Unlicensed Band Sharing Based on Bargaining Game for Heterogeneous Networks

Haixia Cui ,Shujie Zou

1 School of Electronics and Information Engineering,South China Normal University,Foshan 528225,China

2 School of Physics and Telecommunication Engineering,South China Normal University,Guangzhou 510006,China

Abstract:Currently,limited licensed frequency bands cannot meet the increasing demands for various wireless communication applications any more.It is necessary to extend wireless communication networks to unlicensed spectrum.In this paper,we propose a new bargaining framework for unlicensed band access to achieve high spectrum efficiency,where one radio access technology(RAT)(such as macro cellular network)“competes”the unlicensed bands with multiple other RATs(such as small cellular networks or Wi-Fi)virtually.Considering that macro cell can share unlicensed frequencies with multiple small cells which are in the same coverage area for more freedom,we use bargaining game theory to fairly and effectively share the unlicensed spectrum between macro and multiple heterogeneous small cell networks,where bargaining loss and time dissipation loss for virtual “price” of unlicensed bands are mainly considered.In the oneto-many bargaining process,we also develop a multiple RAT alliance game strategy to reduce transmission loss in a joint manner.Simulation results show that the proposed unlicensed band sharing algorithm significantly improves the spectrum efficiency performance compared with the other practical schemes for heterogeneous networks.

Keywords: unlicensed spectrum;bargaining game;alliance game;one-to-many bargaining game

I.INTRODUCTION

With the rapid increase in various types of mobile devices and users,future wireless networks are expected to support much higher capacity.It has been predicted in [1] that mobile data traffic will grow to 30.6 exabytes per month in recent years,which is about 8 times of the mobile traffic in 2015.However,the limited frequency resources in the licensed bands inevitably limits both the capacity of wireless communication networks and the QoS of mobile users.To address the spectrum shortage issue,a possible method is to extend cellular networks to the unlicensed frequency band,currently used by the Wi-Fi networks,and integrate the licensed and unlicensed frequency bands to enhance the network capacity[2].

Unlicensed spectrum is a public resource,which is available to any network operators,including the emerging heterogeneous small cell networks and the conventional Wi-Fi networks.If heterogeneous small cell networks extend their operation in unlicensed spectrum,they must coexist with other radio access technologies (RATs).As a result,future success of wireless networks hinges on the effective co-existing mechanism among RATs.So,it is critical to make sure the heterogeneous networks coexists harmoniously in the unlicensed spectrum.Based on some cooperation rules,the operators may be willing to share the public resource and then obtain some corresponding benefits.Otherwise,heterogeneous networks using the same frequency bands at the same time will cause sever noise interference.

For the adaptive carrier signal transmission scheme in [3],cellular networks periodically transmit on unlicensed bands.In the“Listen-Before-Talk”transmission mode in [4],cellular networks can only transmit when the unlicensed band is idle.The interferenceaware channel selection scheme in [5] allows cellular networks to select channels that are not occupied by Wi-Fi users at that time.As the number of active Wi-Fi users increases,it is inevitable that Wi-Fi networks will occupy the unlicensed band chronically,which makes it difficulty for cellular networks to access the shared bands.Furthermore,random geometry has been used in[6—10]to investigate the coexistence between Wi-Fi and cellular networks and win-win situations can be achieved [7,11,12].For example,a proportional fairness coexistence scheme has been proposed for heterogeneous networks in [6],where cellular networks access the appropriate unlicensed channel with certain probability based on graph theory.

