Resource sharing between a plurality of communication networks

RESOURCE SHARING BETWEEN A PLURALITY OF COMMUNICATION NETWORKS

Field of the invention

The invention relates to resource sharing between a plurality of communication networks and in particular, but not exclusively, to temporary air interface resource re-allocation between broadband Wireless Metropolitan Area Networks (WMAN).

Background of the Invention

In the last decades, wireless communication systems have become ubiquitous. For example, cellular communication systems, broadband Wireless Metropolitan Area Networks (WMAN) and wireless Local Area Networks (WLANs) have become widespread as a means to provide efficient communication services to e.g. mobile communication units. However, the increased prevalence of wireless communication systems have resulted in a dramatically increased need for air interface resources and the need for efficiently and flexibly utilising the available resource has become essential for the further development of wireless systems.

A method that has been proposed for effectively increasing the utilisation of air interface resource is spectrum sharing wherein a number of independent networks may share the same frequency spectrum. The frequency spectrum may be shared by time division wherein the individual networks are allocated distinct time intervals for transmission. However, a static allocation of resource to different networks will typically not result in an optimal utilisation of the available resource as the resource requirements for individual networks tend to vary dynamically. However, current approaches for dynamic allocation of a shared air interface resource to individual networks tend to be complex, result in suboptimal resource sharing and suboptimal performance for the individual networks.

Hence, an improved system for resource sharing would be advantageous and in particular a system allowing increased flexibility, improved resource sharing, improved dynamic performance, reduced complexity and/or improved resource sharing would be advantageous.

Summary of the Invention

Accordingly, the Invention seeks to preferably mitigate, alleviate or eliminate one or more of the above mentioned disadvantages singly or in any combination.

According to a first aspect of the invention there is provided a method of resource sharing between a plurality of communication networks each having a nominal resource allocation of a shared air interface resource and a resource exchange allowance, the method comprising: initiating a temporary resource allocation of a first air interface resource from a nominal resource allocation of a first network; executing a plurality of offer rounds, each offer round comprising determining offer values for the first air interface resource; selecting a second network in response to the determined offer values; sending a resource allocation message to the second network, the resource allocation message indicating a temporary allocation of at least part of the first air interface resource from the first network to the second network; and reducing the resource exchange allowance of the second network by a value determined in response to the resource exchange offer value from the second network; and wherein each offer round comprises: the first network transmitting an offer request to a first plurality of networks; the first plurality of networks transmitting offer messages to the first network, each offer message comprising a resource exchange offer value for at least part of the first air interface resource; and determining the offer values for the first air interface resource in response to the resource exchange offer values.

The invention may allow improved resource sharing between different networks. An efficient management of resource sharing may be achieved. All or some of the nominal resource allocation for one network may temporarily be reassigned to another network (or to a plurality of other networks) without necessitating a complex and/or combined resource allocation. The invention may e.g. allow a temporary resource re-allocation to the network requiring it most through a simple offer mechanism. An efficient dynamic resource sharing is enabled while maintaining the required interworking and coordination between the communication networks. In particular, the iterative nature of the offer rounds allow for an improved resource sharing and distribution to networks most in need of the resource.

Different communication networks may employ independent resource allocation of the allocated air interface allocation and may be independently managed and controlled. The individual networks may be owned and operated by different and independent operators. The communication networks may for example be cellular communication systems such as the Global System for Mobile (GSM) communication or the Universal Mobile Telecommunication System (UMTS). The communication networks may for example also be Orthogonal Frequency Division Multiple Access systems. For example, the communication networks may include Wireless Local Area Networks (WLANs) such as IEEE 802.11 networks or broadband wireless radio access systems such as IEEE 802.16 networks.

The invention may in some embodiments provide a cognitive radio based solution to spectrum utilisation and may in particular allow spectrum reuse opportunities by providing the means to identify/detect the free/available resources for sharing.

The invention may in some embodiments enable or facilitate spectrum sharing in a distributed and real time way. In particular, it may provide the mechanisms for spectrum sharing between base stations using a peer- to-peer arrangement.

The invention may in some embodiments enable or facilitate co-existence of heterogeneous radio access systems using the same frequency band based on collaborative mechanisms.

The invention may e.g. be applied to communication networks using Time Division Duplex (TDD) or Frequency Division Duplex (FDD) communication schemes.

The offer request messages and/or offer messages may be exchanged between individual base stations of the first network and the first plurality of networks.

According to an optional feature of the invention, the offer request of at least one offer round comprises an indication of offer values determined in a previous offer round. This may improve the resource distribution and reallocation and may in particular allow the offering networks to determine a suitable resource exchange offer value.

According to an optional feature of the invention, the first network transmitting offer messages to the first plurality of networks comprises the first network transmitting the offer request to a base station of one of the first plurality of networks, the determination of offer values further comprising: the base station transmitting subscriber station offer requests to subscriber stations of the base station; at least one of the subscriber stations transmitting a subscriber station offer message to the base station, the subscriber station offer message comprising a subscriber station resource exchange offer value; and the base station determining the resource exchange offer value in response to the subscriber station resource exchange offer value and transmitting the resource exchange offer value to the first network.

This may improve the resource distribution and reallocation and may in particular allow a resource distribution that reflects the resource needs of the individual subscriber stations in networks seeking to be allocated a temporary resource.

According to an optional feature of the invention, the sending a resource allocation message to the second network comprises sending the resource allocation message directly to a subscriber station of the second network.

This may facilitate the management and signalling associated with temporary resource reallocation in many embodiments.

According to an optional feature of the invention, the method further comprises: at least one of the subscriber stations transmitting connected equipment offer requests to connected equipment of the at least one of the subscriber stations; at least one of the connected equipments transmitting a connected equipment offer message to the at least one of the subscriber stations, the connected equipment offer message comprising a connected equipment resource exchange offer value; and the at least one of the subscriber stations determining the subscriber station resource exchange offer value in response to the connected equipment resource exchange offer value.

This may improve the resource distribution and reallocation and may in particular allow a resource distribution that reflects the resource needs of the individual equipment connected to the individual subscriber units in networks seeking to be allocated a temporary resource.

According to an optional feature of the invention, the sending a resource allocation message to the second network comprises sending the resource allocation message directly to a connected equipment of the second network.

This may facilitate the management and signalling associated with temporary resource reallocation in many embodiments.

