FIELD OF THE INVENTION

The present invention relates to a relay operable to relay data between a base station and user equipment of a wireless communications system, a relay-base station pair, methods and computer program products.

BACKGROUND

The use of relays within a wireless communications system is known. A relay may be provided within a macro cell in order to provide enhanced coverage within that macro cell. For example, a relay may be provided within a macro cell in an area of high attenuation such as, for example, in the vicinity of a building. The relay communicates with a macro base station and with any user equipment in the area of high attenuation. The macro base station, when communicating with user equipment will determine whether to route data to the user equipment either directly or via the relay. Whilst this arrangement provides for improved coverage, the use of such relays can result in undesirable consequences.

Accordingly, it is desired to provide an improved technique for relaying data between a base station and user equipment of the wireless communication system.

SUMMARY OF THE INVENTION

According to a first aspect, there is provided a relay operable to relay data between a base station and user equipment of a wireless communications system, the relay comprising: queuing logic operable, for each user equipment supported by the relay, to form a pending data queue associated with that user equipment, the pending data queue storing received data intended for that user equipment which has yet to be transmitted by the relay over a communications channel between that user equipment and the relay; and scheduling logic operable to schedule transmissions of pending data to each user equipment based on at least one of a size of the pending data queue associated with each user equipment, priority of pending data and channel state information of the communications channel between each user equipment and the relay.

The first aspect recognises that a problem with existing relay implementations is that the base station implements a centralised approach in which it controls the transmission of data from relays to user equipment. This centralised approach requires control information to be transmitted between the base station and the relays. Furthermore, to enable the base station to make an accurate assessment of the most efficient way to transmit data to user equipment, the base station needs to be aware of the state of any user data queues within the relays, as well as having knowledge of the quality of the communication links between the relay and user equipment. This information needs to be transmitted between the relay and the base station and requires the base station to rapidly process that information in order to make a decision on the best way to service the user equipment. The amount of signalling required over control channels between the base station and relays increases enormously as the number of relays increase, particularly when simple scalar feedback of link quality is not possible such as may be the case with multiple antenna relay configurations . Also, the amount of processing required at the base station in order to make an accurate and timely assessment of the most appropriate data transmissions to perform is high. Hence, careful network planning needs to occur in order to ensure that the base station can operate efficiently and the available resources are not exceeded.

Accordingly, a relay is provided having queuing logic which forms pending data queues, each pending data queue being associated with different user equipment. Each pending data queue stores data which has been received from the base station but has yet to be delivered to the user equipment. Scheduling logic ύ> aiso proviaed which schedules the transmissions of the pending data in the pending data queues to each user equipment. The scheduling of the data transmissions are based on one or more of the pending data queue size, the channel state of the communications channel between a user equipment and the relay and the priority of the pending data. In this way, it can be seen that by moving some of the scheduling decisions towards to relay side, the relay itself can make these decisions and obviate the need to provide control information to those relays from a controlling base station. Also the amount of feedback information which needs to be provided from the relay to the base station is reduced. It will be appreciated that the amount of feedback which is required, particularly where multiple antenna relays are deployed, grows enormously. Hence, the amount of unnecessary traffic being transmitted between the base station and the relays is reduced, the amount processing resources required in the base station is also reduced and, as a consequence, the deployment of relays within the macro network becomes much more scalable. Accordingly, new relays can be readily deployed where needed without requiring complex and careful network planning.

In one embodiment, the scheduling logic is operable to identify that pending data to be transmitted next by scheduling transmissions of higher priority pending data over lower priority pending data. Accordingly, the relay is operable to ensure that where high priority pending data is queued within the pending data queue, that higher priority pending data is transmitted in advance of lower priority pending data. It will be appreciated that examples of such high priority data include real time transmissions or other time-sensitive data.

In one embodiment, the scheduling logic is operable to identify that pending data to be transmitted next from the size of the pending data queue associated with each user equipment and channel state information of the communications channel between each user equipment and the relay. Accordingly, the scheduling logic makes the determination of which data to transmit next based on its knowledge of the size of the pending queue of data stored by the queuing logic for each user equipment considered in combination with the channel state information of the channels between the user equipment and the relay. In this way, it can be seen that a trade-off can be obtained to ensure that the most appropriate data transmission occurs.