In addition,a large amount of prior work has focused on game theory to solve the coexistence problem.Zhou and Tonget al.in [13] have used alliance game to optimize the performance of antennas for longer transmitting distances.Zhanget al.in[14]have exploited alliance game for multiple small cell cooperation to increase the transmission rate of each small cell.Yan and Yanget al.in [15] have investigated the dynamic bargaining game model to optimize the licensed spectrum sharing between secondary users and primary users.Yuet al.in [16] have used bargaining game to help mobile operators negotiate with some venue owners,which can configure a public wireless network to achieve a win-win situation.Gaoet al.in [17] have solved the mobile data unloading with an one-to-many bargaining model.Jehielet al.in[18]and Bagwellet al.in[19]have proposed auction models with only a few bidders to solve the problem of coexistence of RATs.Similarly,Yuet al.in[20]have developed a more general auction game(multiple bidders).Cellular networks can provide Wi-Fi users with a better transmission rate through purchasing the corresponding Wi-Fi bandwidth [21].Bairagiet al.in[22]have proposed cooperative Nash bargaining game and unilateral matching game to solve the coexistence of cellular networks and Wi-Fi.Chenet al.in [23]have used a bargaining game to transfer some Wi-Fi users to cellular networks to achieve a win-win situation.In[24],a hyper access point has been proposed to provide cellular network users with a free-contention time period and Wi-Fi users with a contention time period to promote coexistence issue.Collaborative Kalai-Smorodinsky bargaining games were also studied to optimize RAT coexistence and resource allocation in[25].Tradeoffs between time-sharing and edge offloading for heterogeneous coexistence were studied in[26,27].We refer the reader to[28]for a survey of work in this area.

As pointed out above,the majority of existing literatures on heterogeneous network coexistence in unlicensed bands have not considered the corresponding transmission loss caused by the consumed bargaining time,which may affect the performance of the whole system and make the game process meaningless[29,30].As a result,most of the developed coexistence schemes are suboptimal.In this paper,we study a novel bargaining framework for heterogeneous network coexistence problem in unlicensed bands,where the heterogeneous RATs negotiate with each other to share the public spectrum.Whenever one RAT wants to access the shared unlicensed bands that have been occupied by others,it will pay some corresponding virtual benefits to the heterogeneous network system.Based on this framework,the shared unlicensed spectrum can be used efficiently.

The rest of this paper is organized as follows.Section II introduces the system model.The one-to-one and one-to-many bargaining framework models are presented in Section III.Section IV analyzes the benefits of two RATs and the whole system benefits.Extensive simulation results and discussions are provided in Section V.Finally,VI concludes the paper.

II.SYSTEM MODEL

We consider a heterogeneous wireless network environment where multiple small cell networks are in the coverage of a macro cell network.All heterogeneous RATs should take part in the bargaining game for more benefits and they coordinate their bids through “principal”.The intermediate“principal”may be a private company or a company established by government and it coordinates the interaction for heterogeneous RATs.For ease description,we assume that one small cell network(or Wi-Fi)is occupying the unlicensed spectrum firstly and the whole bargain process is completed in a time slot.Thus,when a macro cell network wants to use the sharing spectrum,it should negotiate with the corresponding small cell network(or Wi-Fi) to “purchase” some unlicensed bands through the“principal”.At the same time,the small cell network(or Wi-Fi) may “sell” some unlicensed spectrum for more benefits.The “principal” transmits the bargaining results between heterogeneous networks to their respective operators.These practical operations can effectively prevent macro cell from communicating directly to all nearby small cell networks and reduce unnecessary transmission loss.Of course,the bargaining business is virtual and the spectrum“price”is only used to reach a win-to-win equilibrium.Note that if the unlicensed bands is used for macro cell network firstly,the bargaining framework is still useful.

On the other hand,the duration of bargaining game process will be longer with the number of small cell networks increasing,resulting in a greater bargaining overhead and time dissipation loss.To avoid this,we select multiple small cells forming an alliance to play a bargaining game with one macro cell.In this case,macro cell is equivalent to play a game with a group rather than with multiple small cells and it can reduce negotiation time and power loss in the negotiation process.The group can share bandwidth to macro cell in exchange for the corresponding virtual“money”(i.e.,transmission rate improving).In return,the macro cell can obtain more frequency bands.Usually,the macro cell negotiates with the group firstly and then a single small cell network under the condition of uniform time consumption and received noise interference of bargaining process.In other words,ifmsmall cells form an alliance group,the group is regarded as a novel virtual network that has the same transmission power andmtimes bandwidth compared to the individualmsmall cells.The obtained benefits of alliance group,including spectrum,are shared by allmsmall cells according to the respective contribution.

