PRICE-BASED SPECTRUM MANAGEMENT IN COGNITIVE RADIO NETWORKS

Fan Wang, Marwan Krunz, and Shuguang Cui

Department of Electrical & Computer Engineering, University of Arizona

Cognitive Radio Oriented Wireless Networks and Communications, 2007. CrownCom 2007

1

Outline2

Introduction System Model Problem Formulation

Utility Function Game Formulation Optimal Pricing Function

Iterative Algorithm Sequential & Parallel

Conclusion Comments

Introduction3

One of the main challenges in an opportunistic CRN How to design an efficient and adaptive

channel access scheme that supports dynamic channel selection and power/rate allocation is a distributed environment Maximize the CRN performance without

disturbing PR (Primary Radio) transmissions. A typical measure of efficiency is the

achievable sum-rate of all CR pairs.

Introduction (cont’d)4

Resource allocation - Iterative water-filling [28] A non-cooperative game was used to model the

spectrum management problem with each user iteratively maximizing its own rate.

This per-user optimization problem is convex and leads to a water-filling solution. For the two-user case, it was shown that the Nash

Equilibrium exists and the IWF algorithm converges to the NE under certain conditions.

However, this NE is generally not Pareto optimal and may be quite inefficient in terms of the sum-rate metric.

Each user tries to maximize its own utility function without considering the overall system performance.

[28] W. Yu. Competition and cooperation in multi-user communication environments. Ph.D. Dissertation, Stanford University, Stanford, CA, 2002.

Introduction (cont’d)5

A centralized spectrum management scheme [4] Improves the system performance over the IWF

scheme by utilizing a centralized spectrum management center

However, such a centralized approach cannot be implemented in a distributed ad hoc CRN

Motivation of this paper Design a channel/power/rate allocation scheme that

overcomes the inefficiency of the classic IWF algorithm can be implemented in a distributed fashion provide incentives to CR users such that they can reach a

more socially efficient NE A commonly used incentive technique is pricing.

Introduction (cont’d)6

Price-based iterative water-filling algorithm We show that this PIWF algorithm maintains the

simplicity and distributed operation of the original IWF algorithm.

A challenging problem The effectiveness of the pricing approach depends on

the appropriate selection of the “pricing function” In this paper, we use a user-dependent pricing

function the sum-rate of the achieved NE after a few iterations. a pricing function can be determined by allowing each

CR user to distributively explore the neighborhood information via control-packet exchanges.

System Model7

A hybrid network Several primary radio networks and one CRN

The CRN contain N CR pairs. The total spectrum consists of K orthogonal

frequency channels (K<N) with central frequencies f1,f2,…,fk

Each CR may simultaneously transmit over multiple channels

Let Mi(fk) denote the total noise-plus-interference level measured by CR user i over channel k This quantity includes the PR-to-CR interference, the

CR-to-CR interference, and the thermal noise.

System Model (cont’d)8

This figure gives a channel allocation example for a CRN with K=3 and N=4.

Denote the set of utilized channels for CR link i as Si

S1 = {f1,f2}

The transmission power vector of CR link i over various channels is denoted by Pi = [Pi(f1), Pi(f2),…,Pi(fk)] Pi(fk) is the transmission power of CR i on

channel k.utilized by a CR Link

System Model (cont’d)9

Constraints Maximum transmission power constraint

The total transmission power of a CR user over the selected channels should not exceed Pmax

CR-to-PR power mask constraint The transmission power of CR i on channel k is

constrained by Pmask(fk), which denotes the power mask associated with channel k.

Pmask defines as [Pmask(f1), Pmask(f2),…,Pmask(fk)] Assume that Pmask is given a priori.

max)( PfPiSk

ki

Problem Formulation10

A normal game can be expressed in the form G = {Ω, P, {Ui}}

Ω={1, 2, …, N} is a finite set of rational players P = P1 x P2 x … x PN is the action space with Pi

being the action set for player I Ui: P R is the utility (payoff) function of player i,

which depends on the strategies of all players Player CR users Actions transmission powers Utility associated with their actions and the

quality of the channels

Problem Formulation (cont’d)

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Utility Function The utility function of user i can be considered as the reward

received by this user from the network.

hii(fk): the channel gain between the transmitter and the receiver of link i over channel k