In one embodiment, the scheduling logic is operable to identify that pending data to be transmitted next in accordance with the following algorithm:

Dfi) = R _k (t)Q>, _J {t),dest(! _l ) e M

where R ₁ (t) is an estimate of the rate for the communications channel /, , the set of all user equipment is denoted as M = {l,...,AT},and Qi _SJ (t),Vi,j € M denotes the size of the queues for user equipment j in the base station and at the i" ¹ relay at the start of time frame t, and the optimal active link for the next time frame is selected as: l' (t) = aigmaxD, (t) . dαt(l,)εM Accordingly, the scheduling logic assesses the available transmission rate for each communications channel and the size of the queue for each user equipment. The pending data which has in combination the largest queue size and best transmission rate will be transmitted next.

In one embodiment, the relay comprises: measurement logic operable to receive information identifying transmissions from other relays; and cooperation logic operable, in response to an indication from the measurement logic that another relay is causing interference, to cause cooperative transmissions between relays. Accordingly, measurement logic is provided which receives information regarding transmissions from other relays. It will be appreciated that such sensing may be performed directly by the relay itself, or from measurement reports made by user equipment. Should an indication be received that another relay is causing inference with transmissions from the relay, the operation logic causes the relays to cooperate in their transmissions. Again, by moving the decision making on scheduling towards the relay side, local, autonomous cooperation between relays becomes possible. Accordingly, interference which would otherwise limit the gains achieved by deploying relays can be reduced though cooperation between relays. Such an approach is possible because by enabling the interfering relays to make near-instantaneous estimates of the amount of interference, cooperation to reduce that inference is possible.

In one embodiment, the cooperation logic is operable to indicate to another relay acceptable transmission characteristics for that relay. Accordingly, when interference is identified, the relay may transmit to another relay information relating to transmissions which could be made to reduce interference. For example, the relay may transmit to that another relay a set of carriers currently allocated to user equipment and that another relay may then be prevented from allocating those carriers. Alternatively, the user equipment could forward to that another relay the set of carriers currently allocated for its transmissions with the relay. Alternatively, when such interference is sensed, a relay may itself decide to avoid such interference by selecting different channels for its own use, thereby avoiding the need to transmit any information to the other relay.

According to a second aspect, there is provided a method of relaying data between a base station and user equipment of a wireless communications system, the method comprising the steps of: forming, at a relay, a pending data queue associated with each user equipment, the pending data queue storing received data intended for that user equipment which has yet to be transmitted over a communications channel to that user equipment; and scheduling transmissions of pending data from the relay to each user equipment based on at least one of a size of the pending data queue associated with each user equipment, priority of pending data and channel state information of the communications channel.

According to a third aspect, there is provided a relay-base station pair, comprising: a base station comprising: base station queuing logic operable, for each user equipment supported by the base station, to form a pending data queue associated with that user equipment, the pending data queue storing received data intended for that user equipment which has yet to be transmitted by the base station over a communications channel between that user equipment and the base station; and base station scheduling logic operable to schedule transmissions of pending data to each user equipment based on at least one of a size of the pending data queue associated with each user equipment, priority of pending data and channel state information of the communications channel between each user equipment and the base station; and the relay of the first aspect.

Accordingly, both the base station and relay may together provide a two-stage distributed scheduling technique where both the base station and the relay make what is assessed by those apparatus to be the most effective scheduling decisions for their pending data transmissions. The base station utilises a similar decision making process to the relay by assessing the priority of the pending data, and by assessing the relative size of the pending data queues at both the base station and the relay, in combination with the quality of the communications channel between the two. This separate but complimentary and synergistic decision process helps to ensure that the pending data is transmitted between the base station and the user equipment in the most efficient way.

In one embodiment, the base station scheduling logic is operable to schedule transmissions of pending data based on at least one of the size of the pending data queue associated with each user equipment, priority of pending data and channel state information of the communications channel directly between each user equipment and the base station and between the base station and any relay supporting each user equipment. Accordingly, the base station scheduling logic will assess the quality of both the communications channel provided directly between that base station and a user equipment, together with the quality of the communications link between the base station and any relay which supports that user equipment. In this way, the base station will select the best possible communications channel for the data to be transmitted.

In one embodiment, the base station scheduling logic is operable to identify that pending data to be transmitted next by scheduling transmissions of higher priority pending data over lower priority pending data. Accordingly, that data having a higher priority will be transmitted in preference to lower priority data to ensure that it is received in the most timely manner possible.