According to an optional feature of the invention, the method further comprises selecting the second network in response to a determination that the resource exchange offer value from the second network for the at least part of the first air interface resource is the highest received resource exchange offer value.

The selection means may for example select the network to which a given resource is temporarily re-allocated as the network providing the highest offer for that specific resource. This may provide a simple and efficient way of providing the available resource to networks most in need of the resource, and may in some embodiments assist in the maximisation of the benefit to the first network of sharing this resource.

According to an optional feature of the invention, the method comprises selecting a plurality of selected networks and allocating different parts of the first air interface resource to the plurality of selected networks so as to maximise the combined resource exchange offer values.

This may allow a flexible resource allocation wherein an available resource is shared between a plurality of networks in accordance with their respective need for the resource, and may in some embodiments maximise the benefit to the first network of sharing the resource.

According to an optional feature of the invention, the first plurality of networks employ a shared Media Access Control (MAC) frame and each of the plurality of communication networks has a nominal allocated time interval of the MAC frame.

The MAC frame may be a shared MAC frame of a radio air interface. The feature may facilitate interoperation and provide a practical system for effective resource sharing. In particular, it may facilitate peer-to-peer based resource sharing over a shared air interface.

According to an optional feature of the invention, the MAC frame comprises a first management subframe for transmission of offer request messages.

This may facilitate interoperation and provide a practical system for effective resource sharing. In particular, it may facilitate peer-to-peer based resource sharing over a shared air interface. According to an optional feature of the invention, the first management subframe is divided into a plurality of different time slots allocated to different networks.

This may facilitate interoperation and provide a practical system for effective resource sharing. In particular, it may facilitate peer-to-peer based resource sharing over a shared air interface.

According to an optional feature of the invention, the first management subframe comprises a transmission time indication for transmission of offer messages from the first plurality of networks.

This may facilitate interoperation and provide a practical system for effective resource sharing. In particular, it may facilitate peer-to-peer based resource sharing over a shared air interface.

According to an optional feature of the invention, the MAC frame comprises a second management subframe for transmission of offer messages.

This may facilitate interoperation and provide a practical system for effective resource sharing. In particular, it may facilitate peer-to-peer based resource sharing over a shared air interface.

According to an optional feature of the invention, the second management subframe is divided into a plurality of different time slots allocated to different networks. This may facilitate interoperation and provide a practical system for effective resource sharing. In particular, it may facilitate peer-to-peer based resource sharing over a shared air interface.

According to an optional feature of the invention, the method further comprises operating a contention scheme for the second management subframe.

This may facilitate interoperation and provide a practical system for effective resource sharing. In particular, it may facilitate peer-to-peer based resource sharing over a shared air interface.

According to an optional feature of the invention, the initiating of the temporary resource allocation comprises transmitting an indication of the availability of the temporary resource allocation to other networks; and the method further comprises the step of at least some of the other networks transmitting an indication of interest in the temporary resource allocation.

The first plurality of networks may be selected in response to the received indications of interest. This may facilitate operation and reduce the number of networks involved in the resource reallocation process.

According to an optional feature of the invention, the communication between the first network and the first plurality of networks in the offer rounds is over a radio air interface.

The invention may provide improved and/or facilitated resource sharing based on radio air interface communication links. Complexity may be reduced and the requirement for dedicated or centralised communication and management means can be reduced or eliminated. According to an optional feature of the invention, the shared air interface resource is a frequency band and the first air interface resource comprises all frequency carriers in the frequency band.

This may provide for a simple sharing of resource which may provide efficient performance and which typically may reduce the impact of the sharing of resource on the first network and/or the second network. The frequency band may be a contiguous or fragmented frequency band.

According to an optional feature of the invention, the at least part of the first air interface resource corresponds to the frequency band in a time interval.

This may facilitate efficient resource sharing.

According to a different aspect of the invention, there is provided a communication system for resource sharing between a plurality of communication networks each having a nominal resource allocation of a shared air interface resource and a resource exchange allowance, the communication system comprising: means for initiating a temporary resource allocation of a first air interface resource from a nominal resource allocation of a first network; means for executing a plurality of offer rounds, each offer round comprising determining offer values for the first air interface resource; means for selecting a second network in response to the determined offer values; means for sending a resource allocation message to the second network, the resource allocation message indicating a temporary allocation of at least part of the first air interface resource from the first network to the second network; and means for reducing the resource exchange allowance of the second network by a value determined in response to the resource exchange offer value from the second network; and wherein the means for executing a plurality of offer rounds is arranged to for each offer round: transmit an offer request to a first plurality of networks from the first network; transmit offer messages from the first plurality of networks to the first network, each offer message comprising a resource exchange offer value for at least part of the first air interface resource; and determine the offer values for the first air interface resource in response to the resource exchange offer values.

These and other aspects, features and advantages of the invention will be apparent from and elucidated with reference to the embodiment(s) described hereinafter.

Brief Description of the Drawings

Embodiments of the invention will be described, by way of example only, with reference to the drawings, in which

FIG. 1 illustrates an example of a combined communication system arrangement comprising three communication networks in accordance with some embodiments of the invention;

FIG. 2 illustrates an example of a Time Division Duplex frame structure for a plurality of networks using spectrum sharing;

FIG. 3 illustrates an example of an apparatus for resource sharing in accordance with some embodiments of the invention; and

FIG. 4 illustrates an example of a method for resource sharing in accordance with some embodiments of the invention; FIG. 5 illustrates an example of a MAC frame format suitable for some embodiments of the invention;

FIG. 6 illustrates an example of a hierarchical arrangement of network nodes;

FIG. 7 illustrates an example of signalling for a temporary resource allocation in accordance with some embodiments of the invention;

FIG. 8 illustrates an example of signalling for a temporary resource allocation in accordance with some embodiments of the invention;

FIG. 9 illustrates an example of a MAC frame format suitable for some embodiments of the invention;

FIG. 10 illustrates an example of a MAC frame format suitable for some embodiments of the invention;

FIG. 11 illustrates an example of a MAC frame format suitable for some embodiments of the invention;

FIG. 12 illustrates an example of a MAC frame format suitable for some embodiments of the invention;

FIG. 13 illustrates an example of a MAC frame format suitable for some embodiments of the invention;

FIG. 14 illustrates an example of a MAC frame format suitable for some embodiments of the invention; FIG. 15 illustrates an example of a MAC frame format suitable for some embodiments of the invention;

FIG. 16 illustrates an example of a MAC frame format suitable for some embodiments of the invention;

FIG. 18 illustrates an example of a MAC frame format suitable for some embodiments of the invention;

FIG. 19 illustrates an example of a MAC frame format suitable for some embodiments of the invention;

FIG. 20 illustrates an example of a MAC frame format suitable for some embodiments of the invention;

FIG. 21 illustrates an example of a resource allocation communication in accordance with some embodiments of the invention; and

FIG. 22 illustrates an example of a resource allocation communication in accordance with some embodiments of the invention.

