Abstract:
There is provided methods for node discovery in a network comprising the following steps:
       performing a first discovery process for discovering at least one first node of said network, using at least one first wireless communication parameter,   adapting said at least one first wireless communication parameter, thereby obtaining at least one second wireless communication parameter coordinated with wireless communication parameters of nodes of at least one group of nodes discovered during the first discovery process, and   performing a second discovery process for discovering at least one second node of said network, using said at least one second wireless communication parameter.       
 
     Embodiments of the invention provide better coordination during node discovery thereby making the node discovery is thus made faster and reducing interferences between the nodes.

Description:
FIELD OF THE INVENTION 
       [0001]    The present invention relates to node discovery methods in communication networks. 
         [0002]    More particularly, the present invention relates to node discovery methods in wireless communication networks. The invention may have applications in ad-hoc wireless communication networks that rely on programmable antennas such as, for example, Wireless PAN (acronym for “Personal Area Network”), wireless multi-display networks, Wireless LAN (acronym for “Local Area Network”) or the same. Such wireless networks may use 2.4 GHz, 5 GHz, 60 GHz radio bands or higher bands. 
       BACKGROUND OF THE INVENTION 
       [0003]    In wireless communication networks, neighbour discovery may be performed by devices such as video projectors, laptops, mobile phones, digital tablets, or the like. 
         [0004]    Wireless ad hoc networks comprise WPAN (“Wireless Personal Area Networks”), WLAN (“Wireless Local Area Networks”), WMAN (“Wireless Metropolitan Area Network”), WWAN (“Wireless Wide Area Networks”), wireless sensor networks etc. The number of applications based on this type of network is increasing. Applications may be video surveillance, video multi-projection, disaster recovery, etc. 
         [0005]    Wireless ad hoc network schemes frequently rely on a mesh communication scheme, which allows collaborating devices to relay information from one device to another across multiple wireless links. Each device has the ability to operate in both transmit and receive modes, either simultaneously or alternately. 
         [0006]    Typically, such wireless mesh networks are setup in a self-organizing way, which means that the network devices do not require a pre-existing infrastructure for performing device discovery along with medium access scheme determination and setup. 
         [0007]    Some wireless ad-hoc mesh networks, even though being self-organizing, may have deterministic topologies. The devices remain static (for example a video surveillance network or a wireless sensor network installed in an office or a housing building). Such wireless networks may be of the IEEE 802.11 WPAN or WLAN type. 
         [0008]    For example, disaster recovery networks are a type of wireless self-organizing networks. Such type of networks is deployed on wide terrains wherein wireless devices are assigned respective restricted operation areas that are arranged symmetrically and of equal sizes. Multi-projection systems, are another type of wireless self-organizing networks wherein spatial topology is typically setup according to an n×m matrix arrangement. 
         [0009]    Some wireless networks, even though being “ad-hoc” in the sense that their actual spatial arrangement is not predetermined, may nevertheless be setup according to some predefined network model settings. In other words, even though their actual spatial topology is not known by the network devices, such devices may intuit it at some point. For example, in case the devices are spatially arranged according to an array topology, each device knows that it is surrounded by up to eight other devices. Each device may thus intuit the positioning of its potential neighbour devices. In the same way, a video projector device belonging to a matrix of video projectors may not know the actual size of the matrix. In case the only communications allowed in the network are communications between devices belonging to the same line or column, a device knows that its potential neighbour devices are located at 0°, 90°, 180° and 270° directions. 
         [0010]    In a wireless self-organizing network, one given device may be able to communicate only with a limited set of devices. Such devices are commonly referred to as “neighbour devices”. In the absence of a master coordinator device, at least upon system start up, each device shall first discover its own neighbour devices before any medium access scheme and associated routing is set up. The process for a device to identify all its neighbours is usually referred to as “neighbour discovery process”. 
         [0011]    Typically, a device that wishes to discover its neighbour devices shall transmit, in broadcast mode in most cases, a probe message and wait for the reception of a probe response message issued by a neighbour device (which has received the probe message). Such probe handshake shall be robust to frame collisions and interferences, which are most likely to occur in an ad-hoc wireless network. Indeed, the interferences and collisions during the “neighbour discovery process” make the process last longer. In order to mitigate the impact of frame collisions and network interferences, probe messages and response frames to/from different neighbours are typically generated repeatedly and transmitted after random delays. 
         [0012]    This neighbour discovery approach, also referred to as the “random access neighbour discovery scheme”, has been specified for the ad-hoc mode of IEEE 802.11 standards as well as for generic mobile ad hoc networks (“MANETs”) by the Internet Engineering Task Force (“IETF”) MANET working group, and is found in many well-known state of the art algorithms, like for instance the “birthday” algorithm or the “coupon collector” algorithm. These algorithms rely on a collision model while requiring the devices to randomly alternate transmit and receive modes, so as to ensure the completion of the handshake discovery process. However, such discovery schemes require a significant amount of contention time slots to guarantee successful discovery, which results in a significant latency before discovery process completion, along with significant bandwidth overhead. 
         [0013]    Document WO 2012/131512 A1 discloses a group-based discovery scheme for reducing the risks of interferences and frame collisions during the neighbour discovery process. 
         [0014]    The group-based discovery scheme is based on the dynamic and iterative selection of a neighbour discovery proxy, amongst a reference group of network devices, by a centralized coordinator device. The selected proxy device is in charge of both performing discovery process handshake(s) with its neighbour device(s) and reporting the results of this discovery process to the centralized coordinator device. Said centralized coordinator device shall then associate the newly discovered neighbour devices to the reference group of network devices and select a new proxy device inside the reference group until a predefined number of devices were discovered. 
         [0015]    Such method requires a network device to be selected for acting as a centralized coordinator device in charge of driving the discovery process. This may considered as in contradiction with the self-organizing network approach. 
         [0016]    Moreover, such method implies that only one device at a time is performing neighbour discovery, which may increase the overall discovery process latency. 
         [0017]    Thus, there is a need for enhancing neighbour device discovery is wireless communication networks. 
         [0018]    The present invention lies within this context. 
       SUMMARY OF THE INVENTION 
       [0019]    According to a first aspect of the invention there is provided a method of node discovery in a network comprising the following steps:
       performing a first discovery process for discovering at least one first node of said network, using at least one first wireless communication parameter,   adapting said at least one first wireless communication parameter, thereby obtaining at least one second wireless communication parameter coordinated with wireless communication parameters of nodes of at least one group of nodes discovered during the first discovery process, and   performing a second discovery process for discovering at least one second node of said network, using said at least one second wireless communication parameter.       
 
         [0023]    According to embodiments, nodes that discovered each other are aggregated into groups of nodes. This makes it possible to reduce network interferences resulting from several devices performing simultaneously discovery process. 
         [0024]    The node discovery is coordinated between the nodes of the network. The overall node discovery is thus made faster. 
         [0025]    Coordination of the wireless communication parameters makes it possible to reduce interferences between the nodes during the discovery. This also makes it possible to avoid redundant discoveries. 
         [0026]    The discovery space where to search for nodes may thus be shared between the nodes that already discovered each other. Each node may discover other nodes in a respective and dedicated direction, according to the coordinated parameters. 
         [0027]    According to embodiments, the method further comprises a step of evaluating a spatial topology of said at least one group of nodes, and wherein said at least one first wireless parameter is adapted based on said evaluated topology. 
         [0028]    For example, the method further comprises transmitting said evaluated spatial topology to at least one node of said at least one group. 
         [0029]    According to embodiments, said spatial topology is evaluated at least based on a topology message received from at least one node of said group. 
         [0030]    For example, said topology message comprises information relating to a spatial topology of a group of nodes to which it formerly belonged. 
         [0031]    For example, evaluating said spatial topology comprises updating a spatial topology array representative of a current spatial topology of said group of nodes. 
         [0032]    According to embodiments, said spatial topology array is further representative of communication paths between nodes of the group of nodes. 
         [0033]    According to embodiments:
       said wireless communication parameters comprise at least one antenna parameter, and   said adaptation step is performed in view of performing said second discovery process according to a respective discovery direction corresponding to a subdivision of a node discovery space.       
 
