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Downlink Channel Assignment and Power Control for Cognitive Radio Networks

Downlink Channel Assignment and Power Control for Cognitive Radio Networks. Anh Tuan Hoang, Member, IEEE Ying-Chang Liang, Senior Member, IEEE Institute for Infocomm Research (I2R), Singapore IEEE Transactions on Wireless Communications 2008. 1. 1. Outline. Introduction

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Downlink Channel Assignment and Power Control for Cognitive Radio Networks

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  1. Downlink Channel Assignment and Power Control for Cognitive Radio Networks Anh Tuan Hoang, Member, IEEE Ying-Chang Liang, Senior Member, IEEE Institute for Infocomm Research (I2R), Singapore IEEE Transactions on Wireless Communications 2008 1 1

  2. Outline • Introduction • Problem Definition • Channel/Power Allocation with Global Knowledge of Active CPEs • Channel/Power Allocation with LocalKnowledge of Active CPEs • Results • Conclusions 2 2

  3. Cognitive Radio Networks • The concept of opportunistic spectrum access allows secondary cognitive radio networks to opportunistically exploit the under-utilized spectrum • The overall spectrum utilization can be improved • Transmission from cognitive nodes can cause harmful interference to primary users of the spectrum • Two important design criteria for cognitive radio networks • maximize the spectrum utilization • minimize interference caused to primary users

  4. Environment • We consider a cognitive radio network that consists of multiple cells • Within each cell, there is a base station (BS) supporting a set of customer premise equipments (CPEs) • Each CPE can be either active or idle and a BS needs exactly one channel to support each active CPE • The spectrum of interest is divided into a set of multiple orthogonal channels using FDMA • We assume that the channel usage pattern of the PUs is fairly static over time • cognitive radio network can carry out primary-user detection and thereby avoiding interfering with PU’s operation

  5. Goal and Constraints • The objective is to maximize the number of active CPEs that can be supported, subject to the following conditions: • R1: The total amount of interference caused by all cognitive transmissions to each PU must not exceed a predefined threshold. • R2: For each supported CPE, the received signal to interference plus noise ratio (SINR) must be above a predefined threshold

  6. System Model • Model • K channels • M primary users (PUs) • N CPEs across B cells • BS needs exactly one channel to support each active CPE • only consider downlink scenario (BSs to CPEs) • CPE is active with probability pa

  7. Notations

  8. Operational Requirements (1) • SINR requirement for CPEs • For a given channel c, the SINR at CPE i can be calculated by • No is the noise • is the total interference caused by all primary transmissions on channel c to CPE i • For reliable transmission toward CPE i • can be the minimum SINR required to achieve a certain bit error rate (BER) performance at each CPE

  9. Operational Requirements (2) • Protecting Primary Users • For each PU, the total interference from all opportunistic transmissions does not exceed a predefined threshold ζ

  10. Joint Channel Assignment and Power Control Schemes (1) • Let A be an N × K channel assignment matrix where • Let P be an N × K power control matrix where

  11. Joint Channel Assignment and Power Control Schemes (2)

  12. Feasibility Check (1) • Feasibility • There exists a vector of positive transmit power levels such that • all the SINR constraints of the m CPEs are met • the interference caused to PUs operating on channel c does not exceed the acceptable threshold • Because each BS can support at most one CPE on each given channel, we must have m CPEs i1, i2, ..., im associated with different BSs

  13. Feasibility Check (2) • Define an m × 1 vector Uc and an m × m matrix Fc • The SINR constraints of m CPEs i1, i2, ..., imcan bewritten compactly as • where I is the m × m identity matrix

  14. Feasibility Check (3) • From the Perron-Frobenious theorem ([8], [11], [27], [28]), (7) has a positive component-wise solution Pc if and only if the maximum eigenvalue of Fcis less than one • The Pareto-optimal transmit power vector is [ 8 ] J. Zander, “Performance of optimum transmitter power control in cellular radio systems,” IEEE Trans. Veh. Technol. 1992. [11] D. Mitra, “An asynchronous distributed algorithm for power control in cellular radio systems,” in Proc. 4th WINLAB Workshop on Third Generation Wireless Information Networks, Rutgers University, New Brunswick, NJ, Oct. 1993. [27] F. R. Gantmacher, The Theory of Matrices. Chelsea Publishing Company, 1959. [28] E. Seneta, Non-Negative Matrices. New York: John Wiley & Sons, 1973.

  15. Two-step Feasibility Check Algorithm • Step 1 • Check if the maximum eigenvalue of Fc defined in (6) is less than one. • If not, the assignment is not feasible • otherwise, continue at Step 2 • Step 2 • Using (8), calculate the Pareto-optimal transmit power vector Pc∗ • check if Pc∗ satisfies the constraints for protecting PUs in (3) and the maximum power constraints, i.e. Pc∗ ≤ Pmax • If yes, conclude that the assignment is feasible and Pc∗ is the power vector to use • Otherwise, the assignment is not feasible

  16. Channel/Power Allocation with Global Knowledge of Active CPEs (1) • Without loss of generality, we assume that all N CPEs in the network are active • The problem of maximizing the number of CPEs served can be formulated as the following mixed-integer linear programming (MILP)

  17. Channel/Power Allocation with Global Knowledge of Active CPEs (2)

  18. Dynamic Interference Graph Allocation (DIGA) (1) • Construct interference graphs • Vertex i represents CPE i • Two vertices i and j will be connected by an edge if and only if CPE i and j cannot be simultaneously supported on channel c • employ the Two-Step Feasibility Check to determine the existence of an edge between a pair of vertices • Procedure • start with no CPEs being assigned any channel • allocate a channel to one CPE at a time, until either all CPEs are served, or there is no more feasible assignment • At each step, construct an interference graph that represents the interference between pairs of unserved CPEs • This interference graph must also take into account the aggregated interference caused by transmissions that have been allocated channels in previous steps