Detailed Description of Some Embodiments of the Invention

The following description focuses on embodiments of the invention applicable to broadband Wireless Metropolitan Area Networks (WMAN) such as the IEEE 802.16 , and Wireless Local Area Networks (WLANs) communication networks such as 802.11 but it will be appreciated that the invention is not limited to this application but may be applied to many other communication networks such as for example GSM (Global System for Mobile communication) or UMTS (Universal Mobile Telecommunication System) cellular communication systems.

FIG. 1 illustrates an example of a combined communication system 5 arrangement comprising three different individual broadband Wireless Metropolitan Area Networks (WMAN) 103, 107, 111.

Each of the networks 103, 107, 111 comprises all the required functionality for supporting communication services in accordance with

10 the Technical Specifications of the WMAN system. In the specific example, the networks 103, 107, 111 comprise functionality for supporting communications over an IEEE 802.16 air interface. Thus, in particular each network 103, 107, 111 comprises at least one base station 101, 105, 109 which can transmit and receive signals over the air interface of the

15 individual communication system (for clarity the base stations 101, 105, 109 are shown coupled to the networks 103, 107, 111 in FIG. 1 but it will be appreciated that they are to be considered part of the networks 103, 107, 111)

20 In the example of FIG. 1, the three networks 103, 107, 111 employ spectrum sharing wherein the same frequency spectrum is used by the air interface communications of all three networks 103, 107, 111. In the specific example, the three networks use time division such that the three networks 103, 107, 111 have access to the full frequency spectrum at

25 different times. Specifically, each of the three networks can use OFDM and OFDMA based communications in the full frequency spectrum.

Specifically, the three networks are arranged to use the same MAC (Media Access Control) frame structure on the air interface. The networks 103, 30 107, 111 are furthermore synchronised such that the MAC frames for transmissions over the air interface are frame synchronised. In the example, each of the networks is allocated a nominal resource allocation corresponding to a specified time interval in each frame. Specifically, the downlink (forward link) and uplink (reverse link) MAC frames comprise three time intervals of equal size with one time interval being allocated to each of the networks 103, 107, 111. Each time interval can be used by different systems while the time intervals are interleaved.)

Thus, within an allocated time interval, the appropriate network 103, 107, 111 is free to communicate over the air interface but this is not allowed during the time intervals allocated to other networks 103, 107, 111.

FIG. 2 illustrates an example of a frame structure for a plurality of networks 103, 107, 111 using spectrum sharing. In the example, for each time interval, the network 103, 107, 111 which is nominally allocated the resource is denoted the master network and the other networks are denoted slave networks.

The individual networks 103, 107, 111 independently manage and control the operation of the networks. Specifically, each of the networks is at any time allocated a given air interface resource and the management of this air interface resource allocation is performed without any consideration of the operation of the other networks 103, 107, 111. Thus, specifically, the allocation of resource to individual calls and base stations in the individual network 103, 107, 111 is performed with consideration of the allocated resource but without consideration of how other communication systems are managing the resource allocated to them.

Although spectrum sharing may allow an efficient sharing of resource, a static allocation is inefficient as it may not take into account the dynamic and different resource requirements of the individual networks 103, 107, 111.

In the system of FIG. 1, the resource sharing of the common frequency band may be improved by a temporary resource allocation of resource from the nominal resource allocation of one network to another network.

In the system, each of the networks 103, 107, 111 is allocated a resource exchange allowance which may be used when borrowing resource from another network. In the system, a resource may temporarily be allocated from one network to another. In response, the resource exchange allowance of the network receiving the resource will be reduced whereas the resource exchange allowance of the network providing the resource is increased.

The communication system of FIG. 1 specifically comprises a resource exchange allowance processor 113 which stores the resource exchange allowances of the networks 103, 107, 111. The stored resource exchange allowances are updated when resource is temporarily re-allocated and thus the resource exchange allowance provides an indication of the resource the individual has borrowed to or from other communication networks.

FIG. 3 illustrates an example of an apparatus 201 for resource sharing in accordance with some embodiments of the invention. The apparatus may be implemented in any suitable location and/or may be distributed between different locations and between different networks. In the specific example, the apparatus 201 is implemented in the first base station 101. The apparatus 201 comprises a transceiver 203 which is arranged to communicate with subscriber stations supported by the base station as well as base stations of the other networks 107, 111.

The apparatus 201 further comprises a sharing instigation processor 205 which is coupled to the transceiver 203. The sharing instigation processor 205 is arranged to initiate a temporary resource allocation of a first air interface resource from a nominal resource allocation of the first network.

For example, the sharing instigation processor 205 can detect that the first network 103 has spare resource that is not used and which it can allow other networks to use. In response, the sharing instigation processor 205 can generate resource availability messages and offer request messages which are transmitted over the air interface to other networks by the transceiver 203.

In response, the transceiver 203 can receive offer messages from the other networks 205, 209. Each offer message will comprise a resource exchange offer value for at least some of the resource available for sharing. The resource exchange offer value is indicative of an amount of reduction in its resource exchange allowance that the network transmitting the offer message is willing to accept in return for a temporary allocation of the specified resource.

As will be described later, the apparatus 201 is arranged to iterate the offer process of transmitting offer request messages and receiving offer messages until a termination criterion is met (e.g. that a certain duration has passed).

The apparatus 201 further comprises a selection processor 207 which is coupled to the transceiver 203 and which is fed the received resource exchange offer values following the plurality of offer rounds. In response, the selection processor 207 proceeds to select a specific network to which the given resource is to be temporarily re-allocated. It will be appreciated that resource may be allocated to a plurality of other networks in many embodiments.

For example, for a given resource, the selection processor 207 can simply select the network which has the highest resource exchange offer value, i.e. to the network which is willing to accept the highest reduction in its resource exchange allowance. As this reduction can be seen as a penalty value for the temporary borrowing of resource, the selection processor 207 can automatically select the network which is most in need of the available resource and thus an efficient resource sharing can be achieved through a low complexity system.

