AN ENERGY-AWARE AUCTION FOR HYBRID ACCESS IN HETEROGENEOUS NETWORKS UNDER QOS REQUIREMENTS

Transcription

1 AN ENERGY-AWARE AUCTION FOR HYBRID ACCESS IN HETEROGENEOUS NETWORKS UNDER QOS REQUIREMENTS Fei Shen, Pin-Hsn Lin +, Lca Sanginetti, Meroane Debbah, Edard A. Jorswieck + Large Networks and System Grop (LANEAS, CentraleSpélec, Université Paris-Saclay, Gif-sr-Yvette, France + Technische Universität Dresden, Commnications Laboratory, Dresden, Germany Dipartimento di Ingegneria dell Informazione, University of Pisa, Pisa, Italy Mathematical and Algorithmic Sciences Lab, Hawei France, Paris, France ABSTRACT We consider a heterogeneos network (HetNet in which mltiple small cell base stations (SBSs aim to offload a qantity of macro cell ser eqipments (s to redce the energy consmption of the network while garanteeing the QoS reqirements of all UEs. We design an ascending-bid action mechanism to achieve this goal. Uniqe and closed form soltions for the demand and spply qantities of offloading s are derived. When the MBS has knowledge abot the tilities and strategies of the SBSs, the proposed action can be formlated as a Stackelberg game where the clinching bid price is obtained in closed form. Nmerical reslts verify the theoretical analysis for different scenarios and show that the proposed action clinches fast at the niqe clinching price, thereby reslting in a win-win soltion that improves the energy consmption of the HetNet. Index Terms ascending-bid action, hybrid access, heterogeneos network, QoS reqirement. INTRODUCTION Heterogeneos networks (HetNets are considered as a key technology for 5G []. This paper investigates the ser eqipment (UE and base station (BS association for a network with a single macrocell base station (MBS and mltiple small cell base stations (SBSs, where each UE has a rate-based QoS reqirement to be garanteed by the serving BS. The three basic access control mechanisms for HetNets are closed, hybrid and open access [, 3]. Among them, the hybrid access is considered as the most promising for redcing the energy consmption of the network. Since the transmit power of each UE is highly related to the total nmber of UEs served in each cell, it is important for the MBS to stimlate the SBSs for the hybrid access. When mltiple SBSs exist, action is a powerfl tool to model, analyze, and solve the problem for offloading the qantity of macrocell UEs (s in the hybrid access. There exist several works in which resorce allocation is performed sing game theory and action [4, 5]. The ser-cell association for massive MIMO networks is considered in [6] and addressed sing non-cooperative game theory. In [7], the ser association and spectrm allocation problems are addressed to stabilize the HetNet and to minimize the transmission delay. In [8, 9], two action mechanisms for allocating the received power among a grop of UEs sbject to a constraint on the interference are proposed for Part of this research has been spported by the ERC Starting Grant 353 MORE. relay selection and relay power allocation, leading to a weighted max-min fair allocation. To motivate an efficient and fair resorce allocation for spectrm-sharing femtocell networks, Vickrey-Clarke- Groves (VCG action is proposed to ensre that small cell ser eqipments (s sbmit their tilities trthflly despite of their selfish natre []. The single clster of macro-femtocell hybrid access is discssed in [, ] where a Stackelberg game is designed to maximize the system energy consmption. A compensation framework is proposed for motivating the hybrid access in conjnction with a time division mltiple access (TDMA strategy [3]. In this work, the mltiple SBSs are modelled as bidders that compete among each other to offload a certain nmber of s and receive the corresponding compensation paid by the MBS. Two different scenarios are envisaged. In the first one, we assme that the MBS and SBSs belong to different operators and ths have no knowledge of the tilities and strategies of each other. In this context, a low-complexity ascending-bid action is proposed, in which each SBS bids for the demand qantity of the offloading s only based on their local information and the given bid price. The fast convergence of the clinching price at market clearance is garanteed. In the second scenario, we assme that the MBS and SBSs belong to the same operator and exploit the knowledge of the tilities and