CHAPTER

Auction-based spectrummarkets in cognitive radionetworks

Xia Zhou1, Heather Zheng1, Maziar Nekovee2, andMilind M. Buddhikot31University of California Santa Barbara, United States2BT Research and University College London, United Kingdom3Alcatel-Lucent, United States

17

17.1 INTRODUCTIONAccess to the radio spectrum is a key requirement for continuous wireless growthand deployment of new mobile services. Given the fast-growing demand for radiospectrum, regulators around the world are implementing much more flexible andliberal forms of spectrum management, often referred to as dynamic spectrummanagement. This new model dynamically redistributes and reassigns spectrumwithin and across different wireless systems, adapting spectrum usage to actualdemands and achieving much more efficient use of the precious spectrum resource.Within the new model, two prominent approaches are being considered by theregulators: spectrum trading and cognitive spectrum access. In this chapter, wefocus on examining the challenges and solutions in the area of spectrum trading.

Spectrum trading is a market-based approach for spectrum redistribution thatenables a spectrum license holder (for example, a cellular operator) to sell orlease all or a portion of its spectrum to a third party [623]. The third party can,in principle, change the use of spectrum or the technology to be used, providedcertain conditions are satisfied. Note that this is an important departure from thecommand and control management model, where spectrum licenses are grantedby regulators for the provision of a specific service using a predefined technology,and license holders were not allowed to reallocate their spectrum to different tech-nologies or other users. Exposing the radio spectrum to market forces has become

c© 2010 Elsevier Inc. All rights reserved.Doi: 10.1016/B978-0-12-374715-0.00017-4 489

490 CHAPTER 17 Auction-based spectrum markets in cognitive radio networks

FIGURE 17.1

From command and control to market-driven spectrum allocation in the United Kingdom(courtesy of Ofcom - Spectrum Framework Review, Feb. 2005).

increasingly popular. For example, the U.K. regulator, Ofcom, is aiming that, by2010, 71.5% of its available spectrum should be operating under market forces [10](see Figure 17.1). The rationale for the approach is that market mechanisms willallocate spectrum to those that value it most, thereby ensuring that the (eco-nomically) most efficient utilization of this resource is achieved. However, at leastinitially, one expects that such forms of spectrum trading would take place only ona macro-scale (e.g., between two cellular service providers) involving large blocksof spectrum and timescales that are still dictated by complex and cumbersomebureaucratic procedures involved in such wholesale forms of trading.

17.1.1 Dynamic Spectrum Micro-AuctionsCognitive access to ceratin “publicly owned" licensed bands, such as TV and mili-tary bands, are being actively pursued by regulators. However, it is very doubtfulthat, without any economic incentive, this form of access can be extended to“privately owned” licensed bands, such as 3G spectrum, for which the incumbentshave already paid billions of dollars, pounds, or euros to ensure their exclusiveuse. Therefore, market mechanisms on a micro-scale need to be implemented tocreate economic incentives for license holders to share their spectrum locally andtemporarily with cognitive radios.

For market players (cognitive radios and incumbent systems) to make econom-ically efficient deals, they require a market environment that enables them tonegotiate such that mutually acceptable bargains are reached. Auctions are amongthe best-known market-based allocation mechanisms due to their perceived fairnessand allocation efficiency. Indeed, the FCC (Federal Communications Commission)and its counterparts across the world have extensively used auctions for wholesaleallocation of spectrum in the last decade and intend to use this mechanism in thefuture. However, an FCC-style spectrum auction targets long-term national/regional

17.2 Rethinking Spectrum Auctions 491

leases, requiring huge upfront investments. In this chapter, on the other hand, ourfocus is on micro-auction mechanisms that allow for the trading of spectrum rightsat the network level. These types of auction mechanisms could be highly attractiveto network operators: they provide a flexible and cost-effective means for dynamicexpansion of their spectrum resources without the need for costly capital invest-ments in new spectrum. The spectrum obtained through micro-auctions can beused for congestion relief during peak loads in traffic or to enhance existing ser-vices and provide new services without the need for acquiring additional spectrum.More generally, users will be able to dynamically and locally vary their operatingfrequencies and access the best available spectrum on a just-in-time basis. Thismay happen either upon instruction from a cognitive base station that acquiresspectrum on behalf of users [357] or autonomously by user devices themselves.

17.1.2 The Role of Cognitive RadiosCognitive functionality is essential in the realization of such types of micro-auctions,because wireless devices can understand the regulatory, technical, and economiccontext within which they perform the required negotiation and decision-makingtasks. The scope of this chapter, however, is not on developing such cognitive func-tionalities. Instead, we assume that these functionalities will be available in futuredevices and focus on developing and modeling appropriate auction algorithmsto ensure fast and efficient redistribution of the spectrum on the network level.Furthermore, we have no assumptions regarding the underlying network accesstechnologies that a cognitive device uses for its transmissions once it acquiresa portion of the spectrum. However, following [624], we envisage that accesstechnologies such as OFDMA will play an important role in enabling our micro-auction mechanisms. These technologies support dynamic bandwidth availabilityand permit grouping, subdividing, and pooling of pieces of the spectrum intoneatly packaged spectrum channels.