Thus,to achieve the expectant theoretical gains,there are two important issues that need to be addressed: How to form the alliance group from the multiple small cells? How to allocate the benefits of alliance group accurately so that small cells are guaranteed a fair spectrum sharing? To answer these two questions,the cooperative small cells should be set within the transmission range of each other and know the distribution ranges of the “contribution” values themselves while the respective“contribution”amount to the alliance group is not public.According to the distribution of “contribution” values,each small cell can approximately estimate whether it can obtain better benefits from nearby small cells through cooperation alliance.In this paper,we will adopt the Shapley distribution rule[14]based on the corresponding“contribution”to the group and allocate the whole benefits to each participant accurately.

In this case,the total benefit of macro cell that takes part in the bargaining with all small cells in its transmission field can be expressed as

whereUL,irepresents the obtained benefit when the macro cell finishes bargaining with thei-th small cell or thei-th small cell group.

The small cell network can cooperate with other small cells or alone to negotiate with macro cell.Correspondingly,after finishing bargaining process,the total benefit obtained by all small cells is given by

whereUw,irepresents the benefit obtained by thei-th small cell.Then,the overall benefit of heterogeneous networks can be expressed as

Our ultimate goal is to maximize the overall system benefit,i.e.max(U),subject to transmission loss in the bargaining process,i.e.,sc.Here,the value of virtual spectrum pricepis defined as the obtained rate per unit bandwidth.It will not affect the total system benefit although it is helpful to reach game Nash equilibrium.

The main parameters and some of the optimization variables (introduced later) are captured in Table 1.Note that some are private information of small cell networks,such as,Ni.

Table 1.List of parameters and key optimization variables.

III.PURCHASING MECHANISM BASED ON BARGAINING GAME

In this section,taking the alliance game theory into account,we develop a purchasing mechanism with twobargaining game models to improve the spectrum efficiency performance of heterogeneous networks.We first present a specific one-to-one bargaining algorithm by the mathematical benefit analysis and then extend it into a one-to-many bargaining model.In addition,we introduce an alliance game algorithm to fulfil the purchasing mechanism for heterogeneous networks.

3.1 One-to-One Bargaining Model

We focus on the case of one-to-one RAT bargaining game for spectrum sharing firstly.As shown in figure 1,there is only one small cell in the coverage field of a macro cell which is willing to participate in spectrum sharing.To maximize respective benefits,the two heterogeneous RATs negotiate the cooperation spectrum pricespaccording to their own channel status,service requirement,and available spectrum resource.Because it is one-to-one bargaining,there is no time dissipation loss although some bargaining loss is still existing.The macro cell network wants to purchase some sharing bands based on the spectrum price that the small cell offers to maximize its own benefit and the small cell also can balance its network loads by selling the appropriate bands.Here,the virtual benefits can be used to transform wireless spectrum resource.The expression of benefit function for the macro cell network can be expressed as

whereB1,1is the purchased bandwidth from macro cell to small cell;PLis the transmission power of macro cell;N1is the noise from small cell to macro cell;N0is the noise power spectral density;pis the spectrum price;αandβare unit uniform coefficients.Similar to the macro cell,the expression of benefit function for the small cell network can be expressed as

whereBw,1is the total sharing bandwidth of small cell network;B2,1is the bandwidth sold by small cell to macro cell;PWis the transmission power of small cell.

If the buyer and the seller reach an agreement,the spectrum bargaining game can reach a Nash equilibrium.Otherwise,both the macro cell and small cell change its own expected spectrum price until the bargaining game reaches an agreement.To summarize,the details of the bargaining game algorithm are presented in Algorithm 1.

Algorithm 1.Bargaining game algorithm.

