FORM 2

The Patent Act 1970
(39 of 1970)
&
The Patent Rules  2005

COMPLETE SPECIFICATION
(SEE SECTION 10 AND RULE 13)

TITLE OF THE INVENTION

“Method to allocate resources for Peer-to-peer Communications in Cellular Networks”
APPLICANTS:

Name Nationality Address
Alcatel Lucent France 3 Avenue Octave Greard 75007  Paris

The following specification particularly describes and ascertains the nature of this invention and the manner in which it is to be performed:-

FIELD OF INVENTION
[001] The embodiments herein relate to peer-to-peer communications and more particularly to allocate resources to user devices for peer-to-peer communications in cellular networks.

BACKGROUND
[002] Wireless telecommunications refer to the transfer of information between two or more devices that are not physically connected. The distance between the communicating devices can be ranging from a few meters to thousands of kilometers. The increased popularity of wireless telecommunications led to the emergence of numerous devices such as cellular phones  PDAs  wireless headsets  etc  which can send or rather transmit data to the destinations provided that the communicating devices are within each other’s range. Wireless communications can be achieved via three modes-radio frequency communication  microwave communication and infrared short-range communication. An emerging networking technology based on a radio network is a cellular network popularly used for transmitting data over cells each connected to a base station which comprises of a transmitter  a receiver and a control unit and acts as a hub or a gateway for transmitting data in wireless networks. Each cell in a cellular network uses a different set of frequencies in order to avoid interference with other adjacent cells. Also  in an LTE (Long Term Evolution)  the frequencies across the different cells can be reused to enable an optimum utilization of the network capacity and its coverage. In most of the cases  the mobile/cellular traffic occupies few channel resources in a licensed spectrum and leaves a large subset of channel resources unused/vacant leading to an inappropriate utilization of the available bandwidth. Since radio spectrum is a limited resource efforts are being made to utilize the available bandwidth more efficiently.
[003] The most common mode of communication that has widely gained popularity in the recent times is a Peer-to-peer communication mode. A wide range of technologies for peer-peer networking are available which include Bluetooth  GPRS  WLAN and WiMax. The efficiency of the applications of wireless communication systems led to the emergence of peer-peer networks prominently used in cellular telephones  personal digital assistants (PDAs)  headsets  etc. Through widely used  these technologies have few other disadvantages such as rate of data transfer is low  range limitations  power consumption  signal interference  etc which ultimately reduce the quality of service provided to the users. Another disadvantage of existing P2P systems is that they do not provide means to facilitate P2P communication using cellular spectrum which provides wide coverage for communication.

SUMMARY

[004] In view of the foregoing  an embodiment herein provides a method for allocating licensed spectrum resources to a plurality of user devices for peer to peer (P2P) communication in a cellular network  the method comprises grouping the plurality of user devices to a virtual user group by a base station (BTS); sending available channel resource information to the virtual user group by the base station; selecting at least one channel resource from the available channel resources by at least one of the plurality of user devices and establishing P2P communication with another user device using the selected channel resource by the user device.
[005] Also  disclosed herein is a system for allocating licensed spectrum resources to a plurality of user devices for peer to peer (P2P) communication in a cellular network  the system provided with at least one means configured for grouping the plurality of user devices to a virtual user group using a base station (BTS); sending available channel resource information to the virtual user group using the base station; selecting at least one channel resource from the available channel resources by at least one of the plurality of user devices and establishing P2P communication with another user device using the selected channel resources by the user device.
[006] These and other aspects of the embodiments herein will be better appreciated and understood when considered in conjunction with the following description and the accompanying drawings.

BRIEF DESCRIPTION OF THE FIGURES
[007] The embodiments herein will be better understood from the following detailed description with reference to the drawings  in which:
[008] FIG. 1 is a block diagram of the proposed peer-peer resource allocation system  as disclosed in the embodiments herein;
[009] FIG. 2 is a block diagram which shows various components of a base station of a cellular network  as disclosed in the embodiments herein;
[0010] FIG. 3 is a flow diagram which shows various steps involved in the process of allocating resources to peer to peer devices for communication  as disclosed in the embodiments herein;
[0011] FIG. 4 illustrates an example sequence diagram which shows the sequence of messages communicated between a base station and a P2P user device considering P2P communications in an LTE spectrum  as disclosed in the embodiments herein; and
[0012] FIG. 5 is an example diagram illustrating allocation of resources to various users in a licensed spectrum  as disclosed in the embodiments herein.