The resource exchange offer values can be an offer value for a given unit of resource. For example, the received resource exchange offer values can specify an amount of reduction in the resource exchange allowance the specific network is willing to accept for the allocation of a single carrier in each time interval of, say, 17100^th of the MAC frame duration. The total offer values compared by the selection processor 207 can in such a case be determined by multiplying the specific offer value with the number of carriers and the number of time intervals of the resource that may be allocated.

The selection processor 207 is coupled to an allowance message generator 209 which is arranged to transmit an allowance message to the resource exchange allowance processor 113 causing the resource exchange allowance for the selected network to be reduced. The communication can for example be over the air interface by the transceiver or can be through the first network via a suitable network interface (not shown). Specifically, the allowance message generator 209 can calculate a resource exchange allowance reduction in response to the resource exchange offer value and can send this value to the resource exchange allowance processor 113. Thus, the allowance message generator 209 causes the resource exchange allowance of the selected network to be reduced by a value determined in response to the resource exchange offer value from the second network.

If the resource exchange allowance processor 113 identifies that the resource exchange allowance of the network receiving the temporary allocation falls below zero, it may notify the apparatus 201 of this fact. In response, the apparatus 201 will prevent the reallocation of resource to this network.

The selection processor 207 is further coupled to an allocation message generator 211 which is further coupled to the network interface 203 and which is arranged to transmit a resource allocation message to the selected network. The resource allocation message comprises an indication of the temporary allocation of at least part of the available resource.

Following receipt of the resource allocation message, the selected network can proceed to use the borrowed resource. Specifically, air interface transmission in a re-allocated time interval nominally allocated to the first network 103 can be scheduled in the selected network.

FIG. 4 illustrates an example of a method for resource sharing in accordance with some embodiments of the invention. The method will be described with reference to the apparatus of FIG. 3.

The method initiates in step 401 wherein the resource exchange allowance processor 113 is initialised with a resource exchange allowance for each network 103, 107, 111. In the following exemplary description, the resource exchange allowance will be measured in an arbitrary unit referred to as a credit token. The resource exchange allowance processor 113 may for example be initialised with each network 103, 107, 111 being allocated a predetermined amount of credit tokens.

Step 401 is followed by step 403 wherein a temporary resource allocation of an air interface resource from the nominal resource allocation of a network is initiated.

The initiation may be initiated by the network seeking to temporarily lend resource or may be initiated by a network seeking to borrow resource.

For example, as previously described, the sharing instigation processor 205 can detect that some resource is not used in the first network 103 or that some resource is only used by low priority services and that it would be desirable to temporarily re-allocate this resource in return for credit tokens. The sharing instigation processor 205 can accordingly send out messages indicating that resource is available to be shared.

As a specific example, the first network 103 can send a resource availability message indicating that the frequency band is available from starting time Tstart to ending time Tend (Tend - Tstart). This time interval will thus make the time frame interval allocated to the first network 103 available to other networks for a fraction of the duration. The first network 103 may in addition include an indication of a minimum number of credit tokens required per time interval for the first network 103 to be willing to temporarily reallocate the resource. Step 403 is followed by step 405 wherein offer rounds are executed. In each offer round, the first base station 101 transmits offer request messages to base stations 105, 109 of the other networks 107, 111.

The base stations 105, 109 of the other networks 107, 111 then determine resource exchange offer values for at least part of the first air interface resource and transmit these back to the first base station 101 in offer messages. The offer messages can specifically indicate a number of credit tokens offered per resource unit, such as the number of credit tokens per time interval and/or per carrier.

Specifically, the other networks 107, 111 can send an offer message comprising an offer in the form of an offer vector (BIDk where k is an index for the network) which specifically may include the following information:

■ The amount of credit tokens offered per time unit (CTk),

■ The fraction Xk of the offered time the offer CTk applies to and/or,

■ The time interval [Tstart k, TEnd k] to which the offer applies (where

[Tstart k, TEndk] C [Tstart, TEnd]).

Thus the offer vector may specifically be denoted by BIDk = {CTk, Xk, Tstart k, TEndk}

The first base station 101 then proceeds to determine offer values for the other base station 105, 109 from the received offer messages. Specifically, the offer value for a given network can be determined as the number of credit tokens offered per resource unit.

The first base station 101 then proceeds to transmit a second offer request message comprising the determined offer values. Upon receiving this offer request message, the other base stations 105, 109 can determine whether to increase the previous offer value. The offer rounds may be repeated until for example a given offer value per resource unit has been reached or until a predetermined time interval has passed.

Step 405 is followed by step 407 wherein a network may be selected to be temporarily allocated an air interface resource. Specifically the network having provided an offer value corresponding to the highest number of credit tokens over the requested renting time period and the requested amount of carriers) can be selected to be temporary allocated the requested resource.

Step 407 is followed by step 409 wherein resource allocation messages identifying the awarded air interface resource is transmitted to the individual networks 107, 111.

Step 409 is followed by step 411 wherein a resource exchange allowance message is transmitted to the resource exchange allowance processor 113. The resource exchange allowance message comprises an identification of the credit tokens which each network being allocated resource has offered for that resource.

In response, the resource exchange allowance processor 113 updates the stored values for the resource exchange allowances of the different networks 103, 107, 111. Specifically, it can reduce the networks 103, 107, 111 having been allocated air interface resource by the corresponding number of credit tokens.

In addition, the resource exchange allowance processor 113 can increase the resource exchange allowance of the first network 103 e.g. by the total number of credit tokens offered by the other networks in return for the allocated resource. Thus the system can also provide the means to award networks 103, 107, 111 with additional resource exchange allowance in return for the sharing of their resource. This can provide an incentive for networks to share resource.

In some embodiments, each of the base stations may support one or more subscriber stations which again support one or more connections for connected equipment executing an application requiring an air interface resource between the BS and the subscriber station.

Specifically, the system can comprise a plurality of IEEE 802.16 networks. In such a nested system, the base stations can communicate directly in peer to peer using a shared MAC structure divided into time intervals for each system. Such an exemplary system will be described in detail in the following.

In the example, a dynamic inter base station spectrum sharing algorithm based on a plurality of iterations is described. In the system, distributed signalling mechanisms over the air interface are used to support the credit tokens transactions (selling, purchase and awarding) between base stations. During the offer rounds, the nested level transaction mechanisms are used to derive an offer value BS_CTk that is used for each iteration. Specifically, the description provides details of the implementation of an air interface distributed signalling mechanisms using a MAC frame as illustrated in FIG. 5.