         [0036]    For example, said node discovery space is subdivided into discovery directions and each node of said group of nodes performs a respective discovery process according to a respective discovery direction. 
         [0037]    For example, said subdivision is an angular subdivision. 
         [0038]    According to embodiments:
       said performing of a first discovery process comprises emitting a probe message and receiving, from at least one node of said at least one group of nodes, a discovery message in response to said probe message, and   the method further comprises transmitting, to said at least one node of the network, a confirmation message.       
 
         [0041]    According to a second aspect of the invention, there is provided a method of image data projection, by a multi-projection system, comprising the following steps:
       discovering projection nodes of a network of the multi-projection system, according to the first aspect,   subdividing at least one image according to projection nodes discovered, and   projecting respective image subdivisions by said projection nodes discovered.       
 
         [0045]    According to a third aspect of the invention, there are provided computer programs and computer program products comprising instructions for implementing methods according to the first and/or second aspect(s) of the invention, when loaded and executed on computer means of a programmable apparatus. 
         [0046]    According to a fourth aspect of the invention, there is provided a node device configured for implementing methods according to the first aspect. 
         [0047]    Such device may comprise a processing unit configured to perform a first discovery process for discovering at least one first node of said network, using at least one first wireless communication parameter, to adapt said at least one first wireless communication parameter, thereby obtaining at least one second wireless communication parameter coordinated with wireless communication parameters of nodes of at least one group of nodes discovered during the first discovery process, and to perform a second discovery process for discovering at least one second node of said network, using said at least one second wireless communication parameter. 
         [0048]    The processing unit may be further configured to evaluate a spatial topology of said at least one group of nodes, and wherein said at least one first wireless parameter is adapted based on said evaluated topology. 
         [0049]    For example, said processing unit is further configured to transmit said evaluated spatial topology to at least one node of said at least one group. 
         [0050]    For example, said spatial topology is evaluated at least based on a topology message received from at least one node of said group. 
         [0051]    For example, said topology message comprises information relating to a spatial topology of a group of nodes to which it formerly belonged. 
         [0052]    For example, evaluating said spatial topology comprises updating a spatial topology array representative of a current spatial topology of said group of nodes. 
         [0053]    For example, said spatial topology array is further representative of communication paths between nodes of the group of nodes. 
         [0054]    According to embodiments:
       said wireless communication parameters comprise at least one antenna parameter, and   said adaptation is performed in view of performing said second discovery process according to a respective discovery direction corresponding to a subdivision of a node discovery space.       
 
         [0057]    For example, said node discovery space is subdivided into discovery directions and each node of said group of nodes performs a respective discovery process according to a respective discovery direction. 
         [0058]    For example, said subdivision is an angular subdivision. 
         [0059]    According to embodiments:
       said performing of a first discovery process comprises emitting a probe message and receiving, from at least one node of said at least one group of nodes, a discovery message in response to said probe message, and   the processing unit is further configured to transmit, to said at least one node of the network, a confirmation message.       
 
         [0062]    According to a fifth aspect of the invention, there is provided a system comprising at least one node device according to the fourth aspect. 
         [0063]    For example, the system is a multi-projection system, for projection of image data, comprising a plurality of projection nodes according to the fourth aspect, wherein said projection nodes are further configured to subdivide at least one image according to projection nodes discovered, and wherein the projection nodes discovered are further configured to project respective image subdivisions. 
         [0064]    The objects according to the second, third, fourth and fifth aspects of the invention provide at least the same advantages as those provided by the method according the first aspect of the invention. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0065]    Other features and advantages of the invention will become apparent from the following description of non-limiting exemplary embodiments, with reference to the appended drawings, in which: 
           [0066]      FIGS. 1-2  are schematic illustrations of exemplary communication networks; 
           [0067]      FIG. 3  is a schematic illustration of a node according to embodiments; 
           [0068]      FIGS. 4   a  and  4   b  schematically illustrate exemplary radio beams of antennas; 
           [0069]      FIG. 5  illustrate exemplary complementary radio settings; 
           [0070]      FIG. 6  illustrates an exemplary software architecture for nodes according to embodiments; 
           [0071]      FIGS. 7-8  are flowcharts of steps of methods according to embodiments; 
           [0072]      FIG. 9  illustrates an exemplary topology array for describing a network topology; 
           [0073]      FIGS. 10   a ,  10   b ,  11   a  and  11   b  illustrate exemplary message formats exchanged during discovery processes according to embodiments; 
           [0074]      FIG. 12  illustrates an exemplary wireless medium access scheme according to embodiments; 
           [0075]      FIG. 13  depicts an exemplary multi-projection wireless communication network according to embodiments. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0076]    With reference to  FIG. 1  and  FIG. 2  illustrative wireless self-configuring networks are described. 
         [0077]      FIG. 1  is a schematic illustration of a wireless self-configuring network  100  comprising a plurality of nodes  110 ,  111 ,  112 ,  113 ,  114 ,  115 ,  116 ,  121 ,  122 ,  123 ,  130 ,  131 ,  132 ,  133 ,  140 ,  141 ,  142  and  143 . For example, the network is designed to resist a disaster scenario. For example, the network nodes comprise wireless sensors, mobile phones, or any other device that may be typically found in a wireless ad hoc network, like for instance IEEE 802.11 WPAN or WLAN or 802.15.4 wireless sensor networks. Each of these network nodes  110 ,  111 ,  112 ,  113 ,  114 ,  115 ,  116 ,  121 ,  122 ,  123 ,  130 ,  131 ,  132 ,  133 ,  140 ,  141 ,  142  and  143  is assigned a geographic area, like for instance areas  150 ,  151  and  152 . Each of these network nodes embeds at least one communication module, which includes at least one antenna (the communication modules are described hereinafter in more details with reference to  FIG. 4 ). 
         [0078]      FIG. 2  is another schematic illustration of a wireless self-configuring network  200  comprising a plurality of nodes  210 ,  211 ,  212 ,  213 ,  220 ,  221 ,  222 ,  223 ,  230 ,  231 ,  232 ,  233 ,  240 ,  241 ,  242  and  243 . For example, the network is designed for a cubicle office environment. Cubicles  270 ,  271 ,  272 ,  273 ,  274 ,  275 ,  276 ,  277 ,  278 ,  279 ,  280 ,  281 ,  282 ,  283 ,  284  and  285  are typically rooms in an office or housing building. Each cubicle has a typical dimension ranging from 3 m×3 m up to 5 m×5 m. The cubicles are separated by a light office or wall partition wall, like for instance partition  290 , characterized by a penetration loss, which typical value is 2 dB. 
         [0079]    The network nodes are typically computers, laptops, video surveillance cameras, wireless sensors or any other devices that may be typically found in a wireless ad hoc network, like for instance IEEE 802.11 WPAN or WLAN or 802.15.4 wireless sensor networks. Each of these network nodes  210 ,  211 ,  212 ,  213 ,  220 ,  221 ,  222 ,  223 ,  230 ,  231 ,  232 ,  233 ,  240 ,  241 ,  242  and  243  embeds at least one communication module, which includes at least one antenna (the communication modules are described hereinafter in more details with reference to  FIG. 4 ). 
         [0080]    According to exemplary embodiments, communication networks  100  and  200  are full wireless communication networks. Thus, all the communication links may be wireless. The wireless communication networks may be operated in one or several of the 5 GHz unlicensed spectrum, the 2.4 GHz unlicensed spectrum, the 57-66 GHz millimeter-wave unlicensed spectrum, or higher frequency bands (e.g. THz bands). 
         [0081]      FIG. 3  is a schematic block diagram of an exemplary communication device  300  configured for performing a node discovery method according to embodiments. The device may be a video projector, a micro-computer, a workstation, a light portable device or any other type of network node. The device comprises a communication bus connected to:
       a central processing unit  301  (CPU);   a random access memory  302  (RAM for “random access memory”), for storing the executable code of a computer program according to embodiments as well as the registers adapted to record variables and parameters for the execution of such code; the memory capacity thereof can be expanded by an optional RAM connected to an expansion port for example;   a read only memory  303  (ROM for “read only memory”), for storing computer programs for implementing a method according to embodiments or input data for such implementation;   a network interface  304  connected to a communication network over which digital data to be processed are transmitted or received. The network interface  304  can be a single network interface, or comprise a set of network interfaces (for instance wired and wireless interfaces, or different kinds of wired or wireless interfaces). The wireless interface comprises antennas (as described hereinafter with reference to  FIG. 4 ). Data packets are written to the network interface for transmission or are read from the network interface for reception under the control of the software application running in the CPU;   a user interface  305  for receiving inputs from a user or to display information to a user;   a hard disk  306  (HD); and   an I/O module  307  for receiving/sending data from/to external devices such as a video source or display.       
 
