Spatio-Temporal Dynamic Spectrum Allocation ... - Semantic Scholar

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.

Spatio-Temporal Dynamic Spectrum Allocation with Interference Handling László Kovács, Attila Vidács∗ , János Tapolcai∗ Dept. of Telecommunications and Media Informatics Budapest University of Technology and Economics H-1117 Budapest, Magyar tudósok krt. 2., Hungary Tel: +361 463 1925, Fax: +361 463 3107 E-mail: {kovacsl, vidacs, tapolcai}@tmit.bme.hu Abstract— As for today, radio spectrum resource is rigidly partitioned for dedicated purposes. The exclusive license of fixed size spectrum blocks separated by guard bands easily solves the interference problems; however, the rigid allocation of spectrum is clearly inadequate for providing optimal spectrum efficiency for spatially and temporarily varying loads. Dynamic Spectrum Allocation (DSA) is a new and promising alternative where the assigned spectrum blocks may vary in time and space, too. In this paper we describe a spatio-temporal DSA model that splits the complex problem into Temporal and Spatial Dynamic Spectrum Allocation. In our architecture the spectrum is allocated by Regional Spectrum Brokers (RSB) that also coordinate spectrum access between regions. The problem of interference between different regions and providers is handled by a flexible description using the proposed geographical and radio technology coupling parameters. We also show how the optimal allocation can be found by giving the ILP solution to the problem. To evaluate the efficiency of the proposed DSA method, different gains are defined from the regulator’s point of view. The performance evaluation is carried out using computer simulations, and the results are compared with the cases where either there is no interference allowed at all, or interference does not occur between regions.

I. I NTRODUCTION Nowadays radio spectrum is allocated as fixed size spectrum blocks separated by guard bands for dedicated purposes. However, communication networks are designed for “busy hours”, which is the time of the peak use of the network. The demands for different services depend on location as well. Consequently, a substantial fraction of the spectrum may be wasted at a given time and place. This is the motivation for a more spectrum efficient technique, called Dynamic Spectrum Allocation (DSA), where the assigned spectrum blocks may vary in time and space. The concept of DSA first came up in the DARPA XG Program [1], where the goals were to develop, integrate, and evaluate the technology in order to enable equipment that automatically selects spectrum and operating modes to both minimize disruption of existing users, and to ensure operation of U.S. systems. Due to the military application there is no central entity, it requires complex spectrum sensing at individual radio nodes and distributed coordination protocols. *A. Vidács and J. Tapolcai are a grantee of the János Bolyai Scholarship of the Hungarian Academy of Sciences. This work has been partially supported by grant OTKA 42559.

Buddhikot et al. gave a detailed description of an implementation architecture for coordinated DSA [2]. In their model a spectrum broker controls and provides a time-bound access to a band of spectrum to service providers. They also investigated algorithms for spectrum allocation in homogenous CDMA networks [3] and executed spectrum measurements in order to study the achievable spectrum gain [4]. The IST-DRiVE project [5] dealt with the coordinated DSA problem as well. The goal was to develop methods for dynamic frequency allocation and for co-existence of different radio technologies in one frequency band in order to increase the total spectrum efficiency. They investigated only the coexistence of UMTS and DVB-T technologies [6] [7] and had some interesting results [8] [9]. The IST-OverDRiVE project [10] dealt with the problem in more details. They defined ‘DSA areas’ in which the traffic demands of different RANs are rather constant in space (yet they may be time variant). Only one gain, called ‘Grade of Service’ (GoS), was defined, which is the fraction of the maximum traffic that can be carried by the allocated spectrum and the traffic demand. In the proposed model they insert unused spectrum blocks (extra guard bands) at the border areas in order to avoid interference. The approach we use in our model is similar to that of [10] with the following key differences. Our paper describes a spatio-temporal coordinated DSA framework where interference is modeled by general “coupling” parameters between regions and providers. In our model the interference cause spectrum efficiency degradation. Although the utilization decreases, it is not necessary to insert extra guard bands at the borders, allowing the providers (and also the regulator) to achieve larger gains. We define DSA regions in which the spatial distribution of the traffic demand is homogenous, only temporal changes are allowed. We also use distributed architectural elements, called Regional Spectrum Brokers (RSB), to coordinate the spectrum allocation inside each region. We define different gains from the regulator’s point of view. We derive the optimal spectrum allocation for the region-based DSA model, which maximizes the guaranteed regulator gain. The rest of the paper is organized as follows. Section II describes the proposed architecture, while Section III details our DSA model, introduces a general and flexible description

