TRANSMISSION RESOURCE FOR MOBILE STATIONS AND METHOD AND APPARATUS FOR PROVIDING INFORMATION THEREFOR

FIELD OF THE INVENTION [0001] Embodiments of the present invention generally relate to the field of a wireless network technology, and more particularly, relate to a method and apparatus for determining feedback transmission resource for mobile stations based on game theory and a method and apparatus for providing information at a mobile station for determining feedback transmission resource for mobile stations.

BACKGROUND OF THE INVENTION

[0002] It has been well recognized that the channel state information (CSI) is of great importance for the downlink transmission of closed-loop wireless networks. The CSI can be sent to the transmitter side through a feedback channel, which may affect the closed-loop capacity gains. With the knowledge of the wireless channel conditions, it is possible for the transmitter to adapt to the propagation conditions by use of a variety of channel adaptive techniques. Particularly, in a multiple mobile station (MS) scenario, with the knowledge of the channel to nearby co-channels MSs, it is possible to actively suppress the signal to the interfered users and maximize the effective signal power. In this case, the base station (BS) can obtain the required channel coefficients through a feedback channel from the MSs and then employ mechanisms such as multiple-antenna pre-coding to mitigate the effects of the interferences and to exploit spatial dimensions to increase the capacity of the wireless network.

[0003] However, the feedback channel has a limited capacity and thus it is important to investigate how to control the amount of the feedback overhead according to the individual requirements so as to improve quality of service (Qos) and preserve fairness among the MSs. Many studies have been made on the above problems, but a perfect feedback of CSI is typically unavailable due to complexity or practicality constraints and thus the infinite feedback of CSI is hard to realize in practice. Additionally, in the existing wireless network, it typically treated each MS independently and researched the multi-MS CSI problem in physical layer for example from the point of view of either communication theory or information theory, which means that interactions among the MSs are not taken into account. Therefore, in the prior art, it cannot efficiently model interactions among self-interested mobile users in wireless system. Moreover, in case that the feedback channel is limited, there will exist conflicts in effective CSI feedback-rates between respective MSs, that is to say, if one MS transmits too much CSI, it will result in reduction of CSI feedback amounts of other MSs and thus will degrade other MSs' performance.

[0004] Hence, it will be desirable in the art to find a solution tackling the competition problem and having a balance in the multi-MS feedback scenario and further achieving a better QoS.

SUMMARY OF THE INVENTION

[0005] In view of the foregoing, the present invention provides a new feedback transmission resource control solution for mobile stations so as to solve or at least partially mitigate at least part of problems in the prior art.

[0006] According to an aspect of the present invention, there is provided a method for determining feedback transmission resource for mobile stations based on game theory, wherein a game utility for each of the mobile stations at any price factor for feedback transmission resource is optimized in a distributed way under the feedback transmission resource constrain. The method can comprise searching a best price factor at which the game utility for each of the mobile stations has a maximum value; and determining a value of the feedback transmission resource corresponding to the best price factor as the feedback transmission resource for each of the mobile stations.

[0007] In an embodiment of the present invention, searching the best price factor can comprise performing the following operations repeatedly until the best price factor is found: sending a price factor for feedback transmission resource to the mobile stations; receiving the game utility at the price factor for at least one of the mobile stations; and determining the price factor as the best price factor if the game utility at the price factor is the maximum value, or adjusting the price factor if the game utility at the price factor is not the maximum value.

[0008] In another embodiment of the present invention, adjusting the price factor can comprise increasing the price factor by a fixed amount.

[0009] In a further embodiment of the present invention, the price factor can have an initial value of zero.

[0010] In a yet further embodiment of the present invention, the game utility at the price factor for a mobile station can be performance gain obtained through using the feedback transmission resource by the mobile station minus the cost paid therefor at the price factor.

[0011] In a still further embodiment of the present invention, the performance gain obtained can be determined based on the feedback transmission resource used by the mobile station and historical determined feedback transmission resource of other mobile stations.

[0012] In a still yet further embodiment of the present invention, the cost paid is a linear function of the feedback transmission resource used by the mobile station.

[0013] In another embodiment of the present invention, it can be determined that the game utility at the price factor is the maximum value if the game utility at the price factor is greater than a game utility at a price factor increased subsequently.

[0014] In a further embodiment of the present invention, the method can further comprise receiving values of feedback transmission resource corresponding to the price factor from respective mobile stations; and sending the received values of feedback transmission resource to each of the mobile stations.

[0015] In a yet further embodiment of the present invention, the feedback transmission resource can comprise any one of feedback rate and feedback bandwidth.

[0016] According to another aspect of the present invention, there is also provided a method for providing information at a mobile station for determining feedback transmission resource. The method can comprise receiving a price factor for feedback transmission source; determining the game utility at the price factor for the mobile station such that the game utility is optimized in a distributed way under the feedback transmission resource constrain; and sending the determined game utility at the price factor for the mobile station to a base station for using in determining feedback transmission resource.

