions of the latter. Subsequent to the request, the control station simulates the optimum evolution of the radioelectric coverages of the satellite so as to include, both on emitting and receiving, the calling and called stations in respective coverages with guaranteed minimum antenna gains. The total power of the satellite and the positions of the stations are notably considered in this simulation. If the result of simulation is positive, an emission authorization is sent by the control station to the calling station, and satellite antennae are reconfigured by phase shift and power control values emitted by the control station.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates very generally to telecommunications between earth 
transmitting-receiving stations via a satellite. 
More exactly, the invention relates to a satellite radioelectric beam 
coverage reconfiguration method thereby dynamically managing beam 
coverages as a function of requests from earth stations, while maintaining 
beam coverages with minimum size to meet a power balance within the 
satellite. The radioelectric coverages of the satellite are reconfigured 
as a function of the variations in the traffic volume and the positions of 
stationary or moving earth stations using the satellite as radioelectric 
relay. This reconfiguration adapts the resources of the payload in the 
satellite to the characteristics of the traffic at each moment. The 
invention is especially suited for cases of sporadic traffic such as that 
generated by VSAT (Very Small Aperture Terminal) or mobile stations. 
2. Description of the Prior Art 
Initially the satellites were designed to route communications from one 
point to another, as via a cable, and the extended coverage of the 
satellite was utilized to set up long distance links. Thus the "Early 
Bird" satellite linked two stations on either side of the Atlantic Ocean. 
Owing to the limited performance of these satellites, earth stations 
equipped with large antennae and hence very costly, had to be used. The 
increase in size and power of the satellites has subsequently reduced the 
size of the earth stations and hence their cost and consequently 
multiplied the number of these stations. Another quality of the satellite 
resulting from its extended coverage and hence its capacity to diffuse or 
collect, has thus been utilized: instead of transmitting signals from one 
point to another, an emitter in a given station can emit to a large number 
of station receivers via the satellite or, conversely, a large number of 
station can emit to a central station. 
The first designed satellites uses single-beam antennae which have certain 
drawbacks: either the satellite provides the coverage of a large earth 
surface but the satellite's antenna gain is limited by the aperture angle 
of the beam; or the satellite provides the coverage of a small earth 
surface and in this case the antenna gain is higher but the beam cannot 
cover stations that are geographically too distant. Thus with a 
single-beam satellite a choice must be made between firstly an extended 
coverage but with low antenna gain, and hence links with high error rates, 
and secondly, a reduced coverage with a high antenna gain but whereby 
stations that are too distant cannot be interconnected. 
The multi-beam antenna techniques harmonize these two alternatives. The 
area coverage of the satellite is extended because it results from the 
juxtaposition of several beams, and each beam offers an antenna gain all 
the higher that the aperture of the beam is reduced. Typically the 
multi-beam antennae on board a satellite consist of radiating elements, 
and combined respectively with beam-forming networks. A beam-forming 
network supplying the radiating elements of an antenna further comprises 
phase-shifters and power dividers whereby the associated antenna can be 
configured in a special way. Both on receiving and on emitting the antenna 
is thus programmed for particular radiation patterns. A radiation pattern 
is notably expressed by a gain as a function of on an angle with respect 
to the antenna axis. 
According to the prior art, two methods are chiefly used within the context 
of a multi-beam satellite. 
According to a first method known as "scanning beam"-type, predetermined 
coverage areas are illuminated cyclically by a same antenna beam whose 
orientation is controlled by special control values programming a 
beam-forming network. The stations located in a given coverage area only 
emit or receive information when said area is illuminated by the beam. In 
the absence of any memorization unit on board the satellite, at least two 
beams are necessary at each time: one to establish an uplink from the 
emitters in the earth stations to the satellite, the other to establish a 
downlink from the satellite to the receivers in the earth stations. 
According to a second known method, the proposal is to use on receiving and 
emitting a certain number of respective beams and allocate respective 
variable capacities to the beams by modifying the pass-band in each one of 
them. To do so a dynamic allocation of the payload channels is obtained 
between the beams as a function of the traffic request in these beams. 
Thus, according to the prior technique, no beam coverage reconfiguration 
method is available to satisfy requests from earth stations as a function 
of their geographical positions and the traffic volumes. 
OBJECTS OF THE INVENTION 
The main object of the invention is to provide a method for reconfigurating 
antenna beam coverages in a satellite network, based on modifications or 
reconfigurations of beam radioelectric coverages on the ground, contrary 
to the known methods consisting in modifying capacities for predetermined 
beam coverages. 