strategies to formlate a Stackelberg game. This allows s to compte the clinching price in closed-form withot the need of any iterative procedre. The otline of the paper is as follows. In order to motivate the energy-aware hybrid access for the two-tier HetNet, an ascendingbid action is proposed in Sec.. The tilities of the MBS and SBSs are provided as fnctions of the bid price and the qantity of offloading s in Sec. 3.. Uniqe and closed form soltions for the demand and spply qantities of offloading s are derived in Sec. 3. by maximizing the tilities of the MBS and SBSs, respectively. A Stackelberg game is analyzed in Sec. 4 wherein a closed-form clinching price is derived. Nmerical reslts are given in Sec. 5 to assess the performance of the proposed soltions and validate the analysis... System model. NETWORK MODEL We consider the plink of a two-tier HetNet in which the MBS and SBSs operate over different freqency bands. We denote by M the nmber of s that are served by the MBS and assme that N SBSs serve L i s each. We assme also that all UEs and BSs are eqipped with a single antenna and that a certain QoS reqire-

2 ? SBS K b MBS b K SBS Fig.. The considered system model. Sharing Spectrm Bid Price Bid Qantity? ment mst be garanteed to each UE (no matter it is served by the MBS or by the SBSs. Within this setting, we are interested in redcing the energy consmption of the network. To this end, we assme that the MBS is willing to compensate a given SBS for offloading a qantity of s. Clearly, when N > this gives rise to a competition among the SBSs, which is modelled and solved in this work throgh an ascending-bid action mechanism as described in the next section. We consider a block flat-fading channel model and denote by the channel gain of a generic UE i. Call S i the total nmber of UEs associated to the MBS or SBS serving UE i. Then, for a given S i the plink power reqired by UE i to meet the rate reqirement is given by [4] as p i[s i] = S i( +. ( We denote the Shannon ratelog(+sinr i as the criterion of the rate reqirement measred in [bit/s/hz]. When all the UEs meet the rate reqirement with eqality, p i[s i] is derived in a simple expression as ( where the CSI or SINR of other UEs is contained in. From the above eqation, it follows that a positive power allocation and the feasibility of achieving for all UEs in the HetNet are ensred only if the total nmber S i in the network is sch that S i.. Action-based Hybrid Access. ( In a generic ascending-bid action mechanism, the actioneer calls a bid price and the bidders respond with demand qantities by maximizing their own tilities. Meanwhile, the actioneer optimizes the spply at the given bid price in each rond. The process iterates with increasing bid prices ntil the market clears or the demand is no less than the spply [5]. The ascending-bid action mechanism sed in this work to offload s operates as follows. The MBS acts as the actioneer, which annonces a bid price b to all the SBSs (the bidders and calls for demand qantities {K i ;i =,...,N}. Each K i corresponds to the maximm nmber of s that can be offloaded by SBS i in order to maximize its own tility fnction U S i while taking into accont that the reward from the MBS is bk i. At the same time, the MBS optimizes its spply qantity by compting the optimal nmber K of offloading s by maximizing its own tility U M. If the sm of the demand qantities is less than the spply, i.e., N i= K i < K, then the actioneer increases the bid price b by a given qantity b. The process contines ntil the market clinches or, eqivalently, ntil the following condition is satisfied N i= K i = K. The above ascending-bid action mechanism is smmarized in Algorithm. Algorithm Action-based Hybrid Access : Inpt M, N,,{L i}, b,u M and{u S i }. : Otpt K,{K i },b. 3: Setb = ; 4: repeat 5: Setb = b+ b; 6: Compte K i = argmax Ki,,...,M U S i ; 7: Compte K = argmax K,,...,M U M ; 8: ntil N i= K i = K When the actioneer MBS has no knowledge abot the tility and strategies of the SBSs, the action is rn as shown in Algorithm ntil the market clears. 