[0017] In an embodiment of the present invention, the game utility at the price factor for the mobile station is the performance gain obtained through using the feedback transmission resource by the mobile station minus the cost paid therefor at the price factor.

[0018] In another embodiment of the present invention, the cost paid is a linear function of the feedback transmission resource used by the mobile station.

[0019] In a further embodiment of the present invention, the method can further comprise receiving values of historical transmission resource of other mobile stations, wherein the performance gain obtained is determined based on the feedback transmission resource used by the mobile station and the received values of historical transmission resource of other mobile stations; sending the value of feedback transmission resource corresponding to the determined game utility to the base station or other mobile stations.

[0020] According to a further aspect of the present invention, there is provided an apparatus for determining feedback transmission resource for mobile stations based on game theory, wherein a game utility for each of the mobile stations at any price factor for feedback transmission resource is optimized in a distributed way under the feedback transmission resource constrain. The apparatus can comprise: best factor searching unit for searching a best price factor at which the game utility for each of the mobile stations has a maximum value; and resource value determination unit for determining a value of the feedback transmission resource corresponding to the best price factor as the feedback transmission resource for each of the mobile stations.

[0021] According to a still further aspect of the present invention, there is provided an apparatus for providing information at a mobile station for determining feedback transmission resource. The apparatus can comprise price factor receiving unit for receiving a price factor for feedback transmission source; game utility determination unit for determining the game utility at the price factor for the mobile station such that the game utility is optimized in a distributed way under the feedback transmission resource constrain; and game utility sending unit for sending the determined game utility at the price factor for the mobile station to a base station for using in determining feedback transmission resource.

[0022] With embodiments of the present invention, each mobile station will maximize its performance in a distributed way and a best price factor can be found to achieve the Nash equilibrium, therefore it can result in close optimal performance compared with that of the centralized scheme and thus improve the overall throughout of wireless data network. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The above and other features of the present invention will become more apparent through detailed explanation on the embodiments as illustrated in the embodiments with reference to the accompanying drawings throughout which like reference numbers represent same or similar components and wherein:

[0024] Fig. 1 schematically illustrates a diagram of system wherein embodiments of the present invention can be implemented;

[0025] Fig. 2 schematically illustrates a flow chart of a method for determining feedback transmission resource for mobile stations based on game theory according to an embodiment of the present invention;

[0026] Fig. 3 schematically illustrates a flow chart of an exemplary approach for searching a best price factor according to an embodiment of the present invention;

[0027] Fig. 4 schematically illustrates a flow chart of a method for providing information at a mobile station for determining feedback transmission resource for mobile stations according to an embodiment of the present invention;

[0028] Figs 5 A to 5H illustrate graphs of simulation results of embodiments of the present application;

[0029] Fig. 6A illustrates a block diagram of an apparatus for determining feedback transmission resource for mobile stations based on game theory according to an embodiment of the present invention;

[0030] Fig. 6B illustrates a block diagram of a best factor searching unit for searching the best price factor according to an embodiment of the present invention;

[0031] Fig. 6C illustrates a block diagram of an apparatus for determining feedback transmission resource for mobile stations based on game theory according to another embodiment of the present invention; and

[0032] Fig. 7 illustrates a block diagram of an apparatus for providing information at a mobile station for determining feedback transmission resource for mobile stations according to an embodiment of the present invention. DETAILED DESCRIPTION OF EMBODIMENTS

[0033] Hereinafter, a method and apparatus for determining feedback transmission resource for mobile stations based on game theory and a method and apparatus for providing information at a mobile station for determining feedback transmission resource for mobile stations will be described in detail through embodiments with reference to the accompanying drawings. It should be appreciated that these embodiments are presented only to enable those skilled in the art to better understand and implement the present invention, not intend to limit the scope of the present invention in any manner.

[0034] It should be first noted that this invention is illustrated in particular sequences for performing the steps of the methods. However, these methods are not necessarily performed strictly according to the illustrated sequences, and they can be performed in reverse sequence or simultaneously based on natures of respective method steps. Beside, the indefinite article "a/an" as used herein does not exclude a plurality of such steps, units, devices, and objects, and etc.

[0035] Additionally, in the present invention, [.] ^T denotes transpose of a vector or matrix; [.] ^H denotes a conjugate transpose of a vector or matrix; [.]* denotes a conjugate of a vector or matrix; ||x|| denotes x x; and Var[x] represents the variance of x.