DETAILED DESCRIPTION OF INVENTION
[0013] The embodiments herein and the various features and advantageous details thereof are explained more fully with reference to the non-limiting embodiments that are illustrated in the accompanying drawings and detailed in the following description. Descriptions of well-known components and processing techniques are omitted so as to not unnecessarily obscure the embodiments herein. The examples used herein are intended merely to facilitate an understanding of ways in which the embodiments herein may be practiced and to further enable those of skill in the art to practice the embodiments herein. Accordingly  the examples should not be construed as limiting the scope of the embodiments herein.
[0014] The embodiments herein achieve a method for allocating channel resources to user devices for peer-to-peer communications in cellular networks. Referring now to the drawings  and more particularly to FIGS. 1 through 5  where similar reference characters denote corresponding features consistently throughout the figures  there are shown embodiments.
[0015] FIG. 1 shows a block diagram of the proposed peer-peer (P2P) resource allocation system  as disclosed in the embodiments herein. The P2P resource allocation system comprises of a Base Station (BTS) 101 and a Virtual User Set 102. The virtual user set further comprises a plurality of P2P user devices 103.a  103.b and103.c  which are connected to the BTS 101 for establishing P2P communication with any other device. The BTS 101 is equipment that facilitates a wireless communication between P2P user devices by allocating them channel resources in a licensed spectrum. It basically transmits and receives signals from various P2P user devices and processes them accordingly. In a P2P resource allocation system  the BTS 101 divides the available bandwidth among primary and secondary users for communication purposes. Primary users are the mobile/cellular users whereas the secondary users refer to the users who want to communicate in a P2P environment.
[0016] On receiving a connection request from a P2P user device 103  the BTS 101 may initially perform an authentication check. If the P2P user device 103 fails in the authentication checking phase  then the process of connecting the device to the BTS 101 is terminated. If the device is authenticated  the BTS 101 assigns it with a unique user ID and thereby establishes a dedicated control channel mapped to the unique user ID of the P2P user device 103. The BTS 101 hereafter communicates with the P2P user device 103 via its control channel. Further  upon receiving a Resource Request (RR) message  the BTS 101 assigns the P2P user device 103 to a virtual user group and communicates the virtual group’s user ID to the P2P user device 103 over its control channel. Grouping the various P2P user devices 103 into a single virtual user group improves the efficiency of the BTS 101 in allocating resources since the BTS 101 now has to allocate the channel resources only to a single virtual user instead of managing multiple P2P user devices 103 individually. The P2P user device 103 can now access the channel resources allocated to the virtual user group as and when required. The P2P user device 103 decodes the data received.
[0017] Further  the BTS 101 sends a schedule of the unused/vacant channel resources in the available bandwidth to the P2P user devices 103 over the control channel mapped to the virtual user set 102. In an embodiment  the available bandwidth for P2P communication and corresponding vacant channel resource number may change continuously according to bandwidth usage by the primary users as well as secondary users. In various embodiments  the bandwidth allocation for P2P communication may be static or dynamic modes. In static mode  one portion of the available bandwidth may be permanently reserved for the secondary user communication i.e. P2P communication. In dynamic mode  amount of bandwidth allocated for primary and secondary user communication may change on the fly depending on the traffic in the network.
[0018] In an embodiment  using any of the available MAC protocols  the P2P user devices 103 contend among each other to avail the channel resources allotted to the virtual user set 102. In another embodiment  the BTS 101 may schedule each P2P user device 103 in a certain time slot in the bandwidth allotted to the virtual user set 102. All the P2P user devices 103 assigned to the Virtual user set 102 may get scheduled in different time slots to communicate with each other thereby reducing the scope of any kind of signal inferences during the process of communication. Further  the data communicated between various P2P user devices 103 using the network may be encrypted using suitable a coding mechanism so as to ensure data security.