After the above process,we can obtain the total system benefit by the one-to-one bargaining model as following

When the bargaining game reaches equilibrium,i.e.,the optimal uniform spectrum pricepis obtained by(B1,1=B2,1=B) whereBis a constant,the total system benefit can be written as

Up to now,we can see that when the bargaining game reaches an equilibrium,the virtual “money”B1,1ppaid by macro cell and the received virtual“money”B2,1pby small cell can offset each other.So,the total system revenue is only related to the bandwidth,signal-to-noise ratio,and bargaining loss.The spectrum pricepis only a medium for the virtual transaction.Besides,we also find that the system benefit is meaningful only with a consistent sharing bandwidth.Otherwise,the bargaining business equalization is impossible.In summary,the complexity of the proposed one-to-one bargaining game algorithm isO((b ?a+1)(c ?d+1)),wherea,b,c,anddare described in Algorithm 1.

3.2 One-to-Many Bargaining Model

After discussing one-to-one model,we now extend it into the one-to-many bargaining game case,which is more practical for heterogeneous networks since there are usually multiple small cells in the coverage field of one macro cell,as shown in figure 2.If the small cells take turns to negotiate with the macro cell one by one,the transmission bargaining delay is too long.So,both bargaining overhead loss and time dissipation loss should be considered in this case.We set the time dissipation loss,st,proportional to transmission delay,to represent the time consumption of one-to-many bargaining process.Note thatstonly relates to the size of small cell networks.

The major difficulty of one-to-many bargaining game lies in which way the macro cell network would choose to negotiate with the small cells.The existing methods mainly include as follows.

? The macro cell network bargains with each small cell network in a random order;

? According to some characteristics from good to bad,the macro cell network selects small cell to participate in the bargaining process in turns based on Bayesian game scheme.

3.3 Alliance Game

In order to decrease the time dissipation loss,we adopt alliance game to solve this issue.When multiple small cells cooperate to form a group,the corresponding time dissipation loss can be significantly reduced since the time loss will be split by the members of the cooperative group.Otherwise,the macro cell will bargain with small cells in a random order,which brings more time loss to the whole heterogeneous networks.The“money”paid by macro cell is used to serve small cell users and the corresponding load balancing will be allocated according to the contribution of small cell users in the alliance community.When several small cells cooperate an alliance,the macro cell will bargain with the alliance group preferentially,as shown in figure 2 in which the solid lines represent the ongoing bargaining game and the dotted lines represent the small cells waiting for negotiating.It is worth noting that each small cell neither knows the contribution of others to the alliance group nor the corresponding obtained benefits,which avoids conflict among group members effectively.

For convenience of description,we assume that there areksmall cells within the macro cell coverage and all of them trade with the macro cell in a specific period.Thus,they may form alliances as

wherem ∈[1,k] is the number of small cells in the cooperation group andis the number of the cooperation groups;xandyare random numbers from 1 tok.

The details of the alliance game algorithm that can formulate the corresponding group are shown in Algorithm 2.Here,the alliance group includes the following two characteristics.

Algorithm 2.Alliance game algorithm.

? To avoid conflicts,each small cell does not knowthe benefit “contributions” of others in the same group.

? There may be multiple cooperation groups in the heterogeneous networks and they do not know the benefits of others which can prevent them from leaving the group effectively.

Based on the above process,we can distribute the received benefit of cooperation group to each alliance member according to its contribution by Sharpley distribution theory [14].DenoteN=[N1,N2,N3,···,Nk],k ≥2,as the noise vector set of small cells and setmsmall cells for an alliance cooperation group,the noise of the whole alliance group can be expressed as

The Shapley value of each small cellican be calculated as

where,

whereIis the largest cooperation group;srepresents all small alliance groups belonging to the largest cooperation groupI;V(s) is the obtained benefit of each alliance group;V(s/{i}) represents the benefit of cooperative group without small celli.The Shapley value represents the received benefit of each small cell from the community.For example,if the largest cooperation group isI={1,2,3},all small alliance groups ares={1,2,3},{1,2},{1,3},{2,3},{1},{2},{3}.In fact,both sides of the above bargaining game can reach a better win-win situation.This leads to the total complexity ofO(k!) to compute the alliance game algorithm 2 forksmall cell networks.