17.2 RETHINKING SPECTRUM AUCTIONSIn the past decade, the radio spectrum has been auctioned in terms of prepar-titioned bulk licenses that cannot match time-varying market demands. Suchmismatch led to several consequences. First, forced to bid in the unit of bulklicenses, buyers face huge upfront costs. As a result, past auctions involved only avery few large (incumbent) players, required significant manual negotiations, andoften took months or years to conclude. Second, winning buyers that receivedthe licenses could not efficiently utilize the assigned spectrum because their traf-fic varies significantly in time and space. Finally, while winning buyers’ spectrumsits unused, new entrants and new wireless technologies are either blocked orforced to crowd into highly unreliable unlicensed bands. If not addressed, suchinefficiency will soon put a stop to wireless growth and innovation.

492 CHAPTER 17 Auction-based spectrum markets in cognitive radio networks

Solving such inefficiency requires us to rethink the way the spectrum is dis-tributed, and redesign spectrum auctions to provide networks with spectrummatching their individual demands. Recent works have proposed an eBay-like,open marketplace concept to enable dynamic spectrum trading [625,626]. In thismarketplace, existing spectrum owners (as providers) gain financial returns byleasing their idle spectrum to new spectrum users, and new users (as buyers)obtain the spectrum they desperately need. This marketplace differs significantlyfrom conventional FCC-style spectrum auctions in three aspects:

■ Multiparty trading with spectrum reuse. Spectrum auctions are funda-mentally different from (and much more difficult than) conventional multiunitauctions because of the spectrum’s unique property of reusability. Unliketraditional goods (e.g., paintings, bonds, electricity), the spectrum can bespatially reused concurrently. Although two conflicting bidders must not usethe same spectrum bands simultaneously, well-separated bidders can. While aconventional auction with n bidders and k bands can have at most k winners,a spectrum auction can have more than k winners. Therefore, unlike FCC-style auctions, which have one provider (i.e., the FCC) and sell one license toonly one buyer, the new marketplace supports multiparty trading. Multipleproviders can selectively offer their idle spectrum pieces, and each spectrumpiece can be sold to multiple “small” buyers. In this way, the new marketplacecan exploit spectrum reusability in spatial and temporal domains to improvespectrum usage efficiency.

■ On-demand spectrum trading. Instead of forcing buyers to purchase pre-defined spectrum licenses, the new marketplace enables buyers to specifytheir own demands. Given these demands, the marketplace intelligentlyselects winners and allocates spectrum to best utilize the spectrum offered byproviders and supported by buyers. Such flexibility not only attracts a largenumber of participants, but also enables the system to effectively multiplexspectrum supply and demand, further improving spectrum utilization.

■ Economic robustness with spectrum reuse. Without good economicdesign, spectrum auctions easily can be manipulated by bidders, sufferinghuge efficiency loss. Auctioneers are forced to apply Bayesian settings, placingstrong (and often wrong) assumptions on the distribution of bidder valua-tions [627]. The heavy overhead and the vulnerability would easily discourageboth providers and players from participation. Therefore, only by preventingmarket manipulation can an auction attract bidders and new entrants and effi-ciently distribute spectrum to make the best use of this important resource.While conventional auction design has proposed novel solutions to achieveeconomic robustness, the requirement on spectrum reuse opens up newvulnerabilities in existing solutions [625]. New auction rules are required toachieve economic robustness while enabling spectrum reuse.

With these three requirements in mind, we now describe several ongoing effortsby which to design dynamic spectrum auctions. We start presenting a spectrum

17.3 On-Demand Spectrum Auctions 493

allocation algorithm to enable fast auction clearing. We then describe two recentworks on adding economic robustness to auction designs, including a single-sidedspectrum auction system, where spectrum buyers bid for spectrum from a singleauctioneer, and a double spectrum auction system, where spectrum sellers andbuyers can trade spectrum by each interacting with an auctioneer.

17.3 ON-DEMAND SPECTRUM AUCTIONSAn on-demand spectrum auction must distribute spectrum on-the-fly to a largenumber of bidders. Spectrum auctions are multiunit auctions, where the spectrumoften is divided into a number of identical channels for sale. Users wish to obtaindifferent amount of spectrum at their desired power levels and may be willing topay differently depending on the assignment. Toward this goal, we need a compactbidding language to allow buyers to conveniently express their desire and doit so compactly, and an efficient allocation algorithm to distribute spectrum inreal-time subject to the complex interference constraints among bidders.

