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Spectrum Sharing in OFDM-Based Cognitive Radio Networks

Spectrum Sharing in OFDM-Based Cognitive Radio Networks. C. Rosenberg. This work was done in collaboration with Dr. L. Le, Profs. P. Mitran & A. Girard. Outline. Introduction to Dynamic Spectrum Sharing Our 3 Resource Allocation Problems Models Formulations Results Heuristics

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Spectrum Sharing in OFDM-Based Cognitive Radio Networks

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  1. Spectrum Sharing in OFDM-Based Cognitive Radio Networks C. Rosenberg This work was done in collaboration with Dr. L. Le, Profs. P. Mitran & A. Girard.

  2. Outline • Introduction to Dynamic Spectrum Sharing • Our 3 Resource Allocation Problems • Models • Formulations • Results • Heuristics • Description • Results • Des • Conclusions

  3. The Spectrum and Its Management • Most governments consider the electromagnetic spectrum to be a public resource. • It is usually allocated by a governmental organization (FCC, CRTC, ETSI, ARIB, etc.) that defines the spectrum management policy. • Most of the spectrum is currently licensed to users to further the public good, e.g., radio, television, etc. • Examples of licensing • TV channels, radio, • Cellular service, • Unlicensed “free for all”, subject to some constraints (e.g., 900 Mhz cordless phones, 2.4 Ghz wireless WiFi). • Common belief: we are running out of usable radio frequencies. Is that true?

  4. Current Spectrum Management Policy • Fixed allocation • Rigid requirements on how to use • Little sharing

  5. Spectrum Usage in Space, Time, & Frequency Actual measurements by the FCC have shown that many licensed spectrum bands are unused most of the time. In NYC, spectrum occupancy is only 13% between 30 MHZ – 3.0 GHz.

  6. Spectrum Usage • Good quality spectrum is under-utilized. • Hence the problem is more a spectrum management policy issue than a physical scarcity. • The problem is begging for a solution based on dynamic spectrum management or access. There are many possibilities. • Cognitive Radio is a (BAD but CATCHY) synonym of dynamic spectrum access.

  7. Dynamic Spectrum Sharing • There are 3 ways to share the spectrum dynamically • Dynamic Exclusive Access: extension to the current licensing policy. Flexible licensing. An improvement but not “fast” enough. • Open Sharing Model: horizontal sharing, a generalization of the unlicensed band policy. All users/nodes have equal regulatory status. Based on the huge success of WiFi and other technologies working in the ISM band. • Hierarchical Access Model: vertical sharing. All users do not have equal regulatory status (i.e., primary users and secondary users). Secondary users can opportunistically access the spectrum as long as it does not affect the primary users’ performance. Allows for prioritized spectrum sharing provided no harmful interference caused to primary users.

  8. Harmful Interference • What is harmful interference? • Ultimately depends on the application. • There are generally two broad approaches to avoid harmful interference: • Interference avoidance (spectrum overlay)‏ • Interference control (spectrum underlay) • Of course they can be combined (overlay) (underlay)‏

  9. Spectrum Overlay: Interference Avoidance • Spectrum overlay approach impose restrictions on when and where the secondary users may transmit. Secondary users have to identify and exploit the spectrum holes defined in space, time, and frequency. • Compatible with the existing spectrum allocation –legacy systems can continue to operate without being affected by the secondary users. • Regulatory policies define basic etiquettes for secondary users to ensure compatibility with legacy systems. • In principle, interference avoidance involves only two steps: • Look for holes in spectrum/time. • Transmit only in those bands at those times. • Sounds a lot easier than it is. • Detection of spectral holes is difficult due to the large range of potential modulation/coding schemes: careful measurements based on actual primary signal statistics and signatures is needed. • Hidden terminal problem: we have to protect the primary receivers (but where are they?). • Fast detection time needed.

  10. How to Use Holes? • Suppose that after some sophisticated signal processing, we determine that spectrum occupancy is: • How do we use these (non-contiguous) holes? • OFDM based approach solves the problem naturally. • OFDM has the advantages that • It is low complexity (FFT and IFFT based) • Can be naturally adjusted to fit almost any configuration of spectral holes. • Is growing in popularity (802.11a, 802.16, 802.22)

  11. Spectrum Underlay: Interference Control • Interference avoidance is worst-case design • In practice, this may be too “soft” and overly limit throughput of secondary users. • Spectrum underlay approach constraints the transmission power of secondary users so that they operate below the interference temperature limit of primary users (i.e., the receivers). • Interference temperature introduces new opportunities at a cost: • Additional difficulties • Secondary user needs to measure/know temp. at primary receivers. • Secondary measurements • Feedback from primary • Treats interference as noise.

  12. Spectrum Opportunity • Channel is available at A (tx) if no primary rx nearby. • Channel is available at B (rx) if no primary tx nearby. • Channel is an opportunity if available at both A and B.

  13. A Definition of Cognitive Radio (CR) • A cognitive radio is an unlicensed communication system • that is aware of its environment • learns from its environment • adapts to the statistical variations of its environment • and uses these to • achieve reliable communication and spectral efficiency by employing spectral holes or opportunities and does not generate harmful interference to the incumbents.  Cognitive Radios will be complex devices.

