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Opportunistic Scheduling with Reliability Guarantees in Cognitive Radio Networks

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Opportunistic Scheduling with Reliability Guarantees in Cognitive Radio Networks

Rahul Urgaonkar, Michael J. Neely

University of Southern California

http://www-rcf.usc.edu/~urgaonka/

*Sponsored in part by the DARPA IT-MANET Program, NSF OCE-0520324

Cognitive Radio Networks

- Radio spectrum: a precious commodity
- recent FCC auction of 700MHz band ~$20 billion

- Existing static allocation of spectrum considered inefficient
- “white spaces” observed

- Motivation: Improve spectrum usage by dynamic spectrum access
- Key enabler: Cognitive Radio
- here, cognitive radio ~ dynamic operating frequency

- Primary (licensed) and Secondary (unlicensed) users
- Basic requirement: To ensure secondary users take advantage of the unused spectrum without adversely affecting primary users
- Challenges:
- potentially oblivious primary users
- imperfect “channel state information” may cause collisions
- network dynamics (mobility, traffic)
- distributed solutions desirable

- Develop a throughput optimal control algorithm for cognitive radio networks
- general mobility and interference models

- Notion of collision queues
- inspired by the virtual power queue technique of [1]
- worst case deterministic bound on maximum number of collisions
- prior works give probabilistic guarantees

- Consider full effects of queueing
- yields bounds on average delay

- Constant factor distributed approximation
- in a special case

[1] M. J. Neely, Energy Optimal Control for Time Varying Wireless Networks, IEEE Transactions on Information Theory, July 2006

- M primary, N secondary users
- Primary users static, each has a unique channel
- channels orthogonal in frequency or space

- Secondary users mobile, no licensed channel
- set of channels they can access time-varying
- H(t) : 0/1 channel accessibility matrix

- Mobility model
- time-slotted
- resulting channel accessibility matrix H(t) Markovian

Example Network

hij(t) = 1 if SU i can access channel j in slot t

H(t) evolves according to a finite state ergodic Markov Chain, transition probabilities unknown

- Interference model
- Sm(t) : actual state for channel m (busy, idle)
- at most one transmission per channel per slot
- additionally, interference sets Inm
- conditions for successful SU transmission

I21 = {1, 2}

Important special case

Inm= {m} for all n,m

- Channel State Information model
- probability Pm(t) = E{Sm(t)|S(t-1)}
- known at slot t
- obtained by sensing the channels or knowledge of PU traffic statistics or combination etc.
- models imperfect channel state information

2 state Markov chain example. Assume know ε, δ

E{S(t)|S(t-1) = ON} = 1- ε

E{S(t)|S(t-1) = OFF} = δ

- Secondary user queues Un(t)
- Flow control decision Rn(t)
- how many new packets to admit

- Transmission decisions μnm(t)
- subject to network model constraints

Goal: Maximize secondary user throughput utility subject to maximum time average rate of collisions ρm with any primary user m

Rn(t) = admitted data for SU n in slot t

Cm(t) = collision variable for PU m in slot t

Let

can solve if know all parameters

challenge: unknowns

mobility, Λ, dynamics

- Lyapunov Optimization technique [2]
- generalization of backpressure technique
- [2] also covers related work

- Unifies stability and utility optimization
- Main idea: Convert time average constraints into queueing stability problems
- notion of virtual queues

- Then, use Lyapunov Stability argument to design an optimal control algorithm

[2] Resource Allocation and Cross-Layer Control in Wireless Networks, Georgiadis, Neely, Tassiulas, NOW Foundations and Trends in Networking, 2006

- Define a collision queue Xm(t) for channel m

Observation: If this queue is stable, then the constraint on the maximum time average rate of collisions is met

This is exactly the collision constraint in our optimization problem

- Define our state as Q(t) = (U(t), X(t))
- Define Lyapunov function
- Compute Lyapunov drift
- Every slot, take control actions to minimize (V≥0)
- Compare with a stationary, randomized policy
- Delayed drift analysis for Markovian dynamics

Cognitive Network Control Algorithm

- “cross-layer” algorithm decoupled into 2 components. (V≥0)
- Flow control: Each secondary user chooses the number of packets to admit as the solution to:
- - simple threshold policy, implemented separately at each SU

- Scheduling transmissions of secondary users: Choose a resource allocation that maximizes:
- subject to network constraints
- - a generalized Maximum Weight Match problem

CNC Performance Theorem

- Strong reliability bound: The worst case number of collisions suffered by any primary user m is no more than ρmT + Xmax over any finite interval T (where Xmax is a constant)
- - deterministic performance guarantee

- Bounded worst case queue backlog: The worst case queue backlog is upper bounded by a finite constant Umax for all secondary users
- - Umaxlinear in V

- Utility-Delay tradeoff: The average secondary user throughput achieved by CNC is within O(1/V) of the optimal value

Distributed Implementation

- Focus on the case with Imn = {m}
- The resource allocation problem becomes the Maximum Weight Match problem on a Bipartite graph
- NxM Bipartite graph, N secondary users, M channels

- Constant factor (1/2) distributed approximation using Greedy Maximal Match Scheduling
- Reliability guarantees stay the same

Simulation example

- Cell partitioned network with 9 static primary users, 8 mobile secondary users, moving according to a Random Walk
- One channel per primary user
- Here, greedy maximal match = MWM

7

2

4

1

3

8

5

6

Total average congestion vs.

input rate for different V

(also no flow control case)

Simulation example

7

2

4

1

Throughput

vs. Input rate

for different V

3

8

5

6

- All collision constraints met
- The achieved throughput is very close to the input rate for small values of the input rate
- The achieved throughput saturates at a value depending on V, being very close to the network capacity for large V