Another object of the invention is to satisfy requests from earth stations 
as a function of their geographical positions and volume traffics. 
SUMMARY OF THE INVENTION 
Accordingly, a method for reconfiguring coverages of in respective beams a 
satellite re-transmitting telecommunications set up between earth 
emitting-receiving stations 
by modifying the phase shifting and power control values of beam-forming 
means associated respectively to radiating means of said beams in said 
satellite, both on receiving for telecommunications emitted by first earth 
stations amongst said earth emitting-receiving stations to said satellite 
and on emitting for said telecommunications to be re-emitted by said 
satellite to second earth stations amongst said earth emitting-receiving 
stations, predetermined numbers of telecommunication channels being 
associated to said beams, respectively, 
to set up a telecommunication link between calling one and called one of 
said earth emitting-receiving stations via said satellite, 
said method being preceded by the transmission of a link setting-up request 
from said calling station to a control station, via a signalling channel 
of said satellite, 
said method comprising, by simulation in said control station, one of first 
and second alternatives separately for each of the calling and called 
stations, then a final step, 
(a.sub.1)--said first alternative, wherein said each of the calling and 
called stations is not located in any of said coverages, comprising the 
first steps of: 
(a.sub.10)--determining amongst all said coverages, a coverage nearest to 
said each of the calling and called stations into a nearest coverage, 
(a.sub.11)--iteratively, reducing in size each of the coverages other than 
said nearest coverage, until said nearest coverage is modified to include 
in said nearest coverage said each of the calling and caller stations with 
a first antenna gain, and 
(a.sub.12)--deriving a simulated link setting-up authorization for said 
each of the calling and called stations when one of said channels 
associated to said nearest coverage is free, and 
(a.sub.2)--said second alternative wherein said each of the calling and 
called stations is located in one of said coverages comprising one of said 
two steps of, 
(a.sub.20)--when at least one of said channels associated to said one of 
the coverages is free, deriving of a simulated link set up authorization 
for said each of the calling and called stations, 
(a.sub.21)--when all said channels associated to said one of the coverages 
are busy, searching a coverage adjacent to said each of the calling and 
called stations and having a associated free channel, and in response to a 
searching having a positive result, exchanging of station load between 
said one of the coverages and said adjacent coverage by reducing said one 
of the coverages and increasing said adjacent coverage so that said each 
of the calling and called stations is located in said adjacent coverage, 
and deriving a simulated link setting-up authorization for said each of 
the calling and called stations, and 
(b)--said final step comprising, when simulated link setting-up 
authorizations are derived both for said calling and called stations, 
emitting an emission authorization to said calling station, and phase 
shift and power control values from said control station to said satellite 
to reconfigure said radiating means in said satellite. 
According to another embodiment of the invention, said first alternative 
comprises parallel to said first steps, the steps of: 
(a.sub.10 ')--determining amongst all said coverages a lowermost surface 
coverage, 
(a.sub.11 ')--iteratively, reducing in size each of said coverages other 
than said lowermost surface coverage whilst maintaining in said converages 
stations which are active prior to said link setting-up request, until 
said lowermost surface coverage is increased to include in said lowermost 
surface coverage said each of the calling and called stations with a 
second antenna gain, then 
(a.sub.12 ')--selecting one of said lowermost surface coverage and nearest 
coverage into a selected coverage as a function of the higher of said 
first and second antenna gains to include said station in said selected 
coverage, and 
(a.sub.13 ')--deriving a simulated link setting-up authorization for said 
each of the calling and called stations when one of said channels 
associated to said selected coverage is free. 
However, as an alternative, the first two steps in the first alternative 
can be replaced by the determinating and reducing steps (a.sub.10 ') and 
(a.sub.11 ') indicated above. 
The control station comprises simulation digital processing means whereby 
all the computations relating to the aforesaid steps can be made. In order 
to make operational the method embodying the invention, notably in terms 
of simulation time by the control station, the beam coverages are 
memorized at each time in the control station in the form of discrete 
points associated to the contour points of said coverages, in a 
transformed reference system defined by: 
EQU u=sin .theta. cos .PHI. 
EQU v=sin .theta. sin .PHI. 
in which .theta. and .PHI. respectively designate elevation and azimuth 
coordinates in a spherical reference system centered on said radiating 
means of the satellite. 
This approximation of the coverage real contours by polygonal contours 
allows advantageous processes of computation by the control station. 