         [0089]    The executable code may be stored either in the ROM, in the hard disk or on a removable digital medium such as for example a disk. The executable code of the programs may also be received by means of a communication network, via the network interface, in order to be stored in one of the storage means of the device, such as the hard disk, before being executed. 
         [0090]    The CPU is configured to control and direct the execution of the instructions or portions of software code of the program or programs according to embodiments. The instructions are stored in one of the aforementioned storage means. The CPU is configured to execute instructions from the main RAM relating to a software application after the instructions have been loaded from the program ROM or the hard-disc for example. Any steps of the algorithms described hereinafter, with reference to  FIG. 7 ,  FIG. 8  and  FIG. 11  may be implemented by software by execution of a set of instructions or program by a programmable computing machine, such as a PC (“Personal Computer”), a DSP (“Digital Signal Processor”) or a microcontroller; or else implemented by hardware by a machine or a dedicated component, such as an FPGA (“Field-Programmable Gate Array”) or an ASIC (“Application-Specific Integrated Circuit”). 
         [0091]    With reference to  FIGS. 4   a  and  4   b , exemplary antenna modules are described. The antenna modules may be integrated to communication modules of nodes of communication networks such as networks  100  and  200  described hereinabove with reference to  FIGS. 1 and 2 . 
         [0092]    The antenna  410   a  in  FIG. 4   a  has a single narrow main beam  420   a . The antenna  410   b  in  FIG. 4   b  has a single wide main beam  420   b.    
         [0093]    For each antenna, two modes may be defined: a directional mode and a wide mode. Each mode is used for transmitting and receiving discovery protocol messages, as described in what follows with reference to  FIGS. 10   a ,  10   b  and  FIG. 11 , in order to perform neighbour device discovery according to algorithms as described in what follows with reference to  FIG. 7  and  FIG. 8 . 
         [0094]    In the directional mode, the antenna focuses transmit and/or receive power towards one direction. Steering an antenna to a given direction (or orientation) corresponds to controlling its parameters (for example the weighting coefficients associated with the elements of an antenna array) such that the radiation pattern, in case of emission, or the antenna sensitivity pattern, in case of reception, is accentuated in that given direction relatively to other directions. 
         [0095]    In  FIG. 4   a , the antenna  410   a  transmits a signal via the single narrow main beam  420   a . For example, the antenna&#39;s gain at a 5° angle is −3 dBi from the maximum, where “dBi” represents a measure of antenna gain relatively to an isotropic antenna. The antenna&#39;s main beam gain is relatively high, for example 25 dBi. The antenna has thus different gain characteristics at different reception angles. A maximum gain is obtained in the direction of the main beam. 
         [0096]    Alternatively, in wide mode, an antenna performs a transmission towards or reception from a plurality of transmission paths which can be affected simultaneously (covering simultaneously a plurality of directions). In  FIG. 4   b  the antenna  410   b  has a single 210° wide main beam  420   b . The main beam gain is thus relatively small, approximately 4 dBi. A wide beam or near omni-directional antenna can be implemented as a single dedicated antenna element. Alternatively, an antenna array comprising a plurality of antenna elements dedicated to directional transmission can be reused by activating a single antenna element among the array of antenna elements. 
         [0097]    It may not be possible to cover all the directions even with a single antenna in wide mode. Therefore, complementary antennas may be used in the same device, each one covering areas in different directions. For instance, in the case wherein a device has 2 antennas, the first antenna may cover the area defined by the angular directions between 0 and 180 degrees and a second antenna may cover the area defined by the angular directions between 181 and 360 degrees. Consequently, when a device has to send a message towards a given direction, it selects the antenna which covers it. 
         [0098]    For the sake of conciseness, it may be considered that the antennas of a same device are either all in wide or all in directional mode. Consequently, when the antennas of a device are all in wide mode, the device is considered as being “in omnidirectional antenna mode” (since the antennas of such device are complementary). Also, when the antennas of a device are all in directional mode, the device is considered as being “in directional antenna mode”. 
         [0099]    A given antenna is either transmitting—i.e. ready to send data—or receiving—i.e. ready to receive data. For the sake of conciseness, the antennas of a device are either all in transmission mode or all in reception mode. Consequently, when the antennas of a device are all in transmission mode (respectively in reception mode), the device is considered as “in transmission mode” (respectively “in reception mode”). 
         [0100]    Consequently, four antenna modes can be considered for a given device (or network node):
       Emission/Wide: the device is in transmission mode and in wide antenna mode;   Emission/Directional: the device is in transmission mode and in directional antenna mode;   Reception/Wide: the device is in reception mode and in wide antenna mode; and   Reception/Directional: the device is in reception mode and in directional antenna mode.       
 