In the following the following notation will be used:

■ BSN denotes the base station BS belonging to the master network NWN, where the master network is the network providing the additional resource. ^■ BSk denotes the base station belonging to the slave network NWk, where the master network is the network providing the additional resource.

^■ SSj,k denotes subscriber station "j" attached to base station BSk, ^■ CCij,k denotes connection "i" (or connected equipment "i") connected to SS_jlk.

In the example:

^■ Each CCij,k can dynamically generate an offer value CC_CT⁽ⁿ⁾ij,k at the n^th iteration. This offer value corresponds to an amount of credit tokens per domain unit (where the domain unit can be a time and/or frequency domain unit) the CC wants to spend to win the "extra" bandwidth during the n^th iteration of the offer rounds,

^■ Each SSj;k can dynamically generate an offer value SS_CT⁽ⁿ⁾j,k at the n^th iteration. This offer value corresponds to the amount of credit tokens per domain unit corresponding to the {CCij.k} attached to that SSj,k during the n^th iteration of the offer rounds,

■ Each BSk can dynamically generate an offer value BS_CT⁽ⁿ⁾k at the n^th iteration. This offer value corresponds to the amount of credit tokens per domain unit corresponding to the {SSj,k} attached to that

BSk during the n^th iteration of the bidding phase.

In the example, a hierarchical arrangement of network nodes as illustrated in FIG. 6 is thus implemented. In this system, a dynamic auctioning/bidding cycle between one BSN of master NWN and several BSk of different slave NWk is implemented by iteratively executing offer rounds. FIG. 7 and 8 illustrate the signalling for a temporary resource allocation based on such offer rounds. For simplicity and brevity, the process is illustrated for one BSN (the first base station 101) and one BSk (the second base station 105) and corresponding SSj,k and CCij,k of a given slave NWk (the second network 107). The cycle is composed of different phases, and each phase is composed of several sequences.

In the following a description of a super MAC frame that is used by the detailed example is described.

Specifically, the implementation of the different phases of the dynamic resource allocation uses a management mechanism introduced in the MAC frame structure presented in FIG. 5. The super MAC frame structure illustrated in FIG. 9 is used in the system. This super MAC frame is structured as follows (for the sake of simplicity, the illustration only considers 3 BSs - one BS (BSN-101) for the master NW (103) , one BS (BSk - 105) for slave NWk (107) and one BS (BSj - 109) for slave NWj (109):

^■ Each MAC frame is divided into the super MAC Downlink (DL) and

Uplink (UL) subframe,

^■ A dedicated super MAC DL management subframe is used for the management of the DL subframe (and similarly a dedicated super MAC UL management subframe is used for the management of the UL subframe). The super MAC DL management subframe can specifically be used for transmission of messages from the master network to slave networks, and specifically for transmission of messages that may be considered offer request messages in that they provide information or indications in response to which the slave networks proceed to determine and submit offer values.

Similarly, the MAC UL management subframe can specifically be used for transmission of messages from the slave networks to the master networks, and specifically for transmission of messages that may be considered offer messages in that they provide offer information to the master network. ^■ The content of the super MAC DL and UL management subframes is structured to support the communications between the master BSN and any of the slave BSk during the different involved phases of the cycle, ^■ Each master or slave subframe is composed of several MAC frames dedicated to the operation of one BS.

The position and the duration of the super MAC management subframes:

■ can e.g. be set for each frame and agreed between all NWs from the beginning (static approach),

■ can e.g. be periodically adapted between the NWs as function of time depending on the needs (dynamic approach). This could be achieved, for example, by wired information exchange between local BS databases via IP communication (via a server) between the involved NWs.

The super MAC DL management subframe is illustrated in FIG. 10 and is divided into two subframes as follows:

■ A broadcasting and a multicasting subframe,

■ Each is also divided into subframes. Each subframe is dedicated to one BS,

■ The broadcasting subframe is reserved for the "advertising/awareness" phase which will be described further later.

■ The multicasting subframe is reserved for: o the "first iteration (n = 1) of the credit tokens based offer rounds" o the "n^th iteration (n > 1) of the dynamic credit tokens based offer rounds" , and o the "final pricing and payment" phase (which will be described further later).

The super MAC UL management subframe is illustrated in PIG. 11 and is divided into two subframes as follows:

^■ A contention and a data transmission subframe,

^■ Each subframe is further divided into subframes. Each subframe is dedicated to one BS,

^■ The contention subframe is reserved for the "Interest expressing phase",

" The data transmission subframe is reserved for: o the "first iteration (n = 1) of the credit tokens based offer rounds" o the "n^th iteration (n > 1) of the dynamic credit tokens based offer rounds, and o the "final pricing and payment" phase.

The organisation (in terms of position and duration) of the broadcasting, multicasting, contention and data transmissions subframes: ■ can e.g. be set fixed for each frame and agreed between all NWs from the beginning (static approach),

■ can e.g. be periodically adapted between the NWs as function of time depending on the needs (dynamic approach). This could be achieved, for example, by wired information exchange between local BS databases via IP communication (via a server) between the involved NWs.

In the following a specific example of a temporary resource allocation process using the described super MAC frames will be described with reference to the signalling example of FIGs. 7 and 8. The process will be described with reference to different phases which correspond to different steps of FIG. 4. For each phase the communication and MAC frame mechanisms applied are described.

Phase 1: Advertising/Awareness phase (corresponding to step 403 of FIG. 4)

This phase is divided into two sequences: (1) and (2) (ref FIG. 7): o In sequence (1), the master BSN us broadcasts the following information to the surrounding slave BSkS using an air interface broadcast channel: Tstart, TEnd, Tstart Renting, TEnd

Renting, RPA (Reserve Price Auction) value.

The MAC frame mechanisms enabling these operations can be implemented in the super MAC DL Management subframe illustrated in FIG. 12.

o In sequence (2), the BSk interested in this additional bandwidth for its own purpose, broadcasts this information to its SSj,kto examine if these SSj,k are interested to enter into the bidding phase. At the MAC level, this information can be added in the existing broadcast messages (e.g. DL_MAP,

DCD in IEEE 802.16) which are used in each slave BS (BSk,

BSj) subframe in DL.

