Broker Based Secondary Spectrum Trading

Transcription

1 Broker Based Secondary Spectrum Trading Joseph W. Mwangoka, Paulo Marques, and Jonathan Rodriguez Instituto de Telecomunicações, Campus Universitário de Santiago, Aveiro, PORTUGAL {joseph, pmarques, Abstract Radio spectrum license is multi-dimensional in nature. This suggests that matching a bid to buy and an offer to sell has to be done across the multiple dimensions to maximize spectrum usage in terms of economic efficiency. In addition, creating a functioning secondary market for trading spectrum requires an intermediary for both pooling the resources and matching the supply and demand sides of the equation. This paper proposes a multiple-dimension auctioning mechanism through a broker to facilitate an efficient secondary spectrum market. A broker for orchestrating the market is proposed describing its basing functionalities. Two trading negotiation protocol modes are discussed,.i.e, merchant and auction. Related signaling for the trading mechanisms are also presented. Focusing on the auction mode, the multiple-winner determination problem (mwdp) is defined and cast into a multidimensional multiplechoice knapsack problem (MMKP). Since the MMKP is NPcomplete, two heuristic algorithms to solve the mwdp namely () area-by-area (ABA), and (2) maximum-utility-first (MUFA) are presented. Numerical studies illustrating the potential of the algorithms are presented. The numerical studies indicate that MUFA is better in addressing the exposure problem. I. INTRODUCTION The proliferation of the Internet usage in people s daily activities has led to an increase in the need for connectivity anytime anywhere. This need has spurred the demand for more spectrum to which some regulators have responded by allowing secondary spectrum usage through trading or opportunistic access parallel with command and control. Moreover, the development of frequency efficient digital terrestrial television (DTV) has lead to the clearing/release of bands which were used for analogue TV. To avoid interference to co-channel or adjacent channel DTV transmitters, the bands are geo-graphically interleaved forming the TV white spaces. The cleared bands and the unused geographical interleaved spectrum bands provide an opportunity for deploying new wireless services. This paper presents a broker based approach for the usage of the TV white spaces. The exploitation of the TV white spaces, although conducive to more decentralized methods of spectrum usage, present risks and challenges which necessitate the introduction of centralized coordination or enabling intermediaries [] [2] [3] [4]. Such centralized co-ordination through intermediaries, like a broker, will have a positive impact to the development of regulatory policies, business models and enabling technologies. For regulation, it would ensure conformance to policies, hence help in achieving economically efficient usage of spectrum. For businesses, it would provide a mechanism for interaction between TV white space supply and demand sides, hence lowering transaction costs by centralizing the access to information on the availability of spectrum. For technology, it would reduce the complexity of cognitive devices by eliminating the need for sensing modules for spectrum acquisition [5], which in turn will boost investment in the development of cognitive technology based services. Therefore, research of an effective intermediary mechanism for supporting secondary spectrum usage is prerequisite to achieve these goals. Initial spectrum assignment mechanisms could affect incentives to spectrum trading due to windfall gains in secondary spectrum trading market [6]. However, the TV white spaces presents a different scenario where the bands have to be reused while the incumbents are sill operational. In this work, we assume that the TV white spaces are acquired from a secondary spectrum market which orchestrated by the broker. Furthermore, through the broker, dynamic spectrum access will allow the TV white spaces to be traded to allow wireless service providers (WSPs), such as Super-WiFi, LTE, WiMAX, etc., acquire or lease chunks of spectrum on a short-term basis [4]. In this case the broker both pools the white spaces and provide a platform for their trading. This suggests that matching a bid to buy and an offer to sell has to be done across the multiple dimensions defining the temporary secondary spectrum rights namely frequency band, bandwidth, maximum emission power, geographic region, availability duration, benchmark price, etc. This means choosing multiple-winners to maximize the economic efficiency of the bands is the main challenge. The auction winner determination problem in secondary spectrum trading has been studied in [4], where the solution is determined through game theoretic means. However the exposure problem has not been addressed. This work proposes a holistic approach for secondary spectrum trading based on the broker. The broker architecture and the negotiation protocols for secondary spectrum trading are proposed. Focusing on the auction mode, the multiple-winner determination problem (mwdp) is defined and cast into a multidimensional multiplechoice knapsack problem (MMKP). Since the MMKP is NPcomplete, two heuristic algorithms to solve the mwdp are proposed. Numerical studies are given to illustrate the potential of the algorithms in terms of their ability to address the exposure problem. The rest of this work is presented in the following order. Section II presents the multi-dimensionality scenario of exploiting the white spaces as well as the challenges and requirements. Section III proposes a broker architecture for facilitating secondary spectrum trading. The section also presents the merchant and auction based negotiation protocols.