In this section, we discuss recent ongoing efforts on spectrum allocation algo-rithms to support dynamic spectrum auctions. We focus on a recent work [628] thatproposed a computationally efficient auction framework with simple and effectivebidding and fast auction clearing algorithms. Specifically, spectrum buyers (bid-ders) use a compact and yet expressive bidding format to express their desiredspectrum usage and willingness to pay, while an auctioneer executes fast clearingalgorithms to derive prices and allocations under different pricing models.

17.3.1 Bidding Format: Piecewise Linear Price-Demand BidsAssume there are K channels in total, Fi is the set of channels assigned to bidder i,and hence the normalized spectrum assigned to i is fi = |Fi|/K. With the piecewiselinear price demand (PLPD), bidder i expresses the desired quantity of spectrumfi at each per-unit price pi using a continuous concave piecewise linear demandcurve. That is, the bidder would like to pay pi × fi for fi channels. An PLPD curvecan be expressed as a conglomeration of a set of individual linear pieces. A simpleexample is a linear demand curve:

pi( fi) = −aifi + bi, ai ≥ 0, bi > 0, (17.1)

where the negative slope represents price sensitivity of buyers—as the per-unitprice decreases, demands in general increase.

17.3.2 Pricing ModelsWithout considering economic robustness, the auction pricing follows directlyfrom each bidder’s bid. Bidder i that obtains fi spectrum is charged pi( fi) × fi asspecified by its bid. In this case, the revenue produced by each bidder is a piecewisequadratic function of the price:

494 CHAPTER 17 Auction-based spectrum markets in cognitive radio networks

Ri(pi) = bipi − pi2

ai. (17.2)

For linear demand curves, the revenue is a quadratic function of price, with aunique maximum at pi = bi/2. We can further divide the pricing models intotwo types: uniform and discriminatory pricing. In uniform pricing, the auctioneerchooses a single clearing price p for all the winners. Each bidder obtains a fractionof spectrum fi(p) = (bi − p)/ai and produces a revenue of Ri(p) = (bip − p2)/ai.Any bidder i with bi ≤ p gets no assignment. In discriminatory pricing, theauctioneer sets nonuniform clearing prices across bidders.

17.3.3 Fast Auction Clearing by Linearizing the InterferenceConstraints

Given the bids and the pricing model, the auction clearing problem is to maxi-mize the auction revenue

∑i Ri(pi) by choosing the winners and their pricing pi

subject to the interference constraints. This optimization problem is in general NP-hard because of the underlining interference constraints grow exponentially withthe number of bidders. The authors of [628] propose to reduce the interferenceconstraints into a set of linearized constraints that grow linearly with the numberof bidders. Specifically, they propose the node-L interference (NLI) constraints.Consider two nodes i and j located at coordinates (xi, yi) and (xj, yj). Node i is tothe left of node j if xi < xj. If xi = xj, then the node with the smaller index isconsidered to be to the node to the left. The constraint becomes: Every neighborof i to the left of i, and i itself, should be assigned with different channels:

fi +∑

j∈NL(i)

fj ≤ 1, i = 1, 2, . . . , N , (17.3)

where NL(i) is the set of neighbors of i lying to its left. It has been shown that thenew constraints are stricter than the original constraints and lead to a feasible butsuboptimal solution within a distance 3 from the optimal solution.

Using the new interference constraints, the auction clearing problem can besolved using linear programming (for the uniform pricing model) or separableprogramming [629] (for the discriminatory pricing model). Both solutions havepolynomial complexity. Readers should refer to [628] for additional details on thealgorithms and proofs. In practice, both algorithms run efficiently in real time.Using a standard desktop with a 3.0 GHz processor and 1 GB of RAM and assuming3500 bidders, the auction clearing finishes in 0.05 sec for the uniform pricing and80 sec for the discriminatory pricing model.

17.4 ECONOMICALLY ROBUST SPECTRUM AUCTIONSWhen it comes to resisting market manipulation, the dominant paradigm is truthfulauction design. A truthful auction guarantees that, if a bidder bids the true valuationof the resource, its utility will be no less than that when it lies. Hence, the weakly

17.4 Economically Robust Spectrum Auctions 495

dominating strategy is for a bidder to bid its true valuation. As we will show, a truth-ful auction charges a winner independent of its actual bid, which is different fromthe auction design in the previous section. To bidders, a truthful auction eliminatesthe expensive overhead of strategizing about other bidders and prevents marketmanipulation. Thus, it can attract a wide range of network nodes/establishmentsto engage in the marketplace. To the auctioneer, by encouraging bidders to revealtheir true valuations, a truthful auction can help the auctioneer increase its rev-enue by assigning the spectrum to the bidders who value it the most. For the samereason, many classic auction systems are made truthful, including the sealed-bidsecondary-price [630], k-position [631,632], and VCG auctions [633,634].