[0019] FIG. 2 is a block diagram which shows various components of a base station 101 of a cellular network  as disclosed in the embodiments herein. The BTS 101 comprises of a transceiver 201  an authentication module 202  resource allocation module 203  scheduler 204  memory module 205  power amplifier 206  duplexer 207  control function 208 and a processor 209. The transceiver 201 is a device that comprises both a transmitter and a receiver for transmitting and receiving signals between the BTS 101 and other network elements. Whenever a transceiver 201 receives a signal indicating an attempt by a P2P user device 103 to connect to the Base Station 101  the authentication module 202 is invoked. The authentication module 202 maintains integrity of the users and the data in the network by authenticating each and every user device that tries to connect to the BTS 101 for resource allocation. Once a P2P user device 103 is authenticated  the authentication module 202 assigns it with a unique user ID which will be used by the P2P user device for further communication process. Also a dedicated control channel mapped to its unique user ID is established which will be used for further communications between the BTS 101 and the P2P user device.
[0020] Further  to establish a P2P connection with a user device; say user device 103.c  another device; say 103.a sends a Resource Request (RR) message to the BTS 101 over its control channel. Upon receiving the resource request from the BTS 101 adds the user to a virtual user set 102. The resource allocation module 203 of the BTS 101 responds to the P2P user device 103.a on its control channel and sends the unique user ID of the Virtual User set 102 using corresponding control messages. This control message may also act as an acknowledgment to the P2P user confirming the successful transmission of the Resource Request message to the BTS 101. The P2P user device 103.a will then listen on the control channel dedicated /assigned to virtual user group and waits for the allocation of channel resources.
[0021] The Scheduler 204 divides the available channel resources between the cellular users and the virtual P2P users. In an embodiment  the scheduler 204 allots channel resources to the cellular users and then allots a subset of the remaining resources to the virtual P2P users. The allocation of channel resources to the P2P users therefore changes dynamically depending on the traffic of the primary/mobile/cellular users in the network. Since  the mobile/cellular users are preferred while allocating the channel resources  the P2P users will avail the resources only if the cellular traffic is less than the total network capacity. In another embodiment  the scheduler 204 may allocate a certain amount of channel resources permanently to the P2P user devices. The allocation of channel resources to P2P users in this method is static and hence may not get affected by the network traffic. Once the channel resources are available  information regarding the same is communicated to the virtual user over the control channel mapped to its unique user ID. Scheduling information does not necessarily correspond to an assignment for the next channel resource; it may be an assignment of channel resources for a slot in the future.
[0022] A memory module 205 stores the information regarding the various virtual user sets and the users assigned to each of them accessing the network for communication. It stores the user IDs of the individual P2P user devices as well as the Virtual user sets and updates its database as and when required.
[0023] A power amplifier 206 is used to amplify the signals received from the transceiver for transmission through antennas to the different user devices. A duplexer 207 allows a bidirectional communication over a single antenna port by separating the sending and receiving signals to/from the antenna. A control function 208 manages the various base stations available and performs functions such as software upgradations  status changes  etc. Finally  a processor 209 processes the information and the instructions received thereby facilitating the other modules of the base station 101 work and coordinate efficiently.
[0024] FIG. 3 is a flow diagram which shows various steps involved in the process of allocating resources to peer-peer devices for communication  as disclosed in the embodiments herein. A P2P user device tries to connect to a base station to avail channel resources for transmitting data to another user device. On receiving the connection request from the user device 103  the BTS 101 checks whether the device is authenticated i.e. if the device has rights to connect to the BTS 101 or not. Authentication may be performed using any suitable protocols such as Remote Authentication Dial-In User Service (RADIUS)  Extensible Authentication Protocol (EAP)  and so on. In a preferred embodiment  the P2P user device (UE) 103 may be permitted to establish connection with the BTS 101 only if the user is an existing cellular user/a pre-registered P2P user device that may be authenticated using the user information available in the network’s databases. In another embodiment  the P2P user devices may have to register/subscribe with the base station so as to use the licensed spectrum for P2P communication. Further  user data obtained during registration may be used to authenticate the user when he/she tries to access the licensed spectrum for P2P communication. If authentication fails  the connection request from the UE 103 is terminated (303). If the authentication succeeds  the UE 103 is assigned (304) with a unique user ID and a dedicated control channel is assigned which is mapped to its unique user ID. Further communication between the BTS 101 and the device 103 will be carried out over this dedicated channel mapped to the User ID of the device 103.
