WO2010150050A1 - Method and apparatus for allocating power for cooperative communications - Google Patents

Abstract

A method, apparatus and computer program product are provided for determining an appropriate power allocation for each of at least two devices to utilize in conjunction with the relaying of data of the other device in furtherance of a cooperative communications technique. Additionally, a method, apparatus and computer program product are provided for responding to the power allocations that have been determined and then cooperating with another device to relay the communications signals of the other device by expending power in accordance with the power allocation. The power allocations may be determined in accordance with a bargaining solution, such as a Nash bargaining solution.

Description

METHOD AND APPARATUS FOR ALLOCATING POWER FOR COOPERATIVE

COMMUNICATIONS

TECHNICAL FIELD

Embodiments of the present invention relate generally to cooperative communications and, more particularly, to allocating power for cooperative communications.

BACKGROUND

As users become increasingly dependant upon wireless networks for business and personal needs, the desire for faster and more widely accessible wireless communications increases. In some instances, wireless networks may employ various techniques, such as hardware or software solutions, to increase the bandwidth and transfer rates, and the quality of service. However, user equipment (UE), such as a mobile terminal, is commonly dependent upon battery power for its operation and, as such, conservation of battery power is also a consideration.

One technique for increasing the data rate of a UE relies upon relaying the communications signals of a UE, such as to a base station. Although dedicated relay nodes may be employed to facilitate the communications of a UE, the use of dedicated relay nodes increases the cost of the network and is only useful in those regions in which relay nodes have been deployed.

In order to enjoy the benefits of relaying while overcoming at least some of the drawbacks of fixed relay nodes, cooperative communications has been proposed in which one UE relays the communications signals of another UE, such as to a base station, an access point or the like (hereinafter generically referenced as a base station). For example, if two UEs are geographically close to one another, each UE may receive the communications signals from the other UE even though the communications signals are intended for another recipient. In accordance with cooperative communications, each UE may relay copies of the communications signals from the other UE to a base station for delivery to the intended recipient. By cooperatively communicating in this fashion, data may be transmitted more reliably at a higher rate.

Although cooperative communications offers advantages, cooperative communications has not been widely adopted. Although the reasons may be myriad, one reason for the failure of cooperative communications to be widely adopted may be that users must consume additional power in order to relay the communications signals of another UE. Since the battery power of a UE is generally limited, it may be counterintuitive to some users that their expenditure of additional battery power to relay the communications signals of another UE could lead to more reliable communications signals at a higher rate as a result of cooperative communications

BRIEF SUMMARY

A method, apparatus and computer program product are provided in accordance with exemplary embodiments of the present invention for determining an appropriate power allocation to thereafter utilize in conjunction with the relaying of data of the other device Additionally, a method, apparatus and computer program product are provided according to other embodiments of the present invention for responding to the power allocations that have been determined and then cooperating with another device to relay the communications signals of the other device by expending power in accordance with the power allocation By determining the power allocations in accordance with a bargaining solution, such as a Nash bargaining solution, each device may benefit not only from communication that is conducted in a more reliable fashion with various network elements, such as base stations, access points and the like, but also in the conservation of battery resources since the battery power that is conserved by more reliably communicating with the network (as a result of the reduction in the need to retransmit data) exceeds the additional battery power that is consumed in relaying the data of the other device As such, cooperative communications are advantageously supported by embodiments of the present invention

In one exemplary embodiment, a method is provided in which a power allocation of a respective device to be utilized to relay communications signals of another device is determined A bargaining solution, such as a Nash bargaining solution, may be utilized in order to determine the power allocation The method of this exemplary embodiment also facilitates cooperation with the other device to relay the communications signals of the other device by expending power in accordance with the power allocation In some embodiments, a different power allocation may be determined for each device

In embodiments in which a Nash bargaining solution is utilized to determine the power allocation, the power allocation may be determined in such a manner as to be based upon a utility of each device as defined by a total amount of data transmitted by a respective device in proportion to the total energy expended for transmission of the data In this regard, determining the power allocation based upon the utility of each device may include determining the power allocation based upon a product of the utility of each device and a respective disagreement point The disagreement point of a respective device may include a long-term non-cooperative payoff of the respective device

In another exemplary embodiment, an apparatus is provided which includes at least one processor, and at least one memory including computer program code In this embodiment, the at least one memory and the computer program code are configured to, with the at least one processor, cause the apparatus to determine a power allocation of a respective device to be utilized to relay communications signals of another device A bargaining solution, such as a Nash bargaining solution, may be utilized in order to determine the power allocation The at least one memory and the computer program code of this exemplary embodiment are also configured to, with the at least one processor, cause the apparatus to facilitate cooperation with the other device to relay the communications signals of the other device by expending power in accordance with the power allocation.

In embodiments in which a Nash bargaining solution is utilized to determine the power allocation, the at least one memory and the computer program code may also be configured to, with the at least one processor, cause the apparatus to determine the power allocation in such a manner as to be based upon a utility of each device as defined by a total amount of data transmitted by a respective device in proportion to the total energy expended for transmission of the data. In this regard, the at least one memory and the computer program code may also be configured to, with the at least one processor, cause the apparatus to determine the power allocation based upon the utility of each device by determining the power allocation based upon a product of the utility of each device and a respective disagreement point. The disagreement point of a respective device may include a long-term non-cooperative payoff of the respective device.

The apparatus of one embodiment is a mobile phone that further includes user interface circuitry and user interface software configured to facilitate user control of at least some functions of the mobile phone through use of a display and configured to display at least a portion of a user interface of the mobile phone. In accordance with this embodiment, the display and display circuitry are configured to facilitate user control of at least some functions of the mobile phone.

In a further exemplary embodiment, a computer program product is provided which includes at least one computer-readable storage medium having computer-readable program instructions stored therein. In this embodiment, the computer-readable program instructions are configured to cause an apparatus at least to determine, for each of at least two devices, a power allocation of a respective device to be utilized to relay communications signals of another device. A bargaining solution, such as a Nash bargaining solution, may be utilized in order to determine the power allocation. The computer-readable program instructions of this exemplary embodiment are also configured to cause an apparatus to facilitate cooperation with the other device to relay the communications signals of the other device by expending power in accordance with the power allocation to at least one of the devices.

In embodiments in which a Nash bargaining solution is utilized to determine the power allocation, the computer-readable program instructions may also be configured to cause an apparatus at least to determine the power allocation in such a manner as to be based upon a utility of each device as defined by a total amount of data transmitted by a respective device in proportion to the total energy expended for transmission of the data. In this regard, the computer- readable program instructions may be configured to cause an apparatus at least to determine the power allocation based upon the utility of each device by determining the power allocation based upon a product of the utility of each device and a respective disagreement point. The disagreement point of a respective device may include a long-term non-cooperative payoff of the respective device.

A method is also provided in accordance with another embodiment of the present invention which accesses a power allocation to be utilized to relay communication signals of another device and facilitates cooperation with the other device to relay the communications signals of the other device, such as by relaying the communications signals of the other device to a base station, by expending power in accordance with the power allocation. The power allocation may be determined in accordance with a bargaining solution, such as a Nash bargaining solution. The method of this exemplary embodiment may also rely upon cooperation by the other device to relay the communications signals transmitted by the respective device.

In another exemplary embodiment, an apparatus is provided which includes at least one processor, and at least one memory including computer program code. In this embodiment, the at least one memory and the computer program code are configured to, with the at least one processor, cause the apparatus to access a power allocation to be utilized to relay communication signals of another device and to facilitate cooperation with the other device to relay the communications signals of the other device, such as by relaying the communications signals of the other device to a base station, by expending power in accordance with the power allocation. The power allocation may be determined in accordance with a bargaining solution, such as a Nash bargaining solution. The at least one memory and the computer program code may also be configured to, with the at least one processor, cause the apparatus to rely upon cooperation by the other device to relay the communications signals transmitted by the respective device.