While prior works have enforced truthfulness in conventional auctions, existingtruthful designs either fail or become computationally prohibitive when applied tospectrum auctions. The fundamental reason is that, unlike goods (e.g., paintings,bonds, electricity) in conventional auctions, the spectrum is reusable among bid-ders subject to the spatial interference constraints. Because interference is only alocal effect, bidders in close proximity cannot use the same spectrum frequencysimultaneously, but well-separated bidders can. These heterogeneous interdepen-dencies among bidders make secondary-price and k-position auctions no longertruthful. Furthermore, these constraints make the problem of finding the optimalspectrum allocation NP-complete, and hence a real-time spectrum auction withmany bidders must resort to greedy allocations that are computationally efficient.Unfortunately, it has been shown that the VCG auction loses its truthfulness undergreedy allocations.

In the following, we describe VERITAS [625], a truthful dynamic spectrumauction framework. VERITAS achieves truthfulness with computationally efficientspectrum allocation and pricing mechanisms, making it feasible for online short-term auctions. In addition, VERITAS provides the auctioneer with the capabilityand flexibility of maximizing its customized objective and allows bidders to requestspectrum by the exact number of channels they want to obtain or by a range definedby the minimal and maximal number of channels.

Consider the typical sealed-bid auction in Figure 17.2. The auctioneer sells kchannels by running an online auction periodically. Each bidder requests spectrumby the number of channels and the per-channel price it would like to pay. Afterreceiving the bids, the auctioneer determines the winners, their spectrum alloca-tions, and prices, based on the bids and the interference condition among bidders.As shown in Figure 17.2, the interference condition is represented by a conflictgraph [635] G = (V , E), where V is the collection of the bidders and E is thecollection of edges where two bidders share an edge if they conflict. Table 17.1summarizes the notations used to define an auction problem.

Using these notations, we now define a truthful auction, and a truthful andefficient spectrum auction.

Definition 1. A truthful auction is one in which no bidder i can obtain higherutility ui by setting bi �= vi.

496 CHAPTER 17 Auction-based spectrum markets in cognitive radio networks

PeriodicAuction

Bids

Submit Bids

Interference Constraints underPredefined Power LevelsMay Change over Time

Auctioneer

Bidder Bidder

Bidder

BidderEC

DF

B

A A

B

D

C

F

E

FIGURE 17.2

A dynamic spectrum auction scenario: (left) an auctioneer performs periodic auctions ofspectrum to the bidders; (right) a conflict graph illustrates the interference constraints amongbidders.

Table 17.1 Summary of Auction Notations

Notations Description

Channel request di The number of channels requested by bidder i

D = {d1, d2, ..., dn} The set of demands across all the n bidders

Per-channel bid bi The per-channel bid submitted by bidder i or themaximum price bidder i is willing to pay for a channel

B = {b1, b2, ..., bn} The set of bids submitted by all the n bidders

Per-channel valuation vi The true valuation a bidder i has for a channel. Inmost cases, vi is private and known only to bidder i

Channel allocation dai The number of channels an auction winner i receives

Clearing price pi The price charged to an auction winner i; in a truthfulauction, pi ≤ da

i × vi

Bidder utility ui The utility of bidder i, or the residual worth of thechannels: ui = vi · da

i - pi if i is an auction winner and0 otherwise

In the context of spectrum auctions, the design must ensure truthfulness andenable spectrum reuse across auction winners to improve spectrum utilization.

Definition 2. An efficient and truthful spectrum auction is one that is truthfuland maximizes the efficiency of spectrum usage subject to the interferenceconstraints.

17.4 Economically Robust Spectrum Auctions 497

In building a truthful and efficient spectrum auction, VERITAS integrates agreedy spectrum allocation with a carefully designed pricing mechanism. Let usstart from a simple scenario, where bidders’ channel requests are strict: a bidder irequests di channels and accepts allocations of only either 0 or di channels.

17.4.1 Spectrum AllocationIn determining the auction winners, VERITAS applies a greedy solution. It first sortsthe bid set B by a descending order of bi, then allocates bidders sequentially fromthe highest one to the lowest one. From each bidder i, the algorithm first checkswhether there are enough channels to satisfy i’s request di. If so, it assigns i withdi’s lowest indexed channels that have not been assigned to i’s conflicting peers.Such monotonic allocation is critical to achieve auction truthfulness.

17.4.2 Winner PricingVERITAS charges each winner i with the bid of its critical neighbor multiplied bythe number of channels allocated to i. The price reflects the minimum value ofi’s bid to win the auction. It is independent of i’s actual bid, and is always nomore than i’s actual bid multiplied by the number of channels allocated to i. Thisproperty is also referred to as the individual rationality. A critical neighbor isdefined as follows:

Definition 3. Given {B \ bi}, a critical neighbor C(i) of bidder i is one of i’sneighbors where if i bids lower than C(i), i will not be allocated, and if i bidshigher than C(i), i will be allocated.