In one embodiment, the base station scheduling logic is operable, when the pending data to be transmitted next is to be transmitted using the communications channel between the base station and a relay, to decide which pending data to transmit based on a difference in associated pending data queue sizes at the relay and the base station. Accordingly, the scheduling logic will determine the relative difference in the size of the data queues at the base station and the relay. If the data queue at the base station for one user is very high, but the data queue at the relay for that user is low, then that data may take preference over data for another user where the pending data queue at the base station is low, but the pending data queue at the relay is high.

In one embodiment, the base station scheduling logic is operable to identify that pending data to be transmitted next in accordance with the following algorithm:

= dest{l) eM

^D ' ^{t > - (ή,0}}, if dest(l) = RS _i where Q _B ^J _S (t) denotes the size of the queue at the base station for the j ^m user equipment at time t.

In one embodiment, the relay is operable to provide an indication of the size of each pending data queue to the base station.

In one embodiment, the relay is operable to provide an indication of a change in size of each pending data queue to the base station. Accordingly, rather than having to report on the size of each queue all the time, it may be more efficient to only transmit information indicating when the size of a queue changes.

According to a fourth aspect, there is provided a method of relaying data between a relay-base station pair and user equipment of a wireless communications system, the method comprising the steps of: forming at a base station, for each user equipment supported by the base station, a pending data queue associated with that user equipment, the pending data queue storing received data intended for that user equipment which has yet to be transmitted by the base station over a communications channel between that user equipment and the base station; scheduling transmissions of pending data to each user equipment based on at least one of a size of the pending data queue associated with each user equipment, priority of pending data and channel state information of the communications channel between each user equipment and the base station; and the method steps of the third aspect. According to α fifth aspect, there is provided a computer program product operable, when executed on a computer, to perform the method steps of the second aspect.

According to a sixth aspect, there is provided a computer program product operable, when executed on a computer, to perform the method steps of the fourth aspect.

Further particular and preferred aspects are set out in the accompanying independent and dependent claims. Features of the dependent claims may be combined with features of the independent claims as appropriate, and in combinations other than those explicitly set out in the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention will now be described further, with reference to the accompanying drawings, in which: Figure 1 illustrates a general relay deployment within one macro cell;

Figure 2 illustrates the main components of the relays shown in Figure 1 according to one embodiment;

Figure 3 illustrates the main components of the base station shown in Figure 1 according to one embodiment; and Figure 4 is a flow chart illustrating the main processing steps of the relays and base station shown in Figure 1.

DESCRIPTION OF THE EMBODIMENTS

Figure 1 illustrates an example deployment of relays within a macro cell supported by a base station. User equipment UE roam through the wireless communication system. Base stations BS are provided which support respective macro cells. Typically, a number of such base stations BS are provided, which are distributed geographically in order to provide a wide area of coverage to the user equipment UE. When user equipment UE is within a macro cell supported by the base station BS then communications may be established between the user equipment UE and the base station UE over an associated radio link. Each base station BS typically supports a number of sectors. Typically, a different antenna or antenna array within a base station BS supports an associated sector. Accordingly, each base station BS has multiple antennas and signals sent through the different antennas are electronically weighted to provide a sectorised approach. Of course, it will be appreciated that Figure 1 illustrates a small subset of the total number of user equipment and base stations that may be present in a typical communications system. Within α macro cell is proved a number of relays RSi, RS2. The relays RSi, RS2 provide local wireless coverage to support user equipment in their vicinity. In this example, RSi supports user equipment UEi and UE2. Likewise, the relay RS2 support user equipment UE3, IIE4 and UE5. Of course, relays may support more user equipment than this and user equipment may be supported by more than one relay. Wireless communications links, I, are provided between each relay and the support user equipment. As mentioned previously, the state of these wireless communications links will vary with time, dependent on local conditions such as the relative locations of the relay to the user equipment and any interfering transmissions or other noise. Accordingly, at any particular time, the data rate supported on each of these links will vary, with some links being able to support a higher data rate than others. Each relay RSi, RS2 maintains a data queue, Q, which stores pending data packets which have been received from the base station EJS but have yet to be transmitted to the intended user equipment. In normal operation, the size of these pending data queues will grow and shrink depending on the rate at which data packets are received from the base station BS over a communications link between that relay and the base station EiS and the rate at which these data packets can be relayed onto the intended user equipment over their associated communications links.