Thus, according to a first aspect of these computation processes, the step 
of determining a coverage nearest to said each of the calling and called 
stations further comprises the steps of 
incrementing a director coefficient to define a sheaf of straight lines 
each passing through a point associated to said each of the calling and 
called stations and intercepting coverage polygon sides into respective 
intersection points, 
computating distances between said point associated to said each of the 
calling and called stations and said intersection points, and 
selecting of a minimum distance from said computed distances thereby 
determining a coverage whose a side is nearest to said associated point. 
According to a second aspect of the computation processes said step of 
reducing in size each of the coverages other than said nearest coverage 
further comprises, for each side of a polygon associated to said each of 
the coverages in said transformed reference system, the steps of 
incrementing a parameter to define a sheaf of straight lines parallel to 
said each side, and 
determinating an intersection point associated to a first active station 
which is located in said each of the coverages with a straight line 
segment of said sheaf so that said straight line segment forms a side of 
said polygon of said each of the coverages reduced in size.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Referring to FIG. 1 a satellite network installation for carrying out the 
method embodying by the invention comprises a satellite 1, a plurality of 
earth stations S.sub.1 to S.sub.8 and a control station SC. On receiving, 
an antenna of satellite 1 is configured to provide a constant global 
coverage CG of a given earth surface including all the earth stations 
S.sub.1 to S.sub.8 and the control station SC, owing to a aperture angle 
of beam FC very wide. Any earth station S.sub.1 to S.sub.8 wishing to set 
up a link through the satellite network to transmit information to another 
earth station, sends a request to set up a link to the control station SC 
via satellite 1. This request is carried by a signalling channel of the 
global coverage receive beam FC in direction of satellite 1, to be 
re-transmitted to the control station SC. In response to the request the 
control station SC computes, by simulation, new beam coverages of 
satellite 1, both on emitting and receiving, and, through a specific link, 
transmits beam-forming network control values to program the coverages of 
the beams of several variable coverage antennae of satellite 1. 
By way of example, referring to FIG. 1, it is assumed that earth station 
S.sub.5 has to emit information to the called station S.sub.l ; it is 
necessary both to reconfigure, on emitting, the downlink beam FD whose 
transmission coverage CD does not include station S.sub.5 and, on 
receiving, the uplink beam FM whose receive coverage CM does not include 
station S.sub.1. 
As will be shown hereafter the beam-forming network control values 
transmitted by control station SC control, in the satellite, phase 
shifters and power dividers transmitting/receiving signals to/from 
radiating element(s) of transmit/receive antennae of satellite 1, 
respectively. 
The invention is not limited to the insertion of earth stations in the new 
beam coverages, but also comprises the reduction of the coverages so as to 
maintain a high antenna gain and hence good quality links in terms of 
error rate, the exchange of capacity between adjacent coverages so as to 
remedy the capacity saturation of a beam, etc. 
As shown schematically in FIG. 2, an antenna with radiating elements, for 
example of the flat antenna type, comprises a plurality of radiating 
elements ER.sub.1 to ER.sub.N, whose the number can be very high, 
distributed over the surface of the antenna. The antenna assumed here to 
operate on emitting, is preceded by a beam-forming network. This 
beam-forming network further includes variable power dividers and variable 
microwave phase shifters associated with the radiating elements, 
respectively, and controlled by beam orientation modifying means. Through 
suitable choices of phase shifts in the phase shifters and power 
distributions through power dividers, various antenna radiation patterns 
are produced. The variations in these phase shifts and power distributions 
modify the inclination of the phase plane with respect to the surface of 
the radiating elements and the antenna gain and thus the orientation of 
the beam produced by the antenna and the beam aperture. Different 
radiation patterns are obtained in terms of gain as a function of the 
angle .beta. between the direction of radiation and the axis z'z of the 
antenna. 
The radiating elements are spaced very slightly therebetween in view of 
optimum coupling and, at each point M located at a given distance from the 
antenna, the radiation results from the respective contribution of each 
radiating element. 
On receiving, the principle of operation of the antenna is identical: phase 
shifters and power dividers are controlled in a suitable way to confer an 
optimum gain on the antenna for a given solid angle of the antenna of 
satellite 1, defining a reception beam. 
The principle of operation of the radiating element antennae will not be 
dealt with further detail as it is assumed known to those skilled in the 
art. 
Likewise, the computation by the control station SC of the phase and 
amplitude control values for the radiating elements of emitting and 
receiving antennae as a function of the optimum beam coverages obtained by 
simulation within the context of the method according to the invention 
will not be detailed. Nevertheless it will be remembered that the control 
station SC includes computing means to extract these control values which 
are transmitted, via the specific link, to the beam-forming networks in 
satellite 1. Digital processes of computing these control values as from 
desired beam coverages are for example the min-max method and the least 
squares method. 