[0025] The device 103 which requires a channel resource for data transmission sends (305) a Resource Request (RR) message to the BTS 101 over the control channel mapped to its unique user ID. On receiving the RR message  the BTS 101 acknowledges and responds to the P2P user device 103 on its control channel by sending the unique user ID of the virtual user set V. The BTS 101 further adds (306) the P2P user device 103 to the Virtual user set V. Further  the BTS 101 assigns a control channel to the created virtual group. The BTS 101 can communicate (307) information such as available channel resource information  scheduled channel resource information and so on to the virtual group through the assigned control channel preferably in an encoded format. Further  the P2P devices present in the virtual group may receive and decode the received information. The virtual grouping may eliminate need for the BTS 101 to communicate individually to all P2P devices connected to it.
[0026] The number of vacant channel resources available in the network at a certain point of time may vary depending on the method used by the Scheduler 204 to allot the channel resources to the mobile/cellular users and the P2P user devices 103. In an embodiment  the scheduler 204 may allot a certain pre-decided number of channel resources specifically to the P2P user. In another embodiment  the scheduler 204 may allot the channel resources dynamically to the P2P users. Here  the mobile/cellular users are preferred by allocating the available channel resources to them and then allocating a subset of the remaining channel resources to the P2P users. In this case  the P2P users get allocated with the channel resources only if the available bandwidth to the virtual user set 102 exceeds the amount of resources allocated to the mobile/cellular traffic. The P2P users are allocated with channel resources left unused by the cellular users in the network. In another embodiment  the P2P users may be allocated resources in the available channel resources and the unused channel resources are then allocated to the cellular users. The method used for allocating the channel resources may vary depending upon the traffic in the network or any other relevant factors. Upon receiving the schedule of the vacant channel resources  the P2P user devices 103 of the virtual user set contend among each other using any of the existing MAC protocols to obtain the channel resources allocated to the virtual user. The P2P user devices 103 then transfer data/communicate with each other in the specified time slot as allotted by the BTS 101.
[0027] The BTS 101 may periodically check (308) if any of the P2P user devices 103 in the virtual user set 102 have finished communication. In a preferred embodiment  the BTS 101 may receive a Resource Detach (RD) message from the P2P user device 103 when the communication is completed. Upon receiving the RD message from the P2P user device 103 over its control channel  BTS 101 detaches (310) the user device 103 by removing the P2P user device 103 from the set of active users and acknowledges the same to the user through a message mapped to its control channel. Further  the channel resource that the user device had been using for P2P communication is released.
[0028] In a preferred embodiment  in order to ensure that the user device 103 which has already been removed from the virtual user group 102 does not receive or listen to any more information transmitted to the virtual user set 102  the BTS 101 may change virtual user id of the user group. In an embodiment  the BTS 101 may change virtual user ID every time a P2P user device 103 is removed from the user group. In another embodiment  the base station can periodically update the virtual user ID. Further in either case  the new ID is communicated to the users present in the virtual user set 102 over their respective control channels mapped to their unique user IDs. Depending on the traffic patterns  the base station can adopt any available methods to change the virtual user ID in specific time intervals. Such a method of periodically updating the virtual user ID is appropriate when the frequency of P2P users arriving at and leaving the network is high.
[0029] FIG. 4 illustrates an example sequence diagram which shows the sequence of messages communicated between a base station and a P2P user device considering P2P communications in an LTE spectrum  as disclosed in the embodiments herein. A P2P user device; say user device 103.a tries to establish a connection with the BTS 101. The BTS 101 authenticates the device and if successful  the device 103.a is allowed to connect to the BTS 101. The P2P user device 103.a then gets assigned with a unique user ID RNTI (Radio Network Temporary Identifier) by the BTS 101 which is communicated over a paging channel. On receiving the unique user ID the device 103.a sends a Resource Request (RR) message to the BTS 101 over the control channel mapped to its unique user ID RNTI. The BTS sends the unique user ID RNTIV of the virtual user set 102 to the user device which is thereby added to the virtual user set 102. The device 103.a now starts listening to the downlink control channel mapped to the user ID of the virtual user set V. The BTS 101 sends a schedule of the vacant/unused channel resources in the network to the virtual user set V over the control channel mapped to its user ID RNTIV. The various P2P users get scheduled using any available MAC protocols and continue with their communication process. After the completion of communication/ transmission  the P2P user device 103.a sends a message to the BTS 101 which then removes the device from the virtual user set and acknowledges the same to the device. The BTS 101 then changes the user ID RNTIV of the virtual user set V and relays the new RNTIV to the active users in the network.