In a further exemplary embodiment, a computer program product is provided which includes at least one computer-readable storage medium having computer-readable program instructions stored therein. In this embodiment, the computer-readable program instructions are configured to cause an apparatus at least to access a power allocation to be utilized to relay communication signals of another device and to facilitate cooperation with the other device to relay the communications signals of the other device, such as by relaying the communications signals of the other device to a base station, by expending power in accordance with the power allocation. The power allocation may be determined in accordance with a bargaining solution, such as a Nash bargaining solution. The computer-readable program instructions may also be configured to cause the apparatus to rely upon cooperation by the other device to relay the communications signals transmitted by the respective device.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

Having thus described exemplary embodiments of the invention in general terms, reference will now be made to the accompanying drawings, which are not necessarily drawn to scale, and wherein:

Figure 1 is a block diagram of a system for supporting cooperative communications in accordance with example embodiments of the present invention;

Figure 2 is a graphical representation of the Nash bargaining solution for the utility function of two UEs in accordance with example embodiments of the present invention;

Figure 3 is a graphical representation of the results of numerical simulations within the Pareto frontier and the resulting Nash bargaining solution in accordance with one embodiment of the present invention; Figure 4 is a graphical representation of the average rate in bits per second per Hertz for two UEs as a function of the expected channel gain between one of the UEs and a base station in instances employing cooperative communications in accordance with example embodiments of the present invention and in instances that do not employ cooperative communications;

Figure 5 is a graphical representation of the average power for two UEs as a function of the expected channel gain between one of the UEs and a base station with the UEs employing cooperative communications in accordance with example embodiments of the present invention;

Figure 6 is a graphical representation of the utility for two UEs as a function of the expected channel gain between one of the UEs and a base station in instances employing cooperative communications in accordance with example embodiments of the present invention and in instances that do not employ cooperative communications;

Figure 7 is a graphical representation of the average Nash bargaining solution powers, e.g., the square root of the Nash product in bits per joule, for two UEs as a function of the expected channel gain between one of the UEs and a base station with the UEs employing cooperative communications in accordance with example embodiments of the present invention;

Figure 8 is a block diagram of an apparatus for determining power allocations in accordance with example embodiments of the present invention;

Figure 9 is a flowchart of the operations performed to determine power allocations in accordance with example embodiments of the present invention;

Figure 10 is a block diagram of an apparatus, such as a UE, for relaying the communications signals of another device in accordance with example embodiments of the present invention; and

Figure 11 is a flowchart of the operations performed to relay the communications signals of another device in accordance with example embodiments of the present invention.

DETAILED DESCRIPTION

Example embodiments of the present invention will now be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all embodiments of the invention are shown. Indeed, the invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. Like reference numerals refer to like elements throughout. The terms "data," "content," "information," and similar terms may be used interchangeably, according to some example embodiments of the present invention, to refer to data capable of being transmitted, received, operated on, and/or stored.

As used herein, the term 'circuitry' refers to all of the following: (a) hardware-only circuit implementations (such as implementations in only analog and/or digital circuitry); (b) to combinations of circuits and software (and/or firmware), such as (as applicable): (i) to a combination of processor(s) or (ii) to portions of processor(s)/software (including digital signal processor(s)), software, and memory(ies) that work together to cause an apparatus, such as a mobile phone or server, to perform various functions); and (c) to circuits, such as a microprocessor(s) or a portion of a microprocessors), that require software or firmware for operation, even if the software or firmware is not physically present.

This definition of 'circuitry' applies to all uses of this term in this application, including in any claims. As a further example, as used in this application, the term "circuitry" would also cover an implementation of merely a processor (or multiple processors) or portion of a processor and its (or their) accompanying software and/or firmware. The term "circuitry" would also cover, for example and if applicable to the particular claim element, a baseband integrated circuit or applications processor integrated circuit for a mobile phone or a similar integrated circuit in server, a cellular network device, or other network device.

In accordance with example embodiments of the present invention, game theory is employed to provide a mathematical framework for considering the decision-making of users with conflicting interests, for example, UEs considering cooperative communications in an energy- limited environment. In this regard, game theory may provide a fair, systematic technique to balance, for example, the performance of each UE relative to the energy expended by another UE. In accordance with example embodiments of the present invention, cooperative game theory facilitates a determination of how much a UE should cooperate, and/or how much energy a UE should expend in relaying communications signals of another UE.

In order to illustrate embodiments of the present invention, Figure 1 illustrates a network environment in which two UEs designated UE 1 and UE 2 communicate with a common base station 14 to access the remainder of the network 16. While Figure 1 and the ensuing discussion mention only two UEs, three or more UEs may cooperatively communicate with the common base station in accordance with other embodiments of the present invention with the two UEs merely provided by way of illustration and not limitation.

In addition, while the UEs are shown and described to cooperatively communicate with a base station 14, the UEs may cooperatively communicate with other network devices, such as access points or the like. As such, reference herein to a base station is also by way of example, and not of limitation.

To eliminate inter-user interference, the UEs' transmissions may be time-division duplexed with UE 1 transmitting its data to the base station 14 during odd time blocks such that UE 1 is active and UE 2 is idle, and UE 2 transmitting its data to the base station during even time blocks such that UE 2 is active and UE 1 is idle. However, to introduce cooperation, the idle UE may choose to relay signals for the active UE in order to increase its rate. In other words, during odd time blocks (when UE 1 operates as a source to transmit its data), UE 2 may act as a relay node, while during even time blocks (when UE 2 operates as a source to transmit its data), UE 1 may act as a relay node. The two UEs and the base station may therefore form a three-terminal relay channel in which the roles of source and relay are exchanged each time block. As a result of the cooperation, during any time block the active UE may transmit its data directly to the base station (as shown in solid lines in Figure 1) and the idle UE may relay the same data (of the active UE) to the base station (as shown in dashed lines in Figure 1). In this regard, Figure 1 depicts the flow of data from UE 1 during odd time blocks by the arrows designated 1 and the flow of data from UE 2 during even time blocks by the arrows designated 2. By potentially receiving the same data via two different channels, the likelihood that the base station will successfully receive the data is increased.

For purposes of example, a narrowband, Rayleigh, block-fading Gaussian channel model may be assumed, although embodiments of the present invention are also applicable to other channel distributions. In a narrowband, Rayleigh block-fading Gaussian channel model, however, the UEs' transmissions are multiplied by the (complex) channel gains and corrupted by Gaussian noise. Without loss of generality, the channel gains may be scaled such that the noise power at each receiver is unity. By the block-fading assumption, channel gains remain constant over a single time block, and channel gains at different time blocks are statistically independent. The channel gains of this example embodiment are Rayleigh distributed, and the channel statistics remain stationary. As shown in Figure 1 , let /?₁₃ and /?₂₃ denote the channel gains between UE 1 and UE 2 and the base station 14, respectively, and let h^ and Λ_2i denote the channel gain between from UE 1 to UE 2 and from UE 2 to UE 1 , respectively. Then, the channel statistics may be described by the expected magnitudes -Ξ[|ft₁₃|²], E[|/723|²], E[I^d²], and E[|/7₂₁|²], where £[•] represents the statistical expectation.

At each time block t, \e\. pi(t) and p₂(t) denote the power level of UE 1 and UE 2, respectively. To model the limitations of the UEs' power amplifiers, an upper bound may be placed on p-,(t) and p₂(t). Again normalizing the channel gains, the power constraints may be defined without loss of generality as:

0 < p₁rø < 1, f = 1, 2, ^{• • •} (1)

0 < p₂rø < 1 , f = 1 , 2, ^{• • •} (2)

Finally, it may be assumed in one example embodiment that each UE uses full power to transmit its own data, meaning that pi(t) = 1 for all odd t and p₂(t) = 1 for all even t. In other words, UEs of this example embodiment are automatically willing to use all of their power for their own transmissions with the UEs only needing to determine how much power they are willing to use for relaying.

In order to determine the achievable rates in accordance with one example embodiment, it may be assumed that UEs can transmit and receive simultaneously, which permits full-duplex transmission. It may also be assumed that full channel state information is available at the UEs and base station 14. Finally, since the exact capacity of the relay channel is unknown, it may be assumed that the UEs employ decode-and-forward relaying via block Markov encoding, although other types of relaying may be employed in other embodiments. In this example embodiment, however, the achievable rates for UE 1 are: r^{irø =} max mln{to&fl + |ΛbWPfl-β²;λ O≤β≤i

Og₂(I + IΛ13I² + |Λ₂₃|² P₂(O + 2 Jp₂(WIh₁₃ Wh₂₃I) )_' for odd f. A similar expression holds for UE 2 for even t. The two terms in the min{} function correspond to the two possible bottlenecks of the decode-and-forward relay channel: the (point-to- point) channel between source and relay, and the broadcast channel formed by the source, relay, and destination. The rate of the relay channel is therefore limited by the rate of the bottleneck component.