Referring to FIG. 3, a process for memorizing the contours of the beam 
coverages by control station SC is now referred to. This control station 
SC has to check, after reception of a request and the simulated 
modification of beam contours as will be described below, that the minimum 
gain for each beam coverage contour is greater than a minimum level 
corresponding to a minimum quality of the links for said beam. Such a 
computation of minimum gain can not be envisaged for the whole contour of 
the beam coverage. This solution would, in fact, involve the use of 
complex algorithms and hence very long computation times. 
Thus, in practice, similarly to the processes of representing earth 
surfaces by digital processing computers, control station SC memorizes the 
beam coverage contours in a discrete form. Thus the gain computations on 
the coverage contour of each beam are only made for a certain number of 
discrete points on this contour. 
For this purpose an angular spacing is chosen to define a "step" between 
each discrete point of the representation of the coverage. This angular 
spacing results from a compromise between the accuracy of the processings, 
or computations, achieved for the coverage contours and the speed of these 
processings by digital processing means in control station SC. 
Moreover, as from this discrete beam coverage representation, the real 
coverage can be obtained by using algorithms of min-max or least squares 
type. From the real coverage are deduced beam forming network control 
values. As shown in FIG. 3, in a three-dimensional Cartesian system (O, x, 
y, z) centered on a radiating element antenna of satellite 1, any point P 
of the space is plotted by spherical coordinates (.theta., .PHI., r). To 
characterize a beam and hence a solid angle, only the angular coordinates, 
elevation .theta. and azimuth .PHI., are needed. Nevertheless it is more 
advantageous for the memorization of beam coverages by central station SC, 
to work within a transformed Cartesian system (u, v). 
In this transformed reference system (u, v), the spherical coordinates 
(.theta., .PHI.) needed to parameter a solid angle, here a beam, are 
transformed into coordinates (u, v) in the form: 
EQU u=sin .theta.. cos .PHI. 
EQU v=sin .theta.. sin .PHI.. 
Through the bijective nature of this transformation, any result of 
computation made in the transformed reference system (u, v) can be 
transposed into the spherical coordinate system. 
Thus in control station SC, each beam coverage contour is memorized in the 
form of a number of discrete points around said contour in the sampling 
transformed reference system (u, v). Elements additional to the notions 
described above are disclosed in the article "Spacecraft multi-beam and 
contoured-beam antennas" by P. Balling, published in Agard Lecture Series 
LS-151, pages 4-1 to 4-23, 1987. 
As shown in FIG. 4, all beam coverage, whose form is substantially circular 
on the ground is represented in a discrete form in the transformed 
reference system (u, v) by a closed polygonal contour C.sub.1, C.sub.2, 
C.sub.3 shown by straight line segments. Each contour constitutes an 
isogain contour inside which the gain is greater than a guaranteed minimum 
gain corresponding to an error rate or a determined quality of link. 
The main steps of the satellite beam coverage reconfigurating method are 
now indicated referring to FIG. 5. 
At the start of an initial step E.sub.00, a station S.sub.k having to set 
up a link with a station S.sub.l so as to emit information thereto, 
previously sends a link setting-up request a link moreover comprising its 
address k and the address l of the called earth station S.sub.1. This 
request, carried by the signalling channel of the global coverage receive 
beam CG, is received by satellite 1 and re-emitted to control station SC. 
Control station SC comprises simulating means for carrying out the method 
embodying the invention, and notably means for memorizing in reference 
system (u, v) discrete digitized representation of the global coverage on 
the ground seen from the satellite. In response to this request, station 
SC derives an emission authorization, or else a rejection, or else a 
demand to queue the request. 
This answer is re-emitted to earth station S.sub.k via the signalling 
channel. 
As previously signalled, the beam-forming networks associated to the 
antennae of satellite 1 are reconfigured both on receiving in order for 
the calling earth station S.sub.k to be included in a minimum gain receive 
coverage of an antenna of satellite 1, and on emitting so that the 
emission beam coverage of an antenna of satellite 1 covers the called 
station with a minimum antenna gain. This latter point is high-lighted in 
step E.sub.01 of the algorithm in FIG. 5. Thus one of two following series 
of steps E.sub.1 and E.sub.2 is performed, by simulation in the station 
SC, for the calling station S.sub.k and for the called station S.sub.l 
respectively, and the emission authorization or the rejection of the 
request is produced by station SC respectively according to whether the 
simulation according to the algorithm in FIG. 5 leads to a simulated 
authorization for the two calling and called stations S.sub.k and S.sub.l, 
or to a simulated rejection for at least one of the two stations S.sub.k 
and S.sub.l. In the rest of the description the two stations S.sub. k and 
S.sub.l are designated as station S, whilst being aware that the next 
series of sub-steps to be simulated for both stations S.sub.k and S.sub.l 
and provide simulated authorization results respectively for the two 
station S.sub.k and S.sub.l so that the emission authorization is 
transmitted from control station SC to station S.sub.k. 