Mi(PR)(fk): the PR-to-CR interference at the receiver of CR link I over

channel k Ni(fk): the received thermal noise power on channel k

Nash Equilibrium (after several iteration and under certain condition)

CR-to-CR interferencePR-to-CR Noise

Problem Formulation (cont’d)

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The resulting NE may be far from the Pareto Optimum those in which any change to make any person

better off is impossible without making someone else worse off. (Wiki)

wi : the weight assigned to user i

A new utility function for user i

Problem Formulation (cont’d)

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ci(fk): the pricing function for user i on channel k =

Our goal is to choose a user-dependent pricing function that can drive the CR users to converge to an “social-efficient” NE

Problem Formulation (cont’d)

14

Game Formulation

The game in our setup can be easily shown to be a concave game if the following two properties are satisfied:1.The action space P is a closed and bounded convex set.2.The utility function Ui(Pi) is concave over its strategy A concave game always admits at least one Nash EquilibriumProposition 1: For any given Pmax and Pmask values, there is at least one NE for the game G

Problem Formulation (cont’d)

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Optimal Pricing Function In power control context, pricing is often

used as an incentive mechanism to improve the efficiency of the NE

Fixed pricing factor for players isn’t suitable for distributed manner.

One contribution of this paper: Introducing a user-dependent linear pricing function that drives the NE close to the Pareto optimal frontier with each player knowing only partial information about the networks.

Problem Formulation (cont’d)

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Proposition 2 Consider the game G with utility function U~i,

i=1…N, as defined in (3) , and let the pricing function ci(fk) be given by ci(fk) = λi(fk)Pi(fk). Then, the game has at least one NE solution (from proposition 1).

Further, if this NE solution is Pareto optimal, then the pricing factor λi(fk) must be:

can be proved by the Lagrange function and KKT-condition

Problem Formulation (cont’d)

17

Intuitively, a higher pricing factor λi(fk) will prevent user i from using a large transmission power on channel k. If a neighbor j is to transmit over channel k, it

needs to broadcast its transmission power Pj(fk), the measured total noise and interference Mj(fk), and the channel gain hjj(fk) between the transmitter and the receiver of link j.

The above information can be incorporated into MAC control packets

Iterative Algorithms18

Each CR user, say i, first adjusts its linear pricing factor λi(fk) over all channels, and then determines its best response The optimal channel/power/rate combination

based on the measured Mi

The best response of user i is to maximize its individual utility function subject to the constraints C1-C3

The same procedure converges, then by definition, it has to converge to a NE of the game.

Iterative Algorithms (cont’d)19

Proposition 3 By treating the other users’ transmissions as

interference, the best response of user i is given by:

the analysis provided in [23] can be extended to arrive at the result in Proposition 3.

β: the water level, is determined by user i as the minimum non-negative value that results in satisfying the total power constraint C2.

[23] G. Scutari, D. P. Palomar, and S. Barbarossa. Asynchronous iterative water-filling for Gaussian frequency-selective interference channels: A unified framework. Submitted to IEEE Transactions on Information Theory, August 2006.

price

interference

channel gaintransmission power

Iterative Algorithms (cont’d)20

Sequential Price-based Iterative algorithm

converge condition

Iterative Algorithms (cont’d)21

Proposition 4 Suppose that the pricing function takes a linear

form with a fixed pricing factor over a few iterations. Then, the sequential update procedure converges to the unique NE if one of the following two sets of conditions is satisfied.

From above, the convergence and the uniqueness of NE are ensured if the CRs that share the same channel are far apart, and thus inflict weak interference on each other.

Iterative Algorithms (cont’d)22

Parallel Price-based Iterative algorithm

Iterative Algorithms (cont’d)23

Compare with the classic approach Sequential vs. Parallel

Iterative Algorithms (cont’d)24

Relaxation Algorithm more robust to occasional estimation errors

and channel oscillations at the cost of slower convergence speedSequential algorithm’s best response

Parallel algorithm’s best response

A larger α (0≤α<1) means a longer memory (less adaptation to the environment), but slower convergenceAs proved in [23],

Conclusions25

Proposed two priced-based iterative water-filling algorithm that overcome the inefficiency of the classic approach.

The parallel algorithm can converge faster than the sequential one, especially for a large number of users.

Comments26

A different approach (game theory) to solve the power control problem

Use pricing manner as the cost function to control the selfishness of CR user

Consider the overall system performance!