In this example embodiment, the parameter β is the correlation coefficient between the source signal and the relay signal, which may be tuned to maximize the rate. When possible, the optimal value of β is the value that makes the two terms inside the min{} function equal. In this case, the two terms may be equated and it may be solved for β. Suppressing time arguments, this solution gives:

\h_u \² (1 - β²) = \h_l3\² + |/ι₂₃ |² P2 + 2y/pϊβ |Λ₁₃ | |Λ₂₃ |

(3)

Equation (3) is a quadratic whose unique positive solution is:

-V^ IM IM + V(IM - IM XIM - I* IM") β

\h 12 (4)

When the terms inside the min{} function cannot be equated, the optimal choice is β = 0, and the second term is left greater than the first. This situation only occurs, however, when UE 2 gives too much power, that is, if the second term is larger even when β - 0, then p₂ may be decreased without impacting the rate. Therefore, without any loss of performance, the power may be constrained such that the second term does not exceed the first, even when β = Q:

IM + IM P2 ≤ IM h 12 - \h 13

Vi ≤

\h ^. (5)

Of course, the relay power cannot go negative. So, combining equation (5) with the original constraint in equation (1), the combined constraint may be represented as follows:

The constraint of equation (6) may be intuitive. In this regard, when l^sl ≥ l^d , UE 1 may communicate at a higher rate with the base station than with UE 2, which precludes UE 2's contributing to the achievable rate. Similarly, if the gap between

is small compared to I^Λ23| , UE 2 may only contribute a small amount of power before the point-to-point link between the UEs becomes the bottleneck. With the relay power constrained by equation (6), the achievable rate simplifies to a single term:

τι {i) = log₂ (l + |/ii₃|² + IM² P₂ + 2VS/ΦIS| |/i23|) , (7) for t odd and β chosen according to equation (4). Note that when p₂ = 0, equation (7) simplifies to the capacity of the point-to-point channel between UE 1 and the base station 14.

The above discussion applies equally well to the rates for UE 2. Thus, the relay power P₁ may be restricted such that:

giving an achievable rate of r₂it)

, ₍₉₎ for t even and β chosen according to

To formally define a game, (a) the set of players, (b) the set of strategies those players may enact, and (c) the utilities or payoffs that each player derives from the strategies enacted are defined. With reference to the example embodiment of Figure 1 , the players are the two UEs and their possible strategies are the relay powers pi(t) and p₂(t) provided by the UEs for relaying the communication signals of the other UE. Since it is assumed for one example embodiment that the UEs use full power for their own transmissions, p-,(t) need only be defined for even time blocks and p₂(t) need only be defined for odd time blocks. In addition, the UEs may be restricted to causal power allocations with p-,(t) and p₂(t) not depending on future decisions or channel realizations. The power allocations of the example embodiment are also memoryless and depend only on the current channel realizations. Thus, P₁ (t) = Pi(h₂₃(t), (h₂₁(t), (h₁₃(t)) = p-ι(\\(t)) and p₂(t) = Pi(hi₃(t), (hi₂(t), (h₂₃(t)) = p₂(h(t)), where the channel realizations may be combined into the vector h(t) for notational convenience. As described above, the power allocations must also satisfy:

»<,^, _M ⁾ <»«(o^,-^.|^i.

(11) for /, j e {1 ,2} / ≠j. For future use, let λ denote the set of power allocation functions that satisfy equation (11).

Due to the time-varying nature of the channels and the power allocations, the UEs' utility functions are defined at each time block. Since the UEs' energy is scarce, both energy expenditure and achievable rate are incorporated into the utility functions. At each time block t, each player's, e.g., each UE's, utility is defined as the total amount of data it has transmitted to the base station 14 (measured in bits) divided by the total energy it has expended (in joules). So, up to a multiplicative constant, the utilities are:

(12) for UE 1 and

for UE 2, where the rates r^h(τ), p₂(h(τ))) and r₂(h(τ), P₁(In(T))) may be calculated according to equations (7) and (9), respectively. Since, as discussed above, each UE uses unit power for its own data, the utilities simplify to:

for UE 1 and

U₂ (p_l , P₂ , t)

for UE 2 where [_-_|and | ^• |are the floor and ceiling functions, respectively.

The utility functions (14) and (15) are coupled in that by increasing its relay power, a UE improves the utility of the other UE while decreasing its own utility. In game theory, each player is assumed to be self-interested and therefore concerned solely with maximizing its own utility without regard for the benefit of others. This leads to the classic Nash equilibrium, which is any set of strategies such that no single player may improve its utility by unilaterally changing its strategy. This definition does not preclude, however, the possibility of utility gain if players simultaneously change strategies. Instead, the Nash equilibrium defines a point such that selfish players — acting alone — cannot increase their utility.

In general, the Nash equilibrium is not unique. However, in this instance, at any fixed time t, the unique Nash equilibrium is to set the relay power equal to zero. Since unilaterally reducing relay power increases a UE's utility, self-interested players will always choose p, = p₂ = 0 if they make decisions at a single time step. Selfishness and short-sightedness may drive UEs to non- cooperation, even though higher utility is possible for both UEs through cooperation, as shown below.

If players consider future plays in making decisions, it is possible for self-interest to stimulate and reinforce cooperation. For example, rather than myopically making decisions in a single time step, players in an infinitely-repeated game (or any game for which the players do not know when the game will end) have incentive to consider how their present choices may effect future payoff. Thus, reciprocity is introduced into decision-making in that players may reward or punish other players for "good" and "bad" behaviors. In this instance, one UE may agree to relay if the other UE agrees to do so in the future. Such agreements may be enforced via "grim trigger" threats, that is, if a UE reneges on its agreement, the other UE responds by refusing to relay for the rest of the game. In this way, cooperative strategies may be sustained as Nash equilibria. More formally, the long-term non-cooperative payoff may be defined as:

(16)

NC

Ui = IhO₀ U₁ [O^ t) = E_h [log₂(l + |/_ll3|²)] u₂ ^NC = t l-i→moo W₂(O₁ O₁ O = JS_h L FlOg₂(I + \h₂₃ \²) J] , ₍₁₇₎ where E_h[-] is the expectation taken over the channel coefficients, and the equality in the previous equations is in the almost sure sense due to the law of large numbers. The non-cooperative utilities υ^^c and uψ represent the utilities garnered if players refuse to cooperate. Similarly, the long-term utilities may be defined as:

^U ₁(P_{1 1} P₂J

^U ₂(Pi₁ P₂) = lim U₂ (Pi ,P2, 0 = y_F ^{2 (}?^{l )]} ₁ , t^→∞ 1 + ^h [p₂] ₍₁₉₎ where the dependence on h has been suppressed for convenience, and again the utilities converge almost surely. Then, any strategies which result in U₁ > ιζ^c and u₂ ≥ «f^c may be sustained as a Nash equilibrium through grim trigger threats. Therefore, power allocations P₁ and p₂ may be freely chosen as long as the associated long-term utilities are at least as great as the non-cooperative utilities, with the guarantee that they may be sustained as a Nash equilibrium. However, there may be an infinite number of Nash equilibria for the repeated game, forcing a non- arbitrary means of choosing among them to be found.

A bargaining solution may therefore be employed in accordance with the example embodiments of the present invention to choose a unique set of strategies. While various bargaining solutions may be employed, a Nash bargaining solution (NBS) may be utilized to choose a unique set of strategies. For purposes of explanation, NBS is first introduced abstractly before being applied to the problem.

In this regard, a two-player bargaining game may be formally defined by a set of feasible utilities U e R² and a disagreement point δ e U . The disagreement point represents the status quo prior to bargaining or utility guaranteed to each player should bargaining fail. A bargaining solution is a mapping /( u,δ ) to a payoff vector u* e U such that u* ≥ δ. The NBS is an axiomatic solution, that is, it is characterized by a set of reasonable axioms rather than by a concrete bargaining process. The following axioms characterize the NBS:

1) Pareto dominance: If u e U is a vector such that u ≥ u^*, then u = u^*. That is, there is no point u e U such that any player receives higher payoff than under u^* without penalizing the other player. If, for example, there exists u e U such that U₁

* *

> Uj , then U₂ < u-η , and vice versa. Pareto dominance is an axiom of efficiency, ensuring that any points which improve players' payoff without cost to other players are not overlooked.