In control station SC, the coverages of all the beams, both on emitting and 
receiving, of satellite 1 are memorized in discrete form as shown in FIG. 
4, i.e., in the form of polygons in the transformed reference system (u, 
v). The "geographical" position in the system (u, v), and the associated 
address of each station are also memorized in station SC. 
A final processing initial sub-step E.sub.02 of the algorithm consists in 
studying if station S belongs to a emission coverage (when S is a calling 
party) or reception coverage (when S is a called party) with the given 
configuration of the beam-forming networks on receiving the link 
setting-up request. 
According to a first alternative (step E.sub.1), station S does not belong 
to a beam coverage C.sub.i, the other alternative being described 
subsequently referring to FIG. 11. Thus station S is, like stations 
S.sub.1 or S.sub.5 in FIG. 1, located outside a beam coverage. 
Modification of the coverage of one of the beams is therefore necessary to 
include station S in it. The coverages of the beams delimit geographical 
earth areas whose contours define boundaries on which links with satellite 
1 are guaranteed with a minimum quality in terms of antenna gain or 
transmission error rate. These boundaries also define geographical points 
where a minimum link quality with satellite 1 is also guaranteed. 
Two cases are considered according to this invention for the choice of the 
beam coverage to be modified so as to include station S: either according 
to a first case, this beam coverage is the coverage having the lowermost 
earth surface amongst all the beam coverage of the satellite, or else, 
according to a second case, this coverage is the coverage nearest to the 
station S. The two cases are handled separately by the control station and 
the solution offering the highest antenna gain by simulation in station S 
is selected (sub-step E.sub.15). 
According to the first case, the choice of the lowermost surface coverage 
results from the following observation: the lowermost surface coverage 
offers the highest antenna gain and hence is the most adequate to 
"enlarge" so as to include station S whilst maintaining a sufficient 
antenna gain. It is recalled that each beam offers antenna gain all the 
higher when the aperture angle of the beam is low. The determination of 
the coverage with the lowermost surface is made in control station SC by 
locating, in a representation of the type shown in FIG. 4, the coverage 
with a minimum geographical coverage by area computation. 
After the determination by computation of the lowermost surface coverage 
C.sub.d (sub-step E.sub.11a), iteratively each C.sub.i of the coverages, 
with 1.ltoreq.i.ltoreq.I and I designating the number of existing beam 
coverages at the moment of the setting-up request, is reduced according to 
a method (sub-step E.sub.12a) described referring to FIG. 8, and a 
modification of the determined coverage C.sub.d is simulated to include in 
it station S at the level of its boundary (sub-step E.sub.13a). Reductions 
in beam coverages are simulated until a modification of coverage C.sub.d 
to include station S leads to a sufficient antenna gain of the level of 
its modified boundary and hence of station S. As soon as a sufficient 
antenna gain for station S, at the level of its modified boundary of 
coverage C.sub.d, can be obtained after i=L reductions in coverage, a 
simulated gain result is recorded. 
According to the second case, the coverage C.sub.d nearest to the station S 
is firstly determined (sub-step E.sub.11b). Then in the same way as in the 
first case above, each C.sub.i of the coverages, with 1.ltoreq.i.ltoreq.I 
and I being the total number of coverages, is reduced (sub-step 
E.sub.12b), and an insertion of station S in the determined coverage 
C.sub.d is simulated (sub-step E.sub.13b). As a function of the gain 
obtained for station S, at the boundary of the modified coverage C.sub.d 
to include it, other coverages are reduced, and the theoretical gain 
results for station S in the respective modified coverages are recorded. 
It should be noted that the reduction, on emitting or receiving, of a 
satellite beam coverage, has the effect of reducing the power used by the 
satellite for this coverage. In view of a total available power in the 
satellite, the reduction of a coverage C.sub.i enables the enlargement of 
another coverage, in this case C.sub.d. Priorities can be defined in the 
order of selecting the coverages C.sub.i to be reduced. Thus for example, 
it may appear of interest to initially reduce coverage C.sub.d. 