[0036] Before specifically describing embodiments of the present mvention, the system model or the architecture of a system in which the present invention can be implemented will be firstly described with reference to Fig. 1. As illustrated in Fig. 1 , in the system, a number of co-channel MSs are served by one BS. The BS is assumed to know the linear processing performed by the MSs, and in such a way the BS can acquire the required CSI through a feedback channel from the MSs. By using multiple antennas at the BS of a cellular system, it can perform transmit precoding for simultaneous transmission to several co-channel mobile users. The precoder is designed in assuming a stationary scenario in which the fast (Rayleigh) fading is described by its second order properties. Additionally it also assumes narrow-band signals without anytime dispersion, i.e., the channel fading is frequency flat. Hereinafter, for the purpose of simplicity, it also is assumed that the system is equipped with a single receive antenna, but it should be appreciated that the present invention is not limited thereto.

[0037] The illustrated system works in a FDD model where the BS has N _t transmit antennas serving N _s MSs simultaneously in the same frequency band, while each MS feeds back the CSI through different channels in order to better protect the control information by avoiding collisions.

[0038] For the k-th MS, the input signal, Λ¼ is first precoded by complex weights = ^e C ^N ' ^xl before transmitted from the N _t transmit antennas at the BS. The corresponding output after precoding can be written as

S* =WhX _k ; (1) where Sk £ C^'" ¹ . Accordingly, the received signals at the k-th MS, k can be then expressed as

Ns

Ns

+ n ,

(2)

Ns

= ^{h W} k ^X k ^{+ h} k ^T Σ ^W i ^X / ^{+ n} *

i=I,i≠k where h _k = [h _ljk ,■ · ·, h.M,k ] ^{T e} c"' ^*7 represents the channel coefficients from the BS to the Ar-th MS with a zero mean and a unit variance; n* is the AWGN noise CN 0,No _; );

Ns

h _k ^T w"x _k is the desired signal; and h _k ^T ^ wf _j can be treated as the interference. It should be noted that the model can be easily extended to frequency selective channels, by taking both co-channel interference and inter-symbol interference into account.

[0039] In studying the aforesaid system and the solutions which can solve or at least partially mitigate at least a part of problems in this system, the present inventors conceive game theory. Game theory is a mathematical method for analyzing calculated circumstances (games) where a person's success is based upon the choices of others. Such a theory offers a set of mathematical tools to study the complex interactions among interdependent rational players and to predict their choices of strategies. In the present invention, the inventors propose a solution for feedback transmission resource control in the wireless system based on a micro economics model.

In this model, each MS's preference is represented by a game utility function which qualifies the level of satisfaction a user gets from using the system resource. Each MS (or called as player) in the game will maximize the utility function in a distributed fashion. The game settles at Nash equilibrium if one exists. Since users act selfishly, the equilibrium point is not necessarily the best operating from the social point of view.

Therefore, the present inventors further introduce pricing to create cooperation between respective MSs to improve efficiency. The utility function, which every MS in the game tries to maximize, is defined as performance gain obtained by CSI feedback minus the paid cost paid by the mobile station therefor which is preferably a linear function of the CSI feed back transmission resource used by the mobile station.

[0040] Next, reference will be made to Fig. 2 to describe the method for determining feedback transmission resource as provided in the present invention at length. Fig. 2 schematically illustrates a flow chart of a method for determining feedback transmission resource for mobile stations based on game theory according to an embodiment of the present invention.

[0041] As illustrated in Fig. 2, first at step S201, the BS will search a best price factor at which the game utility for each of the mobile stations has a maximum value. In the game, each of the mobile stations will optimize/maximize its individual game utility at any price factor in a distributed way under the feedback transmission resource constrain.

[0042] As mentioned hereinbefore, in embodiments of the present invention, there is introduced a pricing mechanism and the game utility function is defined as performance gain obtained by CSI feedback transmission resource minus the paid cost therefor. Particularly, it introduces a price factor for feedback transmission resource so as to determine the cost paid by a mobile station for the feedback transmission resource such as feedback rate, feedback bandwidth and etc.

[0043] In an embodiment of the present invention, the performance gain obtained by a mobile station is determined based on the used transmission resource by the mobile station and historical transmission resource of other mobile stations. That is to say, each mobile station does not know the selection of other mobile station at the present price factor but it can know the historical transmission resource of other mobile stations, and thus the performance gain for a mobile station is dependent on not only the used transmission resource by the mobile station but also the historically determined transmission resource of other mobile stations. Additionally, the cost paid by the mobile station can be a linear function of the used feedback transmission resource, for example, p _k (rk)=ark, wherein pk denotes the cost paid by the k-th mobile station, ¾ denotes the feedback transmission resource used by the k-th mobile station, and a denotes the price factor per unit feedback transmission resource.

[0044] It has been investigated that in the proposed games, there is a Nash equilibrium at which no player can improve its own utility by changing its own strategy only. By searching a best price factor at which the game utility for each of the mobile stations has a maximum value, the Nash equilibrium point of the game can be found. Hereinbelow, reference will be made to Fig. 3 to describe an exemplary approach about how to find the best price factor according to an embodiment of the present invention.