Phase 2: Interest expressing phase (part of step 403 of FIG. 4) This phase is divided into 4 sequences (ref. FIG. 7) as follows: o In sequence (3), each SSj,k inquires its CCij,k to determine if they are interested in bidding, o In sequence (4), each SSj,k receives from CCij,k the expression of interest (or non interest to participate in the bidding), o In sequence (5), each SSj,k informs the BSk about the willingness (or not) of the SSj,k to participate to the bidding on the basis of the feedback received from sequence (4). At the MAC level, this information can be supported by adapting the existing messages (BW request contention slot + polling messages in IEEE 802.16) which are used by each slave BS (BSk, BSj) subframe. o Finally, in sequence (6), each BSk syntheses the feedback from each SSj,k and informs the master BSN about its willingness (or not) to participate in the bidding based on this feedback. If the BSk is interested, it communicates its idk to the master BSN-

As the number of interested parties (surrounding slave BSs) is unknown but typically will not to be very high, the MAC frame mechanisms enabling sequence (6) can be implemented in the super MAC UL Management subframe by using a contention subframe (contention mini slots). A contention mechanism (see FIG. 13) that can be used is the Slotted Aloha protocol (jointly with a collision resolution algorithm like a binary exponential back-off) but with the following adaptation: once a slave BSk has managed to send its idk information (i.e. it received successful acknowledgement from

BSN), its remains silent to let the others interested BSk transmit their idk.

Phase 3: First iteration (n = 1) of the credit tokens based offer rounds (corresponding to step 405 of FIG. 4)

This phase is divided into 7 sequences as follows: o In sequence (7), the master BSN sends the following information to the slave BSkS that have expressed interest in participating in the bidding: • Tstart Bidding: time from which the bidding phase will start, • Tβnd Bidding: time at which the bidding phase will end

(Tβnd Bidding < Tstart),

• DCD, DL-MAP for the management of the multicasting subframe of the super MAC DL management field. DCD (Downlink Channel Descriptor) provides the information on the physical layer parameters that will be used by the master BSN in the DL. This enables the BSk to know how they have to listen to the message provided by the master BSN. DL_MAP (Downlink Minislot Allocation Protocol) provides information on the organisation of the multicasting subframe of sthen uper MAC DL field, i.e. the sequences of the messages, e.g.: first "UCD/UL-MAP, then "Tstart Bidding", and finally "TBnd Bidding" s

• UCD, UL-MAP for the management of the "data transmission" subframe of the super MAC UL management field. UCD (Uplink Channel Descriptor) provides information on the physical layer parameters that will be used by each slave BSk in the UL. This enables the BSN to know how its has to listen to the message provided by the slave BSk. UL_MAP (Uplink

Minislot Allocation Protocol) provides the information on the organisation of the "data transmission" subframe of the super MAC UL field, i.e. the sequence of the slots i.e. the assignment each slot to a BSk => provides the time when each BSk can transmit and with which information. For this first iteration (n = 1), the initial {idk} is denoted {id⁽¹⁾k}.

The MAC frame mechanisms enabling these operations can be implemented in the multicasting subframe of the super MAC DL management field as illustrated in FIG. 14. : o In sequence (8), each BSk requests from each SSj,k its first (n = 1) offer SS_CT⁽Dj,k, o In sequence (9), each SSj,k requests from CCi j,k its first (n = 1) offer CCLCTWij.k, o In sequence (10), each CCij,k sends its CCMϋTWij.k to its SSj,k, o In sequence (11), each SSj,k collects <img file="WO2007005181A2_D0001.tif" /> computes SS_CT⁽Dj,k = sum(CC_CT⁽ⁱ&gt;ij,k) over i, and sends SS_CT⁽»j,k <img file="WO2007005181A2_D0002.tif" /> o In sequence (12), each BSk collects {SS_CT⁽¹⁾j,k}, computes BS_CTWk = SUm(SS-CTd⁾-MO over j, and sends the following information to BS_N: BID⁽Dk = {BS_CT⁽«k, Xk, Tstartk, T_Endk}. For this first iteration, CCLCTWij.k, SS_CT«⁾j,k and BS_CT⁽¹⁾h are expressed in quantified absolute (aggregate) value unit. Thus, the base station generates an offer value which is based on the individual offer values of the individual subscriber stations and connected equipment.

For this first iteration, the MAC frame mechanisms enabling the transmission of this information can be implemented as follows (see FIG. 14):

■ In the multicasting subframe of the super MAC DL management field, the UCD, UL-MAP provides the information to each BSk from {id⁽%} at which moment each BS_k will be able to transmit its BID⁽¹⁾ij in the data transmission field of the super MAC UL management field.

■ The data transmission field of the super MAC UL management field can be organised as shown in FIG.

15) equence (13), BSN performs the following action:

^■ Given the set of intervals {[Tstartk, TEndk]} received from different offerers {id&lt;%}, BSN partitions {[Tstart, TBnd]} into contiguous time segments {TSm}, ^■ The different offerers {id⁽¹⁾k} assigned to a given TSm are identified by {id⁽¹⁾k,m}. {id⁽%,m} compete for each TSm. Each involved offerer id⁽¹⁾k,m competes with his respective offer BID⁽Dk,

^■ Then, for each TSm, the master BSN calculates the payoff P⁽Dk = BS_CT⁽% * Xk* TRenting *NFrame m for each offerer k, and searches the subset ({id⁽Dk,m}seiected ) of {id⁽¹&gt;k,m} such that sum(xk) = 1 and sum(P⁽¹⁾k) is maximal (a Knapsack algorithm can e.g. be used),

■ For each TSm, BS_N informs all {id⁽D_k&gt;m} about P∞ⁱⁿ&gt; ⁽D _m and P∞ax. ⁽D _m where <img file="WO2007005181A2_D0003.tif" />⁽i⁾_m i_s the minimal payoff from {id⁽Dk_)in}_sei_ecte_d and P∞ax, ⁽ⁱ⁾_m {_s the maximal payoff from {id⁽Dk,_m} selected during the first iteration. With this approach, each BSk is directly informed whether it has been selected or not, and has some information on how far it is from P^min&gt; ⁽D _m while still having some information on P^maχ&gt; ⁽D _m. This approach allows the privacy of competing {id⁽Dk,_m} on TSm to be maintained. Thus, this message can be received by a base station and considered to be an offer request allowing the base station to generate and submit further offer values. Furthermore, the offer request message comprises an indication of the offer values determined in the previous offer round. The MAC frame mechanisms enabling the transmission of this information can be implemented as illustrated in FIG. 16.