As indicated in sub-step E.sub.15 in FIG. 5, as a function of the antenna 
gain results obtained for the two cases, i.e., the selection of the 
lowermost surface coverage and the selection of the coverage nearest to 
station S, the case offering the highest theoretical antenna gain for 
station S in the vicinity of the boundary of coverage C.sub.d is adopted. 
An emission authorization simulated for station S is set up for station 
S.sub.k, aware that at the same time the simulated emission and reception 
authorizations should be obtained for stations S.sub.k and S.sub.l in 
order for the real emission authorization to be sent by control station 
SC. 
The sub-steps E.sub.11a to E.sub.14a and E.sub.11b to E.sub.14b, relating 
respectively to the parallel processings of the two coverage determination 
cases C.sub.d are now detailed, by notably introducing the representation 
of the coverages in the transformed reference system (u, v). 
Sub-steps E.sub.11a to E.sub.14a relating to the first case are first of 
all studied. 
It is recalled that step E.sub.11a determining the coverage with the 
lowermost surface takes place in the transformed system (u, v) by surface 
computation. 
The reduction of any beam coverage C.sub.i during sub-step E.sub.12a is 
described below referring to FIG. 8. In the transformed system (u, v), 
each beam coverage is represented by a polygon and for example the beam 
coverage shown in FIG. 8 is delimited by a polygon with six apexes 
I.sub.1, I.sub.2, I.sub.3, I.sub.4, I.sub.5 and I.sub.6. For each side 
(I.sub.1, I.sub.2), (I.sub.2, I.sub.3), . . . , (I.sub.5, I.sub.6) and 
(I.sub.6, I.sub.1) of the polygon, a sheaf of parametered straight lines 
(.DELTA..sub.o) to (.DELTA..sub.n) parallel to this side is determined. 
These parametered straight lines have the same director coefficients tan 
.alpha..sub.4,5 and are determined by the equations (FIG. 7): 
EQU u=(tan .alpha..sub.4,5)v+B.sub.n, 
in which B.sub.n is a parameter incremented by a predetermined step 
.epsilon., so that the straight lines are secant with the polygon in the 
direction to the interior of the coverage surface. As from each side of 
the polygon, control station SC selects the first of the parametered 
straight lines including an active earth station S.sub.i by using the 
discrete representation of coverage C.sub.i stored in control station SC. 
In FIG. 8, the active stations, emitting when S=S.sub.k or receiving when 
S=S.sub.1, are designated by circles, whereas the inactive stations, i.e. 
neither emitting nor receiving, are designated by crosses. 
Take for example a first active station S.sub.j belonging to a straight 
line of the parallel straight line sheaf nearest to the side (I.sub.4, 
I.sub.5). Two alternatives are considered within the context of this 
invention to reduce the coverage C.sub.i, relative to the side (I.sub.4, 
I.sub.5). 
According to a first alternative the coverage (I.sub.1, I.sub.2, I.sub.3, 
I.sub.4, I.sub.5 and I.sub.6) is transformed into (I.sub.1, I.sub.2, 
I.sub.3, I.sub.4, S.sub.j, I.sub.5 and I.sub.6) for side (I.sub.4, 
I.sub.5). In this discrete representation of the coverages, it is possible 
that several stations S.sub.j, such as two stations S.sub.j1 and S.sub.j2, 
belong simultaneously to a first parametered straight line of the straight 
line sheaf including at least one station. To form the polygon (I.sub.1, 
I.sub.2, I.sub.3, I.sub.4, S.sub.j =(S.sub.j1 or S.sub.j2 ), I.sub.5, 
I.sub.6) is chosen the station, S.sub.j1 or S.sub.j2, for which the sum of 
distances 
EQU (d(S.sub.j, I.sub.4)+d(S.sub.j, I.sub.5)) 
is the minimum, 
in which d designates the distance operator. This reduced polygon 
corresponds to a surface for which the coverage reduction is minimum. 
According to a second alternative the coverage (I.sub.1, I.sub.2, I.sub.3, 
I.sub.4, I.sub.5, I.sub.6) is transformed into (I.sub.1, I.sub.2, I.sub.3, 
P, Q, I.sub.6) relatively to side (I.sub.4, I.sub.5) in which P and Q 
respectively designate two intersection points of a first straight line of 
the parallel straight line sheaf, including at least one active earth 
station, with the sides (I.sub.3, I.sub.4) and (I.sub.5, I.sub.6) adjacent 
to the considered side (I.sub.4, I.sub.5). 