[0045] As illustrated in Fig. 3, first at step 301 , the BS will send a price factor for feedback transmission resource to the mobile stations, for example through the control channel such as PDCCH, and etc. After the price factor is sent to the mobile stations, each of the mobile stations will determine the value of the feedback transmission resource under the condition that the game utility at the price factor for the mobile station is maximized with the feedback transmission resource constrain. That process is a optimization process during which the maximum game utility and the corresponding value of the feedback transmission resource will be determined. The details about the determination of the feedback transmission resource value will be described at length hereinafter with reference to the operations of the mobile stations illustrated in for example Fig. 4, which will not be elaborated herein for the purpose of simplify.

[0046] Then BS will receive the game utility at the price factor from respective mobile stations at step S302. Due to the fact that it has been proved that at the best price factor, the game utility for each of the mobile stations will have a maximum value, it is sufficient to receive the game utility at the price factor form at least one of the mobiles stations.

[0047] After that, at Step S303 it can be determined whether the game utility at the price factor is the maximum value. It can be proved that the game utility will have a maximum value at which Nash equilibrium of the proposed game is reached. If the game utility at the price factor is the maximum value of the game utility function, the price factor will be the best price factor mentioned above and thus it can determine the price factor as the best price factor at step S304 and the process ends. On the other hand, if the game utility at the price factor is not the maximum value, the price factor should be adjusted at step S305 and the process returns to step S301 to continue the searching process.

[0048] Therefore, actually, the searching process is a process for searching a maximum value of the game utility function by adjusting the price factor and it can be implemented by various suitable approaches. For the purpose of illustration, an exemplary embodiment is given to explain the searching process.

[0049] In the exemplary embodiment, the price factor sent to the mobile stations is a price factor per unit feedback transmission resource which will be increased by for example a fixed amount Δ at each time. However, the skilled in the art can be appreciated that the price factor can also be increased in any other suitable manner instead of a constant value or even can be or decreased in any suitable way. The value Δ in the embodiment can be selected appropriately, generally speaking, a small Δα will have a high accuracy but will bring out a large amount of computations which will require more system source, and a large Δα will bring an adverse affect on accuracy of the found Nash equilibrium point but need less amount of computations. The price factor can have an initial value (i.e., the first value sent to the mobile stations) of for example 0, but the skilled in the art can appreciate that any other initial value instead of zero may also be possible. In such a case, it will be determined that the game utility at the price factor is the maximum value if the game utility at the price factor is greater than a game utility at a price factor increased subsequently. However, it should be noted that the present invention is not limited thereto, it can also use any other approaches which can be applied to find the maximum value of a function.

[0050] Referring back to Fig. 2, subsequently, at step S202, the BS will determine a value of the feedback transmission resource corresponding to the best price factor as the feedback transmission resource for each of the mobile stations.

[0051 ] The value of the feedback transmission resource corresponding to the best price factor is feedback transmission resource value at which the Nash equilibrium is achieved. If each mobile station transmits the feedback information using the feedback transmission resource at which the Nash equilibrium is achieved, each mobile station will obtain a better performance.

[0052] In this step, the BS can inform each mobile station of the determined value of the feedback transmission resource by notifying each mobile station of the best price factor, and in such a case, each mobile station will search the value of the feedback transmission resource corresponding to the best price factor. Alternatively, in case that the mobile stations send their respective feedback transmission resource values at the corresponding price factor to the BS, the BS can directly transmit the values of the feedback transmission resource corresponding to the best price factor to the mobile station via a unicast or broadcast message to inform them of the determined feedback transmission resource values.

[0053] In another embodiment of the present invention, the method further receives values of feedback transmission resource corresponding to the price factor from respective mobile stations and sends the received values of feedback transmission resource to each of the mobile stations. As mentioned hereinabove, each mobile station will determine the game utility at the price factor based on not only the used transmission resource by the mobile station but also the historically determined transmission resource of other mobile stations. The historically determined transmission resource can be the transmission resource values which are determined for the previous price factor. Additionally, the process of determining the game utility at a price factor is a solving process for the optimization problem, when the problem is solved, the optimized game utility and the transmission resource values are also determined. Therefore, each mobile station can send their determined transmission resource values to the BS for example together with the game utility so that the BS can collect values of feedback transmission resource from all the mobile stations. Then the collected of feedback transmission resource values can be sent to each of the mobile stations so as to determine the game utility at a new price factor. However, the mobile stations can also transmit their determined transmission resource values directly to other mobile stations.

[0054] Through the process described above, the BS can determine the optimum feedback transmission resource value for the mobile stations and notify them of their respective feedback transmission resource value finally determined. By using the determined feedback transmission resource value to transmit feedback information, it is possible to achieve a close optimal performance and improve the overall throughout of wireless data network.

[0055] Hereinafter, reference will further made to Fig. 4 to describe a method for providing information at a mobile station for determining feedback transmission resource for mobile stations according to an embodiment of the present invention.