At first sight, finding the critical neighbor for each bidder i seems computationallyexpensive. It requires inserting i’s bid immediately after each of its neighbors andrunning the allocation algorithm repeatedly. VERITAS overcomes this problem,using an intelligent pricing algorithm that identifies the critical neighbor for eachbidder by running the allocation algorithm once. For each bidder i, the algorithmfirst removes i from the sorted bid set and runs the allocation. When assigningchannels to i’s conflicting peers, the algorithm removes the assigned channelsfrom i’s available channel set. The first winning conflicting peer that makes i’savailable channels less than its demand di is i’s critical neighbor. The detailedalgorithm description can be found in [625].

17.4.3 Supporting Other Bidding FormatsVERITAS enables bidders to use diverse demand formats. A bidder can requestspectrum by the exact number of channels it would like to obtain (strict requests)or by a range defined by the minimum and maximum number of channels (rangerequests). Using the range request, a bidder i can request di channels but acceptany number of channels between 0 and di. To ensure truthfulness under thisrequest, VERITAS applies an advanced allocation and pricing mechanism. When

498 CHAPTER 17 Auction-based spectrum markets in cognitive radio networks

allocating channels, if the number of available channels is less than i’s demanddi, the algorithm allocates whatever is possible. When determining prices, thealgorithm needs to find multiple (rather than one) critical neighbors for eachwinner because bidding below each critical neighbor results into being allocatedwith different numbers of channels. For each set of additional channels obtainedby bidding higher than the last critical neighbor, the algorithm charges the winnerwith the bid of its last critical neighbor. The clearing price is the sum of pricescharged for all of the bidder’s assigned channels.

17.4.4 Supporting Different Auction ObjectivesVERITAS provides the auctioneer with the capability and flexibility of maximizingits customized objective. By sorting the bid set differently, the auctioneer canconfigure the order of allocation to maximize the auction revenue or the socialwelfare. For example, it has been shown that, to maximize the sum of winningbids, known as the social welfare [632], the best-known greedy algorithm is toassign channels following the descending order of bi/|N(i) + 1| [636], where N(i)is the number of conflict peers of bidder i. VERITAS enables this flexibility byallowing different sorting metrics as long as they are an increasing function of thebid bi and are not affected by the bids of other bidders. Example sorting metricsare: bi, bi/|N(i)| + 1, or bi × |N(i)|.

17.4.5 VERITAS Performance and ComplexityIt has been shown that the VERITAS auction design is truthful by combiningthe monotonic spectrum allocation and the critical-neighbor-based pricing algo-rithm [625]. The computational complexity of VERITAS is on the order of O(N3K),where N is the number of bidders and K is the number of channels auctioned.Among them, O(N log N + K|E|) is from the allocation algorithm and O(NK|E|)is from the pricing algorithm, where |E| is the number of edges in the bidderconflict graph. Such polynomial complexity makes VERITAS suitable for dynamic,on-demand spectrum auctions.

Figure 17.3(a) compares VERITAS’s spectrum utilization to that of the best-known greedy allocation algorithm [636], where VERITAS performs similarly tothe greedy solution. Figure 17.3(b) examines its auction revenue as a function ofthe number of channels auctioned. VERITAS exhibits an interesting trend: As thenumber of channels auctioned increases, the revenue first increases then decreases.This is because VERITAS charges winners by their critical-neighbors’ bids. Increas-ing the number of channels reduces the level of bidder competition. As the numberof winners increases to include all the bidders, the price charged each winner alsodecreases to 0. To maximize its revenue, the auctioneer can choose to control thenumber of channels to be auctioned. To prevent bidder manipulation, the auction-eer must make decision prior to the auction execution. Determining the optimalnumber of channels is a challenging question given the complex interferenceconstraints. A simple heuristic was proposed in [625].

17.5 Double Spectrum Auctions for Multiparty Trading 499

0

10

20

30

40

50

60

70

80

90

60 120 180 240 300

Spe

ctru

m U

tiliz

atio

n

Number of Bidders

Best-GreedyVERITAS

(a)

0

10

20

30

40

50

60

2 4 6 8 10 12 14 16 18 20

Rev

enue

Number of Auctioned Channels

300 bidders200 bidders100 bidders

(b)

FIGURE 17.3

VERITAS performance: (a) Spectrum allocation efficiency versus the number of bidders.VERITAS performs similarly to the best-known greedy algorithm [636]. (b) VERITAS auctionrevenue versus the number of channels auctioned. The auction revenue depends heavily onthe level of bidder competition. As the number of channels auctioned increases, the level ofcompetition decreases and the winners’ prices reduce.