The base station BS stores data packets in a pending data queue, Q, for each user equipment supported by that base station. The size of this queue will also vary depending on the rate at which data packets are received by the base station BS from the core network (not shown) and upon the rate at which these packets may be delivered to the intended user equipment either directly over a communications link, I, between the base station BS and that user equipment, or the rate at which the data packets may be provided to a relay supporting that user equipment.

Figure 2 illustrates in more detail components of a relay R according to one embodiment. It will be appreciated that other components of the relay have been omitted to improve clarity. The relay comprises transceiver logic 10 coupled with a multiple antenna array 20 and operable to communicate both with the base station BS and user equipment over respective links. In this embodiment, the relay is half-duplex, however, it will be appreciated that the relay could be full-duplex. Coupled with the transceiver 10 is queuing logic 30 which is operable to create a first-in first-out (FIFO) queue which stores user data received for each user equipment being supported by that relay. Scheduling logic 40 is provided which interrogates the queuing logic 30 to establish the size of each queue and which receives channel state information indicating an estimate of an instantaneous signal to interference plus noise ratio (SINR) for each wireless communications link between the relay and each user equipment. As will be explained in more detail below, the scheduling logic 40 helps to ensure user- fairness by making scheduling decisions based on the state of each user's queue and on the estimate of instantaneous SINRs which does not assume an orthogonal separation of resources between base station-to-relay links and base station or relay-to- user equipment links. Cooperation logic 50 is also provided which enables cooperation to occur between relays as an effective way to combat interference between transmissions made by those relays, as also will be described in more detail below.

The cooperation logic 50 receives information regarding interfering transmissions via the transceiver logic 10. The cooperation logic 50 will then either cause the relay to adjust its transmissions or will take steps to adjust the transmissions of the interfering relay by transmitting messages to that relay via the transceiver 10.

Figure 3 illustrates the main components of a base station EiS according to one embodiment. Once again, only the main components required to support this embodiment have been illustrated and other components have been omitted to improve clarity. A transceiver 60 is provided which is coupled with an antenna array 30 and which supports wireiess transmissions over wireless communications links between the relays and the user equipment. Coupled with the transceiver 60 is queuing logic 70 which maintains, for each user equipment supported by that base station, a FIFO queue, Q, containing data which has been received from the core network over an Sl link, but has yet to be transmitted to that user equipment either directly or via a relay. Once again, the size of each of these queues will vary dependent on which the rate at which the data is received from the core network at the rate at which this data can be transmitted to the user equipment either directly or via the relays. Scheduling logic 80 is provided which makes scheduling decisions based on the state of the user equipment queues and on an estimate of instantaneous SINRs of the direct wireless link between the base station and the user equipment, and the wireless link between the base station and relays. Cooperation logic 90 is also provided which enables cooperation to occur between relays as an effective way to combat interference between transmissions made by those relays, as also will be described in more detail below.

The cooperation logic 90 receives information regarding interfering transmissions via the transceiver logic 90. The cooperation logic 90 will then either cause relays to adjust their transmissions by transmitting messages to that relay via the transceiver 60. The operation of the base station and each relay is illustrated in more detail in Figure 4. In overview, a distributed, two-phase scheduling scheme is provided which obviates the need to provide channel state information between the relays and base station, and obviates then need to transmit relay control information from the base station to the relays.

In the first phase, the base station BS makes its scheduling decision for the next time slot by taking into account the channel conditions of the wireless links directly between the base station and user equipment, and the channel conditions of the wireless links between the base station and the relays, as well as the size of the user equipment queues in both the base station and the relays. The selected destination for the transmission in the next time slot could be either a relay or user equipment.

In the second phase, because each relay is half-duplex, any relay which has not been selected to receive transmissions from the base station EiS in the first phase makes it scheduling decision for transmissions to user equipment on that time slot by taking into account channel conditions of the wireless links between that relay and the user equipment, and on the state of the user equipment queues in that relay.

Turning now to the operation in detail, at step SlO, the base station EiS checks to see whether a new data packet has been received from the core network. If a new data packet has been received, then that data packet is added to the appropriate user equipment queue. If no new data packet has been received processing proceeds to step S30. Of course, it will be appreciated that the base station BS supports full-duplex and so it is able to receive new data packets and transmit queued data packets in the same time slot.