2) Invariance to positive affine transformations: Let A be a positive affine transformation; that is, /A(s) = [C₁Si + d_1t C₂S₂ + d₂)^rfor positive C₁, C₂ and arbitrary d_1t Cf₂. Then, if /(L/, S) = u^*, then f [A[U), A[S)) = A[u^*). In short, the solution must be independent to the scale and zero level of the players' utilities.

3) Symmetry: Let T be the permutation of the two players. Then, /Cr(L/, T( (5))) = T[u*) whenever f[U, S) = u^*. Here a minimal sense of fairness is imposed on the solution. Since players may be interchanged without effect, each player obtains

* * equal utility u-r = u-~ , if U is symmetric and S₁ = S₂.

4) Independence of Irrelevant Alternatives: If V is another set of utilities such that V => U, then either /(V, S) = /(U, S) or f[V, S) e Vl U. In other words, if new utility vectors are added to the game, the bargaining solution either remains unchanged or it selects one of the new utilities.

The unique Nash bargaining solution that satisfies Axioms 1-4 may be defined as: u^* = f(U, δ) = arg max[κi - <Si]⁺ [u₂ - S₂}⁺ ,

(20) where [-]⁺ = min(-, 0). In other words, the Nash bargaining solution is the utility vector that maximizes the product in equation (20), called the Nash product. The Nash bargaining solution is depicted in Figure 2.

In the example embodiment of Figure 1 , the set of feasible utilities is:

U = ( (U₁ 0₁ , p₂) , Ii₂ (Pi , P₂)) E M² : pi , p₂ £ X, } , and the disagreement point may be chosen as:

Then, rewriting equation (20), the NBS becomes: ar

As exposed by equation (21), the NBS payoffs are at least as great as the non-cooperative payoffs. The NBS is therefore guaranteed to be a Nash equilibrium of the repeated game.

In addition to finding the utilities associated with the Nash bargaining solution, the power allocations P₁ and p₂ that achieve the bargained utilities are also determined. Substituting equations (18) and (19) into equation (21), the following optimization problem may be obtained: m_ax -a MP₂ ⁾] . c] ⁺ [gL!gM - ^c ^'

_Pl ^,p ₂e* [ l + £h b>i] J U + £h [P2] ²

(22)

Equation (22) is non-convex, making it difficult to find the NBS power allocations directly. So, a few results that provide a systematic method for solving equation (22) are next presented. * * *

Lemma 1: Let pj and p-~ be power allocations with average power E_h[pj] = O₁ and

£_h[ pw ] = α₂, respectively. Then, the utility vector (t/i( p j , p-~ ), ι/₂( Py , Pw )) is Pareto dominant only if

(23)

PΪ = arg max E_h [r₂(pi )] subject to E_h [pi] = α_t and

Pa = arg max -5¹ _h [ri (p₂)] p? e x subject to £_h [p₂] = α₂ /_24\

*

Proof The point is argued by contradiction. Supposing that p-r is not a solution to

* * equation (23), then there exists some Pi e χ such that E_h[r₂(Pi)] > E_h[r₂( Pj )] and E_hJp₁] = E_h[ p-r ]

= α_v ThUS₁ U₂(P₁, /j ^ > ^U2 Pj _^ Pw ), but ι/,(p,, /? ^ ) = u₇( />y , /> ^ ). So the point

* * * *

(t/_f( _JPJ , /7-^- ),(u₂( /7γ , /7-^- )), cannot be Pareto dominant, which is a contradiction. Repeating the

* argument for p-j establishes the result.

The content of Lemma 1 is that power must be allocated efficiently. In other words, if a UE decides to commit a certain average power for relaying, then that power should be allocated to increase the other UE's rate as much as possible. It is also noted that the converse of Lemma 1 is not true, as will be seen below. There exist power allocations that are solutions to the optimization problems in equations (23) and (24) and result in utilities that are not Pareto dominant.

A benefit of Lemma 1 is that the optimization of the expected rate is a convex problem. Since the NBS utilities are Pareto dominant, the optimization problem in equation (22) may be transformed into a series of comparatively simple optimizations. Instead of searching over the entire set of permissible power allocations, the solution may be found by only searching over the (Ci₁, α₂) pairs.

* *

Theorem 2: Let p-r and p-η be power allocations for which the utility vector

{Ui{ pj , p-~ ), U₂( Pj , P_W )) is Pareto dominant. Then, pj and />^■=^■ must satisfy:

for /, j e {1 ,2} and i ≠j, where β' is the derivative of /? (calculated according to equations (4) or (10)

* as appropriate) with respect to p j , μ > 0 is an arbitrary constant which determines the average power, and [-]_χ is the projection onto the set X. Proof: By Lemma 1 , the power allocations must be a solution to the maximization problem of equations (23) or (24), which is a constrained convex problem. By the calculus of variations in equation (24), the optimal power allocation must satisfy the Euler-Lagrange equation. Defining the Lagrangian as:

L = log(l + |Λ,₃|² + |/ι,₃ |² P₁ + 2^p-β \h_l3\ |Λ,₃|)/(h)

- ApJ(h), where /(h) is the joint probability density of the channel gains, and λ > 0 is the Lagrangian multiplier associated with the average power constraint. Then, the Euler-Lagrange equation is: dL dp;

IM + 2 IM I /ι_t31 (/3/(2 v/pf) + β'y/pϊ) λ = 0 i + IM + IM P; + Zy/pf^β IM |Λ,₃|

Rearranging and solving for p— , the following is obtained:

I±jM

|Λ. t3

But, p— as defined may not be a member of X. Since members of X only are restricted by an upper and lower bound, the Karush-Kuhn-Tucker (KKT) conditions provide the desired result:

where μ = MK for notational convenience.

However, Theorem 2 gives only an implicit definition of the power allocations with no closed-form solution to equation (25) existing. On the other hand, since the expected rate is convex in the power allocation, any allocation p, satisfying equation (25) is a global optimizer for some power level α,. For the simulations discussed below, the solution to equation (25) numerically using the gradient projection method may be determined.

Lemma 1 and Theorem 2 provide a systematic method for finding the power allocations p_\ and p₂ that achieve the Nash bargaining utilities. First, thresholds μ_? and μ₂ may be chosen and the resulting power allocations P₁ and p₂ may be determined according to equation (25). Then, the Nash product of equation (22) may be evaluated at pi and p₂. Using branch-and-bound techniques, the possible values of μ₇ and μ₂may be efficiently searched until the Nash product is maximized. It is noted that the correlation coefficient β is the primary impediment to finding a closed- form solution. So, to find a low-complexity approximation to the true NBS, β may be forced to equal 0, regardless of the channel gains.

* *

Corollary 3: Let pj and p-^ be power allocations with average power for which the sfc _ fc ric sic utility vector (ιy₇( p-r , p-^ ), u₂( pj , p-^ )) is Pareto dominant. If β = 0, p₇ and p₂ have the form:

for /, y e {1 ,2} and i ≠j, where μ > 0 again is an arbitrary constant which determines the average power.

For this approximate case, the optimization process is the same. Using branch-and-bound techniques, the values of μi and μ₂ may be searched. But, rather than relying on gradient projection to find the resulting power allocations, the power allocations may be defined directly by equation (26), thereby greatly reducing the total complexity. Moreover, the optimality gap associated with this approximation may be searched.

To demonstrate the performance of example embodiments of the present invention, the results of numerical simulations are next presented. First, using Lemma 1 , the Pareto frontier may be numerically swept for the case when the expected channel gains are E[[/7i₂|²] = £[|Λ₂i|²] = £l|ftra|²]

= 1OdB. The space [0,1] x [0, 1] of possible (Ci₁, α₂) pairs is quantized into 20 x 20 grid points, and the power allocations and utilities associated with each point are found. In Figure 3, the results are depicted along with the disagreement point £and the NBS point. First, it may be empirically seen that the converse to Lemma 1 is false. All of the points in Figure 3 are found by solving the convex problems of equations (23) and (24), but most are not Pareto dominant. Also, it may be seen that, since the disagreement point is not Pareto dominant, it is indeed possible to improve both UEs' utility via the NBS.