2 The auction multiple-winner determination problem is defined at the end of this section. The problem is NP-complete, hence Section IV gives two heuristics for solving the problem by considering its nature. To illustrate the proposed algorithms, Section V presents the numerical studies. Section VI concludes the paper giving a glimpse of future work. StationX Broker StationX 2 II. SCENARIO AND CHALLENGES FOR EXPLOITATION OF A. Scenario THE TV WHITE SPACES Figure illustrates an example deployment where white spaces are used to provide wireless access services. Assume there are N frequency bands indexed as {,...,n,...,n}; and M stations or geographic regions indexed as {,...,m,...,m}. In the figure, there are two broadcast channels used marked by F and F 2. In this example, incumbent broadcast stations are marked as X mn with the subscript indicating the m th station operates in the n th band. Similarly, white space access points are marked as WS mn. Each incumbent broadcast station X mn uses frequency band F n transmitting in an area of radius z(x mn,f n ). The intensity of the radio waves (received field intensity) from a transmitting station decreases with distance until reaching the sensitivity limit of the receiving device. For example, broadcasts from StationX can be received between PointsE and G. Similarly, broadcasts from Station X 2 can be received between Points F and H. In practical cases, system planners avoid interference by imposing a protection margin to ensures that the field strength of the radio waves from one station is limed to a lower level than the sensitivity limit of the receiver of signals from another station operating in the same band. Apart from distance, interference can be avoided by operating in different bands as shown in the figure. The white space systems operates between points G and H. Therefore, in order to avoid interfering the incumbent system, the white space systems can transmit in an area of radius z(ws mn,f n ) such that, z(ws mn,f n ) D(X mn,ws mn ) z(x mn,f n ), () where D(X mn,ws mn ) is the distance between the incumbent station and the white space base station. In this work, we assume a centralized TV white spaces acquisition mechanism. The broker stores the information about DTV stations, including respective geo-location information, maximum transmission power, etc. This information is processed to a quality that the broker trades the bands for profit. Spectrum trading denotes a mechanism whereby rights to use spectrum are transferred from one party to another for a certain price or based on some utility exchange agreements. This contributes to a more efficient use of frequencies because a trade will only take place if the spectrum is worth more to the new user than it was to the old user, and therefore reflecting the greater economic benefit the new user expects to derive from the acquired spectrum. The goal is to facilitate transfers by establishing a swift and inexpensive mechanism. If neither Fig.. E G WS 2 Legend Frequency F Frequency band F 2 Field intensity condition for enabling shared use of the same channel the buyer nor the seller behave irrationally or misjudge the transaction, and if the trade does not cause external effects (e.g., anti-competitive behavior or intolerable interference), then it can be assumed that spectrum trading contributes to greater economic efficiency and boosts transparency by revealing the true opportunity cost of the spectrum. Reliable information is vital for successful deployment of wireless services with varying QoS guarantee. For convenience, the broker characterizes this piece of information of a spectrum good as a temporary exclusive right represented by the following generic tuple: L = {F,P max,(x,y),t,...}, where P max is the allowed maximum power in a given band; (x, y) the geo-location coordinates of the region of operation; and T is the time frame that the band can be used. This information of TV white spaces will be stored, managed and distributed by the broker based on dynamic resource allocation algorithms. The broker may earn revenue in the following ways: ) auction mechanism where the white space systems bid for the TV white spaces and the winner(s) is(are) chosen such that the broker s revenue is maximized or the spectrum usage efficiency is maximized. 2) merchant mechanism where the broker directly charge secondary spectrum users based on fixed or negotiated fees derived from market-driven rules; The broker supports both auction and merchant modes. In the merchant mode, the price is decided by the allocation procedure which considers various factors that influence the value of TVWS in a given place. In the auction mode, the broker assigns a benchmark price for the offered bands, then decides the final price based on some auction winner determination mechanism. In fact, the price in the merchant mode can be used as benchmark price in auctioning mode. This allows the broker to be flexible in maximizing its revenue: in case of low demand, the broker may use the merchant mode and adjust prices to attract more usage; whereas in case of high demand, the broker may use the auctioning mode to H F