[0030] FIG. 5 is an example diagram illustrating allocation of resources to various users in a licensed spectrum  as disclosed in the embodiments herein. Here  consider the case of allocating channel resources for P2P communications in LTE. A Frequency-Division Duplexing (FDD) structure is considered wherein the transmitter and receiver of the base station 101 use different carrier frequencies in order to transmit and receive data simultaneously. The figure only represents the uplink channel allocations. The uplink channel resources in the LTE are shared between the mobile users and the P2P users. LTE utilizes Orthogonal Frequency Division Multiple Access (OFDMA) as the communication technique for the physical layer which enables simultaneous data transmission from several users at a time. Physical Resource Block (PRB)  which is the smallest quantum of channel resource in an LTE  is allocated to a user. One PRB consists of 12 subcarriers each having a width of 15 kHz. Hence a PRB has a width of 180 kHz and is spread over a single time slot of 1 millisecond consisting of 14 OFDMA symbols. Mobile users (called UEs) are allocated a set of PRBs for their uplink transmission by the base station (called eNodeB). Each active UE 103 is assigned a unique ID called as RNTI. Any control message sent by the eNodeB to a specific UE 103 is encrypted with the specific RNTI assigned to the UE 103. The eNodeB makes scheduling decisions for each subframe of duration 1 ms. The scheduling decisions for the uplink channel are communicated to the UE""s 103 at least three subframes in advance. Hence  the eNodeB transmits the schedule of assignment of PRBs to UE""s 103 in a subframe  at least three subframes in advance. This transmission is performed over the control channel and each UE can decode the messages sent over the control channel to obtain the PRBs assigned to it for transmission. Then the UEs 103 can schedule their transmissions in the appropriate subframe.
[0031] The embodiments disclosed herein can be implemented through at least one software program running on at least one hardware device and performing network management functions to control the network elements. The network elements shown in Fig. 1 include blocks which can be at least one of a hardware device  or a combination of hardware device and software module.
[0032] The embodiment disclosed herein describes a method and system for allocating licensed spectrum for Peer to Peer (P2P) communication in a cellular network. Therefore  it is understood that the scope of the protection is extended to such a program and in addition to a computer readable means having a message therein  such computer readable storage means contain program code means for implementation of one or more steps of the method  when the program runs on a server or mobile device or any suitable programmable device. The method is implemented in a preferred embodiment through or together with a software program written in e.g. Very high speed integrated circuit Hardware Description Language (VHDL) another programming language  or implemented by one or more VHDL or several software modules being executed on at least one hardware device. The hardware device can be any kind of portable device that can be programmed. The device may also include means which could be e.g. hardware means like e.g. an ASIC  or a combination of hardware and software means  e.g. an ASIC and an FPGA  or at least one microprocessor and at least one memory with software modules located therein. The method embodiments described herein could be implemented partly in hardware and partly in software. Alternatively  the invention may be implemented on different hardware devices  e.g. using a plurality of CPUs.
[0033] The foregoing description of the specific embodiments will so fully reveal the general nature of the embodiments herein that others can  by applying current knowledge  readily modify and/or adapt for various applications such specific embodiments without departing from the generic concept  and  therefore  such adaptations and modifications should and are intended to be comprehended within the meaning and range of equivalents of the disclosed embodiments. It is to be understood that the phraseology or terminology employed herein is for the purpose of description and not of limitation. Therefore  while the embodiments herein have been described in terms of preferred embodiments  those skilled in the art will recognize that the embodiments herein can be practiced with modification within the spirit and scope of the embodiments as described herein.