  14. Resource Allocation for the Secondary Network • The most common network configuration in practice has a star topology. • Because users have different channel gains and bandwidth demands, resources must be allocated carefully (this is always true) • Power • Rate: Modulation/Coding scheme • We will assume OFDM  Not all sub-channels are feasible for all secondary users • There are challenging trade-offs between sub-channel allocation, power allocation and rate. • Since primary users can be mobile, re-allocation must be done in real-time to protect the primary.

  15. Some Examples • Two examples of star networks with cognitive features: • IEEE 802.16h (WiMAX) provides extensions to support unlicensed co-existence • IEEE 802.22 is an explicit cognitive WRAN that will exploit vacant TV broadcast bands TV Transmitter WRAN Base Station Typical ~33km Max. 100km : WRAN Base Station : CPE

  16. A little more about IEEE 802.22 • IEEE 802.22 has the following interesting characteristics: • Has a complex architecture to detect primary users. • Follows the spectrum overlay approach (avoids interfering with primary users altogether) • Is OFDM based

  17. Our Class of Problems • The class of problems we are interested in is resource allocation for star topology cognitive networks. • Our problem is similar to IEEE 802.22, except that we follow the spectrum underlay approach • Our assumptions: • Star based network, downlink only, OFDM, limited instantaneous power budget at the base-station, max-min fair.

  18. Distributed Sensing • We assume N secondary users, M sub-channels, z modulations schemes (rates R1,…,Rz and SNR threshold γ1,…γz). • The BS is the master of distributed sensing and resource allocation, etc. • As a result of distributed sensing, a table T is created, which provides the BS with constraints on its transmit power on any given sub-channel to avoid harmful interference to primary users. • Tdecouples the problem of sensing from that of resource allocation. • Given T, find the “best”joint sub-channel, rate, and power allocation. This allocation has to be computed fast (and often).

  19. Assumptions (the channel dimension) • The bandwidth is divided into M subchannels. • Each subchannel may or may not be used by primary users. • We assume that as a result of channel sensing, transmission power at the base station has a known constraint on each subchannel j (depends on the location of the primary receiver using that subchannel).

  20. Assumptions (the time dimension) • The time is slotted. Each user i sends periodically information on its perception of the primary activity on each channel (mi) & its channel gains (gi). • The BS compute the table T and then a resource allocation (RA) map that is valid for the duration of a frame. • The BS has a power budget on a per time-slot basis to share among all its channels/users.

  21. Assumptions (the time dimension) (A) (B) • If the frame is made of L time-slots (TS), one can consider 3 cases: • A RA problem computed on a one-TS basis. The resulting allocation is then repeated for the F TS of the frame. The RA map then looks like (A). • A RA problem computed on a frame-basis. The RA map looks like (B). • A RA problem on a F TS-basis and then repeated k=L/F times. • These 3 cases can be summarized by taking k in {1,…,L}. The larger k, the better the flexibility and the higher the complexity. Joint sub-channel, rate, and power allocation

  22. Our 3 Resource Allocation Problems • First problem: k=1, table T, no queues. Very similar to a traditional OFDM scheduling problem. The only difference is T. • Second problem: k>1, table T, no queues. Surprisingly, nobody seems to have studied this case even in a traditional OFDM system. • Third problem: k>1, table T, with queues. Clearly introducing queues, will allow us to be more efficient in the way we share the resources. The question is: does that make the scheduler more complicated? • These three problems are NP hard. NP hard does not mean that we should try to solve the problem exactly for reasonable size network! It will blow up but how fast is not clear.

  23. First Optimization Problem • Parameters: : Number of subchannels : Number of secondary users : Number of coding and modulation schemes : Rate of modulation and coding scheme . • Formal optimization problem: max-min rate: sijz =1 if channel j is allocated to transmission between the BS and i with modulation z A channel can only be allocated once Min power to tx from BS to i on subchannel j with mod. z. From sensing Total power constraint

  24. Remarks on Optimization Problem • This is an integer linear program in • There are variables. • Example: N = 40 users, M = 120 channels, z =5 modulation/coding schemes • 24,000 variables, only 120 of which are not zero! • Problem can be “solved” using a commercial integer programing tool such as CPLEX. • Takes seconds to minutes, sometimes only yields bounds • Useful for evaluating fast online heuristics.

  25. Second Optimization Problem • New parameter: • F: the number of TS over which the RA is done (k=L/F). We will refer to it as a subframe. • Formal optimization problem: • Let • Then: Straightforward generalization. The number of variables is now multiplied by F.

