*Sponsored in part by the DARPA IT-MANET Program, NSF OCE Opportunistic Scheduling with Reliability Guarantees in Cognitive Radio Networks Rahul Urgaonkar, Michael J. Neely University of Southern California

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 Cognitive Radio Networks

Design Issues and Challenges 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

Our Contributions 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

Network Model 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

h ij (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 Example Network

Network Model (contd.) Interference model –S m (t) : actual state for channel m (busy, idle) –at most one transmission per channel per slot –additionally, interference sets I nm –conditions for successful SU transmission I 21 = {1, 2} Important special case I nm = {m} for all n,m

Network Model (contd.) Channel State Information model –probability P m (t) = E{S m (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

Queueing Dynamics Secondary user queues U n (t) Flow control decision R n (t) –how many new packets to admit Transmission decisions μ nm (t) –subject to network model constraints

Setting up the problem Goal: Maximize secondary user throughput utility subject to maximum time average rate of collisions ρ m with any primary user m R n (t) = admitted data for SU n in slot t C m (t) = collision variable for PU m in slot t Let can solve if know all parameters challenge: unknowns mobility, Λ, dynamics

Our Approach 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

Collision queue Define a collision queue X m (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

Algorithm Design and Proof sketch 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

“cross-layer” algorithm decoupled into 2 components. (V≥0) 1.Flow control: Each secondary user chooses the number of packets to admit as the solution to: - simple threshold policy, implemented separately at each SU 2.Scheduling transmissions of secondary users: Choose a resource allocation that maximizes: subject to network constraints - a generalized Maximum Weight Match problem Cognitive Network Control Algorithm

1.Strong reliability bound: The worst case number of collisions suffered by any primary user m is no more than ρ m T + X max over any finite interval T (where X max is a constant) - deterministic performance guarantee 2.Bounded worst case queue backlog: The worst case queue backlog is upper bounded by a finite constant U max for all secondary users - U max linear in V 3.Utility-Delay tradeoff: The average secondary user throughput achieved by CNC is within O(1/V) of the optimal value CNC Performance Theorem

Distributed Implementation Focus on the case with I mn = {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

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 Simulation example Total average congestion vs. input rate for different V (also no flow control case)

Simulation example 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 Throughput vs. Input rate for different V