CN101784107B - Non-cooperative repeated game-based power scheduling method in wireless MIMO network - Google Patents

Abstract

The invention discloses a non-cooperative repeated game-based power scheduling method in a wireless MIMO network, belongs to the technical field of wireless communication, and in particular relates to power scheduling in a wireless distributed MIMO network. In the method, power scheduling of each link is modeled as a non-cooperative game capable of maximizing a utility function. A pricing mechanism taking sending power and link quality into consideration is introduced into the utility function so as to acquire Pareto improvement of network throughput. The power scheduling of all sending windows is taken as a repeated game to establish a punishing mechanism for preventing the deviation, of the link, aiming to acquire excess earnings. Simulation results show that, compared with a gradient projection algorithm, the algorithm realizes distributed scheduling of resources at lower computational complexity without obviously sacrificing total throughput.

Description

In the wireless MIMO network based on the power dispatching method of non-cooperative repeated game

Technical field

The invention belongs to wireless communication technology field; That relate to is a kind of wireless multiple-input and multiple-output (Multiple-InputMultiple-Output that is used for; MIMO) method of the distributed power of network scheduling (power scheduling); Specifically being a kind of utilization comes the power dispatching of data transmission link in the wireless MIMO network is carried out modeling based on the power dispatching model of non-cooperative repeated game theoretical (non-cooperative repeated game theory), solves the method for the distributed power scheduling problem of network.

Background technology

Present cordless communication network normally occurs with forms such as cellular network or WLANs.These cordless communication networks and wireless communication technology are to being fixed with replenishing and development of spider lines, and they need the support of static infrastructure, and generally adopt the mode of centralized control.But in some particular surroundings or emergency; For example; The battlefield attendes army's rapid deployment and propelling, occasions such as search and the rescue after the natural calamities such as earthquake, open-air scientific investigation, remote mountain areas, temporary meeting take place presses for a kind of static infrastructure that do not rely on; And can be fast and the cordless communication network of flexible configuration technology, Ad Hoc network produces for satisfying this special applications demand.

Ad hoc network is also referred to as self-organizing network, is made up of some wireless mobile nodes, does not rely on any static infrastructure, is the provisional autonomous networks of a kind of multi-hop ad hoc system that carries out the network interconnection through internodal mutual cooperation.In Ad hoc network; Node can move arbitrarily; Network topology structure also can change thereupon, and the finiteness of wireless network coverage can be broken through in the terminal, make 2 can't direct communication user terminal carry out data communication by means of the packet forward at other terminal.It can be not or be not easy to utilize the back-up environment that a kind of communication network is provided under the situation of existing network infrastructure.Compare with fixed network with common mobile network; Wireless self-organization network has following characteristic: the equity between no center control nodes and the node; From discovery, configuration automatically, self-organizing, self-healing, dynamic network topology structure, wireless transmission limited bandwidth; Portable terminal has energy-conservation requirement, fail safe relatively poor with have a unidirectional wireless channel etc.

Ad Hoc network is mainly used in the occasion that fixation means can not be provided, and node generally provides energy by battery in the network simultaneously, therefore how effectively to utilize node energy to become a major issue in the Ad Hoc network research.Along with increasing of network node, the network capacity in the Ad Hoc network is restricted, and because internodal phase mutual interference, the raising of channel utilization is also limited.Adopt the energy consumption of effective power control can not only reduction network, prolong the node life-span, and can also reduce the phase mutual interference between the user, improve efficiency of resource, improve power system capacity.The MIMO technology is the development space resource fully, utilizes a plurality of antennas to realize MIMO, under the situation that need not increase frequency spectrum resource and antenna transmission power, can improve channel capacity exponentially, is antagonism multipath fading and the effective means that improves power system capacity.