  26. Test Cases • Primary and secondary users are distributed at random inside disks of radius km and km respectively. • Each primary user (receiver) assigned a random primary channel. • Channel gains are mix of Ricean fading and path loss

  27. Test cases • The cognitive constraints are determined by • Limiting received power from the secondary base-station at any primary receiver on its primary channel to at most . • The system is multirate with rates and SINR thresholds:RateSINR (dB)1 102 14.773 18.454 21.765 24.91 By default ω = 0 dB (we double the noise level)

  28. Results (Impact of F and Pmax, Np=0) Average max-min rate for (M;N;Np) = (120; 40; 0), infinite queue backlogs (20 realizations per point)

  29. Results (Impact of F and Pmax, Np=30) Average max-min rate for (M;N;Np) = (120; 40; 30), infinite queue backlogs

  30. Results (Impact of F and Pmax, Np=60) Average max-min rate for (M;N;Np) = (120; 40; 60), infinite queue backlogs

  31. Results (Impact of ω) Average max-min rate for (M;N;Np) = (120; 40; 50), infinite queue backlogs, F=1

  32. Third Optimization Problem (1) • This RA problem takes into account the values of the queues at the BS. • Assumption: the BS has one queue per user i and uses the number qiof packets in the queue when computing the RA at the beginning of a frame. • We want to ensure that we do not give more resources than needed to users. • Formulating an optimization problem that includes the queues is not trivial. • We will say that a user i has its queue fully satisfied if • Let S= {sijzt} be a feasible resource allocation over a subframe (and S be the set of all such feasible RA), i.e., one that satisfies all the constraints in the previous problem. • Let Ω(S) be the set of users whose queues are fully satisfied when performing the feasible resource allocation S and Ωc(S) be its complement. • Then for each feasible RA, S we can compute the minimum rate received by a CPE in Ωc(S) (i.e., whose queue is not entirely satisfied). Our objective is to maximize this minimum over all feasible S:

  33. Third Optimization Problem (2) • To remove the dependence of the min operation over the set of non-bottleneck users Ωc(S) we can write the objective function in an equivalent form as follows: • With μ(x,q) is a function which is defined as: • where Λ is a sufficiently large number. This transformation can be interpreted as follows. For a user i such that is satisfied the objective function is large enough that this user will not be a bottleneck for the min operation. Therefore, the min in the objective function is only applied to users with queue backlogs that are not met. • The problem formulated above is a very large non-linear problem with integer variables. It is very general and captures several important resource allocation problems.

  34. Solution Using An Integer Program Solver • The objective function of the optimal allocation problem is not linear in its optimization variables. Hence its solution cannot be readily obtained by an Integer Program (IP) solver. • We develop an iterative procedure to obtain its solution using a IP solver so that we could compute benchmark results for our heuristics.

  35. Results (Finite Queues) Average max-min rate for (M;N;Np) = (120; 40; 0), finite queue backlogs

  36. Results (Finite Queues) Average max-min rate for (M;N;Np) = (120; 40; 30), finite queue backlogs

  37. Results (Finite Queues) Average max-min rate for (M;N;Np) = (120; 40; 60), finite queue backlogs

  38. Need for Heuristics • There is much literature on downlink resource allocation in OFDM. • Need to develop fast (fast enough to adapt to changing primary behaviour) and efficient heuristics. • There are clearly different approaches to develop heuristics. • A common one is to use the following three steps:1. Power Allocation: Distribute power to subchannels first.2. Channel and Rate Allocation: Allocate subchannels and rate to users given the power allocated to each subchannel.3. Rate and Power Allocation: Perform rate and power allocation given the channel allocation obtained in step 2. • We have adapted these 3 steps to our cognitive framework and added a 4th step that makes the heuristic more accurate. We have also improved step 2 by reallocating power not being used as we go along. • We have also adapted the 4 steps to take queue backlogs into account.  We have created a versatile class of heuristics with different trade-offs between accuracy and speed.

  39. Results (Infinite Queues) Average max-min rate for (M;N;Np) = (120; 40; 0), infinite queue backlogs (20 realizations per point)

  40. Results (Infinite Queues) Average max-min rate for (M;N;Np) = (120; 40; 0), infinite queue backlogs (20 realizations per point)

  41. Results (Infinite Queues) Average max-min rate for (M;N;Np) = (120; 40; 30), infinite queue backlogs (20 realizations per point)

  42. Results (Infinite Queues) Average max-min rate for (M;N;Np) = (120; 40; 30), infinite queue backlogs (20 realizations per point)

  43. Results (Infinite Queues) Average max-min rate for (M;N;Np) = (120; 40; 60), infinite queue backlogs (20 realizations per point)

  44. Results (Infinite Queues) Average max-min rate for (M;N;Np) = (120; 40; 60), infinite queue backlogs (20 realizations per point)

  45. Results (Finite Queues) Average max-min rate for (M;N;Np) = (120; 40; 0), finite queue backlogs (20 realizations per point)

  46. Results (Finite Queues) Average max-min rate for (M;N;Np) = (120; 40; 0), finite queue backlogs (20 realizations per point)

  47. Results (Finite Queues) Average max-min rate for (M;N;Np) = (120; 40; 30), finite queue backlogs (20 realizations per point)

  48. Results (Finite Queues) Average max-min rate for (M;N;Np) = (120; 40; 30), finite queue backlogs (20 realizations per point)

  49. Results (Finite Queues) Average max-min rate for (M;N;Np) = (120; 40; 60), finite queue backlogs (20 realizations per point)

  50. Results (Finite Queues) Average max-min rate for (M;N;Np) = (120; 40; 60), finite queue backlogs (20 realizations per point)

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