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to model interference, and gives the feasibility conditions of an allocation. Section IV defines the achievable DSA gains from the regulator’s point of view. In Section V the task of optimal spectrum allocation is formulated as an ILP problem. The validation of the proposed DSA model is given in Section VI using computer simulations. Finally, Section VII concludes the paper. II. S PATIO - TEMPORAL DSA ARCHITECTURE In the fixed spectrum allocation scheme the problem of allocation is modeled by a conflict graph in which the nodes are the base stations, and the edges denote where conflict exists. In such a way the set coloring problem can be reduced to our frequency assignment problem proving its NP-hardness [11]. If the base stations were to demand unequal spectrum slices, this solution could be generalized for dynamic spectrum allocation as well. However, the demand for radio network resources varies greatly in time and space. The temporal and spatial variations of the demands require frequent reallocation of the spectrum. Considering that the graph of the network contains a large number of nodes, and that the problem is NP-hard it is practically impossible to be solved in real-time. To ease the problem, in our model we consider regions within which we assume that the spatial distribution of the spectrum demand is homogeneous, only temporal changes are allowed. (For example, assume that the spectrum demand in the business quarter of a city, in the suburban region, or on a highway changes with time only.) The spectrum of a given region is owned by the Regional Spectrum Broker (RSB), that grants short-time licenses for the requesters (Network Service Providers). Within the regions Temporal Dynamic Spectrum Allocation (TDSA) is realized. In the TDSA method service providers of the region send their demands for spectrum to the RSB. The RSB allocates disjoint and continuous spectrum blocks to the requesters. The size of the blocks may vary in time. The Spatial Dynamic Spectrum Allocation (SDSA) handles spectrum demands arising at the same time in different regions. The aim of the SDSA is to attune the different demands within different regions the way, that the least interference arises in the overlapping regions. In order to realize this, the RSBs need to have information about the actual spectrum allocation of the neighboring regions. When processing the demands the RSBs query the time-snapshots of the neighbors, and based on this information manage overlapping spectrum allocations accordingly. III. DSA M ODEL Assume that the spectrum block to be distributed, also called as Coordinated Access Band (CAB) [3], is the frequency range (ˇ s, sˆ). The whole area is divided into K non-overlapping regions (Rk ). Within the given region, M network service providers (NSPs) compete for the spectrum. The spectrum block allocated to the mth NSP within the k th region at time t is: sm,k (t), sˆm,k (t)). (1) Sm,k (t) = (ˇ

The notations emphasize that the spectrum allocation is highly dynamic, each provider can be given different spectrum blocks at different regions and different time instants. (To ease the notations, the dependence on time t is not written explicitly in the followings.) Furthermore, let |Sm,k | denote the “size” of the allocated spectrum block, i.e., |Sm,k | = sˆm,k − sˇm,k . The first question is, how much spectrum is needed for the NSPs to provide their service to their customers, taking into account that more NSPs exist within the same arena, competing for spectrum block and possibly interfering with each other. Mapping demands to spectrum volume is the first task in DSA networks. A. Spectrum estimator Users of a service provider do not request for spectrum directly. Instead, they ask for digital transmission channels of given capacity (expressed in Mbps) for their applications. Spectrum estimators are able to relate those capacity requests to the required amount of spectrum to satisfy these requests [3]. However, mapping capacity demands to spectrum requests is not an easy task. It is radio technology specific, relies on the knowledge of network elements, the environment, supported by possible in-field measurements. To formulate it, assume that the mth provider has the capacity request bm . The spectrum estimator relates a spectrum block of size |Sm | to this request, i.e., f (bm ) = |Sm |. Here we assume that the relation between capacity and spectrum is linear. This is the case, for example, when a narrow-band carrier must be allocated for each 64 kbps data channel. In this case f (bm ) = bm s0 where s0 is the size of the carrier. However, in our DSA scenario providers can have different capacity demands in different regions. The spectrum estimator of the mth provider in the k th region gives back the spectrum needed in that particular region, i.e., f (bm,k ) = bm,k s0 . B. Spectrum allocation The task of a regional Spectrum Broker (RSB) is to allocate spectrum to the NSPs so that their demands are satisfied. The RSB divides the CAB into non-overlapping blocks and assigns different blocks to different NSPs within each region, i.e., Sm,k ∩ Sn,k = ∅, for all m, n and k. Allocating strictly disjoint spectrum blocks to NSPs within each region seems to solve the problem at first glance. However, this is not the case in spectrum allocation, since spectrum usage does not stop at region boundaries. Thus, the amount of spectrum needed not only depends on the capacity demand bm,k , but also on the allocations of the neighboring regions causing possible spectrum degradation within the interference zones. C. Interference and spectrum efficiency If the same spectrum slice is allocated to two different providers in neighboring regions, certainly some overlapping occurs, radios will interfere. This problem of interference is also present to some extent in the rigid spectrum allocation used today. As an example, consider national service providers