Traditional power control techniques comprises classical water-filling algorithm ^[1]And derivation algorithm ^[2,3], many for the power of the good channel allocation of channel status, the power of the channel allocation of difference does not even distribute power less, and the throughput of system is mainly by its good channel contribution.In recent years, game theory ^[4]Be applied to the research of wireless system much more more and more, a kind of effective solution be provided in particular for distributed power control problem.Document [8] has been studied the game power control in the cdma system, and it has carried out ingenious design to the game revenue function, has also introduced pricing mechanism and has improved systematic function, makes network throughput obtain Pareto and improves, and has obtained effective distributed power control algolithm.People such as Chao Liang have proposed a kind of link down power control mechanism based on the non-cooperative game opinion ^[5], reduce inter-user interference through interrupting ropy link, improve power system capacity.

Aforementioned algorithm has only been considered space scale, and people such as Yue Rong propose a kind of power dispatching (Space TimePower Scheduling, STPS) mechanism when empty ^[6], the transmission signal covariance matrix of MIMO link is adjusted in time.STPS has increased the time degree of freedom, and network throughput is improved significantly.Time division multiple access (TDMA) is a kind of special circumstances of STPS when disturbing very seriously.But what document [6] adopted when asking optimum solution is gradient projection (gradient projection, GP) algorithm in the Non-Linear Programming ^[7], belonging to center control type algorithm, computation complexity is big, is not suitable for the distributed autonomous characteristic of ad hoc network and the limited resources characteristic of node.

List of references (like patent/paper/standard)

[1]D.Tse，P.Viswanath.Fundamentals?of?Wireless?Communication.Cambridge?UniversityPress，2005.

[2]W.Yu，W.Rhee，S.Boyd，and?J.M.Cioffi.Iterative?water-filling?for?gaussian?vectormultiple?access?channels.IEEE?Transaction?on?Information?Theory，Jan.2004，50：145-152.

[3]M.F.Demirkol，M.A.Ingram.Power-controlled?capacity?for?interfering?MIMO?links.Proc.IEEE?VTC，Oct.2001，vol.1，pp.187-191.

[4]D.Fudenberg，J.Tirole.Game?theory.MIT?Press，Cambridge，MA，1991.

[5]Chao?Liang，Dandekar?K.R.Power?Management?in?MIMO?Ad?Hoc?Networks：AGame-Theoretic?Approach.IEEE?Transactions?on?Wireless?Communications，April?2007，vol.6，no.4，pp.1164-1170.

[6]Yue?Rong，Yingbo?Hua.Optimal?Power?Schedule?for?Distributed?MIMO?Links.IEEETransactions?on?Wireless?Communications，August?2008，vol.7，no.8，pp.2896-2900.

[7] Yuan Yaxiang. the Non-Linear Programming numerical method. Shanghai: Shanghai science tech publishing house, 1993.8.

[8]C.U.Saraydar，N.B.Mandayam，and?D.J.Goodman.Efficient?Power?Control?via?Pricingin?Wireless?Data?Networks.IEEE?Transaction?on?Communication，2002，vol.50，pp.291-303.

Summary of the invention

Technical problem

The present invention is a kind of power dispatching method based on non-cooperative repeated game in the wireless MIMO network, and purpose is to solve the distributed realization of power dispatching and the problem of low complex degree.Power dispatching between link is modeled as and makes the maximized non-cooperative game of utility function; In utility function, introduce the pricing mechanism of considering transmitting power and link-quality; The Pareto that obtains network throughput improves (Pareto Improvement); Regard all power dispatchings that send window as repeated game simultaneously, set up penalty mechanism and prevent that link from being the behavior that deviates from that obtains excess earnings.

Technical scheme

Based on the power dispatching method of non-cooperative repeated game, comprise the steps: in the wireless MIMO network of the present invention

1) in wireless MIMO network, comprise L bar point-to-point link, every link receives the same frequency interference from other L-1 bar link, and each node has N root antenna, and during initialization, each link is with maximum transmit power P _MaxMean allocation is given N root transmitting antenna, and wherein N, L are natural number;

2) the transmission signal x of i link _iBe the multiple random vector of N * 1, the covariance matrix of its N * N Matrix P _iAlso be called as the power division matrix; The transmitted power of i link is tr{P _i}≤P _{Max, i}, P _{Max, i}It is the maximum transmit power of i link; Noise n _iBe the independent same distribution standard normal additive white gaussian vector of N * 1, its covariance matrix I _NBe unit matrix; The baseband receiving signals of i link is:

$y_i=\sqrt{\frac{{\mathrm{\ρ}}_i}{N}}{H}_{i,i}{x}_i+\underset{\underset{j\≠i}{j=1}}{\overset{L}{\mathrm{\Σ}}}\sqrt{\frac{{\mathrm{\β}}_{i,j}}{N}}{H}_{i,j}{x}_j+n_i,$

N * N matrix H wherein _{I, j}Be the channel matrix between j link transmitting antenna and i link reception antenna in this transmission window, ρ _iBe the signal to noise ratio snr of i link, β _{I, j}Be the interference-to-noise ratio INR of the sending node of j link to the receiving node of i link, P _{Max, i}Be the maximum transmit power of i link, and i, j ∈ (1,2,3 ..., L);

3) adopt piece decline block fading model, channel matrix is at T coherence time _cIn be quasi-static, will send the window size and be made as T _c, and be divided into T time slot, the transmission covariance matrix P of each link _iChange in time, promptly Transmitted power is constrained to:

$\frac{1}{T}\underset{t=1}{\overset{T}{\mathrm{\Σ}}}\mathrm{tr}\left\{P_i\left(t\right)\right\}=M\≤P_{\max ,i},i=1,...,L,$

P _i(t)≥0，t＝1，...，T；i＝1，...，L，

4) with the throughput of every link as optimization aim, consider link-quality and the cost of sending signal simultaneously, the game revenue function is:

$u_i(P_i,P_{-i})={\mathrm{\Σ}}_{t=1}^T{\log }_2|I_N+\frac{{\mathrm{\ρ}}_i}{N}{H}_{i,i}{P}_i\left(t\right)H_{i,i}^H{R}_i^{-1}\left(t\right)|-c_i\left(P_i\left(t\right)\right),$

Cost function wherein

$c_i\left(P_i\left(t\right)\right)={\mathrm{\γ}}_i{\mathrm{\Σ}}_{t=1}^T|\∂P_i\left(t\right)/\∂\mathrm{SIN}{R}_i\left(t\right)|\mathrm{tr}\left\{P_i\left(t\right)\right\}$

$={\mathrm{\γ}}_i{\mathrm{\Σ}}_{t=1}^T{\left|({\mathrm{\ρ}}_i/N)H_{i,i}{H}_{i,i}^H{R}_i^{-1}\left(t\right)\right|}^{-1}\mathrm{tr}\left\{P_i\left(t\right)\right\},$

${\mathrm{SINR}}_i\left(t\right)=({\mathrm{\ρ}}_i/N)H_{i,i}{P}_i\left(t\right)H_{i,i}^H{R}_i^{-1}\left(t\right),$ $R_i\left(t\right)=I_N+\underset{j=1,j\≠i}{\overset{L}{\mathrm{\Σ}}}\frac{{\mathrm{\β}}_{i,j}}{N}{H}_{i,j}{P}_j\left(t\right)H_{i,j}^H,$ γ _iBe the price factor;

Upgrade power dispatching:

K representes iterations, judges whether the transmitted power matrix that all twice iteration in links front and back obtain satisfies two norms less than ε, then jumps out iterative cycles if satisfy two norms less than ε, and current transmitted power matrix is the Nash Equilibrium of game and separates; If do not satisfy two norms less than ε, then return step 4 and get into next iteration renewal power dispatching, wherein ε is an arithmetic number that goes to zero, and is 10 ^-4

5) each link uses unified price factor gamma, makes total revenue

The maximum price factor is best price factor gamma _OptInitialization price factor gamma=0 is incremental update price factor gamma ← γ+Δ γ with Δ γ, and if execution in step 4 is u ^{γ+Δ γ}>=u ^γ, then continue to improve the price factor, execution in step 4 with increment Delta γ; Otherwise iteration finishes, and the price factor of getting a preceding game is best price factor gamma _Opt, data to be sent will be according to the best factor gamma of fixing a price _OptThe power dispatching matrix sends, wherein ← the expression assignment, u _iThe prospective earnings of representing the i link;

6) according to step 5) the transmission data are set; Data are sent in the actual gain of adding up each link when T time slot finishes; Compare with the prospective earnings of step 5), actual gain is judged to exist greater than the link of prospective earnings deviate from behavior, after this respectively send window and all set its price factor gamma _i→+∞ participates in game, at this moment γ _iBe 10 ^-4, the i link will be selected transmitted power matrix P _i=0, future profits will be zero, if do not find to deviate from behavior, then the price factor gamma of normal initialization i link _i=0, get into next after operation is accomplished and send window, return step 1).