17.5 DOUBLE SPECTRUM AUCTIONS FOR MULTIPARTYTRADING

We have described an auction design where an auctioneer sells its spectrum chan-nels to buyers. In this section, we describe a double spectrum auction designwhere multiple spectrum sellers and buyers can trade spectrum flexibly by inter-acting with an auctioneer. As shown in Figure 17.4, the auctioneer is a matchmaker

500 CHAPTER 17 Auction-based spectrum markets in cognitive radio networks

Auctioneer

Buyers

Sellers

Channel 1 Channel 2Channel 3

LegacyOwner 1

LegacyOwner 2

LegacyOwner 3

FIGURE 17.4

Multiparty spectrum trading based on double auctions. The auctioneer performs an auctionamong both sellers and buyers. Sellers provide idle spectrum pieces dynamically with regionalcoverage, while buyers request spectrum channels in local areas based on their demands.Each channel contributed by a seller can be reused by multiple, nonconflicting buyers.

between sellers and buyers. It buys spectrum pieces from sellers and sells themto buyers. In this way, existing spectrum owners (as sellers) can obtain financialgains by leasing their selected idle spectrum to new spectrum users; new users (asbuyers) can access the spectrum they desperately need and in the format they trulydesire. By multiplexing spectrum supply and demand in time and space, dynamicauctions can significantly improve spectrum utilization.

To model a double spectrum auction, we define the bid, true valuation, price,and utility of both sellers and buyers. The notations for buyers, Bb

n, V bn , Pb

n, and Ubn ,

follow those in Table 17.1, and the notations for sellers are defined in Table 17.2. Inaddition to truthfulness and spectrum reuse, a double spectrum auction must alsoachieve two additional properties: individual rationality and budget balance.

Table 17.2 Summary of Double Auction Notations Related to Sellers

Notations Description

Seller’s per-channel bid Bsm The minimum payment required by seller m to sell

one channel

Seller’s per-channel valuation V sm The true valuation a seller m has for a channel

Seller’s price Psm The payment a winning seller m receives by selling a

channel

Seller’s utility Usm The utility of seller m Us

m = Psm − V s

m if m wins theauction and 0 otherwise; this is different from thebuyer case

17.5 Double Spectrum Auctions for Multiparty Trading 501

Definition 4. A double auction is individual rational if no winning buyer paysmore than its bid (i.e., Pb

n ≤ Bbn), and no winning seller gets paid less than its

bid (i.e., Psm ≥ Bs

m).

This property guarantees nonnegative utilities for bidders who bid truthfully,providing them incentives to participate in the auction.

Definition 5. A double auction is ex-post budget balanced if the auction-eer’s profit is � ≥ 0. The profit is defined as the difference between therevenue collected from buyers and the expense paid to sellers: � = ∑N

n=1 Pbn −∑M

m=1 Psm ≥ 0.

This property ensures that the auctioneer has incentive to set up the auction.In the following, we describe TRUST [626], a double spectrum auction frame-

work that achieves the four required properties: spectrum reuse, truthfulness,individual rationality, and budget balance. Table 17.3 compares TRUST to exist-ing double auction designs. Conventional double auction designs (VCG [637] andMcAfee [638]) achieve truthfulness but do not consider spectrum reusability. VER-ITAS [625], on the other hand, addresses only single-sided buyer-only auctions andloses the truthfulness when directly extended to double auctions [626].

TRUST [626] breaks the barrier between spectrum reuse and truthfulness indouble spectrum auctions. In essence, it enables spectrum reuse by applying aspectrum allocation algorithm to form buyer groups. It achieves the three economicproperties via the bid-independent group formation and a reusability-aware pricingmechanism. TRUST consists of three components: grouping buyers, determiningwinners, and pricing.

17.5.1 Grouping BuyersTRUST groups multiple nonconflicting buyers into groups so that buyers in eachgroup do not conflict and can reuse the same channel. This is done privately bythe auctioneer performing a spectrum allocation algorithm and organizing buyers

Table 17.3 Comparison of Various Double Auction Designs

Existing Double Spectrum Ex-Post Budget IndividualAuction Designs Reuse Truthfulness Balance Rationality

VCG X√

X√

McAfee X√ √ √

VERITAS extension√

X√ √

RUST√ √ √ √

502 CHAPTER 17 Auction-based spectrum markets in cognitive radio networks

assigned to the same channel to a group. Unlike VERITAS, the group formationis independent of the buyer bids to prevent bidders from rigging their bids tomanipulate the group size and its members.

The group formation can cope with various interference models by using differ-ent spectrum allocation algorithms. If the buyer interference condition is modeledby a conflict graph, the group formation is equivalent to finding the independentsets of the conflict graph [639,640]. If the interference condition is modeled by thephysical signal-to-interference and noise ratio (SINR) [641], TRUST finds multiplesets of buyers who can transmit simultaneously and maintain an adequate receivedSINR [642]. TRUST performs this allocation only to form buyer groups, not toassign specific channels to buyers.