that have exclusive rights to use their allocated spectrum only within the country. Special rules apply to the border region, where operators are not allowed to interfere (above a certain limit) with the operators in the neighboring country. Antennas must be placed accordingly, and transmit powers need to be adjusted to obey the rules. However, the area of this “problematic” border region is very small compared to the size of the country, its effect on the full network is negligible. On the contrary, in our proposed scenario the regions coordinated by dedicated RSBs are relatively small, thus the area of the interference zone is not negligible compared to the size of the region. In our model we take into account interference as a source for spectrum utilization degradation. “Noisy” spectrum cannot be fully utilized. First of all, spectrum utilization is decreased if the same frequency is used by different NSPs in neighboring regions, while NSPs operating within the same band but far away from each other will not interfere. The level of interference mainly depends on the geographic location and size of the regions, and can be expressed by the geographic coupling parameter ε. Let 0 ≤ εkl ≤ 1 denote the coupling between regions Rk and Rl , i.e., it shows how the radios operating at the same frequency simultaneously in both regions disturb each other. It is zero if there is no interference between the two, and it is equal to one if the shared spectrum is completelyunusable because of heavy interference. (We assume that i εki ≤ 1 and εkk = 1.) From the NSPs point of view, the level of interference is the measure of how much their radio technology is affected by competing technologies. It can happen that robust techniques with error-prone encoding are more tolerant to noisy spectrum than others. The level of interference caused by an NSP depends not only on its physical distance but on the radio access technique used, the transmission power as well as the positions and types of radio transmitters. (For example, carefully designed microcell structure with directed and low-power antennas cause much limited interference than a central undirectional transmitter placed in the middle of the region.) The level of disturbance (or jamming) between different NSP radio technologies is captured by the radio technology coupling parameter η. Let 0 ≤ ηm,n ≤ 1 denote the coupling between the radio technologies used by the mth and nth NSPs. By looking at the two extremes, if η is zero the two NSPs having the same spectrum slice in neighboring regions do not affect each other, while η equals one means that the spectrum is ruined if there is an interfering NSP nearby. (We define ηmm = 0.) The cumulative effect of the geographic and radio technology coupling between the mth NSP operating in region Rk and the nth NSP in region Rl having the same spectrum is simply the product of the two factors, namely, εk,l · ηm,n . Let ξ(Sm,k ) denote the efficiency of spectrum block Sm,k that can be calculated as 1 ξ(Sm,k ) = ξm,k (λ) dλ (2) |Sm,k | Sm,k

where ξm,k (λ) is the efficiency of frequency λ from the mth NSP’s point of view in region Rk , that is ξm,k (λ) = 1 −

M K

εk,j · ηm,i · I{λ∈Si,j }

(3)

i=1 j=1

The efficiency is one if no interference occurs, and less than one if there is interference with neighboring regions. D. Feasible allocation In the spatio-temporal DSA case the requirement of feasibility can be interpreted as follows. An allocation S = (S1 , . . . , SM ) with Sm = (Sm,1 , . . . , Sm,K ) is feasible, if the spectrum blocks {Sm,i } used by the NSPs within a region are non-overlapping, and all demands are satisfied, i.e., Sm,k ∩ Sn,k |Sm,k |ξ(Sm,k )

= ∅, ∀m, n, k, ≥ bm,k s0 , ∀m, k ,

(4) (5)

where s0 is a constant (i.e., 5 MHz band). Combining (2) and (5) we get M K bm,k s0 ≤ |Sm,k | − εkj ηm,i I{λ∈Si,j } dλ. (6) Sm,k