Beneficial effect

The present invention has following advantage:

1. the scheme of document [6] needs a central dispatching node transceiver channel state information, the rated output allocation matrix, and the transmitted power of dispatching each link, this makes it become center control type method, is unfavorable in distributed ad hoc network, realizing.The present invention is based on theory of games; Suppose that each link has rational and selfishness property; Can be separately according to the channel condition information that is obtained, through choosing the income of suitable transmitted power maximization self, each link transmitted power converges to the Nash Equilibrium point after the several times game; Belong to distributed method, be applicable to ad hoc network, wireless sensor network distributed network.

2. in non-cooperative game power dispatching algorithm, each link is only known local information, is to be self benefits maximization, the i.e. competition process of a selfishness to the scheduling of power.And arbitrary link increases the revenue function attenuating (not changing at other link under the situation of strategy) that transmitted power all will make other link; This can make affected user also can improve self benefits through increasing transmitted power; Final equilibrium point will be in an all bigger policy groups of each link power and close, and be unfavorable for saving the limited energy of node.Document [8] is introduced pricing mechanism for to impel each link to communicate with lower transmitted power, and structure is proportional to the linear cost function of link transmitted power, and the result shows that system has obtained the Pareto improvement of network throughput.This paper considers the random distribution nature of node on the basis of document [8], each link-quality is different, and system should tend to the measured link of matter, and ropy link is carried out heavier punishment, forces it to reduce transmitted power, has designed cost function

simulation result show the present invention than document [8] at network

There is further Pareto to improve on the throughput.

3. based on the dynamic characteristic of ad hoc network, the attributes such as position of Link State, node all change in time, and the present invention supposes that node is static, and power dispatching is necessary with T coherence time _cFor the time interval repeats, promptly constitute a repeated game (repeated game) ^[4], each sends the game of window and can regard as at certain T _cThe stage game (stage game) carried out of incipient stage.Though the life-span of node receives the restriction of battery in the network, because all can't foreseeing game, the participant of game when finishes, so the game between link can be regarded unlimited repeated game as.According in the repeated game with discount factors δ ∈ (0; 1) method of estimated income; Represent to send window number with w; The average yield of i bar link is:

discount factors δ as the patient tolerance of link cooperation; δ is big more, and then link is more patient, also payes attention to long-term gain more.The value of δ generally has network character and application scenarios decision, and the discount factors of long-standing stable network is greater than the dynamic network of height of interim foundation, and the present invention considers δ → 1.The game equilibrium that deviates from that causes for the selfish characteristic that prevents because of link obtains the excess earnings behavior, and the repeated game process is disciplined introducing as a warning mechanism.To cause corresponding punishment if deviate from behavior; Link will have to consider its cost; That the loss of its future profits is surpassed is current when deviating from the short-term excess earnings that behavior obtains when punishment, and link will deviate from motivation owing to the rational faculty loses, and observe the power dispatching arrangement that the stage game produces.The mechanism of disciplining as a warning of the present invention's design will be utilized the price factor gamma _i→+∞ is as punishment, and according to revenue function, link will be selected P _i=0, this moment u _i=0, promptly after this link can't obtain income, the average yield of link

Obviously the excess earnings that deviates from acquisition can't remedy the loss of losing income indefinite duration, thereby effectively prevents the behavior that deviates from of link.