3 approximate the willingness to pay value of customers above the benchmark price. In this work we consider the first revenue model, i.e., the broker earns revenue through auctioning the TV white spaces to participants. We consider reducing the exposure problem that bidders of multiple-bids encounter in acquiring spectrum, assuming that the broker runs profitable. Region 3GLD Region 2GLD Region GLD GLD :Geo-location database WS Allocation Server WS Broker Spectrum Context Database B. Challenges and requirements We consider a spectrum secondary market environment having a broker as a supplier and several master-slaves communication systems forming the demand side. The broker is a centralized platform for trading spectrum while controlling the amount of bandwidth and power assigned to each user in order to keep the desired QoS and interference below regulatory (or acceptable) limits. The master-slaves communication systems are comprised of cognitive devices, i.e., radios with the ability to reconfigure their bandwidth, center frequency, power, and respond to QoS changes based on user preferences and budget. The master-slaves systems could be cellular operators, highspeed Internet service providers, ad-hoc sensor networks, etc. The market allows the master devices to buy or lease temporary spectrum usage rights from the broker. The setting poses an enormous number of challenges especially when conflicting goals comes in the picture. These includes maximizing the broker s revenue while lowering management overhead; increasing spectrum acquisition flexibility while ensuring reliability; maximizing spectrum usage efficiency while minimizing interference; and the list goes on. These challenges emanates from the following aspects: A. Multi-bands: The TVWS management complexity increases with the increase of the number of bands in the broker s portfolio. A.2 Multi-bids: On the demand sides, different masters systems are posed to request for different bands. A.3 Multiple locations: The broker manages bands across a wide geographic area. Therefore, band reuse has to be considered in order to maximize spectrum usage. The above setting implies that the broker has to simultaneously satisfy conflicting needs in the most efficient and cost effective way. Different goals will lead to different strategies. In this work, while ensuring reasonable revenue for the broker, we aim at maximizing spectrum usage while lowering management overhead. To this end, simple heuristic algorithms to generate the multiple winners of the TVWS bands will be investigated. III. BROKER ARCHITECTURE AND THE AUCTION MULTI-WINNER DETERMINATION PROBLEM In this section, a centralized broker platform to support the trading of the TVWS is introduced. Further, the operation interaction between the broker and users is given. the spectrum users include cellular operators, super-wifi providers, etc. The spectrum broker controls the amount of bandwidth and power Super-WiFi Hot-Spots Fire Brigade Fig. 2. Super-WiFi Provider Public Safety Police etc WS Trading Server The White Space Broker Model Registration & Validation Cellular Operators assigned to each user in order to keep the desired QoS and interference below the interference limits. A. The White Space Broker Model In the broker model part of TVWS is traded as a commodity, therefore, the amount of policing and enforcement of illegal or accidental polluting of spectrum needs improvement from todays standard. In this context, we make suggestions with respect to the digital switchover regulation that is needed towards the realization of true spectrum sharing systems at European level. It is important to note that the broker model has the potential not just to open the market to new players but that it also has the potential to create new business opportunities for the spectrum broker entity - be that in new public sector roles or in the commercial sector. Moreover, the broker is a viable solution to address the cross-border issues among member states. A service provider across diverse geographic regions can easily obtain spectrum from spectrum broker operating in regions. Therefore, the service provider saves the time spent in acquiring spectrum resources in each place. The white space broker is a centralized intermediary that orchestrates the exploitation of the TVWS. As Fig. 2 shows, the broker has the following sub-systems: () Spectrum context database; (2) Dynamic TVWS allocation; (3) Trading and auctioning; and (4) Registration and validation. In short, the sub-systems perform the following respective tasks. ) Spectrum context database: The spectrum context database obtains TVWS information from the national database. The broker then enhances the radio environment map by analyzing availability usage patterns. The database must contain regulatory policies for the specification of secondary spectrum usage rights and obligations and prioritization of