[0056] As illustrated in Fig. 4, first at step S401, the mobile station will receive the price factor for feedback transmission resource which is transmitted from the BS.

[0057] After receiving the price factor, the mobile station will determine the game utility at the price factor at step S402 such that the game utility is optimized under the feedback transmission resource constrain.

[0058] As is known, the game utility is a concept commonly used in microeconomics and refers to the level of satisfaction the decision- taker receives as a result of its actions. In the present invention, the game utility at a price factor for k-th mobile station can be defined as the performance gain obtained through using the feedback transmission resource by the mobile station minus the cost paid therefor at the price factor, which can be expressed by for example the following equation:

u _k ( ^r k » ^r -k) ^{=s C} t (?'k) - Pki ^r k) (3) wherein ¾ denotes the game utility value with the feedback rate ¾ C _k ( Y _k ) denotes the performance gains (particularly the throughput) through transmitting the feedback information at the feedback rate Y _k denotes the SINR of the k-th MS and p _k (i ^* k) denotes the cost paid for the feedback rate at a price factor. Particularly, the cost paid for the feedback rate at a price factor can be a linear function of the feedback transmission resource, i.e., _k (¾) ⁼ α¾, where a is the price factor per unit feedback transmission resource (e.g. transmission bandwidth) received by the mobile station at step 401.

[0059] Based on the above game utility function, the proposed game i.e., non-cooperative feedback control game with price (NFCP), can be modeled for example as follows:

(NFCP) ma u£ (r _k , r _k ) = max ( C _k (yJ - ar _k ) , Vk e ^ (4)

r _k R _k r„eR _t

i.e., for a given price factor, each mobile station will select ¾ under the feedback resource constrain so that the game utility is maximized. Additionally, it should be note that when a=0, the proposed game can be equivalent as non-cooperative feedback control game (NFC) which does not take the pricing into account compared to the NFCP game.

[0060] Actually, the calculation of the throughput C _k ( Y _k ) in the above equation (4) is known in the art, but for the purpose of explanation and completeness, an example of calculation of C _k ( Y _k ) will be described hereinafter.

[0061] First, it has been known that the throughput C _k ( V _k ) can be expressed as follows

Ck( Y k) =B _DL log ₂ (l + _lt (r _!: » r _k )) (5) wherein BDL is the downlink width; _k (r _k , r _k ) is the signal to noise plus interference ratio (SINR) of the k-th mobile station at the feedback resource level r _k selected by the k-th mobile station and the other user's the feedback resource level selection r. than the k-th mobile station. As mentioned hereinbefore, the other mobile stations' feedback resource level selection r. _k can be the historical feedback transmission resource value. Additionally, as mentioned hereinbefore, the received signals at the k-th MS y^ can be expressed by equation (2) and accordingly, the SINR y _k of the k-th mobile station can be written as can be written as

[0062] Therefore, to determine SINR it needs knowh _k and w^ which will be described hereinafter for the purpose of illustration.

[0063] In a closed-loop wireless communication system, the MS will feed the quantized CSI matrix back to the BS so as to perform a transmit precoding. For the purpose of simplicity and without loss of generality, the path loss can be not considered. Therefore, here it will use the equivalent quantized feedback channel by transforming the real channel matrix in terms of feedback rate and distortion. Through CSI quantization, the real channel output for the k-th MS, denoted by h _k €^' ^χ1 can be for example modeled as

where hk £ (f ^txl represents the quantized feedback channel output with zero mean and variance of 1-D _k ; n _s E ^'" ¹ is an independent additive noise matrix with each entry corresponding to an i.i.d. Gaussian variable with distribution Δ^Ο,Ό^) and D _k represents the channel quantization distortion constrain. The quality of feedback information can be measured by the distortion on the source h _k from the quantized CSI hk . The distortion can be defined by

[0064] For given distortion rate D _k , the quantized CSI can be modeled for example as follows:

^ \ _ί = μ}ΐι _ί +νη< ₃ (9) wherein parameters μ and V are the functions of D _k and the element of n _q ec^' ^*1 are i.i.d. Gaussian variables with distribution _2V(0,1). Through channel quantization, the parameter μ can be simply expressed by the following linear function:

μ=χ+γ ΰ/ _ί (10) [0065] Additionally, it is known that the real channel output h _k and its corresponding quantized channel hk satisfy the following linear extreme conditions:

^■ When there is no quantization errors, i.e., V = D^= 0, it can get μ =χ =\ .