Description of drawings

Fig. 1: distributed ad hoc network topology structure;

Fig. 2: the inventive method flow chart;

Fig. 3: network throughput is with the variation relation of interference-to-noise ratio;

Fig. 4: network throughput is with the variation relation of number of links;

Fig. 5: the relation of network total revenue and price factor gamma;

Fig. 6: the stage income that deviates from link;

Embodiment

Be elaborated below in conjunction with the technical scheme of accompanying drawing to invention:

As shown in Figure 2, be the inventive method flow chart.

The scene that the present invention considers is as shown in Figure 1, in wireless MIMO network, comprises L bar point-to-point link, and every link receives the same frequency interference from other L-1 bar link, and each node has N root antenna, and during initialization, each link is with maximum transmit power P _MaxMean allocation is given N root transmitting antenna;

The transmission signal x of i link _iBe the multiple random vector of N * 1, its covariance matrix

N * N matrix P _iAlso be called as the power division matrix, the transmitted power of i link is tr{P _i}≤P _{Max, i}Noise n _iBe the independent same distribution standard normal additive white gaussian vector of N * 1, its covariance matrix

I _NBe unit matrix, the baseband receiving signals of i link is:

$y_i=\sqrt{\frac{{\mathrm{\ρ}}_i}{N}}{H}_{i,i}{x}_i+\underset{\underset{j\≠i}{j=1}}{\overset{L}{\mathrm{\Σ}}}\sqrt{\frac{{\mathrm{\β}}_{i,j}}{N}}{H}_{i,j}{x}_j+n_i$

N * N matrix H wherein _{I, j}Be the channel matrix between j link transmitting antenna and i link reception antenna in this transmission window, ρ _iBe the signal to noise ratio (snr) of i link, β _{I, j}Be the interference-to-noise ratio (INR) of the sending node of j link to the receiving node of i link.

Adopt piece decline (block fading) model, suppose that channel matrix is at T coherence time _cIn be quasi-static, will send the window size and be made as T _c, and being divided into T time slot, each sends covariance matrix P _iCan change in time, promptly

Transmitted power is constrained to:

$\frac{1}{T}\underset{t=1}{\overset{T}{\mathrm{\Σ}}}\mathrm{tr}\left\{P_i\left(t\right)\right\}=M\≤P_{\max ,i},i=1,...,L$

P _i(t)≥0，t＝1，...，T；i＝1，...，L

As optimization aim, consider link-quality and the cost of sending signal with the throughput of every link simultaneously, the game revenue function of the present invention's design is:

$u_i(P_i,P_{-i})={\mathrm{\&Sigma;}}_{t=1}^{\mathrm{<figure-callout\; id="2"\; label="T\; log"\; filenames="H2010100179070E00031.png,H2010100179070E00032.png"\; state="\{\{state\}\}">T</figure-callout>}}{\log }_{}{}_2|I_N+\frac{{\mathrm{\&rho;}}_i}{N}{H}_{i,i}{P}_i\left(t\right)H_{i,i}^H{R}_i^{-1}\left(t\right)|-c_i\left(P_i\left(t\right)\right)$

Cost function wherein

$c_i\left(P_i\left(t\right)\right)={\mathrm{\&gamma;}}_i{\mathrm{\&Sigma;}}_{t=1}^T|\&PartialD;P_i\left(t\right)/\&PartialD;\mathrm{SIN}{R}_i\left(t\right)|\mathrm{tr}\left\{P_i\left(t\right)\right\}$

$={\mathrm{\&gamma;}}_i{\mathrm{\&Sigma;}}_{t=1}^T{\left|({\mathrm{\&rho;}}_i/N)H_{i,i}{H}_{i,i}^H{R}_i^{-1}\left(t\right)\right|}^{-1}\mathrm{tr}\left\{P_i\left(t\right)\right\},$

${\mathrm{SINR}}_i\left(t\right)=({\mathrm{\&rho;}}_i/N)H_{i,i}{P}_i\left(t\right)H_{i,i}^H{R}_i^{-1}\left(t\right),$ $R_i\left(t\right)=I_N+\underset{j=1,j\&NotEqual;i}{\overset{L}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&beta;}}_{i,j}}{N}{H}_{i,j}{P}_j\left(t\right)H_{i,j}^H,$ γ _iBe the price factor;

Each link upgrades power dispatching:

K representes iterations, judges before and after all links transmitted power matrix that twice iteration obtain whether to satisfy two norms (ε is an arithmetic number that goes to zero, and can be made as 10 less than ε ^-4), then jump out iterative cycles if satisfy, current transmitted power matrix is the Nash Equilibrium of game and separates, and then gets into next iteration renewal power dispatching if do not satisfy.