4 TVWS access. Specifically, the spectrum context database contains the following repositories: Trading information repository: stores trading information to maximize revenue, spectrum utilization and fairness such as reserve price and transaction costs. Market and coexistence polices repository: stores regulatory policies for the specification of spectrum usage rights, prioritization of TVWS access, policies for coexistence, cross-border requirements, etc. TVWS occupancy repository: stores real time TVWS channels occupancy information. 2) Dynamic TVWS Allocation: The Broker, through its trading mechanism and price discovery, matches the players requirement with available resources and thus allocates the TVWS based on preset rules. The TVWS allocation mechanism implements an algorithm that uses information from the database to determine the TVWS bands and power at which a secondary user (player) should be allowed to operate to avoid spectrum fragmentation, optimize QoS and guarantee fairness in TVWS access. Having determined the benchmark price of a given band, the Broker creates a spectrum portfolio for potential transactions. The portfolio recommends the bandwidth and power thresholds as well as geographic areas that the band can be used in the form of the tuple L given above. The portfolio is based on spectrum context information analysis by the broker to best match the needs of potential users. Interested parties then bid for the bands based on their needs. 3) Trading and Auctioning: The trading mechanism handles the spectrum transactions between the broker and the customers (players) who buy spectrum. When a player needs extra spectrum, then he/she goes to the broker to buy spectrum resources (TVWS) available. The Broker is an intermediary agent that lets the spectrum supply and demand sides meet and accomplish a spectrum transaction. The main function of the trading mechanism is to determine the revenue maximizing set of buyers or bidders. The broker aims at selling the spectrum rights to the most valuable user(s). The best way to achieve this is through auctioning. Besides discovering the willingness to pay price of the buyer, the broker need to determine a benchmark price to start the auctioning. This ensures profitability, and limits the chances of collusion where buyers collude to lower the spectrum prices. Dealing with collusion is not in the scope of this work. 4) Registration and validation: To support secure spectrum trading, a security framework is required to prevent unauthorized spectrum access. Therefore, tracing users of the brokers service is achieved through a registration and validation mechanism. The tracing of users is also important in case of conflict resolution. B. Negotiation Protocol In this section, the interfacing signaling between the broker and the spectrum user are presented. The signaling interface is the protocol that enable the transaction of spectrum between the broker and the user to take place efficiently. Through this, the Broker maximizes its revenue as well as ensures fairness between players. In the merchant mode, spectrum is sold in terms of first come first serve basis; while in the auctioning mode, the most valuable bidder wins the band. Figure 3 gives the operation sequence of the negotiation protocol. As the figure shows, in the merchant mode: () the broker informs the buyers about the available TVWS portfolio and corresponding prices; (2) network operators and service providers place TVWS orders on first come first serve basis. The broker then, authenticates them; and (3) sends an ACK message that the orders have been received. The broker processes the orders for the temporary spectrum rights from each buyer and proceeds to step (9). The auction mode, on the other hand, behaves differently depending on the type of auction. Referring to the Figure 3, a generic sequence of events in allocating the TVWS through the auction mode proceeds as follows: (4) The broker informs the participants about the start of an auction and; (5) calls for proposal by announcing the initial price (let s say in an English Auction setting). (6) The participants, i.e., network operators and service providers, send their bids for the spectrum, each with a proposal price(s) for the band(s) of interest. After receiving the multiple-bids, (7) the broker solves an auction winner determination problem with the objective of maximizing its utility in terms of revenue or spectrum efficiency. Depending on the auction mechanism, an iteration (6-8a) continues until the bid winner(s) is(are) found. Based on