To summarize,there are two options for each small cell network when it shares the unlicensed spectrum resource with other heterogeneous macro cell network.

? Bargaining game with macro cell directly: In this case,the benefit of participating in alliance is less than that of negotiating with macro cell alone.As a result,the small cell does not choose alliance cooperation and it generates time dissipation lossst.

? Taking part in cooperation alliance to bargain game with macro cell: In this case,the benefit of participating in alliance is more than that of negotiating with macro cell alone.The small cell finds other partners that are willing to cooperate and the whole bargaining queuing delay is saved.

Furthermore,the proposed bargaining framework can be extended to a situation that multiple macro cells bargain with multiple small cells.In this case,if one of macro cells makes a request to the intermediate“principal” to obtain some unlicensed spectrum of small cells,it will consider whether other macro cells are requiring the same spectrum.

3.4 Game Equilibrium Discussion

The efficiency of bargaining game algorithm lies in the convergence characteristic of bargaining process.As time goes by,it is attracted to the optimal virtual spectrum price for the buyer and seller.According to[31],the sufficient equilibrium convergence theorem for Algorithm 1 including the alliance game process(Algorithm 2)is as follows.

Theorem 1.The bargaining game process converges to the global optimal price after sufficient iterations.Proof.Tt is pointed out in Property 3 in [31] that the benefit function of small cell is concave in its own spectrum virtual pricepwhen its spectrum consumption is the optimized purchased amount from the macro cell and the other small cells’ prices are fixed.Also,the small cell price criteria help the macro cell reject the least beneficial small cells according to the Proposition 1 in[31].

IV.BENEFIT ANALYSIS

In this section,we analyze the obtained benefits for heterogeneous networks with different bargaining game models.We first analyze the benefits of macro cell,small cells,and small cell alliance groups and then describe the total system benefit in different situations.

4.1 Benefits of Macro Cell and Small Cells

Denote the indexes of small cells participating in bargaining with macro cell as 1,2,3,···,k,respectively.For clear description,we evaluate the benefits as the following three cases.1.When there is no small cell alliance,the benefit of macro cell is given by

whereB1,irepresents the purchased bandwidth from thei-th small cell.Moreover,the total benefit of all small cells is formulated as

whereB2,irepresents the sold bandwidth of thei-th small cell to macro cell.

2.When there are small cell alliance groups,we name the remaining small cell networks as 1,2,3...except for the members joined in alliances.For the sake of simplicity,we only discuss the case with one small cell alliance group in heterogeneous networks.In this situation,the benefit of macro cell is written as

whereB1,Mrepresents the purchased bandwidth of macro cell from an alliance groupMwithmsmall cells,as shown in Algorithm 2.Meanwhile,the benefit of small cells can be calculated in two different situations.

? If the small cells participate in cooperation alliance,the total benefit of the cooperation alliance is formulated as

whereB2,Mis the sold bandwidth of cooperation alliance to macro cell andBw,Mis the total occupied bandwidth by alliance group.The obtained benefit by each small cell in alliance group can be written as

whereV(s/{j})represents the benefit of cooperative group without small cellj.

? If the small cells negotiate separately with macro cell,the obtained benefit of thei-th small cell is given by

Therefore,the total obtained benefit of all small cells can be written as

3.When all small cells in the macro cell coverage field form an alliance group,the obtained benefit of macro cell can be expressed as

where|M|=m=k.The obtained benefit of alliance community is equal to the total benefit of small cells in the second case above,which will not be repeated here.

4.2 Total Revenue

In this section,we study the whole benefit of heterogeneous networks in bargaining game equilibrium.Similar to the above discussion,there are several different situations.