The price factor gamma _iSetting will influence the performance of system, be to reduce system complexity, each link uses unified price factor gamma, definition makes total revenue

The maximum price factor is best price factor gamma _Opt, initialization price factor gamma=0 is incremental update price factor gamma=γ+Δ γ with Δ γ, carries out power dispatching and upgrades, if u ^{γ+Δ γ}>=u γ then continues to improve the price factor with increment Delta γ, and carry out power dispatching and upgrade, otherwise the iteration end, the price factor of getting a preceding game is best price factor gamma _Opt, data to be sent will be sent according to its power dispatching matrix.

As can beappreciated from fig. 3; Increase along with interference-to-noise ratio; The network throughput of three kinds of algorithms all becomes downward trend, but speed slows down gradually, and the power dispatching method based on gradient project algorithms (STPS-GP) performance that wherein belongs to the center control type is best; The power dispatching method based on non-cooperative game (STPS-NGTH) of considering link-quality and transmitted power obtains the Pareto improvement with respect to the power dispatching method based on non-cooperative game of only considering transmitted power (STPS-NGT); Because back two kinds of methods belong to distributed method, more meet ad hoc network characteristic, have higher combination property.As can beappreciated from fig. 4, network throughput increases with number of links in number of links more after a little while and rises, and the back is because the increase of number of links makes to be disturbed excessive and decline gradually, and the performance of three kinds of algorithms and the analysis of Fig. 3 are similar.

The transmission data of the power dispatching matrix during according to the best price of the acquisition factor; Data are sent in the actual gain of adding up each link when the T time slot finishes; Compare with the prospective earnings of power dispatching; Actual gain is judged that greater than the link of prospective earnings existence deviates from behavior, after this respectively send window and all set its price factor gamma _i→+∞ participates in game (this moment γ _iCan be made as 10 ⁴), can know that according to revenue function this link will select transmitted power matrix P _i=0, future profits will be zero, if find to deviate from behavior with normal initialization factor gamma=0 of fixing a price, operation is accomplished the back and got into next transmission window, reinitializes.

As can beappreciated from fig. 6, deviate from link and make and deviate from behavior sending window 6, obtain excess earnings, but all pay for the income vanishing in respectively sending in the window after this.

Claims (1)

1. In the wireless MIMO network based on the power dispatching method of non-cooperative repeated game, it is characterized in that comprising the steps:

   1) in wireless MIMO network, comprise L bar point-to-point link, every link receives the same frequency interference from other L-1 bar link, and each node has N root antenna, and during initialization, each link is with maximum transmit power P _MaxMean allocation is given N root transmitting antenna, and wherein N, L are natural number;

   2) the transmission signal x of i link _iBe the multiple random vector of N * 1, its covariance matrix

   

   N * N matrix P _iBe the power division matrix; The transmitted power of i link is tr{P _i}≤P _{Max, i}Noise n _iBe the independent same distribution standard normal additive white gaussian vector of N * 1, its covariance matrix I _NBe unit matrix; The baseband receiving signals of i link is:

   $y_i=\sqrt{\frac{{\mathrm{\&rho;}}_i}{N}}{H}_{i,i}{x}_i+\underset{\underset{j\&NotEqual;i}{j=1}}{\overset{L}{\mathrm{\&Sigma;}}}\sqrt{\frac{{\mathrm{\&beta;}}_{i,j}}{N}}{H}_{i,j}{x}_j+n_i,$

   N * N matrix H wherein _{I, j}Be the channel matrix between j link transmitting antenna and i link reception antenna in this transmission window, ρ _iBe the signal to noise ratio snr of i link, β _{I, j}Be the interference-to-noise ratio INR of the sending node of j link to the receiving node of i link, P _{Max, i}Be the maximum transmit power of i link, and i, j ∈ (1,2,3 ..., L);