17.5.2 Determining WinnersNext, TRUST treats each buyer group as a superbuyer and runs the conventionaldouble spectrum auction algorithm to determine the winning sellers and super-buyers. Let G1, G2, ..., GL represent the L groups formed. For any group Gl withnl = |Gl| buyers, the group bid πl is

πl = min{Bb

n|n ∈ Gl

}· nl . (17.4)

TRUST sorts the seller bids in nondecreasing order and the buyer group bids innonincreasing order: B

′ : Bs1 ≤ Bs

2 ≤ ... ≤ BsM , and B

′′ : π1 ≥ π2 ≥ ... ≥ πL. Definek as the last profitable trade:

k = argmaxl≤min{L,M}πl ≥ Bsl . (17.5)

Then the auction winners are the first (k − 1) sellers and the first (k − 1) buyergroups.

17.5.3 PricingTo ensure truthfulness, TRUST pays each winning seller m by the kth seller’s bidBs

k and charges each winning buyer group l by the kth buyer group’s bid πk. Thisgroup price is evenly shared among the buyers in the group l:

Pbn = πk/nl , for all n ∈ Gl . (17.6)

No charges or payments are made to losing buyers and sellers. The uniform pricingis fair because buyers in a winning group obtain the same channel and thus arecharged equally. In addition, to ensure individual rationality, a group bid must notexceed the product of the lowest buyer bid in the group and the number of buyersin the group, which is used in the process of determining winning groups. Withsuch pricing mechanism, the auctioneer’s profit becomes � = (k − 1) · (πk − Bs

k)

and it is easy to show that � ≥ 0.

17.6 Chapter Summary and Further Reading 503

FIGURE 17.5

The percentage of spectrum utilization achieved by TRUST compared to that of pureallocations without economic factors. Four allocation algorithms are considered, includingMax-IS [640], two greedy allocation algorithms [639], Greedy-U and Greedy, and randomallocation RAND.

17.5.4 TRUST Performance and ComplexityAs shown in [626], by integrating the monotonic winner determination and bid-independent pricing, TRUST achieves truthfulness, ex-post budget balance, andindividual rationality while enabling spectrum reuse to improve spectrum uti-lization. One key advantage of TRUST is that it can use any spectrum allocationalgorithm in forming buyer groups. Thus, its complexity depends heavily on theallocation algorithm used.

On the other hand, ensuring these economic properties comes at a cost inspectrum utilization. This is because TRUST selects winning buyer groups by theminimum bid in the group multiplied by the group size, so that groups of differentsizes have equal opportunity in being chosen. On the other hand, the convec-tional spectrum allocation algorithms always choose large groups, leading to anadvantage in spectrum utilization. Figure 17.5 illustrates the ratio of TRUST’s spec-trum utilization to that of conventional spectrum allocations without economicconsideration [639,640]. It examines the performance using random and clusteredtopologies. In random network topologies, TRUST achieves 70–80% spectrumutilization of the conventional spectrum allocation, while in clustered networktopologies, TRUST sacrifices roughly 50% of spectrum utilization in exchange foreconomic robustness. This is because, in clustered topologies, the group sizesbecome much more diverse and TRUST could select a set of small buyer groups,which degrades the overall spectrum utilization.

17.6 CHAPTER SUMMARY AND FURTHER READINGIn this chapter we examine the challenges and solutions in the area of spectrum trad-ing. Unlike the conventional command and control management model, spectrum

504 CHAPTER 17 Auction-based spectrum markets in cognitive radio networks

trading is an open, market-based approach for redistributing the spectrum. Newusers can gain access to the spectrum they desperately need and existing own-ers can gain financial incentives to “lease” their idle spectrum. We focus mainlyon dynamic spectrum auctions, because auctions are among the best-knownmarket-based allocation mechanisms. Dynamic spectrum auctions are fundamen-tally different from (and much more difficult than) conventional multiunit auctionsbecause of their unique requirement of spectrum reusability. With this in mind,we introduce three recent works on on-demand spectrum auctions, truthful spec-trum auctions, and truthful double spectrum auctions. Together, they provide thebasic building blocks for constructing an efficient, economically robust, real-timedynamic spectrum marketplace.

It is important to note that there have been numerous contributions and ongoingefforts on dynamic spectrum allocation, pricing, trading, and auctions. A small setof them are summarized next. Building on these extensive contributions, the use ofspectrum trading is moving from pure research to several commercial deploymentsand ideally will expand to the general public in the near future.