Next, the manner in which the NBS performs in a variety of channel conditions is examined, particularly when the UEs' link qualities are asymmetric. In this regard, the expected inter-user channel gains is set constant at E[|/?1₂|²]

= 15dB. UE 2's channel with the base station also has a constant expected gain of E[|Λ₂₃|²] = 15dB. E[|/7_Y3|²] is allowed to vary between -5dB and 2OdB.

In Figure 4, the average rates for both UEs under single-user transmission (no cooperation), the approximate NBS given in Corollary 3, and the optimal NBS found via Theorem 2 are shown with UE 1 represented by a dotted line and UE 2 represented by a solid line. Of course, both UEs experience an increased rate under both the approximate and optimal NBS. Also, the difference between the optimal rates and the approximate rates is quite small. Finally, a notion of fairness is demonstrated in the bargained rates: when E[|/?_r3|²] is small, UE 1 is at a comparative disadvantage but experiences the greater increase in rates; conversely, when E[|/7₎₃|²] is large, UE 1 is at a comparative advantage and experiences the lesser rate increase. In Figure 5, the average relay power allocated by each UE in accordance with the approximate NBS given in Corollary 3 and the optimal NBS found via Theorem 2 is shown with UE 1 represented by a dotted line and UE 2 represented by a solid line. Again, the fairness is noted with the advantaged UE expending the greater energy in helping the disadvantaged UE. However, as shown in Figure 6, the advantaged UE is not over-burdened by bargaining. In Figure 6 the bits- per-joule utility of both players under single-user transmission (no cooperation), the approximate NBS given in Corollary 3, and the optimal NBS found via Theorem 2 is plotted with UE 1 represented by a dotted line and UE 2 represented by a solid line. As required by the NBS, both UEs obtain greater utility through bargaining than through non-cooperation. As in Figure 4, it is noted that the disadvantaged UE obtains the higher utility, but even the advantaged UE is benefited by bargaining.

Finally, in Figure 7 the square root of the Nash product in accordance with the approximate NBS given in Corollary 3 and the optimal NBS found via Theorem 2 is shown for a respective UE. The square root of the Nash product may be interpreted as the geometric average of the utility gains of the UEs over non-cooperation. Here, a small but discemable gap exists between the approximate and optimal NBS allocations. It is also noted that the increase in (geometric) average utility is highest when E[|/?₁₃|²] is roughly between OdB and 5dB. This suggests that there may be a "sweet spot" in channel statistics in which the NBS is most beneficial to the users. Of course, even in the extreme cases (when E[|ft₁₃|²] is high or low), UEs experience a noticeable increase in bits-per-joule utility.

In sum, and in accordance with the example embodiment of the present invention discussed above, two or more UEs may be in communication with a common base station 14, such as in accordance with time-division duplexing to eliminate inter-user interference. Cooperation is introduced by allowing the idle UE to relay the active UE's data in order to improve the achievable rate. Therefore, the UEs and base station form a three-terminal relay channel, with the UEs exchanging the roles of source and relay at each time block.

To capture the energy limitations of the UEs, each UE's utility function is expressed in terms of its bits-per-joule efficiency. Rather than trying to maximize only the achievable rate, UEs instead aim to improve the ratio of achievable rate and the rate of energy consumption. Under traditional non-cooperative game theory, however, the unique one-stage Nash equilibrium is for each UE to refuse to relay.

So, to facilitate cooperation, the scenario is modeled as an infinitely-repeated game. Here, UEs can reward other UEs who agree to cooperate and punish other UEs who deviate from the agreement, providing incentive even for self-interested UEs to cooperate. The cooperation levels may be defined by the Nash bargaining solution, which axiomatically defines a fair and efficient compromise between the UEs. In this regard, it is shown that the relay power allocations associated with the Nash bargain may be found through a series of convex optimization problems. The foregoing numerical results show that it is possible for both UEs to improve their bits-per-joule performance through bargaining. Each UE experiences increased rate but still allocates power conservatively. Furthermore, the Nash bargain provides a fair distribution of resources: weaker UEs benefit more from cooperation, while stronger UEs are not unduly burdened.

The power allocations described above may be determined by any one or more of a variety of devices. For example, the base station 14 or other network entity may be configured to determine the power allocations of each UE, e.g., UE1 and UE2, and may provide the power allocations to the respective UEs for facilitating subsequent cooperative communications involving the UEs. Alternatively, either or both of the UEs may be configured to determine the power allocations for itself and the other UE and may then provide the power allocations to the other UE.

By way of example, an apparatus 20, such as a base station 14 or UE, that may be configured to determine the power allocations of the UEs is depicted in Figure 8. The example apparatus 20 may include or may otherwise be in communication with a processor 22, a memory device 24, a communications interface 26, and power allocation determination circuitry 28. In some embodiments, the example apparatus 20 may optionally include, for example, when the apparatus 20 is embodied as a UE, a user interface 30.

The processor 22 may be embodied as various means implementing various functionality of example embodiments of the present invention including, for example, a microprocessor, a coprocessor, a controller, a special-purpose integrated circuit such as, for example, an ASIC (application specific integrated circuit), an FPGA (field programmable gate array), or a hardware accelerator, processing circuitry or the like. According to one example embodiment, processor 22 may be representative of a plurality of processors, or one or more multiple core processors, operating in concert. Further, the processor 22 may be comprised of a plurality of transistors, logic gates, a clock (e.g., oscillator), and the like to facilitate performance of the functionality described herein. The processor 22 may, but need not, include one or more accompanying digital signal processors. In some example embodiments, the processor 22 is configured to execute instructions stored in the memory device 24 or instructions otherwise accessible to the processor 22. The processor 22 may be configured to operate such that the processor causes the apparatus 20 to perform various functionalities described herein. Whether configured as hardware or via instructions stored on a computer-readable storage medium, or by a combination thereof, the processor 22 may be an entity capable of performing operations according to embodiments of the present invention while configured accordingly. Thus, in example embodiments where the processor 22 is embodied as an ASIC, FPGA, or the like, the processor 22 is specifically configured hardware for conducting the operations described herein. Alternatively, in example embodiments where the processor 22 is embodied as an executor of instructions stored on a computer-readable storage medium, the instructions specifically configure the processor 22 to perform the algorithms and operations described herein. In some example embodiments, the processor 22 is a processor of a specific device (e.g., a mobile terminal) configured for employing example embodiments of the present invention by further configuration of the processor 22 via executed instructions for performing the algorithms and operations described herein.

The memory device 24 may be one or more computer-readable storage media that may include volatile and/or non-volatile memory. In some example embodiments, the memory device 24 includes Random Access Memory (RAM) including dynamic and/or static RAM, on-chip or off- chip cache memory, and/or the like. Further, memory device 24 may include non-volatile memory, which may be embedded and/or removable, and may include, for example, read-only memory, flash memory, magnetic storage devices (e.g., hard disks, floppy disk drives, magnetic tape, etc.), optical disc drives and/or media, non-volatile random access memory (NVRAM), and/or the like. Memory device 24 may include a cache area for temporary storage of data. In this regard, some or all of memory device 24 may be included within the processor 22.

Further, the memory device 24 may be configured to store information, data, applications, computer-readable program code instructions, or the like for enabling the processor 22 and the example apparatus 20 to carry out various functions in accordance with example embodiments of the present invention described herein. For example, the memory device 24 could be configured to buffer input data for processing by the processor 22. Additionally, or alternatively, the memory device 24 may be configured to store instructions for execution by the processor 22.

The communication interface 26 may be any device or means embodied in either hardware, a computer program product, or a combination of hardware and a computer program product that is configured to receive and/or transmit data from/to a network 16 and/or any other device or module, such as a base station 14, access point or the like, in communication with the example apparatus 20. Processor 22 may also be configured to facilitate communications via the communications interface by, for example, controlling hardware included within the communications interface 26. In this regard, the communication interface 26 may include, for example, one or more antennas, a transmitter, a receiver, a transceiver and/or supporting hardware, including a processor for enabling communications with network 16. Via the communication interface 26 and the network 16, the example apparatus 20 may communicate with various other network entities in a device-to-device fashion and/or via indirect communications via a base station 14, access point, server, gateway, router, or the like.