  19. Dynamic Interference Graph Allocation (DIGA) (2) • At each step, given the prior channel allocation matrix A, for each unserved CPE i, we calculate its degree corresponding to channel c as follows • D(i, c, A)= ∞ if it is not feasible to assign channel c to CPE i while supporting all prior assignments • The feasibility can be checked using the two-step procedure • If it is feasible to assign channel c to CPE i, then D(i, c, A) is the total number of unserved CPEs that can not be assigned channel c anymore when this channel is assigned to CPE i • The algorithm then picks a CPE-channel pair [i∗, c∗] that minimizes D(i, c, A) and assigns channel c∗ to CPE i∗

  20. Dynamic Interference Graph Allocation (DIGA) (3)

  21. Other Algorithms • Power Control Scheduling Algorithm (PCSA) [18] • An interference graph is first constructed • The problem is then converted into the problem of finding a maximum independent set of the interference graph • The interference graph cannot account for the aggregated interference effect, a clean-up step is needed at the end to remove some links and make the set feasible • Minimum Incremental Power Allocation (MIPA) [19] • Allocate subchannels to interfering links so that their rate requirements are met while the total transmit power is minimized [18] A. Behzad and I. Rubin, “Multiple access protocol for power-controlled wireless access nets,” IEEE Trans. Mobile Comput., vol. 3, no. 4, pp.307–316, Oct.-Dec. 2004 [19] G. Kulkarni, S. Adlakha, and M. Srivastava, “Subcarrier allocation and bit loading algorithms for OFDMA-based wireless networks,” IEEE Trans. Mobile Comput 2005.

  22. Channel/Power Allocation with Local Knowledge of Active CPEs • Assume a centralized power controller to coordinate transmit powers of all BSs to protect PUs • Two-Phase Resource Allocation (TPRA) scheme • Phase 1 - Global Allocation • channels and transmit powers are allocated to BSs so that the interference caused to each PU is below a tolerable threshold • at the same time, we aim to cover as many CPEs as possible • do not care whether a CPE is active or idle

  23. Phase 1 - Global Allocation (1) • Intuition for allocation decision making • A BS that is near any PU receiving on channel c should transmit at low power to reduce interference • A BS faraway from all PUs receiving on channel c can transmit at higher power • The K channels are processed one at a time • For channel c, define • denotes the channel gain from base station b to primary user p on channel c

  24. Phase 1 - Global Allocation (2) • Allocation procedure • Sort the base stations in the ascending order of • The BSs will be processed one at a time in this order • For base station bn, determine a particular CPE in that bn should cover • Given the set of CPEs being covered by base stations • Let be the set of all CPEs i in the cell of bn such that is feasible on channel c • Then in is the CPE that has the weakest channel gain from bn

  25. Phase 1 - Global Allocation (3) • After processing all BSs, using (8), determine the transmit power to serve each of these CPEs • i.e. • Finally, based on , determine the N × K coverage matrix C • where C(i, c)=1 means CPE i can be served by the corresponding BS on channel c

  26. Phase 2 - Local Allocation (1) • Based on the coverage matrix C obtained in Phase 1, channel allocation can be carried out within each cell, independent to what happens in the rest • First, determine all active CPEs in the cell • Next, form a bipartite graph • represent the set of active CPEs as a set of vertices which are connected to another set of vertices representing the available channels • an edge exists between CPE i and channel c if and only if C(i, c)=1 • Maximizing the number of active CPEs served is equivalent to maximizing the number of disjoint edges in the newly-formed bipartite graph • This is the maximal bipartite matching problem

  27. Phase 2 - Local Allocation (2)

  28. Phase 2 - Local Allocation (3) • Berge’s Theorem: A matching is maximum if and only if there is no more augmenting path • Step 1: Start with the empty match • For a particular match, if an edge is in the corresponding set of disjoint edges, then we say the edge is occupied, otherwise, the edge is free • Step 2: Find an augmenting path for the current match • The edges within the path must alternate between occupied and free • The path must start and end with freeedges • If there is no augmenting path, the current match is maximal • Step 3: Flip the augmenting path found in Step 2 • Change free edges to occupied and occupied edges to free to get a better matching • After flipping, the number of matches will be increased by 1 • Go back to Step 2

  29. Simulation Environment • Square area: 1000× 1000 m2 • divided into B adjacent cells, B =4 or 9 • a BS is deployed at the center of each cell • Total number of • CPEs: N = 100 • active with probability pa = 0.1 or 0.2 • PUs: M = 5 ~ 20 • Channels: K = 8 • Power • maximum transmit power of BS: Pmax =50 mW • noise: No = −100 dBm • required SINR for each CPE: 15 dB • maximum tolerable interference for each PU: −110 dBm

  30. Performance of Different Schemes with Global Knowledge (1) 4 BS pa = 0.1 pa = 0.2

  31. Performance of Different Schemes with Global Knowledge (2) 9 BS pa = 0.1 pa = 0.2

  32. Percentage of CPEs being Covered

  33. Performance of Different Schemes with Local Knowledge 4 BS pa = 0.1 pa = 0.2

  34. Conclusions • A control framework is formulated to protect primary users from excessive interference and to guarantee reliable communications for cognitive nodes • Global knowledge of active subscribers is available • formulate the optimization problem as a mixed-integer linear programming • propose a suboptimal allocation scheme based on a dynamic interference graph • Only local knowledge of active subscribers is available • propose a scalable two-phase channel/power allocation scheme that achieves good performance

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