3. AUCTION FORMULATION AND SOLUTION Next, we introdce the tility fnctions of MBS and SBSs for the propsoed action framework and then provide its soltion in a closed form. The bid b is provided by the actioneer MBS for the qantity of offloading s. 3.. Action Formlation The tility fnctionsu M andu S i commonly take the following form Utility = Revene Cost. In this work, we assme that U M is compted as U M = v M bk, (3 where v M denotes the Revene for the power saving for each remaining de to the offloading of K s and bk acconts for the total price (or cost paid by the MBS to all SBSs. Denote M and M K to be the sets of s served by the MBS before and after sing the hybrid access, respectively. Thereby, we obtain v M = λ M (p i [M] p i [M K] ( = λ M M( +, (M K( + (4 where λ M denotes the eqivalent revene per nit of power saving of a single ithat remains in the service range of MBS. For each remaining i in the system the term remains the same for both sets M and M K in (. Therefore, is mltiplied to ease the calclation. Note that both the Revene and Cost of the MBS are increasing fnctions with respect to K, i.e., the spply qantity of offloaded s. The tility of SBSiis modelled as: U S i = v S i +bk i E i (5

3 where v S i acconts for the tility of the L i s, bk i is the compensation received from the MBS, and E i is the cost of additional energy of each registered when additional K i s are offloaded to the SBSi. We letv S i = λ L i withλ being the revene per nit of achievable rate whereas E i is compted as E i = λ p i[l i +K i] p i[l i] = λ L i( + (L i +K i( + withλ being the revene per nit of power loss denoted by the ratio of power consmption for a single registered. Observe that E i is an increasing fnction of K i. The tilityu S i is a fnction of only the local information of each SBS and of the bid price b from the MBS. Therefore, there is no need of information exchange among SBSs. 3.. Action Soltion As depicted in Algorithm, for a given b the demand qantity of SBS i at each iteration is obtained as the soltion of the following problem: K i = arg where U S i takes the form max K i {,,...,M} (6 U S i, (7 Ui S (L i( + = λ L i+bk i λ (L i +K i( +. (8 The soltion of the above problem can be obtained in a closed form as follows. Proposition. For a given bid price b, the soltion to (7 is K i = L i( + (L i( +λ. (9 b( Proof. K i in (9 is obtained by checking US i K i = by integer optimization and showing that U S i is a convex fnction of K i. The optimal qantity K i is obtained by solving the first derivative of (8 with respect tok i, i.e., Ui S = b+ λ(li( +( =, K i ((L i +K i( + K i = Li( + (L i( +λ.( b( Now we show that the tility fnction U S i in (8 admits global maximm by checking the second derivative, U S i K i = (L i( +( ((L i +K i( + ((L i +K i( + 4. ( Given the restriction in (, Ui S <. The integer-valed optimization reslt is achieved by K i sing. As seen, for a given b the comptation of K i reqires knowledge of local information as it only depends on the parameters L i,, and λ, which are independent of other SBSs. The MBS determines the optimal spply of offloading s by solving the following problem: K = arg max K {,,...,M} U M ( with U M = λ M( M( + bk. (M K( + Proposition. For a given bid price b, the soltion to ( is K λ = M + M b(. (3 Proof. The proof follows the same procedre as that for Proposition and is ths omitted for space limitations. With the constraint on the total nmber of offloading s K {,,...,M}, the bid price b shold be provided in the following range. Corollary. The rate reqirement can be ensred provided that the bid price b is sch that b min b b max with and b max = λ M ( (M( +, (4 ( b min = max λ M ( λ (,. (5 L i( + Proof. λ M ( b λm ( (M( + is proved by ensring λ ( L i ( + K M. b is to ensre Ki M, therefore Corollary is proved. 4. CLINCHING PRICE-STACKELBERG GAME If the MBS and SBSs belong to the same operator, then it is possible for the MBS to gain knowledge abot the tilities and strategies of the SBSs. The proposed ascending-bid action can be formlated as a Stackelberg game. The MBS acts as the leader by providing the clinching bid price b and the SBSs act as the followers by deciding the bid qantity of offloading s given b. We now proceed compting the clinching bid price in a closed form. If the MBS acqires the information of the SBSs, then it can predict the bidb withot iterations. As described before, the action mechanism is clinched if the market clears or, eqivalently, if the spply is eqal to the total demand, which amonts to saying that K = N i= K i. Then, from the reslts of Propositions and it follows that: Proposition 3. The clinching bid price b can be obtained from the following eqation b = λm + N i= λ(l i( + (+ N i= Li( + M.