         [0105]    With reference to  FIG. 5 , exemplary complementary (or coordinated) radio and antenna settings that may be applied by one or more devices are described. 
         [0106]    Radio and antenna communication scheme  510  involves four communication modules  521 ,  522 ,  523  and  524  (as described hereinabove with reference to  FIG. 4 ) operated in directional mode. 
         [0107]    The antenna of communication module  521  performs antenna sweep according to antenna settings  511 , which specify an angular range of operation between 0° and 90°. 
         [0108]    The antenna of communication module  522  performs antenna sweep according to antenna settings  512 , which specify an angular range of operation between 180° and 270°. 
         [0109]    The antenna of communication module  523  performs antenna sweep according to antenna setting  513 , which specify an angular range of operation between 270° and 0°. 
         [0110]    The antenna of communication module  524  performs antenna sweep according to antenna setting  514 , which specify an angular range of operation between 90° and 180°. 
         [0111]    The antenna settings  511 ,  512 ,  513  and  514  of communication modules  521 ,  522 ,  523  and  524  are complementary (or coordinated) in the sense that they cover the full angular space, ranging from 0° to 360°, when they are all used in emission or in reception mode. 
         [0112]    Radio and antenna communication scheme  530  involves two communication modules  541  and  542  (as described hereinabove with reference to  FIG. 4 ) operated in directional mode. 
         [0113]    The antenna of communication module  541  performs antenna sweep according to antenna setting  531 , which specifies an angular range of operation between 270° and 90°. 
         [0114]    In one embodiment of the present invention, antenna setting  532  is alternately used in reception mode while antenna setting  531  is used in transmission mode or in transmission mode while antenna setting  531  is used in reception mode. 
         [0115]    The antenna of communication module  542  performs antenna sweep according to antenna settings  532 , which specify an angular range of operation between 90° and 270°. 
         [0116]    The antenna settings  531  and  532  of communication modules  541  and  542  are complementary (or coordinated) in the sense that they cover the full angular space, ranging from 0° to 360°, when they are both used in emission or in reception mode. 
         [0117]    Radio and antenna communication scheme  550  involves two communication modules  561  and  562  (as described hereinabove with reference to  FIG. 4 ) operated in wide mode. 
         [0118]    The antenna of communication module  551  covers space between 270° and 90°. The antenna of communication module  552  covers space between 90° and 270°. The antenna settings  551  and  552  of communication modules  561  and  562  are complementary (or coordinated) in the sense that they cover the full angular space, ranging from 0° to 360°, when they are both used in emission or in reception mode. 
         [0119]    Using complementary (or coordinated) antenna settings scheme  510  in a group of four network devices (like for instance group  1370  described hereinafter with reference to  FIG. 13 ) makes it possible to perform a fast discovery process since each network device belonging to this group limits its antenna discovery space to 90°. Such antenna setting scheme also makes it possible to have the four nodes of group  1370  described hereinafter with reference to  FIG. 13  to perform simultaneously their antenna discovery process while avoiding any interference between each other, thereby increasing the efficiency of the discovery process. 
         [0120]    An exemplary software architecture of a network node is described with reference to  FIG. 6 . 
         [0121]    Discovery Management modules  611 ,  621 ,  631  and  641  of network devices  610 ,  620 ,  630  and  640  are configured to determine which discovery messages are to be sent over network interface modules  614 ,  624 ,  634  and  644 . The discovery messages comprise probe, feedback and Confirmation Messages. These messages are described in details hereinafter with reference to  FIGS. 10   a ,  10   b  and  FIG. 11 . The sequencing of these discovery messages may be performed in accordance with the algorithm described in what follows with reference to  FIG. 7 . 
         [0122]    Upon receipt of a feedback discovery message by a network interface module, the topology evaluation module (cf. modules  613 ,  623 ,  633  and  643 ) updates the topology of the group of devices to which it belongs, by including the newly discovered network device that issued the feedback discovery message (as described hereinafter with reference to  FIG. 8 ). Based on the newly computed group topology, the radio configuration module (cf. modules  612 ,  622 ,  632  and  642 ) determines the radio and antenna settings to be used by each network interface module for transmitting and receiving discovery messages, in accordance with the algorithm described hereinafter with reference to  FIG. 8 . 
         [0123]      FIG. 7  is a flowchart of steps of a method for performing a neighbour discovery according to embodiments. With reference to  FIG. 7 , the method is described at a device level. 
         [0124]    The algorithm may be implemented by a discovery management module as described hereinabove with reference to  FIG. 6 . 
         [0125]    In a first step  700 , a network device transmits, through its network interface module, a probe message using radio and antenna settings formerly determined by its radio configuration module. The format of the probe messages is described in what follows with reference to  FIG. 10   a . The probe messages may be transmitted during each of the device&#39;s transmission periods, in accordance with a medium access scheme. An exemplary medium access scheme is described in what follows with reference to  FIG. 12 . 
         [0126]    The network interface uses the radio and antenna settings defined by the radio configuration module. The determination of these radio and antenna settings as performed by the radio configuration module is described in what follows with reference to  FIG. 8 . 
         [0127]    Next, during a step  701 , the network device waits for the receipt of a discovery message issued by a neighbour device, which received a probe message sent by the network device during step  700 . The format of such feedback message is described hereinafter with reference  FIG. 10   b . A network device shall probe the wireless medium during each of its reception periods, in accordance with the medium access scheme described with reference to  FIG. 12 . 
         [0128]    The information embedded in the feedback message is passed by the network interface module to the topology evaluation module. The topology evaluation module then evaluates the new topology of the group to which the network device belongs so as to allow the radio configuration module to define new radio and antenna settings for transmitting and receiving discovery messages. 
         [0129]    During a step  702 , the network device transmits, through its network interface module, a confirmation message using radio and antenna settings formerly determined by the radio configuration module. The format of the discovery confirmation message is described in what follows with reference to  FIG. 11 . 
         [0130]    Finally, during a step  703 , the network device transmits, through its network interface module, a discovery process summary message  1150  (which is described in more details hereinafter with reference to  FIG. 11   b ), to at least one another network device belonging to its current group of devices. For example, the network device transmits, through its network interface module, a discovery process summary message  1150  to all the network devices inside its current group of devices. The network device may also relay, through its network interface module, any discovery process summary message to at least one of the network devices of its current group of devices, so as to ensure that all the devices inside a group of devices share the same knowledge of the discovery process performed by each of the network devices belonging to the group of devices. 
         [0131]    The discovery process summary messages  1150  are used by the topology evaluation modules to evaluate the new topology of the group to which the network device belongs. 
         [0132]    An application of the process described with reference to  FIG. 7  is presented hereinafter in the context of an exemplary network  1300  represented in  FIG. 13 . 
         [0133]    The network  1300  comprises three groups of devices  1350 ,  1360  and  1370 . Group  1350  comprises network devices  1311  and  1312 . It is considered that network devices  1311  and  1312  already discovered each other by applying the process of  FIG. 7  (and also the process described hereinafter with reference to  FIG. 8 ). Group  1370  comprises network devices  1331 ,  1332 ,  1341  and  1342 . It is considered that network devices  1331 ,  1332 ,  1341  and  1342  already discovered each other by applying the algorithms of  FIG. 7  (and also the process described hereinafter with reference to  FIG. 8 ). Group  1360  comprises a single network device  1322 . It is considered that network device  1360  has not discovered any other device yet. This may be due to the fact that network device  1360  was turned on after network devices  1311 ,  1312 ,  1331 ,  1332 ,  1341  and  1342 . 