The communications interface 26 may be configured to provide for communications in accordance with any wired or wireless communication standard. The communications interface 26 may be configured to support communications in multiple antenna environments, such as multiple input multiple output (MIMO) environments. Further, the communications interface 26 may be configured to support orthogonal frequency division multiplexed (OFDM) signaling. In some example embodiments, the communications interface 26 may be configured to communicate in accordance with various techniques, such as, second-generation (2G) wireless communication protocols IS-136 (time division multiple access (TDMA)), GSM (global system for mobile communication), IS-95 (code division multiple access (CDMA)), third-generation (3G) wireless communication protocols, such as Universal Mobile Telecommunications System (UMTS), CDMA200, wideband CDMA (WCDMA) and time division-synchronous CDMA (TD-SCDMA), 3.9 generation (3.9G) wireless communication protocols, such as Evolved Universal Terrestrial Radio Access Network (E-UTRAN), with fourth-generation (4G) wireless communication protocols, international mobile telecommunications advanced (IMT-Advanced) protocols, Long Term Evolution (LTE) protocols including LTE-advanced, or the like. Further, communications interface 26 may be configured to provide for communications in accordance with techniques such as, for example, radio frequency (RF), infrared (IrDA) or any of a number of different wireless networking techniques, including WLAN techniques such as IEEE 802.11 (e.g., 802.11a, 802.11 b, 802.11g, 802.11n, etc.), wireless local area network (WLAN) protocols, world interoperability for microwave access (WiMAX) techniques such as IEEE 802.16, and/or wireless Personal Area Network (WPAN) techniques such as IEEE 802.15, BlueTooth (BT), low power versions of BT, ultra wideband (UWB), Wibree, Zigbee and/or the like. The communications interface 26 may also be configured to support communications at the network layer, possibly via Internet Protocol (IP).

In embodiments of the apparatus 20 that include a user interface 30, such as a UE, the user interface 30 may be in communication with the processor 22 to receive user input via the user interface 30 and/or to present output to a user as, for example, audible, visual, mechanical or other output indications. In this regard, the processor 22 may comprise user interface circuitry configured to control at least some functions of one or more elements of the user interface 30. The processor 22 and/or user interface circuitry of the processor 22 may be configured to control one or more functions of one or more elements of the user interface 30 through computer program instructions (e.g., software and/or firmware, such as user interface software) stored on a memory accessible to the processor (e.g., volatile memory, non-volatile memory, and/or the like). The user interface 30 may include, for example, a keyboard, a mouse, a joystick, a display (e.g., a touch screen display), a microphone, a speaker, or other input/output mechanisms. In embodiments including a display, the display and the associated display circuitry may be configured to facilitate user control of at least some functions of the apparatus.

The power allocation determination circuitry 28 of example apparatus 20 may be any means or device embodied, partially or wholly, in hardware, a computer program product, or a combination of hardware and a computer program product, such as processor 22 implementing stored instructions to configure the example apparatus 20, or a hardware configured processor, that is configured to carry out the functions of the power allocation determination circuitry 28 as described herein. In an example embodiment, the processor 22 includes, or controls, the power allocation determination circuitry 28. The power allocation determination circuitry 28 may be, partially or wholly, embodied as processors similar to, but separate from processor 22. In this regard, the power allocation determination circuitry 28 may be in communication with the processor 22. In various example embodiments, the power allocation determination circuitry 28 may, partially or wholly, reside on differing apparatuses such that some or all of the functionality of the power allocation determination circuitry 28 may be performed by a first apparatus, and the remainder of the functionality of the power allocation determination circuitry 28 may be performed by one or more other apparatuses.

As described above and as shown in Figure 9, the power allocation determination circuitry 28 may be configured to utilize a bargaining solution to determine a power allocation for each of two or more devices, such as UEs. See operation 40, As described above, the power allocation determination circuitry may determine the power allocations in accordance with Theorem 2 and equation (25) with the resulting solution, such as the Nash bargaining solution, being optimized as shown, for example, in Figure 3. Alternatively, the power allocation determination circuitry may determine the power allocations in accordance with the approximation provided by Corollary 3 and equation (26). Once the power allocations have been determined and in instances in which the apparatus 20 that determines the power allocations is different than the device that is to relay communications signals in accordance with the power allocations, the power allocations (that is, a value defining the power allocation as opposed to a quantity of power itself) may be provided to at least one device as shown in operation 42 of Figure 9. For example, in embodiments in which a base station 14 or other network entity determines the power allocations, the network entity may advise each of the devices, such as UE 1 and UE 2, of their respective power allocations. Alternatively, in embodiments in which one of the client devices, such as one of the UEs, determines the power allocations, the power allocation need only be provided to the other client devices, such as the other UEs. In other embodiments, the same device that determines the power allocations then utilizes the determined power allocations to relay communications signals of another device in accordance therewith. For example, each UE may independently determine the power allocations and thereafter cooperate with one another by relaying communications signals of the other in accordance with the determined power allocations. As such, operation 42 of Figure 9 may be optional in that the power allocations that are determined need not be provided to other devices in at least some embodiments.

In operation and once the power allocations have been determined and provided to the UEs, the UEs may facilitate cooperation with each other by relaying the communications signals of the other UE by expending power in accordance with the power allocations in order to support cooperative communications. See operation 44 of Figure 9. Each UE may be embodied in a variety of devices including, for example, a desktop computer, laptop computer, mobile terminal, mobile computer, mobile phone, portable digital assistant (PDA), pagers, mobile communication device, game device, digital camera/camcorder, audio/video player, television device, radio receiver, digital video recorder, positioning device, any combination thereof, and/or the like configured to establish a radio connection with a base station 14, access point or the like. In an exemplary embodiment, the UE is embodied as a mobile terminal, such as that illustrated in Figure 10.

In this regard, Figure 10 illustrates a block diagram of a mobile terminal 50 representative of one embodiment of a UE in accordance with embodiments of the present invention. It should be understood, however, that the mobile terminal 50 illustrated and hereinafter described is merely illustrative of one type of UE that may implement and/or benefit from embodiments of the present invention and, therefore, should not be taken to limit the scope of the present invention. While certain embodiments of the UE are illustrated and will be hereinafter described for purposes of example, other types of UEs may employ embodiments of the present invention.

As shown, the mobile terminal 50 may include an antenna 52 (or multiple antennas 12) in communication with a transmitter 54 and a receiver 56. The mobile terminal may also include one or more processors 58 that provides signals to and receives signals from the transmitter and receiver, respectively. These signals may include signaling information in accordance with an air interface standard of an applicable cellular system, and/or any number of different wireline or wireless networking techniques, comprising but not limited to Wireless-Fidelity (Wi-Fi), wireless local access network (WLAN) techniques such as Institute of Electrical and Electronics Engineers (IEEE) 802.11 , 802.16, and/or the like. In addition, these signals may include speech data, user generated data, user requested data, and/or the like. In this regard, the mobile terminal may be capable of operating with one or more air interface standards, communication protocols, modulation types, access types, and/or the like. More particularly, the mobile terminal may be capable of operating in accordance with various first generation (1G), second generation (2G), 2.5G, third-generation (3G) communication protocols, fourth-generation (4G) communication protocols, Internet Protocol Multimedia Subsystem (IMS) communication protocols (e.g., session initiation protocol (SIP)), and/or the like. For example, the mobile terminal may be capable of operating in accordance with 2G wireless communication protocols IS-136 (Time Division Multiple Access (TDMA)), Global System for Mobile communications (GSM), IS-95 (Code Division Multiple Access (CDMA)), and/or the like. Also, for example, the mobile terminal may be capable of operating in accordance with 2.5G wireless communication protocols General Packet Radio Service (GPRS), Enhanced Data GSM Environment (EDGE), and/or the like. Further, for example, the mobile terminal may be capable of operating in accordance with 3G wireless communication protocols such as Universal Mobile Telecommunications System (UMTS), Code Division Multiple Access 200 (CDMA200), Wideband Code Division Multiple Access (WCDMA), Time Division-Synchronous Code Division Multiple Access (TD-SCDMA), and/or the like. The mobile terminal may be additionally capable of operating in accordance with 3.9G wireless communication protocols such as Long Term Evolution (LTE) or Evolved Universal Terrestrial Radio Access Network (E-UTRAN) and/or the like. Additionally, for example, the mobile terminal may be capable of operating in accordance with fourth-generation (4G) wireless communication protocols and/or the like as well as similar wireless communication protocols that may be developed in the future.