4 Nmber of optimal s M =5, L =,L = =.8 λ M = λ =5 λ = 5 K K Clinching 4 K +K K Fig.. Illstration of clinching bid price at market clearance with =.8. Nmber of optimal s M =5, L =,L = =.8 λ M = λ =5 λ = Clinching K K K + K Fig. 4. Illstration of clinching bid price at market clearance with λ =. K Nmber of optimal s M =5, L =,L = =.3 λ M = λ =5 λ = K K K + K K Clinching Fig. 3. Illstration of clinching bid price at market clearance with =.3. Proof. Imposing K = N i= K i and solving with respect to b yields the above reslt (after simple calcls. If the MBS and SBSs belong to different operators, then the ascending-bid action is rn as shown in Algorithm. This is illstrated in the next section. 5. NUMERICAL RESULTS In order to illstrate the otcome of the proposed action-based hybrid access, the scenario where two small cells exist within the coverage of the macrocell is simlated. However, the reslts are extendable to mltiple small cells. In the following, the identical rate reqirement is set in the range sch that it is achievable for all possible nmbers of UEs in the twotier system no matter in the macrocell or the small cell. We illstrate when the MBS has no knowledge abot the SBSs, how the nmber of s in both demand and spply changes with the bid price for different network parameters. In each rond of the action, both the actioneer MBS and the bidders SBSs optimize their spply and demand qantities of offloading s by maximizing their own tilities, respectively. U M is a decreasing fnction whileu F i is an increasing fnction ofb. The higher the bid price, the more compensation the MBS will pay to the SBSs and ths the lower its spply of s. In contrast, the higher b, the more s the SBSs are willing to serve. There exists a niqe clinching price b sch that the market clears withk = N i= K i. And the step size b can be chosen for fast convergence. We can see from the figres that the bid price clinches only after few iterations, which shows the fast convergence of Algorithm. By comparing Fig. and Fig. 3, we observe that when the rate reqirement of each UE increases, the clinching bid price b is higher and the market clearance qantity K decreases. This is becase the higher rate reqirement, the less the acceptable nmber of UEs in each cell. Moreover, the SBSs need more compensation from the MBS in order to stimlate the acceptance of the additional s. Whenλ increases as shown in Fig. 4, the clinching bid priceb also becomes higher and the market clearance qantityk decreases as well. The reason is that λ shows the importance of the energy loss for the SBSs when concerning to serve additional s. If λ becomes higher, then less Ki s cold be served in order to make sre that the loss in power of the registered s is not significant. The theoretical analysis of b, K, K and K are verified by the simlation reslts. Both the tilities of the MBS and SBSs are maximized. Since there is no overhead on information exchange among different cells, the proposed ascending-bid action is a lowcomplexity mechanism to apply for the hybrid access in HetNets. After optimizing the offloading qantity of s, the MBS can decide the exact s with the shortest distance to the corresponding SBS in order to minimize the total energy consmption of the two-tier HetNet. However, this is beyond the scope of the crrent work. Therefore, the comparison of energy redction remains in or ftre work. 6. CONCLUSION In order to motivate the energy-aware hybrid access in the two-tier macro-small cell network, a novel ascending-bid action-based algorithm is proposed.. The MBS in the macro- cell acts as the actioneer and the SBSs in the small cells act as the bidders. The bid price is provided by the MBS to all the SBSs. The optimal spply and demand qantities and the clinching price are derived in closed form soltions. Nmerical reslts illstrate that the action clinches at the niqe clinching price and the tilities of both the MBS and the SBSs are maximized, showing that the action algorithm reslts in a win-win soltion.

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