the results, the broker (a) rejects the proposal price of some bidders, and (b) accepts the proposal price of the remaining bidders, i.e., the winner(s). (8) In case the broker still has resources, it (a) returns to step (5) with a new call for proposal price, or it (b) informs all the participants about end of auction. Further, in (c) the broker informs the bid winner(s) about the final price to be paid. After the buyers or winners have been determined, (9) the broker processes the bill for their bids and (0) allocates the temporary spectrum rights. Finally, () the broker updates the local TVWS repository and monitors the market.after that, the participants can start to transmit data in the acquired bands with QoS guarantee. C. The Auction Multiple-Winner Determination Problem A provider of wireless service access may wish to buy temporary license rights in a geographic area of a country. This could be for super-wifi, LTE, etc. The provider will need enough bandwidth to cover the whole region to support the service offered. Moreover, the provider will incur less roaming cost of using a competitor s network if wider coverage is achieved [7]. On the other hand, limited coverage may result into loss of a wider customer base leading to decreased profit. Therefore, when bidding for TV white spaces, the provider may prefer (or has incentives) to bid for a combination of white spaces over several geographical regions. Depending on the need, the provider may opt for all-or-nothing bids or prioritize regions according to potential revenue. For example if bandsq,q 2, andq 3 are auctioned, an all-or-nothing bid

5 Participant(s) n n k n Advertise Available TVWS PlaceTVWS Order ACK Receiving Order Inform: Start Auction Call for Proposal: Announce Initial Price Propose Price k- Reject Proposal Price (a) Accept Propose Price (b) k>=2cfp New Price (a) Inform End Auction (b) (Actual Price>= Reserve Price) Request Price (c) Allocate Temporary Spectrum Rights Broker () (2) Authenticate Buyer (3) Process Order (4) (5) (6) (7) (8) (9) Process Payment (0) Update Repository () Auction Mode Merchant Mode combination of these parameters qualifies the boundaries of a spectrum good offer. This has two connotations based on A., A.2 and A.3: One-offering multiple-winners [9]: Since spectrum-bands are interference-limited, then one band offering for auction can receive bids from multiple participants, denoted by set I. Multi-bids: One participant can request for one band in multiple locations forming a multi-bid s problem. Similarly, one participant can bid for multiple bands in the same location. For the bidder, we define a bid as a tuple b i = {qmn,p i i mn,wmn}, i where b i is the bid from participant i I; qmn i is the spectrum band requested; p i mn is the corresponding payment; and wmn i is the weight allocated for the respective band for the given region. This information is part of the broker s bidding language for the participants to encode their preferences. In this particular case, it is used to address the exposure problem. A participant may multi-bid by submitting several requests for a band in different locations or different bands in the same location with constraints on its utility. Assuming the bidder is determined to provide services in several areas M i M. Hence, when the bidder i is in need of spectrum, it submits a set of M i two dimensional bids b i = {b i,...,bmi i }. The exposure problem can be modeled by considering that the bidder i allocates a weight wmn i for each band in each region such that wmn i =. Therefore, a bidder s utility can be defined as Fig. 3. Negotiation Protocol for the merchant and auction modes U i = N M i n=m= w i mnq i mnp i mn, (2) on {q 2,q 3 } will either accept an offer of both q 2 and q 3, or none, this is because, partial allocation may lead to loss of revenue as mentioned above. On the other hand, if the provider only need q 2 additional frequency band to accommodate a traffic surge in a specific region, a partial allocation will be economically feasible. The need for this kind of flexibility bring challenges in determining the auction winner while achieving the goals of the broker. Therefore, appropriate combinatorial auction mechanism has to be designed in order to achieve a viable white space secondary spectrum market. To formalize this problem, let the amount of white space items that the broker simultaneously trades be given by a matrix Q = {q mn }, where the subscripts represents the frequency band index and corresponding geographic regions respectively. The number of master nodes (bidders) is I. As pointed out in [8] [9], auction of spectrum resources differs from other goods in that the former is interferenceconstrained while the latter is quantity-constrained. Therefore, the auctioning of spectrum goods have to consider interference in its definition. In this work, we consider interference