In particular, the DCD/DL-MAP provides the necessary information when each id⁽%,m has to listen to the multicasting subframe so that each id⁽%,m only listens to the part dedicated to it (i.e. related to its TSm).

Phase 4 n^th iteration of the credit tokens based offer rounds (corresponding to step 405 of FIG. 4)

This phase is divided into 6 sequences: o If P⁽¹&gt;k &lt; P¹¹"¹¹' ⁽D m, this means that BSk has not been selected for being granted the resources which it previously made an offer for. In that case, in sequence (14), each BSk requests from each SS_j;k its 2^ (n = 2) offer SS_CT⁽²&gt;j,k. More generally speaking, for n&gt;l, if P⁽ⁿ-% &lt; P∞"¹, ⁽n-i⁾_mj each BS_k requests from each SSj,k its n^th offer SS_CT&gt;&gt;j,k, o In sequence (15), if P&lt;ⁿ-D_k &lt; pmin, ⁽n-i⁾_{mj eac}h SS_j,k requests from CCij,k its n^th offer CC_CTtoy,k&gt; CCCTfe-^Uyj. in case CCij,k wants to keep offering, o In sequence (16), each CCy.k informs its SSj,k if it wants to continue to make an offer, and if so, it sends its new offer CC_CT⁽ⁿ⁾y,k. For the non interested CCy,k, CC-CT^y* = CC_CT⁽*-ⁱ⁾y_)k, o In sequence (17), each SSj,k collects {CC_CT⁽ⁿ^ij,k}, computes

SS_CT&gt;&gt;j,k = sum(CC_CT⁽ⁿ&gt;ij,k) over i, and sends SS_CT&gt;&gt;j,k to its BSk, o In sequence (18), each BSk collects {SS_CT⁽ⁿ⁾j,k}, computes

BS_CTW_k= StUn(SS-CTWj_Js) over j. Next, BSk computes the new PH = BS_CT&lt;^π&gt;k * Xk* Tuenting *NFrame m where

Xk,Titenting and NFrame m are common for all n on TSm. If P&lt;ⁿ&gt;k&gt; P^fr-^k and P&lt;ⁿ&gt;k &gt; P^min&gt; &amp;*^■« _m, BSk expresses its interest to keep on participating in the offer process with the new bid P&lt;ⁿ⁾k. In that case, it sends the new (update) value of BS_CT&lt;ⁿ&gt;k to BSN. In case pω_k = pcn-ⁱ⁾_{k or} P^k &lt; P^min&gt; ^» m, BSk leaves the offering process and will not be granted additional resources.

A MAC frame mechanism enabling the transmission of this information BS_CT⁽ⁿ⁾k can be implemented as follows:

^■ For each TSm, each BSk who has expressed the need to send its BS_CT⁽ⁿ⁾k, enters into a reservation phase in the contention subframe of the super MAC UL management field. This contention subframe (see FIG. 17) enables the BSk to communicate its idk to the BSN.

This is achieved by using contention mini slots (slotted Aloha protocol jointly with a collision resolution algorithm like a binary exponential back-off) but with the following adaptation: once a slave BSk has managed to send its idk information (i.e. it received successful acknowledgement from BSN), it remains silent to let the other interested BSk transmit their idk.

^■ For each TSm, based on the received {idk}, BSN assigns dedicated data slots to each BSk in the data transmission subframe of the super MAC UL management field. This information on data assignment is included in the UCD/UL-MAP field of the multicasting subframe of the super MAC DL management. ^■ For each TSm, in its dedicated data slots, each BSk can transmits its BS_CT⁽ⁿ⁾k in an incremental fashion (instead of providing the absolute value) as follows:

• Based on the knowledge of P«ώi&gt; ⁽n⁾_{m an(}j pmax,

5 &lt;ⁿ⁾ m, BSN proposes several pre defined Q discrete steps {Sm,p} to facilitate each BSk expressing their relative increase between the iteration n-1 and n on TSm. Q is an integer. {Sm,p} can be represented/coded by the field indicated in FIG. 10 18.

• This field is multicast in the "multicasting subframe" of the super MAC DL management field as shown in FIG. 19.

• For each BSk, this relative increase between the 15 iteration n-1 and n is noted Δ⁽ⁿ⁾k and can be expressed as follows: Δ⁽ⁿ&gt;k = BS_CT⁽ⁿ⁾k -

BS_CT⁽ⁿ-^χ&gt;k = ak,lSm,l + ak,2Sm,2 + ...+ak,QSm,Q =

∑ak,pSm,_P over all p, p varying from 1 to Q. Let be Ak = [ak,_P] .

20 • Each BSk calculates eack ak,p to reach

BS_CT&lt;ⁿ&gt;k. Next, BSk transmits Ak to BSN in the data transmission field of the super MAC UL management field as shown in FIG. 20. In the multicasting subframe of the super MAC

25 DL management field, the UCD/UL-MAP provides the information to each BSk from {id⁽ⁿ⁾k} at which moment each BSk will be able to transmit its Ak in the data transmission field of the super MAC UL management field.

30 Specifically, the following two options can be used for this UL data transmission:

• The data transmission field (see FIG. 20) is split into subframes. Each suframe is dedicated to a BSk for the transmission of Ak.

• Each BSk is polled by BSN to transmit its data Ak.

The incremental approach may allow a reduced bandwidth while still providing some flexibility.