^■ When the uantization is completely inaccurate, i.e., μ =0 and O _k - 1, it

so it will have the following relationship:

μ^Ι- D _k (11) [0066] As h _k and ri _q are independent with each other, and thus it can have the flowing equation: Var [hk ] = Var [ di _k +uri _q ] =Var [«]¾]- Var [wi _q ]

[0067] Based on the Shannon's rate-distortion theory of continuous- amplitude sources, the rate-distortion function of a zero-mean and unit variance complex Gaussian source can be given by:

wherein ¾ represents the feedback rate of the k-th mobile station. By Substituting equation (13) into equation (9), the quantized CSI matrix hk can be expressed as a function of the feedback rate /¾;

After normalization, the above equation will become

which can be used to perform precoding at the BS side.

[0068] Additionally, for the purpose of simplicity and without loss of generality, it can only consider a sub-optimal MMSE based precoder design, but it should be noted that any other suitable precoding approaches can also be readily applied in the present invention. The received signals can be written in a matrix form as

y= HWx + n, (16) wherein y =[yi, . . .yNs] ^T≡ C ^A¾xl represent the received signals, H=[hi,. . .hN _S ] ^{T≡ (} f ^sxNt and represents the real channel put , W=[W[, . . .W _S ] ( " ^xlv< and represent the precoder and ^{/V!r l} and represents the noise.

[0069] The general form for the optimal linear precoder can be written as

W = H ^H (H H ^H + ψΐΥ' (17) wherein K and ψ are two free scalar parameters for the optimal linear precoder, H = hi,..., h Ms ] ^T ^ (f ^sxNt _an d represents the total quantized feedback channel output K is a normalization constant used to comply with the unit transmit power constraint (averaged over data symbols) and it can expressed as H ^H (H H ^H + ^/ r' || (18)

The parameter ψ is typically a regularization parameter, which can be expressed as the following form

^ = SINR ^" ' (19) [0070] By setting ψ =0 , the equation (17) can become the simplest and the most common zer -forcing (channel inversion) precoder as follows:

wherein H = [hi ,..., Α Λ¾ ] ^τ , its elements corresponding to h¾ given in equation (15).

[0071] Thus, based on hk and W given in the above equation (20), it can be determined y k, and Ck( y k) an in turn the game utility at the sent price factor can be determined.

[0072] Next, referring back to Fig. 4, at step S403, the mobile station sends the determined game utility at the price factor for the mobile station to a base station for using in determining feedback transmission resource. The BS will determine whether the determined game utility at the price factor will cause the game to reach the Nash equilibrium. If the Nash equilibrium is reached, BS will notify the mobile station the best price factor or the corresponding feedback transmission resource values, otherwise the BS will send a new price factor which has been adjusted to the mobile station and the mobile station will repeat the operations in steps S401 to S403.

[0073] Additionally, in the following, only for the purpose of illustration, the specific algorithms for both the mobile stations and BS are provided. However, it should be noted that the give specific algorithms for both MS and BS are also illustrative, and the skilled in the art can appreciate that any other suitable specific algorithms can be employed.

NFCP algorithm for the k-th MS

1. Set initial CSI vector at time t=0, r(0)=r _0>

2. For all j, such τ,- εΤ

Give r.k(c), compute: r _k (Tj)= argma uj; (r _k ,r _{k (} ,)

NFCP algorithm for the BS

1. Set a=0 and announce α=0 to all MSs;

2. Get U _k from the mobile stations; increase α:=α+Δα and then announce to all MSs;

3. if u _k ^a < _Uk ' α+Δα for all, then go to step 2, else stop and declare , _κ1 =α.

[0074] Hereinafter, reference will be made to Figs. 5 A to 5H to shown the simulation results of the present invention, wherein Figs. 5 A to 5D and Figs. 5E to 5H illustrate the simulation results for FDMA and CSAM respectively. It should be noted that all the simulation are performed over the Rayleigh fading channel with MMSE precoder in equation (18) and for the purpose of simplicity, it is assumed that both the transmit power and the noise variance are normalized to unit. Additionally, in the simulations, FDMA and CSMA system are investigated as two simple examples. However, the skilled in the art can appreciate that the proposed solution in the present invention can be readily applied to any other multiple protocols.

[0075] Reference is first made to Fig. 5A, which illustrate the utility function of MS 1 in term of its CSI feedback rate by fixing the feedback-rate of the other MSs over FDMA channels, wherein the number of the mobile stations is 2 and r ₂ =1 , 3, and 10. As illustrated in Fig. 5A, for FDMA system, when the feedback rates of other users are fixed, the target MS will first experience an increasing throughput as its CSI feedback-rate rj increases, and then the game utility of the MS will begin to decrease for a sufficiently large value.

[0076] Then Referring to Fig. 5B, Fig.5B illustrates the performance of the proposed game over FDMA channels, wherein the number of the mobile stations is 10, B=20, and β=0.01. The simulation result is constructed by letting the NFCP algorithm for the k-th MS given hereinabove reach the Nash equilibrium at each value of a. The best price factor can be found if all mobile users receive worse overall utility than the previous equilibrium utility according to the NFCP algorithm for the BS. It can be also observed from the figure when the pricing factor increases, the total utility and the sum rates first increase, as shown in the small window, and then begin to decrease subsequently. It shows that solution by NFCP with a = CIBEST = 0:025 offers an obvious improvement in total utilities with respect to the NFC when a = 0, where pricing factor is not involved. At high pricing factors, we can see both sum utility and rate converge to a constant value. This is because the system stops requiring users to feedback CSI as it costs too much.

