Cooperative Spectrum Allocation in Centralized Cognitive Networks Using Bipartite Matching

1. Cooperative Spectrum Allocation in Centralized Cognitive Networks Using Bipartite Matching Zhao Chengshi, Zou Mingrui, Shen Bin, Kim Bumjung and Kwak Kyungsup Graduate School of IT and Telecom., Inha University, Korea GLOBECOM 2008 1 1

2. Outline • Introduction • Network Modeling • Bipartite Matching Algorithm • Simulations and Discussions • Conclusion 2 2

3. Introduction • Actual measurements have shown that • Most of the allocated spectrum is largely underutilized • Traditional fixed spectrum allocation may be very inefficient • Cognitive Radio (CR) is a promising radio design method, motivated to increase spectrum utilization • By the method of exploiting unused or low utilization spectrum already authorized to primary systems • Secondary Users opportunistically lease spare spectrum from Primary Users without disrupting their operations

4. Previous Work (1) • In [8]-[9], it is shown that by mapping each channel into a color, spectrum allocation can be reduced to a heuristics graph multi-coloring (GMC) problem • The model obtains conflict free spectrum assignments that closely approximate the global optimum in centralized systems • In centralized systems, effective and efficient coordination heavily depends on fast dissemination of control packets among users [8] Zheng, H., and Peng, C, “Collaboration and fairness in opportunistic spectrum access”. In Proc. ICC’05, pp: 3132-3136 June 2005. [9] Peng, C., Zheng, H., and Zhao, B. Y. “Utilization and fairness in spectrum assignemnt for opportunistic spectrum access”. Mobile Networks and Applications, vol. 11, no. 4, pp:555-576, Aug, 2006.

5. Previous Work (2) • In [11], through illustrative examples and simulation data, authors show that under spectrum heterogeneity • A common channel is rarely available to all users, while users do share significant spectrum with local neighbors • In other words, nearby nodes have very similar views of spectrum availabilities • According to this conclusion, we assume that • Nearby users self-organized into coordination groups and use spectrum cooperatively with neighbors by exchanging control messages through a local common channel in each group • A group is build up according to [10] [10] Cao L, Zheng H. “Distributed spectrum allocation via local bargaining”, in Proc. IEEE SECON’05 [11] Zhao, J., Zheng, H. and Yang, G. H., "Spectrum Sharing through Distributed Coordination in Dynamic Spectrum Access Networks," Wireless Communications and Mobile Computing Journal, 2007

6. Goal • In this paper, centralized spectrum allocation is considered • Environmental conditions such as user location, available spectrums are static during allocation • We look upon the target of spectrum allocation is • To maximize networkutilizationas well as to minimize interference • Fairness across users is also considered to some extent

7. Network Modeling • In this paper, we specify • “Channel” is the network link between two users • “Spectrum band” is the radio electromagnetic frequency range that the channel access to • we consider that spectrum is orthogonal as FDMA, which cuts spectrum into spectrum bands • Each SU has an available spectrum band list and selects one band that avoids interference with PUs and other SUs • Users communicate with each other in a method of semi-duplex, uplink and downlink use same spectrum band

8. Edge-Vertex Transform • Channels are transformed into vertexes • Vertexes choose band from intersection of neighboring users’ available band lists • e.g. {band list of 1} = {band list of I} ∩ {band list of II}

9. Key Components of the Network Model • Assume • A network includes N channels, M spectrum bands • Key components of the network model include • AvailabilityA = {an,m | an,m = 0,1}N×M • an,m = 1 iff band m is available for channel n • Constraints C = {ci,j | ci,j = 0,1}N×N • ci,j = 1 iff channel i and channel j are not allowed to access to a same band simultaneously • Utilities U = {un,m | un,m ≧ 0}N×M • un,m=0 iff band m is not available to channel n • Objective O = {on,m | on,m = 0,1}N×M = argAmax{U} • on,m= 1 iff band m is allocated to channel n