         [0134]    The network devices belonging to groups  1350 ,  1360  and  1370  shall transmit either discovery probe messages  1000  or discovery confirmation messages  1100  during their transmission periods. The devices shall also probe the wireless medium so as to receive discovery feedback messages  1050  during their transmission periods. The medium access scheme is described hereinafter with reference to  FIG. 12 . Each time a discovery confirmation message  1100  is sent by a device belonging to any one of these groups of devices, such device shall send a discovery process summary message  1150  to the other network devices belonging to the same group, if any. The network devices belonging to a same group of device shall use dedicated communication links to exchange the discovery process summary messages. For instance, network devices  1311  and  1312  that belong to group  1350 , use on network communication link  1351  for exchanging their discovery process summary messages  1150 . Network devices  1331 ,  1332 ,  1341  and  1342  that belong to group  1370 , use network communication links  1371 ,  1372 ,  1373  and  1374  for exchanging their discovery process summary messages. For example, communication links  1351 ,  1371 ,  1372 ,  1373  and  1374  are operated in accordance with the medium access scheme described with reference to  FIG. 12 . 
         [0135]    The transmission period for one device transmitting data over such communication links corresponds to a reception period of the network device receiving data over such communication link. 
         [0136]    For instance, if network device  1312  receives a discovery feedback message  1050  in response to a previously sent discovery probe message  1000 , from network device  1322 , it shall send a discovery process summary message to network device  1311 . 
         [0137]    For instance, if network device  1332  receives a discovery feedback message  1050  in response to a previously sent discovery probe message  1000 , from network device  1322 , it shall send a discovery process summary message  1150  to at least one other network device belonging to group  1370 , using communication links  1371  and/or  1372 . The discovery process summary message  1150 , issued by network device  1332 , may be relayed by at least one of network devices  1331  and  1342  to network device  1341  using communication links  1373  and  1374 . 
         [0138]    The method for performing a neighbour discovery is described, at a group of devices level with reference to the flowchart of  FIG. 8 . 
         [0139]    During a first step  800 , a network device receives, through its network interface module, one or several discovery feedback message(s)  1050  from one or several neighbour device(s), which are not currently part of the group of devices to which it belongs. The discovery feedback message(s) received are passed by the network interface module to the topology evaluation module for further group topology evaluation. 
         [0140]    During a second step  801 , a network device receives, through its network interface module, discovery process summary message(s)  1150  from other network devices inside the group of devices to which it belong, and/or discovery feedback message(s) from at least one device inside the predefined subset of devices. Any received discovery process summary message(s)  1050  is passed by the network interface module to the topology evaluation module for further group topology evaluation. 
         [0141]    During a third step  802 , the topology evaluation module of the network device compiles the information embedded in all the discovery feedback message(s)  1050  and discovery process summary message(s)  1150  it recently received. For example, this operation is performed on a regular basis, e.g. every 50 ms. Based on these information, the topology evaluation module builds a spatial topology of the new group of network devices, including the newly discovered neighbour devices (i.e. the network devices for which a discovery feedback message  1050  was received by at least one network device of the current group of devices) 
         [0142]    The description and the storage scheme of such spatial topology is described in what follows with reference to  FIG. 9 . The update of the group&#39;s spatial topology is performed by updating the spatial topology array  900  by adding new entries in this array for each of the newly discovered network devices. 
         [0143]    Back to  FIG. 8 , after step  802 , during a step  803 , the newly computed spatial topology of the group of devices is used by the radio configuration module for defining new complementary (or coordinated) radio and antenna settings for each of the network devices of the updated group of devices. Some examples of complementary radio and antenna settings have already been given in  FIG. 5 . 
         [0144]    Finally, during a step  804 , the network interface module of the network device performs the discovery process, which is managed by the discovery management module, using the radio and antenna settings defined during step  802 . 
         [0145]    An application of the process described with reference to  FIG. 8  is presented hereinafter in the context of an exemplary network  1300  represented in  FIG. 13 . 
         [0146]    Network device  1312  of group  1350  receives (step  800 ) a discovery feedback message  1050  from network device  1322  which belongs to the single-device group  1360 . It is thus considered that network device  1322  actually received a probe message  1000  that network device  1312  had previously sent. 
         [0147]    Since no other device belonging to group  1350  has received a discovery feedback message  1050 , network device  1312  did not receive any discovery process summary message during step  801 . According to the process described with reference to  FIG. 7 , network device  1312  sent a discovery confirmation message  1100  to network device  1322  in response to the discovery feedback message  1050  it received from network device  1322 . 
         [0148]    Using the information embedded in the feedback message received from device  1322 , the topology evaluation module of network device  1312  updates the spatial topology of group  1350  by including network device  1322  (step  802 ). The newly formed group is group  1380 . 
         [0149]    Using the information embedded in the confirmation message received from device  1312 , the topology evaluation module of network device  1322  updates the spatial topology of group  1360  by including network devices  1311  and  1312  (step  802 ). The newly formed group is group  1380 . 
         [0150]    For example, only the device that issues a confirmation message computes the new topology of a newly formed group, and transmits the newly computed topology to the device that sent a feedback message. 
         [0151]    Since network devices  1311  and  1312  were initially part of the same group  1350 , they were using complementary radio and antenna settings, like, for instance antenna settings  532  for network device  1311  and antenna settings  531  for network device  1312 . Also, network device  1322  was initially using antenna settings  551  for its communication module  1326  and antenna settings  552  for its communication module  1325 . 
         [0152]    Based on the topology of the newly formed group  580 , the radio configuration modules of network devices  1311 ,  1312  and  1322  update the antenna settings to be applied by their respective communication modules. For instance, communication module  1317  of network device  1311  keeps using antenna setting  532 . Communication module  1319  of network device  1312  may now use antenna settings  511 . Communication module  1326  of network device  1322  may now use antenna settings  513 . Communication module  1325  of network device  1322  may now use antenna settings  512 . 
         [0153]    Having the knowledge of the topology model of network  1300  can also allow a radio configuration module to determine particularly relevant antenna settings that can optimize network discovery. For instance, knowing that the topology model for network  1300  is a matrix topology allows network devices  1311  and  1322  knowing the presence of network device  1321  as a neighbour device located at 270° from network device  1311  and at 180° from network device  1322 . 
         [0154]    With reference to  FIG. 9 , there is described an exemplary mode of representation of the spatial topology of a wireless communication network. 
         [0155]    A spatial topology may be represented by an array  900  of K rows and K columns, K being the number of communication devices in the network. This array may be referred to as a “spatial topology array”. A non-empty element of the array located at the row i and the column j corresponds to the existence of a communication path between the device i and the device j. An empty element of the array means that there is no possible communication path in any directions between the two corresponding devices, i.e. the communication path between communication modules of the two corresponding devices 
         [0156]    Each element of the array refers to the transmit antenna parameters used by the respective communication modules of device i and device j, which allows identifying the communication path between said two devices i and j. 
         [0157]    In what follows, the considered transmit antenna parameters are the antenna direction and the antenna transmit power. However, other or additional transmit antenna parameters may be used (e.g. transmit antenna gain). 
         [0158]    The communication device identifier considered in a network topology array is referred to as the topology device identifier. It may be different from the typical network device identifier typically based on the MAC address of the device. 
         [0159]    A network topology array is stored in the ROM for each device. The value of the parameters stored in this array may be filled directly by a user, through a dedicated user interface, or by programming the ROM device upon device manufacturing. 
         [0160]    An example of network topology array based on the network topology of wireless communication network  1300  of  FIG. 13  is given hereinbelow. For the sake of conciseness, the distances between the devices  1310 ,  1311 ,  1320  and  1321  are considered as identical and one same value of transmit power can be specified (for instance 0.01 W) as the transmit power to be used by each communication device in the network to perform communication with other communication neighbour devices during the discovery protocol described with reference to  FIG. 7  and  FIG. 8 . 
         [0161]    Therefore, the network topology array for devices  1310 ,  1311 ,  1320  and  1321  of network  1300  of  FIG. 13  only gathers antenna direction information, as follows: 
         [0000]    
       