1.If there is no small cell cooperation alliance,the overall system benefit is simplified intoU=UL+Uw.When the bargaining game between macro cell and small cells reaches equilibrium,i.e.,B1,i=B2,i=Bi,the overall system benefit can be rewritten as

From the above,the overall system benefit is independent of spectrum pricepwhich is only a virtual resource sharing medium.

2.When there are small cell alliance groups,the overall system benefit isU=+UL.After reaching equilibrium of bargaining games between macro cell and small cells withB1,M=B2,M=BMandB1,i=B2,i=Bi,iM,we can calculate the overall system benefit as

3.When all small cells within the macro cell coverage field cooperate for bargaining with the macro cell as an alliance group and the equilibrium has obtained withB1,M=B2,M=BM,|M|=k,the overall system benefit can be given by

V.SIMULATION RESULTS

In this section,we present simulation results to verify the effectiveness of the proposed bargaining game algorithm and alliance algorithm for unlicensed spectrum sharing problem in heterogeneous networks.We assume that all small cell networks in one macro cell coverage field occupy the shared unlicensed spectrum firstly,Bw,1=Bw,2=···=Bw,k=20MHz,N0=0.01W/MHz,PL=5W,PW=0.5W,the noise in each areaN1=0.006W,N2=0.008W,N3=0.01W,and the losssc=st=5Mbpbs.For comparison,we also evaluate the performance of several benchmark schemes,such as traditional optimal algorithm and auction game algorithm.

Figure 3 demonstrates the iterative convergence performance for the one-to-one bargaining game process between small cell and macro cell with a virtual spectrum price.From the figure,when the spectrum pricepis small,the small cell network is unwilling to“sell”(sharing)its bandwidth to the macro cell network while the macro cell wants more bandwidth for benefit.Withpincreasing,both macro cell and small cell begin to adjust their previous decisions on virtual spectrum price until an agreement is reached(i.e.,the bargaining game reaches an equilibrium).However,whenpexceeds its equilibrium point and continues to rise,the equilibrium is broken.Thus,the intersection of the two curves represents the equilibrium point of bargaining.

Figure 1.One-to-one bargaining between macro cell and small cell.

Figure 2.One-to-many bargaining between macro cell and small cells.

Figure 4 illustrates the advantage of cooperation alliance group for bargaining process with different time dissipationscwherek=3 andp=4Mbps/MHz.We observe that all the benefits from different members of alliance group get less when the time dissipation becomes larger.This is because bargaining loss will impact the benefits of heterogeneous networks seriously and it should not be ignored.In other words,the cooperation alliance is helpful to save bargaining loss and improve spectrum efficiency.Yet,no matter how the value ofscchanges,small cell networks that participate in cooperation can obtain more benefits than others.More cells cooperate,the network benefit becomes greater.Although more alliance group members bring higher noise,the received benefit of cooperative group can make up for this shortcoming.Furthermore,scin bargaining process can be shared by the participating members,which further reduces the transmission loss per terminal user.

Figure 3.Iterative process of one-to-one bargaining game model.

Figure 4.The benefits of small cell networks versus bargaining loss sc.

Figure 5.The impact of|M|on each small cell network in alliance group.

Figure 6.Benefits of one small cell network in different situations.

Figure 7.System benefits in different cases.(a)sc= st=8Mpbs;(b)sc=st=2Mpbs.

Figure 8.Comparison of total system revenue under different transmission power.

Figure 9.Comparison of total system revenue under different bandwidth.

In figure 5,we demonstrate the impact of participating number in cooperation|M|on each small cell network in alliance group.From the figure,small cell network would like to “sell” more bandwidth as|M|increasing andpis inversely proportional to|M|.This is because that macro cell network will purchase more bandwidth from alliance group with reducing losses when cooperation alliance group is large.If there are sufficient spectrum resources,small cell networks are willing to“sell”more bandwidth with lower prices for larger sales at a small profit.To demonstrate the superiority of our proposed bargaining game algorithm for each single small cell network,we compare the average benefit in cooperation alliance group in figure 6.From the figure,the benefit of one small cell network gradually increases aspraising and cooperation transmission gains more profits than non-cooperation.This is because that cooperation communication can get prior bargaining chance with less time dissipation loss and the transmission bargaining loss will be shared by more group members.