Some Narrow-band Advanced Mobile Phone System (NAMPS), as well as Total Access Communication System (TACS), mobile terminals may also benefit from embodiments of this invention, as should dual or higher mode phones (e.g., digital/analog or TDMA/CDMA/analog phones). Additionally, the mobile terminal 50 may be capable of operating according to Wireless Fidelity (Wi-Fi) or Worldwide Interoperability for Microwave Access (WiMAX) protocols.

It is understood that the processor 58 may comprise circuitry for implementing audio/video and logic functions of the mobile terminal 50. For example, the processor 58 may comprise a digital signal processor device, a microprocessor device, processing circuitry, an analog-to-digital converter, a digital-to-analog converter, and/or the like. Control and signal processing functions of the mobile terminal may be allocated between these devices according to their respective capabilities. The processor may additionally comprise an internal voice coder (VC) 58a, an internal data modem (DM) 58b, and/or the like. Further, the processor may comprise functionality to operate one or more software programs, which may be stored in memory. For example, the processor 58 may be capable of operating a connectivity program, such as a web browser. The connectivity program may allow the mobile terminal 50 to transmit and receive web content, such as location-based content, according to a protocol, such as Wireless Application Protocol (WAP), hypertext transfer protocol (HTTP), and/or the like. The mobile terminal 50 may be capable of using a Transmission Control Protocol/Internet Protocol (TCP/IP) to transmit and receive web content across the internet or other networks.

The mobile terminal 50 may also comprise a user interface including, for example, an earphone or speaker 60, a ringer 62, a microphone 64, a display 66, a user input interface, and/or the like, which may be operationally coupled to the processor 58. In this regard, the processor 58 may comprise user interface circuitry configured to control at least some functions of one or elements of the user interface, such as, for example, the speaker 60, the ringer 62, the microphone 64, the display 66, and/or the like. The processor 58 and/or user interface circuitry comprising the processor 58 may be configured to control one or more functions of one or more elements of the user interface through computer program instructions (e.g., software and/or firmware, such as user interface software) stored on a memory accessible to the processor 58 (e.g., volatile memory 68, non-volatile memory 70, and/or the like). Although not shown, the mobile terminal may comprise a battery for powering various circuits related to the mobile terminal, for example, a circuit to provide mechanical vibration as a detectable output. The user input interface may comprise devices allowing the mobile terminal to receive data, such as a keypad 72, a touch display (not shown), a joystick (not shown), and/or other input device. In embodiments including a keypad, the keypad may comprise numeric (0-9) and related keys (#, *), and/or other keys for operating the mobile terminal. In embodiments that include a display, the display and display circuitry may be configured to facilitate user control of at least some functions of the mobile terminal.

As shown in Figure 10, the mobile terminal 50 may also include one or more means for sharing and/or obtaining data. For example, the mobile terminal may comprise a short-range radio frequency (RF) transceiver and/or interrogator 74 so data may be shared with and/or obtained from electronic devices in accordance with RF techniques. The mobile terminal may comprise other short-range transceivers, such as, for example, an infrared (IR) transceiver 76, a Bluetooth™ (BT) transceiver 78 operating using Bluetooth™ brand wireless technology developed by the Bluetooth™ Special Interest Group, a wireless universal serial bus (USB) transceiver 80 and/or the like. The Bluetooth™ transceiver 78 may be capable of operating according to ultra-low power Bluetooth™ technology (e.g., Wibree™) radio standards. In this regard, the mobile terminal 50 and, in particular, the short-range transceiver may be capable of transmitting data to and/or receiving data from electronic devices within a proximity of the mobile terminal, such as within 10 meters, for example. Although not shown, the mobile terminal may be capable of transmitting and/or receiving data from electronic devices according to various wireless networking techniques, including Wireless Fidelity (Wi-Fi), WLAN techniques such as IEEE 802.11 techniques, IEEE 802.16 techniques, and/or the like.

The mobile terminal 50 may comprise memory, such as a subscriber identity module (SIM) 82, a removable user identity module (R-UIM), and/or the like, which may store information elements related to a mobile subscriber. In addition to the SIM, the mobile terminal may comprise other removable and/or fixed memory. The mobile terminal 50 may include volatile memory 68 and/or non-volatile memory 70. For example, volatile memory 68 may include Random Access Memory (RAM) including dynamic and/or static RAM, on-chip or off-chip cache memory, and/or the like. Non-volatile memory 70, which may be embedded and/or removable, may include, for example, read-only memory, flash memory, magnetic storage devices (e.g., hard disks, floppy disk drives, magnetic tape, etc.), optical disc drives and/or media, non-volatile random access memory (NVRAM), and/or the like. Like volatile memory 68, non-volatile memory 70 may include a cache area for temporary storage of data. The memories may store one or more software programs, instructions, pieces of information, data, and/or the like which may be used by the mobile terminal for performing functions of the mobile terminal. For example, the memories may comprise an identifier, such as an international mobile equipment identification (IMEI) code, capable of uniquely identifying the mobile terminal 50.

As described above and as shown in Figure 11, the UE and, more particularly, the processor 58 may be configured to access the respective power allocation that has previously been determined and provided to the UE, at least in instances in which the power allocation was determined by another device, such as a base station 14 or other network entity or another UE. See operation 90. Thereafter, the processor may direct that communications signals of another UE be relayed, such as to a base station, with the power of the relayed signals being defined in accordance with the power allocation. See operation 92. For example, the processor may direct that the communications signals of the other UE be relayed at a power level equal to the power allocation. As indicated by operation 94, the processor may also rely upon the other UE to relay communications signals that have been transmitted by the UE, such as under the direction and/or control of the processor, with the other UE correspondingly relaying the communications signals at a power level in accordance with, e.g., equal to, a respective power allocation. As such, the UEs may engage in cooperative communications with the respective power allocations defined in such a manner that each UE benefits not only from the increased reliability of communications with the base station, access point or the like, but also due to a reduction in battery power consumption attributable, for example, to a reduction in the number of communications signals that much be retransmitted to a base station, access point or the like in comparison to more conventional communications techniques.

As described above, Figures 9 and 11 illustrate flowcharts of example systems, methods, and/or computer program products according to example embodiments of the invention. It will be understood that each block or operation of the flowcharts, and/or combinations of blocks or operations in the flowcharts, can be implemented by various means. Means for implementing the blocks or operations of the flowcharts, combinations of the blocks or operations in the flowchart, or other functionality of example embodiments of the present invention described herein may include hardware, and/or a computer program product including a computer-readable storage medium having one or more computer program code instructions, program instructions, or executable computer-readable program code instructions stored therein. In this regard, program code instructions may be stored on a memory device, such as memory devices 24, 68 or 70, of an example apparatus, such as example apparatus 20 or 50, and executed by a processor, such as the processor 22 or 58, and/or the power allocation determination circuitry 28. As will be appreciated, any such program code instructions may be loaded onto a computer or other programmable apparatus (e.g., processor 22, memory device 24, power allocation determination circuitry 28, processor 58, memory devices 68 or 70) from a computer-readable storage medium to produce a particular machine, such that the particular machine becomes a means for implementing the functions specified in the flowcharts' block(s) or operation(s). These program code instructions may also be stored in a computer-readable storage medium that can direct a computer, a processor, or other programmable apparatus to function in a particular manner to thereby generate a particular machine or particular article of manufacture. The instructions stored in the computer-readable storage medium may produce an article of manufacture, where the article of manufacture becomes a means for implementing the functions specified in the flowcharts' block(s) or operation(s). The program code instructions may be retrieved from a computer- readable storage medium and loaded into a computer, processor, or other programmable apparatus to configure the computer, processor, or other programmable apparatus to execute operations to be performed on or by the computer, processor, or other programmable apparatus. Retrieval, loading, and execution of the program code instructions may be performed sequentially such that one instruction is retrieved, loaded, and executed at a time. In some example embodiments, retrieval, loading and/or execution may be performed in parallel such that multiple instructions are retrieved, loaded, and/or executed together. Execution of the program code instructions may produce a computer-implemented process such that the instructions executed by the computer, processor, or other programmable apparatus provide operations for implementing the functions specified in the flowcharts' block(s) or operation(s).