[0077] Fig. 5C illustrate a graph of performance comparisons of NFCP and the centralized scheme in the prior art over orthogonal feedback channels, wherein the number of the mobile stations is 10, B=20, and β=0.01. From the comparisons, it can be seen that the proposed distributed solution in the present invention and the centralized solution in the prior art are asymptotically the same if a in the right region, however, when a is too large, the MSs will be reluctant to feedback and when a is too small, the MSs will feed back in the non-operative manner.

[0078] Fig. 5D shows the uplink bandwidth occupancy in terms of the pricing factor over the orthogonal feedback channel, wherein the number of the mobile stations is 10, B=20, and β=0.01. From Fig. 5D it can see the variations of the sum feedback-rate as well as the individual feedback-rate in term of the pricing factor, where

Ns

B _UL ⁼ ?∑ ^r _k · From the figure we can see that, when a = 0, it requires the maximum amount of feedback, but with increasing of the price, the feedback-rate starts to decrease until zero, which make the throughput dropped to minimum.

[0079] Next, reference is made to Figs. 5E to 5H to describe the simulation results for CSMA system. For simplicity, herein it considers a special case of slotted 1 -persistent CSMA by setting p - 1, i.e., 1 -persistent CSMA. In Fig. 5E, it shows the total throughput against the traffic load. It indicates that there exists an optimal transmission rate corresponding to the maximum throughput. In Fig. 5F, it shows the utility of MS 1 in term of n over CSMA feedback channels, where the number of MSs is 2 and r ₂ = 1 , 3, 10. From Fig. 5F, it can be seen that the utility function of each MS has a maximum point in terms of the feedback-rate, which again proves the effectiveness of the proposed solution in the present invention. In Fig. 5Q it shows the performance of the proposed solution in the present invention over CSMA feedback channels where the number of MSs is 10 and B-20. Fig. 5G indicates that the proposed solution in the present invention provides much better results than the game without considering the pricing. Fig. 5H shows the performance compassions of the proposed solution in the present invention and the centralized scheme over CSMA feedback channels where the number of MSs is 10 and B=20. From the simulation results, it can be seen that the distributed solution and the centralized solution are almost the same when a is adjusted to the optimal working point.

[0080] Therefore, according to the embodiments of the present invention, MS will determine game utilities at price factors based on game theory and transmit to the BS, and the BS will search the best price factor based on the game utilities and determine the feedback transmission resource values corresponding to the best price factor as the feedback transmission resource allocated for each mobile stations. Hence, in the present invention, each mobile station can maximize its performance in a distributed way and the BS will select a best price factor at which Nash equilibrium can be reached, so it is possible to result in close optimal performance compared with that of the centralized scheme in the prior art and improve the overall throughout of wireless data network.

[0081] Additionally, the present invention also provides an apparatus for determining feedback transmission resource for mobile stations based on game theory and an apparatus for providing information at a mobile station for determining feedback transmission resource. Hereinafter, reference will be made to Figs. 6A to 6C and Fig. 7 to describe the apparatuses.

[0082] As illustrated in Fig. 6A, apparatus 600 can comprise a best factor searching unit 601 and a resource value determination unit 602. The best factor searching unit 601 can be configured for searching a best price factor at which the game utility for each of the mobile stations has a maximum value. The resource value determination unit 602 can be configured for determining a value of the feedback transmission resource corresponding to the best price factor as the feedback transmission resource for each of the mobile stations.

[0083] Additionally, as illustrated in Fig. 6B, the best factor searching unit 601 can comprise a price factor sending unit 6011 for sending a price factor for feedback transmission resource to the mobile stations; a game utility receiving unit 6012 for receiving the game utility at the price factor for at least one of the mobile stations; a best price factor determination unit 6013 for determining the price factor as the best price factor if the game utility at the price factor is a maximum value; and a price factor adjusting unit 6014 for adjusting the price factor if the game utility at the price factor is not the maximum value.

[0084] In an embodiment of the present invention, the price factor adjusting unit 6014 can be configured for increasing the price factor by a fixed amount. In another embodiment of the present invention, the price factor can have an initial value of zero.

[0085] In a further embodiment of the present invention, the game utility at the price factor for the mobile station can be performance gain obtained through using the feedback transmission resource by the mobile station minus the cost paid therefor at the price factor.

[0086] In a still further embodiment of the present invention, the performance gain obtained can be determined based on the feedback transmission resource used by the mobile station and historical determined feedback transmission resource of other mobile stations.