10. Bipartite Matching Algorithm (1) • Assume that there are 3 available bands for 5 channels to choose from, and the utility matrix U is assumed as follow • To get the maximum utility of the graph G =(V+B,U), it can be treated as a weighted bipartite graph matching problem

11. Bipartite Matching Algorithm (2) • After perfect matching, we get the result shown in following figure • Utility of the matched network is u3,3+u4,2+u5,1 = 14 • v1 and v2 did not access to any band, they are starved • In fact, they can access some band by improving on the bipartite matching algorithm

12. Max Matching • Berge’s Theorem • A matching is maximum if and only if there is no moreaugmenting path • The edges within the path must alternate between occupied and free • The path must start and end with free edges

13. Max-Weight Matching (1) • A Perfect Matching is an M in which every vertex is adjacent to some edge in M • A vertex labeling is a function ℓ : V → R • A feasible labeling is one such that • ℓ(x) + ℓ(y) ≥ w(x, y), ∀x ∈ X, y ∈ Y • The Equality Graph (with respect to ℓ) is G = (V, Eℓ) where • Eℓ = {(x, y) : ℓ(x)+ℓ(y) = w(x, y)}

14. Max-Weight Matching (2) • Theorem [Kuhn-Munkres]: • If ℓ is feasible and M is a Perfect matching in Eℓ then M is a max-weight matching • Algorithm for Max-Weight Matching • Start with any feasible labeling ℓ and some matching M in Eℓ • While M is not perfect repeat the following: • 1. Find an augmenting path for M in Eℓ; this increases size of M • 2. If no augmenting path exists, improve ℓ to ℓ’ such that Eℓ ⊂ Eℓ’ Go to 1

15. Sharing and Starvation Consideration • Sharing Consideration • v2 can share same band e.g. b1, with v5 • Starvation Consideration • v1 is still starved

16. Solution to Starvation Problem • In each step of matching, vertexes of set B are matched to the starving vertexes first • this method cannot get an overall optimal utility, but starvation is alleviated furthest

17. Solution to Sharing Problem (1) • The allocation is described as follows • Matching starving vertexes first • Assume set B0 is matched to starving vertexes set • Delete vertexes V0; delete the connections between B0 and confliction vertexes of V0 according to matrix C • e.g. c1,2=1, delete vertex v1 and delete the link between b1 and v2 • Considering matrix both C and U to build up possible sharing cases and add sharing cases as fictitious vertexes in set V • possible sharing cases are only {1,3}, {1,4}, {1,5} and {2,5}

18. Solution to Sharing Problem (2) • Delete repeated connections • e.g. v3 is connected to b1, while {1,3} is connected to b1 too, so delete the link between v3 and b1 • Describing the figure in a matrix • The channelscompeting for same band must be put into a column • Fictitious vertexes that sharing same element must be put into a same row

19. Solution to Sharing Problem (3) • U’ is called as extended utility matrix • {i, j} represents a fictitious vertex, and utility U{i, j}= U{i}+ U{j} • It is easily to get that the perfect matching of U’ is {1,3}+{2,5}+{4}=15 • Utility is maximized as well as starvation is avoided • To get the overall optimal result, all of the feasible extended utility matrix must be ransacked

20. Algorithm • Derive extended utility matrixU’ • Use K-M algorithm to U’, get ONXM • If there are other feasible U’, turn to 2 • Compare the results of all ONXM , get the best one from them

21. Simulation Environment • Setting • CR network is assumed by randomly placing users on an area • users within a distance of D will disturb each other if they transmit data using same channel simultaneously • each user is within D distance of the other users at a probability of β • Each band can be a candidate of one’s available band set with probability α • For matrix U, uniform random values are produced from 1 to 20 • number of overall available bands = number of users • Non-Cooperative Case • There is no band-sharing or starvation-restraining • if confliction happens, the user will be rejected to access

22. Results

23. Conclusion • Using bipartite graph matching, a spectrum allocation algorithm that maximizes system utilities and mitigates interference is presented • Experimental results confirm that user cooperation yields significant benefits in spectrum allocation