in terms of geo-location and maximum emission power. The Considering that the TV white spaces have a similar RF properties, n may be dropped.let us define the social utility of the broker as U broker = N n=m= M qmnp mn, (3) where p mn is the price offered by (determined for) the bid winner. Therefore, the broker s objective is to maximize its revenue, that is: Maximize U broker (4) In order to do that, the broker has to determine the k best winners such that its revenue is maximized (and the signaling overhead is minimized), subject to conditions that the total spectrum allocated does not exceed Q. Moreover, in case the bidder bids for all-or-nothing, then the broker must address the exposure problem, that is, ensure that the bidder wins bands in all chosen areas or risk to lose revenue. Therefore, the revenue maximization problem is a multi-objective one. Hence, for the exposure problem of each bidder, one of the

6 constraints that the broker has to consider is, N M i n=m= M i w i mp i mn U i i I; wnm i = m. m= The revenue maximization problem solved by the broker, i.e., the multiple-winners determining problem (mwdp) of the auction is equivalent to a multi-dimensional multiple-choice knapsack problem (MMKP). A multiple-dimensional knapsack problem is one kind of knapsack where the resources are multi-dimensional, i.e., there are multiple resource constraints for the knapsack. The mwdp problem is MMKP. Every instance of the MMKP can be formulated as a mwdp; hence mwdp is NP-hard. For this case, an exact solution is not suitable for such a real time problem, so a heuristic based on approximation algorithm to allocate spectrum among multiple bidders is developed. Moreover, we exploit some characteristics of the problem to find the solution of the mwdp as presented in the next section. Algorithm Area-by-Area Algorithm (ABA) : INPUT: DTV(X,Y), P DTV, Φ, CR(x,y), p max, etc. 2: Pre-processing ) Enhance REM in broker repository and estimate availability index 2) Estimate TVWS demand and benchmark price p bmp 3) Prepare WS portfolio Q 3: Advertise bands for sale (auction) 4: Receive WS bids from interested parties B = {b,...,b M } where b i = {q i,p i,(x i,y i ),t i }. 5: for all Bids do 6: Sort b i in descending order based on price p i. 7: end for 8: for all Q {} do 9: Allocate requested temporary exclusive rights following the sorted order for each bid 0: Update allocated bands as : Update available bands as q i q i and b i {q i} Q Q {q i} Q Q Q c 2: end for 3: Inform winning bidders B = b i 4: Update WS occupancy repository (5) IV. HEURISTICS FOR SPECTRUM ALLOCATION This work considers the nature of the problem to design the heuristics for solving the multiple-winner problem. Generally, wireless service providers prefer to deploy their services in with potential for a higher customer base; for example across populated cities joined by land, sea or air transportations. Therefore, proposed heuristics takes into consideration that a single bidder might bid for several regions to minimize its cost of running. Two heuristics to address the mwdp problem are presented in this section. The heuristics are namely () area-by-area (ABA), and (2) maximum-utility-first (MUFA). The first algorithm simply collects the bids, and group them in area by area basis. The algorithm then sorts the bids from highest price to lowest for the bands in a given areas and match them to the value of the bands in the portfolio for that locality until there is no more bands remaining in the broker s portfolio. Here we assume that the demand exceed supply. This heuristic is summarized in Algorithm. The second heuristics considers the aggregate utilities for the bidders in all regions of interest. The algorithm sorts the bids from the highest aggregate utility to the lowest. The bands are then allocated following the sorted order across the broker s portfolio. This heuristics is summarized in Algorithm 2. Algorithm 2 Maximum-Utility-First Algorithm (MUFA) : INPUT: DTV(X,Y), P DTV, Φ, CR(x,y), p max, etc. 2: Pre-processing ) Enhance REM in broker repository and allocate availability index 2) Estimate TVWS demand and benchmark price p bmp 3) Prepare WS portfolio Q 3: Advertise bands for (auction) 4: Receive WS bids from interested parties B = {b,...,b M } where b i = {q i,p i,(x i,y i ),U i }. 5: Sort b i in descending order based on price U i. 6: for all Q {} do 7: Allocate bands area-by-area following the sorted order 8: end for 9: Inform winning bidders B = b i 0: Update WS occupancy repository The data used in the allocation algorithm is as follows: () Location grid of DTV transmit stations DT V(X, Y) (2) Maximum DTV station transmit power P DTV (3) Operating frequencies Φ (4) Allowable interference threshold(s) (5) Location grid of operating CR transmitter CR(x, y) (6) Required (maximum) transmit power p max (7) Standardization or Regulators constraints.