The incremental method can also be applied in sequence (17) between each SSj,k and its assigned BSk. In the particular case of IEEE 802.16, this can be achieved by adapting the existing "contention slot for bandwidth requests" field of the UL subframe, and the DCD, UCD, DL-MAP, UL-MAP fields.

o In sequence (19), BSN updates {id^^k,..-} into {id⁽ⁿ⁾k,m}. Based on the new received offer values {BS_CT⁽ⁿ⁾k} for each TSm, the master BSN calculates the new payoff P⁽ⁿ⁾k = BS_CT⁽ⁿ⁾k * Xk* TRenting *NFrame m for each offerer k who still participates in the bidding. Then, BSN searches the subset ({id⁽ⁿ⁾k,m} selected) of {id⁽ⁿ⁾k,m} such as sum(xk) = 1 and sum(P⁽ⁿ⁾k) is maximal (the Knapsack algorithm can be used for this purpose). Next, BSN performs the same actions as in sequence (13): for each TSm, BSN informs all {id⁽ⁿ⁾k,m} about P∞™' &lt;ⁿ&gt; m and P∞ax, ⁽n⁾_{m w}here P^min&gt; &lt;ⁿ&gt; m is the minimal payoff from {id⁽ⁿ⁾k,m} selected and P^max&gt; ⁽ⁿ⁾_m is the maximal payoff from {id⁽ⁿ⁾k,m} selected during the n^th iteration. The difference with sequence (13) is that now the MAC frame mechanisms enabling the transmission of {pmin, (n) _m} _an(j {pmax, (n) _m} j_s implemented with an incremental mechanism as used in sequence (18). For each TSm, only the relative values (difference) ΔP^min&gt; &lt;ⁿ⁾_m =

5 Pmin, (n) _m _ pmin, (n-1) _{m an(}J <img file="WO2007005181A2_D0004.tif" />₌ pmax, (n) _m . pmax,

⁽ⁿ-i⁾_mj _are transmitted in the "multicasting subframe" of the super MAC DL management field.

Phase 5: Final pricing and Payment phase (Corresponding to steps 10 407, 409 of FIG. 4)

This phase is composed of the sequences (20) and (21): o In sequence (20), as long as Tεnd Bidding - Tstart Bidding&gt;0 (i.e. the bidding phase duration has not yet elapsed), n is increased and the credit tokens based offer rounds are

15 executed. o In sequence (20), when TEnd Bidding - Tstart Bidding = 0, the offer rounds phase is over. None of the BSk can now make a new offer. {id^{(n final)}k,m} selected is derived. At this point, BSN derives the clearing price auction BS_CPAk (expressed as a number

20 of credit tokens per dimension unit) for each TSm and each k from {id&lt;^{n fiπaI}&gt;k,m}. For each k and m, BS_CPAkcan correspond to the BS_CT^(final)k, or for example can follow the Vickrey's second price auction method. The MAC frame mechanisms enabling the transmission of

25 this information {BS_CPAk} to each BSk from {id&lt;^{n fi}^^m} are implemented in the multicasting field of the super MAC DL management field. BSN sends this information to each BSk in a dedicated slot. o In sequence (21), eack k pays Prk = BS_CPAk * Xk* Titenting

30 *NFrame m on its corresponding TSm. On the basis of the information sent in the multicasting field of the super MAC DL management field in sequence (20), two MAC mechanisms can specifically be used (similar to sequence (18)) for the UL data transmission of Prk: ^■ The data transmission field is split into subframes

(similar to FIG. 20). Each suframe is dedicated to a BSk for the transmission of Prk. ^■ Each BSk is polled by BSN to transmit its data Prk.

Phase 6 Credit tokens based bandwidth granting phase (corresponding to step 409 of FIG. 4)

During this phase, each winning BSk grants its resources to its SSj,k and CCij,k. Currently, grant mechanisms (e.g. in IEEE 802.16-2004) are either per CC or per SS. In the specific detailed example, these mechanisms are extended by being combined with the credit token paradigm. The two following grants options can specifically be used:

o Credit tokens based grant per CC (CtG_CC)

In this case (ref. FIG. 21), the bandwidth is granted at the CC level. Thus, the resource allocation message can be transmitted directly to a connected equipment. The bandwidth is granted to the CCij,k which have participated in the offering rounds. The amount of resources granted to each CCij,k is proportional to the max value of CC_CTij,k that the CCij,k has made an offer for. In this case, the BSk is in charge of the resources scheduling between all CCij,k attached to that BSk.

o Credit tokens based grant per SS (CtGJSS) In this case (ref. FIG. 22), the bandwidth is granted at the SS level. Thus, the resource allocation message can be transmitted directly to a Subscriber Station. The bandwidth is granted to each SSj,k which participated in the offering rounds. The amount of resources granted to each SSj,k is proportional to the max value of SS_CTj,k that the SSj,k has made an offer for. In this case, BSk is in charge of the resources scheduling between all 5 SSj.k attached to that BSk. Then, each SSj,k is in charge of the allocation of resources between all CCy,k attached to that SSj,k.

Depending on the strategy (CtG__CC or CtG_SS) considered, either the sequence (22-1) or (22-2) is used. For both strategies, in the case of IEEE 10 802.16, the MAC mechanisms to be used can be achieved by adapting the existing DCD/DL-MAP, UCD/UL-MAP fields.

It will be appreciated that the above description for clarity has described embodiments of the invention with reference to different functional units

15 and processors. However, it will be apparent that any suitable distribution of functionality between different functional units or processors may be used without detracting from the invention. For example, functionality illustrated to be performed by separate processors or controllers may be performed by the same processor or controllers.

20 Hence, references to specific functional units are only to be seen as references to suitable means for providing the described functionality rather than indicative of a strict logical or physical structure or organization.

5 The invention can be implemented in any suitable form including hardware, software, firmware or any combination of these. The invention may optionally be implemented at least partly as computer software running on one or more data processors and/or digital signal processors. The elements and components of an embodiment of the invention may be

30 physically, functionally and logically implemented in any suitable way. Indeed the functionality may be implemented in a single unit, in a plurality of units or as part of other functional units. As such, the invention may be implemented in a single unit or may be physically and functionally distributed between different units and processors.

Although the present invention has been described in connection with some embodiments, it is not intended to be limited to the specific form set forth herein. Rather, the scope of the present invention is limited only by the accompanying claims. Additionally, although a feature may appear to be described in connection with particular embodiments, one skilled in the art would recognize that various features of the described embodiments may be combined in accordance with the invention. In the claims, the term comprising does not exclude the presence of other elements or steps.

Furthermore, although individually listed, a plurality of means, elements or method steps may be implemented by e.g. a single unit or processor. Additionally, although individual features may be included in different claims, these may possibly be advantageously combined, and the inclusion in different claims does not imply that a combination of features is not feasible and/or advantageous. Also the inclusion of a feature in one category of claims does not imply a limitation to this category but rather indicates that the feature is equally applicable to other claim categories as appropriate. Furthermore, the order of features in the claims does not imply any specific order in which the features must be worked and in particular the order of individual steps in a method claim does not imply that the steps must be performed in this order. Rather, the steps may be performed in any suitable order. In addition, singular references do not exclude a plurality. Thus references to "a", "an", "first", "second" etc do not preclude a plurality.