   3) adopt piece decline block fading model, channel matrix is at T coherence time _cIn be quasi-static; To send the window size and be made as T _c, and be divided into T time slot, the transmission covariance matrix P of each link _iChange in time, promptly

   

   Transmitted power is constrained to:

   $\frac{1}{T}\underset{t=1}{\overset{T}{\mathrm{\&Sigma;}}}\mathrm{tr}\left\{P_i\left(t\right)\right\}=M\&le;P_{\max ,i},i=1,...,L,$

   P _i(t)≥0，t＝1，...，T；i＝1，...，L，

   4) with the throughput of every link as optimization aim, consider link-quality and the cost of sending signal simultaneously, the game revenue function is:

   $u_i(P_i,P_{-i})={\mathrm{\&Sigma;}}_{t=1}^T{\log }_2|I_N+\frac{{\mathrm{\&rho;}}_i}{N}{H}_{i,i}{P}_i\left(t\right)H_{i,i}^H{R}_i^{-1}\left(t\right)|-c_i\left(P_i\left(t\right)\right),$

   Cost function wherein

   $c_i\left(P_i\left(t\right)\right)={\mathrm{\&gamma;}}_i{\mathrm{\&Sigma;}}_{t=1}^T|\&PartialD;P_i\left(t\right)/\&PartialD;\mathrm{SIN}{R}_i\left(t\right)|\mathrm{tr}\left\{P_i\left(t\right)\right\}$

   $={\mathrm{\&gamma;}}_i{\mathrm{\&Sigma;}}_{t=1}^T{\left|({\mathrm{\&rho;}}_i/N)H_{i,i}{H}_{i,i}^H{R}_i^{-1}\left(t\right)\right|}^{-1}\mathrm{tr}\left\{P_i\left(t\right)\right\},$

   ${\mathrm{SINR}}_i\left(t\right)=({\mathrm{\&rho;}}_i/N)H_{i,i}{P}_i\left(t\right)H_{i,i}^H{R}_i^{-1}\left(t\right),$ $R_i\left(t\right)=I_N+\underset{j=1,j\&NotEqual;i}{\overset{L}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&beta;}}_{i,j}}{N}{H}_{i,j}{P}_j\left(t\right)H_{i,j}^H,$ γ _iBe the price factor;

   Upgrade power dispatching: K representes iterations, judges whether the transmitted power matrix that all twice iteration in links front and back obtain satisfies two norms less than ε, then jumps out iterative cycles if satisfy two norms less than ε, and current transmitted power matrix is the Nash Equilibrium of game and separates; If do not satisfy two norms less than ε, then return step 4 and get into next iteration renewal power dispatching, wherein ε is an arithmetic number that goes to zero, and is 10 ^-4

   5) each link uses unified price factor gamma, makes total revenue

   

   The maximum price factor is best price factor gamma _OptInitialization price factor gamma=0 is incremental update price factor gamma ← γ+Δ γ with Δ γ, and if execution in step 4 is u ^{γ+Δ γ}>=u ^γ, then continue to improve the price factor, execution in step 4 with increment Delta γ; Otherwise iteration finishes, and the price factor of getting a preceding game is best price factor gamma _Opt, data to be sent will be according to the best factor gamma of fixing a price _OptThe power dispatching matrix sends, wherein ← the expression assignment, u _iThe prospective earnings of representing the i link;

   6) according to step 5) the transmission data are set; Data are sent in the actual gain of adding up each link when T time slot finishes; Compare with the prospective earnings of step 5), actual gain is judged to exist greater than the link of prospective earnings deviate from behavior, after this respectively send window and all set its price factor gamma _i→+∞ participates in game, at this moment γ _iBe 10 ^-4, the i link will be selected transmitted power matrix P _i=0, future profits will be zero, if do not find to deviate from behavior, then the price factor gamma of normal initialization i link _i=0, get into next after operation is accomplished and send window, return step 1).

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