We compare the system benefits in different situations withsc=st=8Mpbsin figure 7(a) andsc=st=2Mpbsin figure 7(b).It can be observed that the system benefit increases with the growth of bandwidth under different small cells.The total system revenue begins to decline when the sharing spectrum continues to increase.This is because there is much noise power spectrum and it becomes larger as bandwidth increasing.As a result,the system performance begins to decrease.In figure 7(a),we also show the relationship between the system performance and the number of small cells taking part in cooperation alliance.Note that with the growing of cooperation small cells,the whole heterogeneous network performance improves as expected.With more cooperation members,there has high flexibility in time consumption and queuing delay.However,the curve trend in figure 7(b) is in the opposite direction with figure 7(a).With the growing of cooperation small cells,the system benefit declines because the bargaining loss is very weak here.With the bandwidth increasing,the effect of bargaining loss and time dissipation loss on system revenue becomes weak,too.The influence of noise power spectrum in cooperation alliance group(the “contribution” of each member to the group)becomes more and more obvious.In other words,the noise is the main factor for system efficiency now.To summarize,the alliance game has advantages only when the noise interference is relatively weak and the bargaining loss or time dissipation loss is relatively high.That is to say,the non-cooperation bargaining will be better than the cooperation alliance if the bargaining game loss is very low.

Figure 8 compares the performance of the above mentioned schemes with respect to the transmission power of macro cell.In the traditional benchmark algorithm,the macro cell network directly occupies the unlicensed frequency bands if it needs to access.As a result,there may be lots of inter-cell interference and collisions with the running small cell networks in these unlicensed bands.Here,we set the interference factor of macro cell to small cell asα=0.7 and small cell to macro cell asα=0.4.In auction game algorithm,the macro cell served as auctioneer consults with small cells served as bidders and then selects one as best bidder.Due to multiple spectrum sharing pairs assumed in this paper,the auctioneer needs to conduct multiple best bidders and it may occupy the unlicensed band directly if there is no available spectrum sharing pair.From the figure,with increasing transmission power(i.e.,signal-to-noise ratio),the whole heterogeneous network improves its performance gradually.Our proposed one-to-many bargaining game is better than the two others obviously although the traditional benchmark algorithm is better than the other two algorithms when the signal-to-noise ratio is relatively low.This is because proposed one-to-many bargaining model combined with alliance game is used to reduce system loss to the utmost in good communication environment.However,it doesn’t need share the unlicensed spectrum when the transmission channel condition is very bad.Furthermore,the macro cell may occupy the unlicensed bands directly if its received advantages outweigh the loss disadvantages.As shown in Figure 9,the more spectrum resources,the better system performance.Our proposed one-tomany bargaining game is much better than the benchmark scheme and comes close to the theoretical upper limit of social welfare when the bandwidth is enough large.

VI.CONCLUSION

In this paper,we investigated two bargaining game frameworks with alliance game to reduce system transmission loss and improve unlicensed spectrum sharing efficiency for heterogeneous networks.Moreover,we adopt Shapley theory to distribute the total gains to each small cell network in alliance group so that the benefit for each small cell is higher than the non-cooperation sharing.This alliance game algorithm can encourage small cells to participate in cooperation to reduce spectrum sharing loss.The numerical results demonstrate that our proposed bargaining spectrum sharing algorithm can lead to significant performance gains over related techniques currently used in heterogeneous networks.

ACKNOWLEDGEMENT

This work was supported in part by the National Natural Science Foundation of China under Grant 61871433,61828103 and in part by the Research Platform of South China Normal University and Foshan.