         
               
               
               
               
               
             
           
               
                   
               
               
                 Topology 
                   
                   
                   
                   
               
               
                 device 
                   
                   
                   
                   
               
               
                 identifier 
                 1 
                 2 
                 3 
                 4 
               
               
                   
               
             
             
               
                 1 
                 X 
                 d 12 /d 21   
                 d 13 /d 31   
                 X 
               
               
                 2 
                 d 21 /d 12   
                 X 
                 X 
                 d 24 /d 42   
               
               
                 3 
                 d 31 /d 13   
                 X 
                 X 
                 d 34 /d 43   
               
               
                 4 
                 X 
                 d 42 /d 24   
                 d 43 /d 34   
                 X 
               
               
                   
               
               
                 Topology device identifier “1” refers to device 1310; 
               
               
                 Topology device identifier “2” refers to device 1311; 
               
               
                 Topology device identifier “3” refers to device 1320; 
               
               
                 Topology device identifier “4” refers to device 1321; 
               
             
          
         
       
     
         [0162]    In the above array, (d ij /d ji ) refers to the transmit antenna direction d u  (respectively d ji ) to be used by communication device i (respectively j) to communicate with communication device j (respectively i). Moreover, the combination (d ij /d ji ) identifies the communication link L ij  between two communication devices i and j. 
         [0163]    For instance, communication device 1 shall set its transmit antenna configuration to a 0° direction in order to communicate with communication device 2, while communication device 2 shall set its transmit antenna configuration to a 180° direction in order to communicate with communication device 1. Therefore, d 12  value is 0° while d 21  value is 180°. Similarly, d 13  value is 270° while d 31  value is 90°; d 24  value is 270° while d 42  value is 90°; d 34  value is 0° while d 43  value is 180°. 
         [0164]    Depending on the antenna configuration value specified in the network topology array, the communication device may select the appropriate communication module. 
         [0165]    For instance, when considering communication device 1310, communication module  1315  shall handle communications in the directions ranging from 90° to 270°, while communication module  1316  shall handle communications in the directions ranging from 0° to 90° and from 270° to 360°. 
         [0166]      FIG. 10   a ,  FIG. 10   b  and  FIG. 11  illustrate the format of the messages sent during the discovery protocol process described with reference to  FIG. 7  and  FIG. 8  between two devices belonging to the wireless communication network. 
         [0167]      FIG. 10   a  is an illustration of an exemplary probe message  1000 . 
         [0168]    Probe Message  1000  comprises a data field  1010  and a cyclic redundancy check (CRC) field  1040  for checking the validity of the data part  1010 . Data field  1010  is made of two main information fields. Information field  1015  embeds the identifier of the communication device sending the probe message. The identifier of said communication device may be, for instance, the network device identifier—e.g. the MAC address of said communication device or a function of its MAC address—or a unique device identifier (e.g. serial number). Information field  1020  embeds the transmit antenna parameters used by the communication device for sending the probe message. Information field  1020  may embed a plurality of transmit parameters information, like, for instance, the antenna direction value (field  1025 ), expressed in degrees, the transmit power (field  1030 ), expressed in Watts, or the transmit antenna gain or the transmit antenna mode—i.e. directional or wide—(field  1035 ). 
         [0169]      FIG. 10   b  is an illustration of an exemplary feedback message  1050 . 
         [0170]    Feedback Message  1050  depicted in  FIG. 10   b  comprises a data field  1060  and a cyclic redundancy check (CRC) field  1090  for checking the validity of the data part  1060 . Data field  1060  comprises a plurality of information fields. Information field  1065  embeds the identifier of the communication device sending the feedback message. The identifier of said communication device may be, for instance, the network device identifier—e.g. the MAC address of said communication device or a function of its MAC address—or a unique device identifier (e.g. serial number). Information field  1070  embeds the transmit antenna parameters used by the communication device for sending the feedback message. Information field  1070  may embed a plurality of transmit parameters information (as for field  1020  of probe message  1000 ) like for instance, the antenna direction value, expressed in degrees, the transmit power, expressed in Watts, or the transmit antenna gain or the transmit antenna mode—i.e. directional or wide. Information field  1075  embeds the identifier of the communication device that sent the probe message related to the feedback message being sent. Thus, field  1075  shall have the same value as field  1015  of the probe message  1000  associated to the feedback message  1050  being sent. Information field  1080  embeds the transmit antenna parameters used by the communication device that sent the probe message related to the feedback message being sent. Thus, information field  1080  shall have the same value as field  1020  of the probe message  1000  associated to the feedback message  1050  being sent. Information field  1080  may also embed (field  1085 ) information related to the topology of the cluster of devices to which the sender of the feedback message belongs. For example, the topology information may be set according to the topology description scheme described with reference to  FIG. 9 . 
         [0171]      FIG. 11  is an illustration of an exemplary confirmation message  1100 . 
         [0172]    Confirmation message comprises a data field  1110  and a cyclic redundancy check (CRC) field  1120  used for checking the validity of the data part  1110 . Data field  1110  comprises information fields  1111 ,  1112 ,  1113 ,  1114  and  1115 . Information field  1111  embeds the identifier of the communication device sending the confirmation message. The identifier of said communication device may be, for instance, the network device identifier—e.g. the MAC address of said communication device or a function of its MAC address—or a unique device identifier (e.g. serial number). Information field  1112  embeds the transmit antenna parameters used by the communication device for sending the confirmation message. 
         [0173]    Information field  1113  embeds the spatial topology of the group of devices to which the device issuing the confirmation message belongs. For example, spatial topology information  1114  may be set according to the topology description scheme described with reference to  FIG. 9 . Such spatial topology is determined as described with reference to  FIG. 7  and  FIG. 8 . 
         [0174]    Information field  1114  embeds an estimation of the spatial topology of the wireless communication network, like for instance network  100 ,  200  or  1300 , to which the device issuing the confirmation message belongs. For example, spatial topology information  1114  may be set according to the topology description scheme described with reference to  FIG. 9 . Such spatial topology estimation is performed as described with reference to  FIG. 7  and  FIG. 8 . 
         [0175]      FIG. 11   b  illustrates an exemplary format for the discovery process summary messages sent during the discovery protocol process described with reference to  FIG. 7  and  FIG. 8  between two devices belonging to a same group of devices (i.e. devices that already discovered each other). 
         [0176]    The discovery process summary message  1150  illustrated in  FIG. 11   a  comprises a data field  1160  and a cyclic redundancy check (CRC) field  1170  for checking the validity of the data part  1160 . Data field  1160  comprises information fields  1161 ,  1162  and  1163 . Information field  1163  embeds the data fields  1060  related to each of the discovery feedback message  1050  received from newly discovered network devices. The number of data fields  1060  embedded inside information field  1162  is provided in information field  1162 . Information field  1161  embeds the identifier of the communication device sending the discovery process summary message. The identifier of said communication device may be, for instance, the network device identifier—e.g. the MAC address of said communication device or a function of its MAC address—or a unique device identifier (e.g. serial number). 
         [0177]    For example, information field  1163  embeds the data fields  1060  related to each of the discovery feedback messages  1050  received from newly discovered network devices along with data fields  1163  related to each of the discovery process summary messages  1150  received from formerly discovered network devices. 
         [0178]    With reference to  FIG. 12 , there is described a wireless medium access scheme for performing a discovery protocol according to embodiments. 
         [0179]    The communication modules of a given communication device, like for instance communication device  110  of wireless communication network  100 , when performing a discovery protocol (e.g. as described with reference to  FIG. 7  and  FIG. 8 ), alternate between transmission periods, like time periods  1201 ,  1203 ,  1205 ,  1211  and  1213 , and reception periods, like time periods  1202 ,  1204  and  1212 . 
         [0180]    For a given communication device, the duration for both the transmission and the reception periods is chosen randomly. Moreover, when one communication module of a given communication device is in transmission mode the other communication module is in reception mode. 
         [0181]    Embodiments of the present invention may have applications in multi-projections systems. 
         [0182]      FIG. 13  is an illustration of a multi-projection system  1300  comprising multiple projection display apparatus  1310 ,  1311 ,  1312 ,  1313 ,  1314 ,  1320 ,  1321 ,  1322 ,  1323 ,  1324 ,  1330 ,  1331 ,  1332 ,  1333 ,  1334 ,  1340 ,  1341 ,  1342 ,  1343  and  1344  for projecting on a screen, video frames delivered by a source device connected to one or more of these apparatuses. 
         [0183]    A projection display apparatus is typically a video projector that projects a video stream but may encompass any type of projector such as for example a still image projector. Each of these display apparatuses  1310 ,  1311 ,  1312 ,  1313 ,  1314 ,  1320 ,  1321 ,  1322 ,  1323 ,  1324 ,  1330 ,  1331 ,  1332 ,  1333 ,  1334 ,  1340 ,  1341 ,  1342 ,  1343  and  1344  embeds at least one communication module, which includes at least one antenna, as described with reference to  FIG. 3 . For example, each of the display apparatuses  1310 ,  1311 ,  1312 ,  1313 ,  1314 ,  1320 ,  1321 ,  1322 ,  1323 ,  1324 ,  1330 ,  1331 ,  1332 ,  1333 ,  1334 ,  1340 ,  1341 ,  1342 ,  1343  and  1344  embeds two communication modules. For instance, display apparatus  1310  embeds communication modules  1315  and  1316  while display apparatus  1311  embeds communication modules  1317  and  1318 . 
         [0184]    According an exemplary implementation, the communication network  1300  is a full wireless communication network, i.e. all the communication links are wireless. For example, this wireless communication network is operated in the 57-66 GHz millimeter-wave unlicensed spectrum, which provides bandwidth required for the transport of high definition (HD) video data. 
         [0185]    Alternatively, some of the inter-projectors communication paths are wireless communication paths. 
         [0186]    An image to be projected is split into a plurality of sub-images. The number of sub-images per image is typically, but not necessarily, equal to the number of projectors in the multi-projection system. The size and shape of each sub-image is determined so that a full composite image can be reconstructed when all the sub-images are projected by their corresponding projectors. 
         [0187]    In what follows, there is described a method for adjusting the transmit frequency of the probe messages. The method may accelerate the discovery process. 
         [0188]    The number of probe messages  1000  sent during a given time period is referred to as the frequency F. When considering a TDMA medium access scheme, like the one described with reference to  FIG. 12 , several consecutives time slots are defined, the size of which may differ, wherein a node is either in emission or in reception mode. 
         [0189]    It is considered that the communication mode—i.e. emission or reception—to be used in a given time slot is set according to a random scheduler. 
         [0190]    The probability that a node i transmits during the time slot l is denoted p(l,i). 
         [0191]    During a given time slot, a node can send a given number M of probe messages  1000 . Consequently, there is a direct relation between the aforementioned mean frequency F and p(l,i) whereby: 
         [0000]    
       