7 V. NUMERICAL STUDY This section presents numerical studies to illustrate the potential of the proposed algorithm in solving the multiple winner determination problem. The numerical study emphasizes on the potential for addressing the exposure problem prevalent in multi-bid auctions. The band portfolio studied consists of five bands in seven regions. The bands are graded according to an availability score ranging from 0 to. The lower the score, the less the value of the band and the higher the potential for interference - causing interference or being interfered. The higher the score, the higher the value of the band the lower the risk for interference, i.e., being interfered or interfering other systems. For simplicity, we assume that all the bands have the highest score. In this experiment, there are 20 bidders competing for the available bands. Each bidder intends to provide wireless services in several regions in which the broker auctions its bands. The bidder submits bids, indicating its utility for each region, and the aggregate utility for all the regions of interest. For simplicity, we assume that the aggregate utility of the bidders is the sum of the utilities for each region submitted. In selecting the highest bidder, this paper proposes two heuristics: () area-by-area (ABA), and (2) maximum-utilityfirst (MUFA).Figure 4 shows the utility of winning bidders obtained through the two methods compared to expected utility. From the figure, it can be seen that the MUFA heuristic has less of the exposure problem than the ABA. From the brokers perspective, both algorithms could maximize its utility. However, from the operator s angle, MUFA has the potential of lowering running costs by avoiding roaming costs in other provider s networks. This is true especially for providers of mobile services across different regions, or for back-haul. However, for fixed services, ABA algorithm is better, if those services are provided by separate providers. In that case, ABA has the potential of enabling start-ups to acquire spectrum bands and compete in their locality, hence spur innovation. VI. CONCLUSION AND FUTURE WORKS This paper has considered the problem of matching multiple-bids to buy and band portfolio to sell as offered by a spectrum broker. The matching has to be done across multiple dimensions to maximize spectrum usage in terms of economic efficiency. The problem scenario is given to illustrate the multiple-dimensional nature of the problem. A broker for orchestrating the market is proposed with the necessary negotiation protocols to faciitate the matching task. The multiple-winner determination problem (mwdp) is cast into a multidimensional multiple-choice knapsack problem (MMKP), which is NP-complete. Two heuristic algorithms to solve the MMKP mwdp namely () area-by-area (ABA), and (2) maximum-utility-first (MUFA)are presented. The heuristics are based on the nature of the problem. MUFA is shown to better address the exposure problem than ABA Area by area Maximum utility first Expected utility Fig. 4. Illustration of the number of exposed and non-exposed bidders in area by area and maximum utility first algorithms. Further study is needed to address the various needs of the bidders as well as maximization of the broker s revenue. Also, in case demand is less than supply, pricing mechanism to give incentives for spectrum usage has to be studied. ACKNOWLEDGMENT The research leading to these results has received funding from the European Community s Seventh Framework Programme [FP7/ ] under grant agreement No [COGEU]. REFERENCES [] J. Bae, E. Beigman, R. Berry, M. Honig, H. Shen, R. Vohra, and H. 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