[0087] In a yet further embodiment of the present invention, the cost paid is a linear function of the feedback transmission resource used by the mobile station.

[0088] In a still yet further embodiment of the present invention, the best price factor determination unit 602 is configured for determining the game utility at the price factor to be a maximum value if the game utility at the price factor is greater than a game utility at a price factor increased subsequently.

[0089] Besides, as illustrated in Fig. 6C, apparatus 600 can further comprise a resource value receiving unit 603 for receiving values of feedback transmission resource corresponding to the price factor from respective mobile stations; and a resource value sending unit 604 for sending the received values of feedback transmission resource to each of the mobile stations.

[0090] In another embodiment of the present invention, the feedback transmission resource can comprise any one of feedback rate and feedback bandwidth.

[0091] Reference is made to Fig. 7, which illustrates apparatus 700 as provided in the present invention according to an embodiment of the present invention. As illustrated in Fig. 7, apparatus 700 can comprise a price factor receiving unit 701, a game utility determination unit 702 and a game utility sending unit 703. The price factor receiving unit 701 can be configured for receiving a price factor for feedback transmission source. The game utility determination unit 702 can be configured for determining the game utility at the price factor for the mobile station such that the game utility is optimized in a distributed way under the feedback transmission resource constrain. The game utility sending unit 703 can be configured for sending the determined game utility at the price factor for the mobile station to a base station for using in determining feedback transmission resource.

[0092] In an embodiment of the present invention, the game utility at the price factor for the mobile station is the performance gain obtained through using the feedback transmission resource by the mobile station minus the cost paid therefor at the price factor.

[0093] In another embodiment of the present invention, the cost paid can be a linear function of the feedback transmission resource used by the mobile station.

[0094] Additionally, as illustrated in Fig. 7, in a further embodiment of the present invention, apparatus 700 can further comprise historical value receiving unit 704 and resource value sending unit 705. The historical value receiving unit 704 can be configured for receiving values of historical transmission resource of other mobile stations, wherein the performance gain obtained is determined based on the feedback transmission resource used by the mobile station and the received values of historical transmission resource of other mobile stations. The resource value sending unit 705 can be configured for sending the value of feedback transmission resource corresponding to the determined game utility to the base station or other mobile stations.

[0095] Besides, it should be noted that operations of respective units as comprised in the apparatus 600 and apparatus 700 substantially correspond to operations in respective method steps as previously described. Therefore, for detailed operations of respective units in the apparatuses 600 and 700, please refer to the previous descriptions of the methods of the present invention with reference to Figs. 2 to 5H.

[0096] Additionally, the present invention is described mainly with reference with the feedback transmission resource such as feedback rate, but the present invention is not limited thereto. Actually, the skilled in the art can readily appreciated that it can also be true for other transmission resource such as feedback bandwidth and etc.

[0097] In embodiments of the present invention, description is made through taking increasing the price factor by a fixed amount as an example, but actually, the price factor can also be adjusted in any other suitable manner. In such a case, the skilled in the art will modify the corresponding the best factor searching process based on the teaching provided in the application and the knowledge he had known.

[0098] Moreover, in description of the embodiments of the present invention, the feedback information is described with reference to CSI, but the present invention is not limited thereto. The present invention can also be used to determine the feedback transmission resource for any other feedback information such ICI, CQI, ACK/NAC . Moreover, the present invention can also be applied to any other sorts of network such as ad-hoc.

[0099] By far, the present invention has been described with reference to the accompanying drawings through particular preferred embodiments. However, it should be noted that the present invention is not limited to the illustrated and provided particular embodiments, but various modification may be made within the scope of the present invention.

[00100] Further, the embodiments of the present invention can be implemented in software, hardware or the combination thereof. The hardware part can be implemented by a special logic; the software part can be stored in a memory and executed by a proper instruction execution system such as a microprocessor or a dedicated designed hardware. Those normally skilled in the art may appreciate that the above method and system can be implemented with a computer-executable instructions and/or control codes contained in the processor, for example, such codes provided on a bearer medium such as a magnetic disk, CD, or DVD-ROM, or a programmable memory such as a read-only memory (firmware) or a data bearer such as an optical or electronic signal bearer. The apparatus and its components in the present embodiments may be implemented by hardware circuitry, for example a very large scale integrated circuit or gate array, a semiconductor such as logical chip or transistor, or a programmable hardware device such as a field-programmable gate array, or a programmable logical device, or implemented by software executed by various kinds of processors, or implemented by combination of the above hardware circuitry and software, for example by firmware.

[00101] Though the present invention has been described with reference to the currently considered embodiments, it should be appreciated that the present invention is not limited the disclosed embodiments. On the contrary, the present invention is intended to cover various modifications and equivalent arrangements falling within in the spirit and scope of the appended claims. The scope of the appended claims is accorded with the broadest explanations and covers all such modifications and equivalent structures and functions.