CLAIMS
We Claim :
1. A method for allocating licensed spectrum resources to a plurality of user devices for peer to peer (P2P) communication in a cellular network  said method comprises:
grouping said plurality of user devices to a virtual user group by a base station (BTS);
sending available channel resource information to said virtual user group by said base station;
selecting at least one channel resource from said available channel resources by at least one of said plurality of user devices; and
establishing P2P communication with another user device using said selected channel resource by said user device.
2. The method as in claim 1  wherein said grouping at least one of said plurality of user devices to the virtual user group further comprises:
verifying authenticity of said user device on the user device requesting resource for establishing said P2P communication with another user device;
assigning said user device to said virtual user group on said authentication being successful; and
assigning and configuring a control channel with a virtual user Id of said virtual user group.
3. The method as in claim 2  wherein said assigning the user device to the virtual user group further comprises:
configuring a user Id of said user device with the virtual user Id of said virtual user group; and
sending said user Id of the virtual user group to said user device over a control channel that connects said user device to the base station.
4. The method as in claim 1  wherein said sending available channel resource information to the virtual user group further comprises:
detecting free channel resource information in an available bandwidth by said base station; and
sharing said detected free channel resource information with said virtual user group.
5. The method as in claim 4  wherein said sharing detected free channel resource information with the virtual user group further comprises sending said detected free channel resource information over the control channel assigned to the virtual user group.
6. The method as in claim 4  wherein said available bandwidth is assigned statically for said P2P communication.
7. The method as in claim 4  wherein said available bandwidth is assigned dynamically for said P2P communication.
8. The method as in claim 1  wherein said selected channel resource is released upon completion of said P2P communication.
9. The method as in claim 8  wherein said releasing of the selected channel resource further comprises:
receiving a resource detach message from said user device upon completion of the P2P communication;
removing said user device from a list of active users; and
changing a virtual user Id of said virtual user group to a new virtual Id.
10. The method as in claim 9  wherein said new virtual Id is communicated with all active user devices in said virtual user group.
11. A system for allocating licensed spectrum resources to a plurality of user devices for peer to peer (P2P) communication in a cellular network  said system provided with at least one means configured for:
grouping said plurality of user devices to a virtual user group using a base station (BTS);
sending available channel resource information to said virtual user group using said base station;
selecting at least one channel resource from said available channel resources by at least one of said plurality of user devices; and
establishing P2P communication with another user device using said selected channel resources by said user device.
12. The system as in claim 11  wherein said system is further configured for grouping at least one of said plurality of user devices to the virtual user group by:
verifying authenticity of said user device on the user device requesting resource for establishing said P2P communication with another user device using said base station;
assigning said user device to said virtual user group on said authentication being successful using said base station; and
assigning and configuring a control channel with a virtual user Id of said virtual user group using said base station.
13. The system as in claim 12  wherein said system is further configured for assigning the user device to the virtual user group by:
configuring a user Id of the user device with the virtual user Id of said virtual user group using said base station; and
sending said user Id of the virtual user group to said user device over a control channel that connects said user device to the base station using said base station.
14. The system as in claim 11  wherein said system is further configured for sending available channel resource information to the virtual user group by:
detecting free channel resource information in an available bandwidth using said base station; and
sharing said detected free channel resource information with said virtual user group using said base station.
15. The system as in claim 14  wherein said system is configured for sharing detected free channel resource information with the virtual user group by sending said detected free channel resource information over the control channel assigned to the virtual user group using said base station.
16. The system as in claim 14  wherein said system is configured for assigning said available bandwidth statically for said P2P communication using said base station.
17. The system as in claim 14  wherein said system is configured for assigning said available bandwidth dynamically for said P2P communication using said base station.
18. The system as in claim 11  wherein said system is further configured for releasing said selected channel resource upon completion of said P2P communication using said base station.
19. The system as in claim 18  wherein said system is further configured for releasing the selected channel resource by:
receiving a resource detach message from said user device upon completion of the P2P communication using said base station;
removing said user device from a list of active users using said base station; and
changing a virtual user Id of said virtual user group to a new virtual Id using said base station.
20. The system as in claim 19  wherein said system is further configured for communicating said new virtual Id with all active user devices in said virtual user group.

Dated: 21st November  2012 Signature
Dr. Kalyan Chakravarthy
Patent Agent

ABSTRACT

The embodiments herein relate to peer-to-peer communications and more particularly to allocate resources to user devices for peer-to-peer communications in cellular networks. All the user devices requiring the resources for P2P communication are grouped into a single virtual user set and the virtual user set is assigned a unique virtual user group Id. Further  information regarding vacant channel resources at each instant of time is communicated with the devices present in the virtual set. Based on this information  the devices can access channel resources and communicate with any other device. Further  when a user device finishes communication  that device is removed from the virtual set. In order to ensure data security  Id of the virtual group is changed periodically and is communicated with user devices which are present in the virtual set at that instance of time.

FIG. 3