i=1 j=1

IV. DSA GAINS Checking feasibility of a spectrum allocation is a must. However, feasibility on its own does not say anything about the overall efficiency of the allocation. Spectrum can be distributed badly, or in a more clever way. What is good or what is bad depends on how we define the achievable gain. In the following, we describe various gains that can be achieved by DSA. Depending on what we are aiming at, different allocation rules that lead to efficient spectrum usage can be defined. A. Temporal Gains from DSA The gain achieved by TDSA from the regulator’s point of view can be interpreted as follows. (For the achievable gains from the NSPs point of view, please refer to [12].) Since we concentrate on the temporal gains, the dependence on the region is omitted from the notations. Instead, the dependence on time t is explicitly noted. Compared to the rigid spectrum allocation where enough spectrum must be allocated in advance for each NSP to satisfy its peek demand, the Temporal Regulator Gain (TRG) at time t can be computed as M |Si (t)| . (7) T RG(t) = 1 − M i=1 i=1 maxτ {bi (τ )s0 } The average gain of the regulator in time interval T is: T ave −1 T RG =T RG(t) dt.

(8)

0

The minimal gain over the whole time interval can also be defined: (9) T RGmin = min RG(t). t


This is the gain that can be achieved at all times when compared to the fixed spectrum allocation. In other words, the size of CAB can be smaller by this factor than the total spectrum needed for the rigid allocation. Note, that the achievable gain strongly depends on the correlations between the NSP demands.

D. Efficient allocation Depending on what we are aiming at, different allocation rules that lead to efficient spectrum usage can be defined. After ensuring feasibility, the task is to choose the most efficient allocation S∗ that maximizes the guaranteed Regulator Gain, which is equivalent of (see (13) and (15))

B. Spatial Gains from DSA The spectrum demands of an NSP can be different in different regions. The main task of the SDSA is to handle this heterogeneity. (Since we concentrate on the spatial gain, a time snapshot is investigated. Hence the notation of time dependence is omitted.) Using rigid spectrum allocation, the amount of spectrum M that must be allocated in all regions is i=1 maxj {bi,j s0 }. Thus, the Regulator Gain from SDSA in region k is M |Si,k | . (10) SRGk = 1 − M i=1 i=1 maxj {bi,j s0 }

max j

M

|Si,j | → min .

(18)

i=1

V. O PTIMAL SPECTRUM ALLOCATION A. Graph model

C. Spatio-Temporal Gains from DSA

To model the interference of NSPs in neighboring region an undirected graph G = (V, E) is defined with vertex set V and edge set E. Each vertex of the graph is assigned to a specific region and to a NSP providing network service in the region. In some equations a vertex is denoted as a region-NSP duplet in braces (i.e., {m, k} refers to a node corresponding to k th region and mth NSP). Note that, in the proposed model the number of vertices |V | is equal to M × K. We connect two vertices with and edge, if the there can be an interference between the corresponding regions, except if the two vertices correspond for the same network service provider, formally, ({m, k}, {n, l}) ∈ E if m = n and k interfere with l. Let us define a cost function denoted by ce on edges representing the decrease in the efficiency of utilization due to interference. 1, if k = l (19) c({m,k},{n,l}) = ηm,n εk,l , otherwise

Taking into account the temporal and spatial gains simultaneously, the following gains can be defined. The spatiotemporal DSA Regulator Gain is given by M |Si,k (t)| (13) RGk (t) = 1 − M i=1 i=1 maxj,τ {bi,j (τ )s0 }

In such a graph model the spectrum allocation problem can be formulated as a task to define a spectrum interval Si = (ˇ si , sî ) for each node i of the graph. Let us define a variable z(i,j) assigned for each edge in the graph representing the amount of overlap in spectrum assigned to node i and node j, formally:

The achieved average gain over all areas and all times is T K RGave = T −1 (Aj /A) RGj (t) dt. (14)

z(i,j) = |Si ∩ Sj | = max {0, min{ˆ si , sˆj } − max{ˇ si , sˇj }} (20)

The average gain over the whole controlled area is SRGave =

K

(Aj /A)RGj ,

(11)

j=1

where larger areas are taken with higher weights in the sum. The minimal gain that is guaranteed to be achieved in all regions is given by SRGmin = min SRGj . j

(12)

0

j=1

The minimal (or guaranteed) achievable gain that is guaranteed at time t is (15) RGmin (t) = min RGj (t). j

If we look for the minimum at all times, we have RGmin

= =

min RGj (τ ) j,τ

(16) M

maxj,τ i=1 |Si,j (τ )| . 1 − M i=1 maxj,τ {bi,j (τ )s0 }

B. ILP Solution Based on the proposed model, we formulate the problem as an Integer Linear Program (ILP). By solving the ILP problem with an ILP solver [13] we can get the optimal solution. Note that, the worst case runtime of ILP solvers is exponential compared to the size of input. The ILP has following constraints: First, the spectrum block of each NSP is limited to fit into the coordinated band S: sˇ ≤ sˇi ≤ sî ≤ sˆ ∀i ∈ V

(17)

Eq.(17) gives the gain that is guaranteed in the sense that in each region and at any time the achieved gain is at least as much as this value.