The two coverage reduction sub-steps E.sub.12a and E.sub.12b of the main 
algorithm in FIG. 5, according to the two alternatives, are summarized in 
the algorithm in FIG. 7. It should be noted that the reduction of the 
coverage of beam C.sub.i is not achieved only relatively to one side, such 
as side (I.sub.4, I.sub.5), of the polygon associated to the coverage in 
the transformed reference system (u, v), but also relatively to all the 
sides of the polygon. After these various polygon reductions numbering not 
more than the number of sides of the polygon, the corresponding beam 
coverage reduction, when emitting or receiving, in satellite 1 is 
controlled by control station SC by programming beam-forming networks 
associated to the corresponding antenna of the satellite. This programming 
is achieved after the simulated emission/reception authorizations have 
been obtained for the calling station S.sub.k and called station S.sub.l. 
Referring to FIG. 9, sub-step E.sub.13a for inserting station S in the 
determined coverage C.sub.d, here of lowermost surface, by simulation in 
control station SC is now detailed. In the diagram in FIG. 9, the polygon 
associated to a beam coverage C.sub.i comprises, for example, four apexes 
I.sub.1, I.sub.2, I.sub.3 and I.sub.4. The start of this insertion 
sub-step consists in determining the side (I.sub.p, I.sub.p+1) nearest to 
station S, here (I.sub.2, I.sub.3). Then the beam coverage (I.sub.1, 
I.sub.2, I.sub.3, I.sub.4) is modified into coverage (I.sub.1, I.sub.2, S, 
I.sub.3, I.sub.4) whose surface is increased by adding the triangle 
(I.sub.2, S, I.sub.3), station S being the calling station S.sub.k or 
called station S.sub.1 to be included in the beam, on receiving or 
emitting, of an antenna of satellite 1. 
Concerning sub-steps E.sub.11b to E.sub.14b of the main algorithm, the 
sub-steps E.sub.12b and E.sub.13b are identical to sub-steps E.sub.12a and 
E.sub.13a described above, and sub-step E.sub.11b consists in the 
determination, by simulation in control station SC, of the coverage 
C.sub.d nearest to station S, i.e., station S.sub.k or S.sub.l. 
Referring to FIG. 10, relative to sub-step E.sub.11b, i.e., C.sub.i with 
i=1, 3 or 4, the coverage nearest to a station S, calling station S.sub.k 
or called station S.sub.l, should be modified to include this station in 
it. A straight line sheaf (.DELTA..sub.t) passing through S with 
coordinates u.sub.S and v.sub.S is determined by the equations (FIG. 6): 
EQU u=(tan .alpha..sub.t)v+[u.sub.S -(tan .alpha..sub.t).v.sub.S)] 
by discretely incrementing a director coefficient tan .alpha..sub.t as from 
that of a predetermined line .DELTA..sub.o of this sheaf. For each 
straight line (.DELTA..sub.t) a/some point(s) of intersection of straight 
line (.DELTA..sub.t) with the polygon side(s) nearest to station S is/are 
computed. Thus by way of example in FIG. 10, the straight line 
(.DELTA..sub.t) possesses two intersection points M.sub.t1 and M.sub.t4 
with two respective sides, such as (I.sub.p, I.sub.p+1), of the polygons 
associated to coverages C.sub.1 and C.sub.4. By successive iterations of 
the incrementation of the director coefficient tan .alpha..sub.t 
parametering the straight line sheaf and the search for intersection 
points, a set of points: 
EQU .zeta..sub.MT =.zeta.M.sub.t .DELTA..sub.k .andgate.(I.sub.p, 
I.sub.p+1).noteq.{.PHI.}.zeta. 
is obtained. 
The minimum distance between the point associated to station S and any one 
of points M.sub.t is then determined. The side to which the intersection 
point M.sub.t with a minimum distance from station S belongs, is that of 
the beam coverage determined as the coverage nearest to station S. 
The algorithm in FIG. 6 shows various sub-steps for determining the 
coverage nearest to station S (E.sub.11b). In this algorithm the minimum 
distance is determined iteratively for each new parametered straight line 
(.DELTA..sub.t) by comparison of the distance of point M.sub.t of this 
straight line (.DELTA..sub.t) belonging to any segment of a coverage with 
the minimum distance measured until now. 
Until now, only the first alternative has been dealt with according to 
which station S, S.sub.k or S.sub.1, is not located within a emitting or 
receiving coverage of an antenna of satellite 1. As indicated by stage 
E.sub.2 of the main algorithm (FIG. 5), the second alternative according 
to which station S is located within a beam coverage C.sub.i is now dealt 
with reference to FIG. 11. 
It is assumed that the frequency bands are dedicated respectively to the 
beams of satellite 1, and that each of the beams carries channels in 
predetermined number NC, for example multiplexed frequency channels or 
resulting from any other type of multiplexing. 