At step S30 an assessment is made of whether to transmit in the next time slot to a user equipment using a wireless link directly between the base station BS and that user equipment. This assessment is made in the following way. The set of all transmitters within the macro base stations is denoted as T = {l,...,N + l} . corresponding to the N relays and the single base station BS. Similarly, the set of all users is denoted as

M = {l,..., K) . The total number of wireless links that the base station considers is given by the L = N + K, which includes all the wireless links between the base station and the users and between the base station and the relays. For a generic link I, for simplicity the transmission rate can be estimated using the Shannon Formula as

Λ, (/) = log ₂ (l + [bits /sec/ Hz] . Where SINR^ (t) is the SINR at the destination of the I ^th link at the time frame t, assuming that all other simultaneously active links are interfering. Accordingly, different from the centralised scheduling approach a transmitter set is activated without taking into account the interference generated to the scheduled receivers in order to maximise spatial reuse. On the other hand, the relays are operable to tackle interference by using cooperative scheduling as will be described in more detail below. Let Q _B ' _S (/), j e M and Qj _sj {t) denote the size of the queues at the base station for user equipment j in the macro cell and at the I ^th relay for user equipment j, respectively, at the start of the next time frame. To enable the base station to make that assessment, the relays will transmit information enabling the base station to determine the size of the queues at the relays as will be described in more detail below. Let us define D ₁ (t) as

J R ₁ (t)Q _B ^J _S {t), if/ = dest{l) e M

^D ' V> ^~ |Λ, (f)max{max{βi _s (t)-Q^ (t), θ}}, if dest (I) = RS ₁ where the first case corresponds to the transmission directly to a user equipment and the second case corresponds to the transmission to the I ^th relay. The optimal active link for the next time frame t is selected as follows: r (t) = aτgτnzx.D, (t)

;=(i. .L)

If transmission directly to a user is selected, then the scheduling logic 80 causes the next data packet within the associated user queue stored by the queuing logic 70 to be transmitted via the transceiver 60 to that user equipment and processing returns to step SlO. If the optimal link is selected to be a link between the base station BS and the I ^th relay for the next time frame, then processing proceeds to step S50.

At step S50, the user equipment whose packets will be transmitted over this link is selected in accordance with the following algorithm: j]. (t) = argmaxjmaxtø, {t)-Q^ (t),θ}}

At step S60, the scheduling logic 80 causes the queuing logic 70 to transmit the next data packet stored within that user equipments queue via the transceiver logic 60 to the selected relay.

Meanwhile, at each relay, an assessment is made by that relay of whether control information from the base station indicates that that relay has been selected to receive a data packet in the next time frame. Because each relay is half-duplex this will mean that it is therefore unable to also transmit data packets to user equipment in that time slot. However, if the relay was full-duplex, then concurrent reception and transmission of data packets would be possible.

If the relay has been select to receive data packet, the received data packet is added to the appropriate user equipment queue. If no data packet is to be received from a base station, then processing proceeds to S90.

At step S90, the second phase of the scheduling begins at the relay. The scheduling logic 40 selects which relay to user equipment wireless link should be used to transmit data packets. Considering the I ^th relay, lets us define D ₁ (/) as

D, {t) = R ₁ (I)Qi ₄ (IUeStQ ₁ ) ^ M where R ₁ (t) is an estimate of the rate for the link I, taking into account the scheduling decision of the base station BS. The optimal link for the next time frame t is selected as follows: l,' (t) = arg max D, (t) desl(l _t )eM

At step Sl 20, interference between the relay transmission and the transmission of other relays is identified so that local cooperation can occur. Such local cooperation can be an effective way to combat interference between two relays. For example, user equipment UE2 may be served by relay RSi but sees relay RS2 as a strong interferer. Accordingly, low-rate cooperation occurs between relays Rsi and RS2. The identification of transmission interference occurs as follows. The user equipment receives pilots from different transmitters such as relays or base stations. It selects the best transmitter as a function of the received power and identifies the dominant interfering transmitter(s) by looking at its pilot power. Considering the example where relay RSi is the best transmitter and relay RS2 is the dominant interferer, we define gamma γ as the ratio between power received from relay RSi and the power received

P from relay RS2, γ = — . If γ < γ for a given threshold, then the user equipment requires

cooperation between the relay RSi and relay RS2.