Exploitation of market mechanisms for dynamic allocation and redistribution ofspectrum has been the topic of several other recent research investigations, andthe literature on this topic is growing. Important also, the use of such mechanismsis starting to move from the realm of pure research into that of development andcommercial exploitation. For example, Spectrum Bridge Inc. [643], a U.S.-basedcompany, developed a real-time online marketplace that enables spectrum ownersand users to buy, sell, and lease FCC-licensed spectrum. According to the company’sweb site, its online marketplace, SpecEx, provides access to over 200 billion unitsof spectrum that the FCC made eligible for secondary market transactions. Forthe benefit of the reader we summarize in the remaining of this section some ofthe most recent research on the use of market mechanisms for dynamic spectrumaccess.

A framework for coordinating dynamic spectrum access among serviceproviders was proposed in [357]. The scheme proposed in this work relies ona spectrum broker that controls the allocation of spectrum among the requestingoperators. This work was later extended to cases where the interference amongbidders is modeled by pairwise and physical interference models and the bid-ders can bid for heterogeneous channels of different widths using generic biddingfunctions [644].

The price dynamics of a dynamic spectrum market was explored in [645]. Theauthors considered a marketplace consisting of spectrum agile network serviceproviders and users. Competition among multiple primary users to sell their spec-trum are modeled in this work as a noncooperative game. An interesting featureof this work is that the analysis takes into account differences in evaluation of thequality of the offered spectrum by buyers. For example, radio waves at lower fre-quencies, such as UHF, travel longer distances and penetrate more readily throughwalls. Therefore, buyers may value spectrum in such bands highly for applica-tions that require good penetration properties. Also, depending on their operating

17.7 Problems 505

wireless technology, some spectrum buyers may value contiguous segments ofspectrum higher than noncontiguous ones.

The dynamics of multiple-seller and multiple-buyer spectrum trading in dynamicspectrum access networks is considered in [646]. In this work it is assumed thatthe secondary users can adapt their spectrum buying behavior to the variations inprice and quality of spectrum offered by different primary users. At the same timethe primary users can adjust their behavior in selling their spectrum to achievethe highest utility. Similar to [645] the competition among primary users in sellingspectrum is modeled using a noncooperative game formulation. At the same time,evolution in the spectrum buying behavior of secondary users are analyzed usingthe deterministic and stochastic models of evolutionary games.

One of the early papers that explores the use of auctions for dynamic alloca-tion of spectrum is [647]. The authors consider a scenario where multiple codedivision, multiple-access operators bid for the spectrum to a spectrum manager.They present an optimal bidding and pricing mechanism with the objective ofmaximizing the revenue of the operators based on the willingness of users to pay.Auction-based mechanism for dynamic spectrum access are also explored in [648],where an optimization problem is formulated to maximize the revenue of spectrumowners through pricing and spectrum assignment. In [624] the authors describe acombinatorial clock auction mechanism for trading of spectrum in the context ofan OFDMA-based cognitive radio network. Combinatorial clock auctions [649] areused when a range of items are on sale that may be logically grouped together intomany packages to suit either the buyer, the seller, or both. In these auctions, bidsfor such packages are made throughout a number of sequential open rounds and afinal sealed-bid round. During the sequential rounds buyers have an opportunity toexplore the bid space as their bids are either accepted or rejected until there is nochange in the winners or no new bids are submitted. The authors of [624] presenta modified version of the combinatorial clock auctions to reduce the complexityof the mechanism for cognitive radios that attempt to buy and sell spectrum onbehalf of users.

17.7 PROBLEMS1 What is spectrum trading? How does it differ from the command and control

model?

2 This chapter deals mainly with auction-based mechanisms to enable efficientdeals between spectrum buyers and sellers. Name and explain at least one othermarket mechanism that can be used for trading spectrum.

3 How does spectrum differ from other natural resources, such as gas andelectricity? How do these differences affect the use of auctions in tradingspectrum?

506 CHAPTER 17 Auction-based spectrum markets in cognitive radio networks

4 Explain what a conflict graph is. Use MATLAB to construct and visualize conflictgraphs for a collection of 100 nodes uniformly distributed in a 1 km2 rectangulararea. Assume that all nodes have a 100 m transmission radius.

5 What are the limitations of FCC-style auctions?

6 What are the differences between single-sided auctions and double auctions?

7 Consider the first-price auction where the winner is charged by its bid.What revenue trend would you expect as the number of channels auctionedincreases? Explain your conjecture by comparing it to Figure 17.3.

8 Critical neighbor is defined in VERITAS for determining each winner’s price.Consider a winner i in VERITAS, and among i’s unallocated neighbors (i.e., i’sneighbors who did not win any channel in the auction), let j be the one withthe highest bid. Is j always i’s critique neighbor? If it is, explain the reason, andif it is not, give a counterexample.

9 Buyer group formation is an important step for TRUST to enable spectrumreuse. Given the conflict graph of buyers and the set of bids of sellers, do youthink it is a good idea to make the buyer group size more balanced? Explainyour conclusion.