As signalled in sub-step E.sub.2 in FIG. 11, control station SC checks the 
availability of the NC channels of coverage C.sub.i covering station 
S.sub.o. If at least one of the NC channels is free for coverage C.sub.i, 
i.e., if a modulation carrier associated to coverage C.sub.i can be used 
for receive or emit by station S, then a simulated authorization is given 
to station S. It is recalled that the real emission/reception 
authorization is conditioned in control station SC by simulated 
authorizations, both relating to the calling station S.sub.k and called 
station S.sub.l. 
When all the NC channels of coverage C.sub.i are busy, the control station 
searches from amongst the coverages adjacent to coverage C.sub.i including 
station S, one of those whose a beam has a free channel. This search is 
made according to a predetermined order of priority of adjacent coverages 
and/or preferably by selecting the coverage with the smallest number of 
busy channels. Two beam coverages are said to be "adjacent" when their 
angular separation is such that their is no coverage inserted between 
them. 
If none of the examined coverages adjacent to coverage C.sub.i possesses at 
least one free channel, then the setting-up request from station S is 
rejected or placed in the queue of station SC. When the station is the 
calling station S.sub.k or called station S.sub.l, the link between the 
two stations S.sub.k and S.sub.l is not then set up. 
If a first coverage adjacent to coverage C.sub.i and including at least one 
free channel is detected, a sub-step is then carried out for exchanging 
loads between the beams of these coverages, as indicated in E.sub.24 in 
FIG. 11. 
This sub-step of exchanging loads between beams is shown graphically in 
FIG. 12. According to this FIG. 12, take C.sub.i as the beam coverage 
initially including station S and having all its channels busy, and 
C.sub.i+1 a coverage adjacent to coverage C.sub.i with at least one free 
channel, these two coverages being initially delimited by continuous line 
polygonal contours. 
First of all, side (I.sub.p, I.sub.p+1) of the polygon of coverage C.sub.i 
nearest to station S is determined in the transformed reference system (u, 
v). This side is preferably determined in the same way as in sub-step 
E.sub.11b, by using a straight line sheaf with incremented director 
coefficient. In FIG. 12 this side of the coverage C.sub.i is (I.sub.2, 
I.sub.3). Then coverage C.sub.i is reduced by joining the two apexes 
I.sub.2 and I.sub.3 of this side to the point of station S so that the 
side (I.sub.2, I.sub.3) is replaced by the two sides (I.sub.2, S) and (S, 
I.sub.3), as shown by a broken line in FIG. 12. Nevertheless the reduction 
of the coverage C.sub.i can be accomplished according to the second 
alternative shown in FIG. 8 for which the side (I.sub.2, I.sub.3) is 
replaced by a side (P,Q) parallel to it and passing through point S. 
Then, for coverage C.sub.i+1 adjacent to coverage C.sub.i and possessing at 
least one free channel, two sides of the polygon delimiting coverage 
C.sub.i+1 nearest to station S are determined. As previously in sub-step 
E.sub.11b, this determination is obtained by means of a sheaf of straight 
lines passing through S, with incremented director coefficients. In FIG. 
12, these two sides of the coverage C.sub.i+1 are (I'.sub.4, I'.sub.5) and 
(I'.sub.5, I'.sub.1). Then coverage C.sub.i+1 is enlarged so as to include 
station S in it, by joining the two far end apexes I'.sub.1, I'.sub.4 of 
these two sides (I'.sub.4, I'.sub.5) and (I'.sub.5, I'.sub.1) to the point 
of station S, so as to form two sides (I'.sub.4, S) and (S, I'.sub.1) as 
shown in broken line in FIG. 12. Thus station S is included in modified 
coverage C.sub.i +1, and a free channel of the beam of this coverage 
C.sub.i+1 is allocated by control station SC to station S to emit or 
receive. 
Simultaneously, the address of station S is withdrawn from the channel 
allocation memory in station SC associated to coverage C.sub.i, and this 
coverage C.sub.i initially covering station S is reduced by controlling a 
reduction in emission or reception power, of the antenna of satellite 1 
supplying coverage C.sub.i, by modifying the control coefficients of the 
phase shifters and power dividers of the configuration network of this 
antenna as a function of coverage C.sub.i thus defined. 
Thus the invention provides an original method for reconfiguring satellite 
beams, taking account of the limited power, both for emit and receive, in 
the satellite, and makes use of discrete points for each beam contour in 
the transformed reference system (u, v) considerably simplifying certain 
steps or sub-steps in the method.