(21)

We can guarantee bandwidth bi s0 for each NSP in each region z(i,j) · c(i,j) ≥ bi s0 ∀i ∈ V (22) sî − sˇi − ∀(i,j)∈E


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Then we need to set variable ze for each e ∈ E according to (20). Unfortunately, (20) is not linear thus we need to introduce two working binary variables yˇ(i,j) and yˆ(i,j) for each edge, such that yˇ(i,j) = I{ˇsi ≤ˇsj } and yˆ(i,j) = I{ˆsi ≤ˆsj } . Next, the four cases of (20) can be expressed as: z(i,j)

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When the guaranteed Regulator Gain is maximized (i.e., the size of the spectrum block is minimized) we have one additional set of constraints with on a new real working variable s : (24) sî ≤ s ∀i ∈ V Finally, for the cost function we have to minimize s . Solving the ILP problem we obtain the optimal allocation. VI. S IMULATIONS RESULTS To evaluate the spectrum allocation efficiency of the proposed DSA method, simulation experiments were performed. We examined three different regions (downtown, business quarter, residential area) with different spectrum demands (see Fig. 1) as an example. In each region five NSPs operate in the CAB. There are two mobile speech service providers, one digital broadcast provider and two wireless internet service providers. NSPs demand spectrum in discrete units (5 MHz carriers). The spectrum was reallocated in every 2 hours. We examined the minimal spectrum requirement to fulfill the demands in all regions for three different situations. In the first case the regions are completely isolated, no interference can occur. This can be modeled by setting all of the geometrical coupling parameters to zero, i.e., εk,l = 0 for all k = l. This “ideal” case requires the least bandwidth, thus it can be seen as a lower bound for the more realistic cases. This scenario is referred to as ‘3-islands’ setup. In the second case the regions are neighboring, the same frequencies used in more

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than one region would interfere, but no interference is allowed at all. This is achieved by setting both the geographic and radio technology coupling parameters to one, i.e., ηm,n = εk,l ≡ 1 for all NSPs and regions. This strict burden requires disjoint spectrum allocations for providers even if they operate in different regions. This assumption yields similar results as the OverDRiVE proposal in [10]. The third case refers to our proposed spectrum allocation method, where all geographic coupling was set to 20% in between all region pairs, while the radio technology coupling parameter was 0.5 for each NSP pair. The feasible and optimal spectrum allocation was calculated based on the ILP description in section V-B. As for comparison, we note that in case of fixed spectrum allocation 51 carriers are necessary to fulfill the requests of all providers. Fig. 2 shows the minimal spectrum requirement for the three situations as a function of time. When the traffic intensity is low (e.g., from 2h to 4h) or the demands are concentrating on one region (e.g., from 20h to 22h in the residential area) the three situations provide the same result. However, in the busy hours the proposed DSA model provides better results than the OverDRiVE proposal. The guaranteed regulator gain in our model is 26,15%, in contrast to the OverDRiVE proposal’s 17,65% gain, and is close to the maximal achievable gain of 27.45% of the 3-islands model. Fig. 3 details the individual allocations for all five NSPs during the busy-hours (10h - 12h) in all three regions, and for all three allocation strategies. The plot gives an explanation for the different gains achieved: In the 3-islands case there is no need to pull apart spectrum blocks allocated for different providers in neighboring regions, since no interference occurs between regions. Thus, blocks are allocated as tightly as possible. Although in our proposed DSA model overlapping between spectrum blocks in neighboring regions is possible, it is avoided as much as possible to reduce spectrum degradation. As a result, there are no gaps between spectrum blocks in the most heavily loaded region. When overlapping between neighboring regions is strictly prohibited (see OverDRiVE allocation), even in the most heavily loaded region there is