         
           
             F 
             = 
             
               
                 
                   p 
                    
                   
                     ( 
                     
                       l 
                       , 
                       i 
                     
                     ) 
                   
                 
                 × 
                 M 
               
               Slot_duration 
             
           
         
       
     
         [0192]    Since all the nodes in the network are equivalent, it may be of particular interest to determine the value of p(l,i) that optimizes the probability p i,j  that a node i discovers a node j, so as to allow faster discovery process. 
         [0193]    Each network node embeds at least one directional antenna. Each antenna is steerable and each antenna can be used either in transmission or reception. 
         [0194]    When considering a transmission time slot, let θ the area covered by the antennas belonging to a given network node, θ being comprised between 0 and a coverage area CA (for instance 2π at the beginning). CA is the discovery space representing the angle range over which probe messages  1000  are sent. The area θ can be a sum of θ i  wherein θ i  is the beam width of a directional antenna: 
         [0000]    
       
         
           
             θ 
             = 
             
               
                 ∑ 
                 
                   n 
                   = 
                   1 
                 
                 N 
               
                
               
                   
               
                
               
                 θ 
                 n 
               
             
           
         
       
     
         [0195]    When considering a reception time slot, the receive antenna configuration mode is wide, so as to maximize the probability of reception of the discovery messages. 
         [0196]    The probability that a node j transmits in the range of the node i is: 
         [0000]    
       
         
           
             θ 
             CAi 
           
         
       
     
         [0197]    Where CAi is the coverage area of the node i. 
         [0198]    Depending on the actual network topology, a network node may be surrounded by a plurality of network nodes, which may differ from one topology to another. Therefore, an estimated neighbor density K is defined, which indicates for each node, the number of nodes that are in its reception range. 
         [0199]    A node i discovers a node j if: 
         [0200]    1) Node i is in reception mode, and 
         [0201]    2) Only one node j in the neighborhood of node i (the density of which is K i ), transmits towards node i—i.e. if two nodes transmit simultaneously a probe message  1000  towards node i, node i cannot discover any of these two nodes. 
         [0202]    Document Vasudevan et al. “ On neighbor discovery in wireless networks with directional antennas ” is a study of the neighbor discovery problem in static wireless ad hoc networks with directional antennas. This document discloses several probabilistic algorithms and the following formula for expressing the probability p i,j  that one node i discovers a node j: 
         [0000]    
       
         
           
             
               p 
               
                 i 
                 , 
                 j 
               
             
             = 
             
               
                 θ 
                 
                   2 
                    
                   
                       
                   
                    
                   π 
                 
               
                
               
                 
                   
                     p 
                     t 
                   
                    
                   
                     ( 
                     
                       1 
                       - 
                       
                         
                           θ 
                           
                             2 
                              
                             
                                 
                             
                              
                             π 
                           
                         
                          
                         
                           p 
                           t 
                         
                       
                     
                     ) 
                   
                 
                 
                   k 
                   - 
                   2 
                 
               
                
               
                 ( 
                 
                   1 
                   - 
                   
                     p 
                     t 
                   
                 
                 ) 
               
             
           
         
       
     
         [0203]    Based on the aforementioned considerations, we can derive from the above formula the following one: 
         [0000]    
       
         
           
             
               p 
               
                 i 
                 , 
                 j 
               
             
             = 
             
               
                 ( 
                 
                   1 
                   - 
                   
                     p 
                      
                     
                       ( 
                       
                         l 
                         , 
                         i 
                       
                       ) 
                     
                   
                 
                 ) 
               
                
               
                 θ 
                 CAi 
               
                
               
                 p 
                  
                 
                   ( 
                   
                     l 
                     , 
                     i 
                   
                   ) 
                 
               
                
               
                 
                   ( 
                   
                     1 
                     - 
                     
                       
                         θ 
                         CAi 
                       
                        
                       
                         p 
                          
                         
                           ( 
                           
                             l 
                             , 
                             i 
                           
                           ) 
                         
                       
                     
                   
                   ) 
                 
                 
                   
                     k 
                     i 
                   
                   - 
                   2 
                 
               
             
           
         
       
     