Accordingly, execution of instructions associated with the blocks or operations of the flowchart by a processor, or storage of instructions associated with the blocks or operations of the flowcharts in a computer-readable storage medium, support combinations of operations for performing the specified functions. It will also be understood that one or more blocks or operations of the flowcharts, and combinations of blocks or operations in the flowcharts, may be implemented by special purpose hardware-based computer systems and/or processors which perform the specified functions, or combinations of special purpose hardware and program code instructions.

Many modifications and other embodiments of the inventions set forth herein will come to mind to one skilled in the art to which these inventions pertain having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. Therefore, it is to be understood that the inventions are not to be limited to the specific embodiments disclosed and that modifications and other embodiments are intended to be included within the scope of the appended claims. For example, although at least some of the foregoing examples were in the context of memoryless power allocations, other embodiments of the present invention may, instead, cast the game as a dynamic programming problem so as to permit causal power allocations to be determined that may depend on previous actions. Additionally, other embodiments of the present invention may determine power allocations in instances in which the channel state information is unknown and/or in instances that rely upon a different channel model. Further, although at least some of the foregoing examples assumed that the UEs utilized full power for its own transmissions, other embodiments need not make this same assumption. Still further, other embodiments of the present invention may define the utilities in terms of outage probability instead of achievable rate as described above.

Moreover, although the foregoing descriptions and the associated drawings describe example embodiments in the context of certain example combinations of elements and/or functions, it should be appreciated that different combinations of elements and/or functions may be provided by alternative embodiments without departing from the scope of the appended claims. In this regard, for example, different combinations of elements and/or functions other than those explicitly described above are also contemplated as may be set forth in some of the appended claims. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.

Claims

THAT WHICH IS CLAIMED:

1. A method comprising: determining a power allocation of a respective device to be utilized to relay communications signals of another device, wherein determining the power allocation comprises utilizing a bargaining solution in order to determine the power allocation; and facilitate cooperation with the other device to relay the communications signals of the other device by expending power in accordance with the power allocation.

2. A method according to Claim 1 wherein utilizing a bargaining solution comprises utilizing a Nash bargaining solution.

3. A method according to Claim 2 wherein utilizing a Nash bargaining solution comprises determining the power allocation based upon a utility of each device as defined by a total amount of data transmitted by a respective device in proportion to the total energy expended for transmission of the data.

4. A method according to Claim 3 wherein determining the power allocation based upon the utility of each device comprises determining the power allocation based upon a product of the utility of each device and a respective disagreement point.

5. A method according to Claim 4 wherein the disagreement point of a respective device comprises a long-term non-cooperative payoff of the respective device.

6. A method according to Claim 1 wherein determining the power allocation comprises determining a different power allocation for each device.

7. An apparatus comprising: at least one processor; and at least one memory including computer program code, the at least one memory and the computer program code configured to, with the at least one processor, cause the apparatus at least to perform: determine a power allocation of a respective device to be utilized to relay communications signals of another device by utilizing a bargaining solution in order to determine the power allocation; and facilitate cooperation with the other device to relay the communications signals of the other device by expending power in accordance with the power allocation.

8. An apparatus according to Claim 7 wherein the at least one memory and the computer program code are configured to, with the at least one processor, cause the apparatus to determine the power allocation by utilizing a Nash bargaining solution.

9. An apparatus according to Claim 8 wherein the at least one memory and the computer program code are configured to, with the at least one processor, cause the apparatus to utilize a Nash bargaining solution by determining the power allocation based upon a utility of each device as defined by a total amount of data transmitted by a respective device in proportion to the total energy expended for transmission of the data.

10. An apparatus according to Claim 9 wherein the at least one memory and the computer program code are configured to, with the at least one processor, cause the apparatus to determine the power allocation based upon the utility of each device by determining the power allocation based upon a product of the utility of each device and a respective disagreement point.

11. An apparatus according to Claim 10 wherein the disagreement point of a respective device comprises a long-term non-cooperative payoff of the respective device.

12. An apparatus according to Claim 7 wherein the at least one memory and the computer program code are configured to, with the at least one processor, cause the apparatus to determine the power allocation by determining a different power allocation for each device.

13. An apparatus according to Claim 7 wherein the apparatus is a mobile phone further comprising user interface circuitry and user interface software configured to facilitate user control of at least some functions of the mobile phone through use of a display and configured to display at least a portion of a user interface of the mobile phone, the display and display circuitry configured to facilitate user control of at least some functions of the mobile phone.

14. A computer program product comprising at least one computer-readable storage medium having computer-readable program instructions stored therein, the computer-readable program instructions configured to cause an apparatus at least to perform: determining a power allocation of a respective device to be utilized to relay communications signals of another device, wherein determining the power allocation comprises utilizing a bargaining solution in order to determine the power allocation; and facilitate cooperation with the other device to relay the communications signals of the other device by expending power in accordance with the power allocation.

15. A computer program product according to Claim 14 wherein the computer-readable program instructions are further configured to cause the apparatus to utilize a bargaining solution by utilizing a Nash bargaining solution.

16. A computer program product according to Claim 15 wherein the computer-readable program instructions are further configured to cause the apparatus to utilize a Nash bargaining solution by determining the power allocation based upon a utility of each device as defined by a total amount of data transmitted by a respective device in proportion to the total energy expended for transmission of the data.

17. A computer program product according to Claim 16 wherein the computer-readable program instructions are further configured to cause the apparatus to determine the power allocation based upon the utility of each device by determining the power allocation based upon a product of the utility of each device and a respective disagreement point.

18. A computer program product according to Claim 17 wherein the disagreement point of a respective device comprises a long-term non-cooperative payoff of the respective device.

19. A computer program product according to Claim 14 wherein the computer-readable program instructions are further configured to cause the apparatus to determine the power allocation by determining a different power allocation for each device.

20. A method comprising: accessing a power allocation to be utilized to relay communication signals of another device, wherein the power allocation is determined in accordance with a bargaining solution; and facilitating cooperation with the other device to relay the communications signals of the other device by expending power in accordance with the power allocation.

21. A method according to Claim 20 further comprising relying upon cooperation by the other device to relay the communications signals transmitted by the respective device.

22. A method according to Claim 20 wherein facilitating cooperation with the other device comprises relaying the communications signals of the other device to a base station.

23. A method according to Claim 20 wherein the power allocation is determined in accordance with a Nash bargaining solution.

24. An apparatus comprising: at least one processor; and at least one memory including computer program code, the at least one memory and the computer program code configured to, with the at least one processor, cause the apparatus at least to perform: access a power allocation to be utilized to relay communication signals of another device, wherein the power allocation is determined in accordance with a bargaining solution; and facilitate cooperation with the other device to relay the communications signals of the other device by expending power in accordance with the power allocation.

25. An apparatus according to Claim 24 wherein the at least one memory and the computer program code are configured to, with the at least one processor, cause the apparatus to rely upon cooperation by the other device to relay the communications signals transmitted by the respective device.

26. An apparatus according to Claim 24 wherein the at least one memory and the computer program code are configured to, with the at least one processor, cause the apparatus to facilitate cooperation with the other device by relaying the communications signals of the other device to a base station.

27. An apparatus according to Claim 24 wherein the power allocation is determined in accordance with a Nash bargaining solution.

28. An apparatus according to Claim 24 wherein the apparatus is a mobile phone further comprising user interface circuitry and user interface software configured to facilitate user control of at least some functions of the mobile phone through use of a display and configured to display at least a portion of a user interface of the mobile phone, the display and display circuitry configured to facilitate user control of at least some functions of the mobile phone.

29. A computer program product comprising at least one computer-readable storage medium having computer-readable program instructions stored therein, the computer-readable program instructions configured to cause an apparatus at least to perform: accessing a power allocation to be utilized to relay communication signals of another device, wherein the power allocation is determined in accordance with a bargaining solution; and facilitate cooperation with the other device to relay the communications signals of the other device by expending power in accordance with the power allocation.

30. A computer program product according to Claim 29 wherein the computer-readable program instructions are further configured to cause the apparatus to rely upon cooperation by the other device to relay the communications signals transmitted by the respective device.

31. A computer program product according to Claim 29 wherein the computer-readable program instructions are further configured to cause the apparatus to facilitate cooperation with the other device by relaying the communications signals of the other device to a base station.

32. A computer program product according to Claim 29 wherein the power allocation is determined in accordance with a Nash bargaining solution.