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a need to have gaps between blocks to avoid interference. Fig. 4 shows the detailed spectrum allocations for all five providers in the three regions. Although the allocated blocks are scattered and there are gaps in between them, in each time period there is a region where spectrum blocks are allocated tightly without unused slices in between. I.e., during the middle of the day the business quarter is responsible for the highest overall spectrum demand, while the peak in the residential area occurs during the evening hours. We should also note that Fig. 4 reveals that the position of allocated spectrum block for a particular NSP in a given region can change from time-to-time, even if the provider’s demand remains the same. This is because in our proposed solution the spectrum allocation task is accomplished independently from the previous runs. In practical situations, however, it can be desirable from the NSPs’ point of view to allocate the same (or slightly resized) spectrum blocks as before whenever it is possible. To implement this constraint in the proposed algorithm remains for further study. VII. C ONCLUSION In our paper we introduced a new model for Dynamic Spectrum Allocation (DSA). We described an architecture that splits the complex problem into Temporal DSA and Spatial DSA parts. The Temporal Dynamic Spectrum Allocations (TDSA) are coordinated by Regional Spectrum Brokers (RSBs). An RSB handles the spectrum demands of the Network Service Providers (NSPs) within one region, while taking into account spectrum allocations of neighboring regions as well. Based on this information the RSB can handle interference between regions by modeling it by the so-called geographic and radio technology coupling parameters. The use of the two coupling parameters makes our proposed DSA model general and flexible. By the proper setting of these parameters different cases of interference handling can be incorporated in the model. After giving the requirements for a feasible spatio-temporal spectrum allocation, we defined various achievable gains from the regulator’s point of view, taking into account the spatial and temporal inhomogeneities of spectrum usage. The solution to find an optimal spectrum

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allocation was given using the ILP formulation of the problem. The achievable DSA gain was shown using computer simulations, where we shoved a real-like scenario example with downtown, business quarter and residential regions having different daily profiles in spectrum demands. The results have shown that—when interference is allowed but is kept under control—the achievable gain is higher in our solution than using the proposed models from the literature. R EFERENCES [1] “DARPA XG program,” http://www.darpa.mil/ato/programs/xg/. [2] M. Buddhikot, P. Kolodzy, S. Miller, K. Ryan, and J. Evans, “DIMSUMnet: New directions in wireless networking using coordinated dynamic spectrum access,” in Position Paper in IEEE International Symposium on a World of Wireless, Mobile and Multimedia Networks (IEEE WoWMoM 2005), Taromina/Giardini Naxos, Italy, Jun 2005. [3] M. Buddhikot and K. Ryan, “Spectrum management in coordinated dynamic spectrum access based cellular networks,” in Proc., First IEEE International Symposium on New Directions in Dynamic Spectrum Access Networks, Baltimore, MD, 8-11 Nov 2005. [4] T. Kamakaris, M. Buddhikot, and R. Iyer, “A case for coordinated dynamic spectrum access in cellular networks,” in Proc., First IEEE International Symposium on New Directions in Dynamic Spectrum Access Networks, Baltimore, MD, 8-11 Nov 2005. [5] “IST-DRiVE project,” http://www.ist-drive.org. [6] P. Leaves, S. Ghaheri-Niri, R. Tafazolli, L. Christodoulides, T. Sammut, W. Stahl, and J. Huschke, “Dynamic spectrum allocation in a multiradio environment: Concept and algorithm,” in Proc., IEE Second International Conference on 3G Mobile Communication Technologies, London, United Kingdom, 26-28 March 2001, pp. 53–57. [7] P. Leaves, J. Huschke, and R. Tafazolli, “A summary of dynamic spectrum allocation results from DRiVE,” in Proc., IST Mobile and Wireless Telecommunications Summit, Thessaloniki, Greece, 16-19 June 2002, pp. 245–250. [8] J. Huschke and P. Leaves, “Dynamic spectrum allocation algorithm including results of DSA performance simulations, DRiVE Deliverable D09,” Jan 2002. [9] P. Leaves and R. Tafazolli, “A time-adaptive dynamic spectrum allocation scheme for a converged cellular and broadcast system,” in Proc., IEEE Getting the Most Out of the Radio Spectrum Conference, United Kingdom, 24-25 October 2002, pp. 18/1–18/5. [10] “IST OverDRiVE project,” http://www.ist-overdrive.org. [11] E. Malesinska, “Graph-theoretical models for frequency assignment problems,” 1997. [Online]. Available: citeseer.ist.psu.edu/malesinska97graphtheoretical.html [12] L. Kovács and A. Vidács, “Spatio-temporal spectrum management model for dynamic spectrum access networks,” in Proc., First International Workshop on Technology and Policy for Accessing Spectrum (TAPAS 2006), Boston, USA, 1-5 Aug 2006. [13] “CPLEX,” http://www.ilog.com/products/cplex/.