         [0204]    Where: 
         [0205]    (1−p(l,i)) is the probability that the node i is in reception mode during the slot l, 
         [0000]    
       
         
           
             θ 
             CAi 
           
         
       
     
         [0000]    is the probability mat a node j transmits in the range of the node i, 
         [0206]    p(l, i) is the probability that a node j transmits during the time slot l and 
         [0000]    
       
         
           
             
               ( 
               
                 1 
                 - 
                 
                   
                     θ 
                     CAi 
                   
                    
                   
                     p 
                      
                     
                       ( 
                       
                         l 
                         , 
                         i 
                       
                       ) 
                     
                   
                 
               
               ) 
             
             
               
                 k 
                 i 
               
               - 
               2 
             
           
         
       
     
         [0000]    is the probability that the other node nodes (excepted i and j) do not transmit in the range of the node i 
         [0207]    Finally, the probability that node i discovers node j within t time slots is: 
         [0000]        P   i,j ( t )=1−(1− pi,j ) t  
 
         [0208]    The objective is then to find p(l,i) that optimizes P i,j . 
         [0209]    The probability p(l,i) that a node j transmits in the range of the node i, which optimizes P i,j  is equal to: 
         [0000]    
       
         
           
             
               p 
               
                 ( 
                 
                   l 
                   , 
                   i 
                 
                 ) 
               
             
             = 
             
               
                 
                   ( 
                   
                     2 
                     + 
                     
                       
                         ( 
                         
                           
                             K 
                             i 
                           
                           - 
                           1 
                         
                         ) 
                       
                        
                       
                         θ 
                         
                           CA 
                           i 
                         
                       
                     
                   
                   ) 
                 
                 - 
                 
                   
                     
                       ( 
                       
                         2 
                         + 
                         
                           
                             ( 
                             
                               
                                 K 
                                 i 
                               
                               - 
                               1 
                             
                             ) 
                           
                            
                           
                             θ 
                             
                               CA 
                               i 
                             
                           
                         
                       
                       ) 
                     
                     - 
                     
                       4 
                        
                       
                           
                       
                        
                       
                         K 
                         i 
                       
                        
                       
                         θ 
                         
                           CA 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   K 
                   i 
                 
                  
                 
                   θ 
                   
                     CA 
                     i 
                   
                 
               
             
           
         
       
     
         [0210]    With K i  being the number of nodes in the reception range of node i. 
         [0211]    The optimal (l,) can be computed but the problem is not resolved because K i  is not known. Only estimation of K i  can be used. 
         [0212]    With KT i  being the true value of K i  corresponding to the actual number of nodes in the reception range of node i:
       If K i &gt;KT i , the transmission probability is underestimated and consequently, the channel is under-utilized and some discovery events are missed.   If K i &lt;KT i , the transmission probability is overestimated and consequently, more collisions are generated.       
 
         [0215]    The algorithm described with reference to  FIG. 8  makes it possible to adjust the value of the coverage area CA each time the radio settings are determined for performing further discovery process (step  803  of the algorithm). For instance, adjusting the antenna configuration of a given node i from configuration  531  to configuration  511  (see  FIG. 5 ) makes it possible to restrict the coverage area from 180° to 90°. The adjustment of the coverage area CA i  allows performing a new estimation of the number of nodes K i  related to this new coverage area. 
         [0216]    Therefore, the probability that a node j transmits in the range of the node i during the slot l is defined as follows: 
         [0000]    
       
         
           
             
               p 
               
                 ( 
                 
                   l 
                   , 
                   i 
                 
                 ) 
               
             
             = 
             
               
                 
                   ( 
                   
                     2 
                     + 
                     
                       
                         ( 
                         
                           
                             K 
                             i 
                           
                           - 
                           1 
                         
                         ) 
                       
                        
                       
                         θ 
                         
                           CA 
                           i 
                         
                       
                     
                   
                   ) 
                 
                 - 
                 
                   
                     
                       ( 
                       
                         2 
                         + 
                         
                           
                             ( 
                             
                               
                                 K 
                                 i 
                               
                               - 
                               1 
                             
                             ) 
                           
                            
                           
                             θ 
                             
                               CA 
                               i 
                             
                           
                         
                       
                       ) 
                     
                     - 
                     
                       4 
                        
                       
                           
                       
                        
                       
                         K 
                         i 
                       
                        
                       
                         θ 
                         
                           CA 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   K 
                   i 
                 
                  
                 
                   θ 
                   
                     CA 
                     i 
                   
                 
               
             
           
         
       
       
         
           
             Then 
              
             
               : 
             
           
         
       
       
         
           
             
               p 
               
                 ( 
                 
                   l 
                   , 
                   i 
                 
                 ) 
               
             
             = 
             
               
                 
                   
                     
                       
                         ( 
                         
                           2 
                           + 
                           
                             
                               ( 
                               
                                 
                                   
                                     K 
                                     i 
                                   
                                    
                                   
                                     ( 
                                     l 
                                     ) 
                                   
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                              
                             
                               θ 
                               
                                 
                                   CA 
                                   i 
                                 
                                  
                                 
                                   ( 
                                   l 
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                       - 
                     
                   
                 
                 
                   
                     
                       
                         
                           ( 
                           
                             2 
                             + 
                             
                               
                                 ( 
                                 
                                   
                                     
                                       K 
                                       i 
                                     
                                      
                                     
                                       ( 
                                       l 
                                       ) 
                                     
                                   
                                   - 
                                   1 
                                 
                                 ) 
                               
                                
                               
                                 θ 
                                 
                                   
                                     CA 
                                     i 
                                   
                                    
                                   
                                     ( 
                                     l 
                                     ) 
                                   
                                 
                               
                             
                           
                           ) 
                         
                         - 
                         
                           4 
                            
                           
                               
                           
                            
                           
                             
                               K 
                               i 
                             
                              
                             
                               ( 
                               l 
                               ) 
                             
                           
                            
                           
                             θ 
                             
                               
                                 CA 
                                 i 
                               
                                
                               
                                 ( 
                                 l 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   
                     K 
                     i 
                   
                    
                   
                     ( 
                     l 
                     ) 
                   
                 
                  
                 
                   θ 
                   
                     
                       CA 
                       i 
                     
                      
                     
                       ( 
                       l 
                       ) 
                     
                   
                 
               
             
           
         
       
     
         [0217]    The coverage area is modified according to the discovered neighbors. Consequently, the value of K i —i.e. the number of nodes in the reception range of node i—is also modified. One may, for instance, consider a linear model for adjusting the value of K i : 
         [0000]    
       
         
           
             
               
                 K 
                 i 
               
                
               
                 ( 
                 l 
                 ) 
               
             
             = 
             
               
                 
                   K 
                   i 
                 
                  
                 
                   ( 
                   
                     l 
                     - 
                     1 
                   
                   ) 
                 
               
               * 
               
                 
                   
                     CA 
                     i 
                   
                    
                   
                     ( 
                     l 
                     ) 
                   
                 
                 
                   
                     CA 
                     i 
                   
                    
                   
                     ( 
                     
                       l 
                       - 
                       1 
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0218]    While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive, the invention being not restricted to the disclosed embodiment. Other variations to the disclosed embodiment can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure and the appended claims. 
         [0219]    In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. A single processor or other unit may fulfill the functions of several items recited in the claims. The mere fact that different features are recited in mutually different dependent claims does not indicate that a combination of these features cannot be advantageously used. Any reference signs in the claims should not be construed as limiting the scope of the invention.