Accordingly, at step 130, any ameliorative action is taken. For example, assuming OFDMA modulation, relay RSi transmits to relay RS2 either directly or via the user equipment, the set of the carriers allocated to that user equipment, and the relay RS2 avoids allocating those carriers. The same approach could be used to allocated orthogonal beams, assuming multiple antennas at the relay side.

At step SlOO, the scheduling logic 40 causes the queuing logic 30 to transmit the next data packet from the appropriate user equipment queue via the transceiver 10 to the user equipment over its wireless link.

At step SI lO, the change in size of that user equipment's queue is transmitted to the base station EJS via the control channel. Of course, it will be appreciated that any increase in the user equipment queues caused by data packets being received from the base station can be inferred by the base station BS without need to transmit this change in size. However, the increase in size of the user equipment queue could also be transmitted, if required.

This procedure is repeated for each relay. It can be seen that for this distributed scheduling approach each relay needs to feedback to the base station only an update of the queue sizes. Unlike in the centralised approach, any feedback concerning the channel state information between the relay and its supported user equipment is not required. Feedback concerning the channel state information can require a considerable amount of bits, particularly when multiple antennas are deployed and a scalar feedback is not sufficient to estimate the SINR of a given link. However, there will be embodiments where such a feedback (or partial feedback) will be transmitted from relays to the base station.

Accordingly, it can be seen that a distributed relay scheme for down link transmissions is provided where a given user equipment can be either served by a base station or a relay in an opportunistic way. Such a distributed approach allows reduced feedback with respect to the centralised approach, particularly when a simple scalar feedback is not sufficient for estimating the channel quality. As a result of the reduced feedback requirement, the system becomes more scaleable and new relays can be deployed where needed without the need for careful network planning. By using a distributed approach, local, low rate relay-to-relay and relay-to-base station cooperation can be implemented even between relays belonging to different cells.

A person of skill in the art would readily recognize that steps of various above-described methods can be performed by programmed computers. Herein, some embodiments are also intended to cover program storage devices, e.g., digital data storage media, which are machine or computer readable and encode machine-executable or computer-executable programs of instructions, wherein said instructions perform some or all of the steps of said above-described methods. The program storage devices may be, e.g., digital memories, magnetic storage media such as a magnetic disks and magnetic tapes, hard drives, or optically readable digital data storage media. The embodiments are also intended to cover computers programmed to perform said steps of the above-described methods.

The functions of the various elements shown in the FIGs., including any functional blocks labeled as "processors" or "logic", may be provided through the use of dedicated hardware as well as hardware capable of executing software in association with appropriate software. When provided by a processor, the functions may be provided by a single dedicated processor, by a single shared processor, or by a plurality of individual processors, some of which may be shared. Moreover, explicit use of the term "processor" or "controller" or "logic" should not be construed to refer exclusively to hardware capable of executing software, and may implicitly include, without limitation, digital signal processor (DSP) hardware, network processor, application specific integrated circuit (ASiC), field programmable gate array (FPGA), read only memory (ROM) for storing software, random access memory (RAM), and non volatile storage. Other hardware, conventional and/or custom, may also be included. Similarly, any switches shown in the FIGS, are conceptual only. Their function may be carried out through the operation of program logic, through dedicated logic, through the interaction of program control and dedicated logic, or even manually, the particular technique being selectable by the implementer as more specifically understood from the context.

It should be appreciated by those skilled in the art that any block diagrams herein represent conceptual views of illustrative circuitry embodying the principles of the invention. Similarly, it will be appreciated that any flow charts, flow diagrams, state transition diagrams, pseudo code, and the like represent various processes which may be substantially represented in computer readable medium and so executed by a computer or processor, whether or not such computer or processor is explicitly shown.

The description and drawings merely illustrate the principles of the invention. It will thus be appreciated that those skilled in the art will be able to devise various arrangements that, although not explicitly described or shown herein, embody the principles of the invention and are included within its spirit and scope. Furthermore, all examples recited herein are principally intended expressly to be only for pedagogical purposes to aid the reader in understanding the principles of the invention and the concepts contributed by the inventor(s) to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions. Moreover, all statements herein reciting principles, aspects, and embodiments of the invention, as well as specific examples thereof, are intended to encompass equivalents thereof.