improved utility-based cooperative cognitive...

Improved Utility-Based Cooperative CognitiveRadio Networks

by Team10Haobing Wang

Ren MaoFei YeLi Li

June 9, 2009

by Team10 Haobing Wang Ren Mao Fei Ye Li Li Improved Utility-Based Cooperative Cognitive Radio Networks

CRNCCRN

Part I

Introduction


CRNCCRN

Cognitive Radio Network


CRNCCRN


In Cognitive Radio Network, two kinds of users exists:


CRNCCRN



Primary Users(PU): PU has a higher priority to access thechannel, and they have the right to improve their ownperformance.


CRNCCRN




Secondary Users(SU): SU has no license to access theband, so they should pay to the PU for proportional accesstime.


CRNCCRN




Secondary Users(SU): SU has no license to access theband, so they should pay to the PU for proportional accesstime.

Problem: In previous research, there is no inter-cooperationbetween PU and SUs. So we wonder if we introduce acooperative pattern, the performance of the whole networkmay be improved.


CRNCCRN

Cooperative Cognitive Radio Network


CRNCCRN


Cooperative Pattern:


CRNCCRN



Leveraging SUs as the cooperative relays for the PU’stransmission, the rate can be dramatically increased.


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Similarly, PU can serve as SU’s relay, which can improvethe rate of SU’s transmission.


CRNCCRN




Similarly, PU can serve as SU’s relay, which can improvethe rate of SU’s transmission.

If we can select a subset of the SUs as relays properly, PU’sdata can be transferred in a shorter interval of time, whichcorrespondingly lead to more spare time for SU’s datatransferring, and also PU may get more pay from the SUs. So,we can see that it is a win-win situation.


ModelProtocol

Part II

Model


ModelProtocol

System Model


ModelProtocol

System Model

In our system Model, a slot is separated into three parts:


ModelProtocol

System Model


Step 1: In the first (αβ) fraction of slot, PU trasmit data toselected SUs.


ModelProtocol

System Model



Step 2: In the second (α(1 − β)) fraction of slot, both PUand SUs transmit data cooperatively.


ModelProtocol

System Model



Step 2: In the second (α(1 − β)) fraction of slot, both PUand SUs transmit data cooperatively.

Step 3: In the third (1 − α) fraction of slot, each SUi isprovided an interval of time for transmitting with respect toits payment ci . And for each SUi, PU is used as a relayand the fraction of time for PU is γi .


ModelProtocol

Transmission Rate


ModelProtocol

Transmission Rate

We calculate several transmission rate in all three steps:Step 1:

RPTST (S) = log2 (1 +mini∈S |hPTST ,i |2Pp

No) (1)


ModelProtocol

Transmission Rate



No) (1)

Step 2:

RPSPR(S) = log2 (1 +|hp|2Pp

No+

∑

i∈S

|hSTPR,i |2Ps

No) (2)


ModelProtocol

Transmission Rate



No) (1)

Step 2:


No+

∑

i∈S

|hSTPR,i |2Ps

No) (2)

Step 3:

RSTPT ,i(S) = log2 (1 +|hSTPT ,i |2Pp

No) (3)


ModelProtocol

Transmission Rate


ModelProtocol

Transmission Rate

Note: S is the set of chosen relay SUs.


ModelProtocol

Transmission Rate

Note: S is the set of chosen relay SUs.Thus, for PU,

RP(α, β, S) = min (αβRPTST (S), α(1 − β)RPSPR(S)) (5)


ModelProtocol

Transmission Rate

Note: S is the set of chosen relay SUs.Thus, for PU,

RP(α, β, S) = min (αβRPTST (S), α(1 − β)RPSPR(S)) (5)

For SUi,

Ri = min ((1 − α)γiRSTPT ,i(S), (1 − α)(1 − γi)RSPSR,i(S)) (6)


ModelProtocol

Utility Function


ModelProtocol

Utility Function

The utility function of PU is

UP = wPUR(RP(α, β, S)) +∑

i∈S

ci (7)

where wP is a predefined equiavalent revenue per unit data rateutility contributes to the overall utility and

UR(RP(α, β, S)) =1

1 + e−a(RP(α,β,S)−Ro)(8)

a measure of PU’s degree of satisfaction and Ro is PU’s trafficrequirement.


ModelProtocol

Utility Function


ModelProtocol

Utility Function

The utility function of SU is

ui = wsRi(|hSTPR,i |2Ps

∑

i∈S |hSTPR,i |2Pswx +

ci∑

i∈S ci) · 1

1 + wx− ci (9)

where ws is the equivalent revenue per unit transmission ratecontributes to the overall utility and wx is the weighted constantbetween price and transmission contribution.


ModelProtocol

Implementation Protocol


ModelProtocol


1 PU collects the information of all existing channels.


ModelProtocol


1 PU collects the information of all existing channels.2 By predicting the performance of SUs and in purpose of

maximizing its own utility, PU make a decision of α, β andthe set of SUs for relaying.


ModelProtocol


1 PU collects the information of all existing channels.2 By predicting the performance of SUs and in purpose of

maximizing its own utility, PU make a decision of α, β andthe set of SUs for relaying.

3 Depending on the strategies PU sets, the chosen SUsmake a decision of ci and γi to maximize its utility.


ModelProtocol

SU’s Strategy Selection Game


ModelProtocol


It can be inferred from the definition of SU’s utility function thatui is an increasing function of Ri .


ModelProtocol


It can be inferred from the definition of SU’s utility function thatui is an increasing function of Ri .Moreover, Ri is the minimum of (1 − α)γiRSTPT ,i and(1 − α)(1 − γi)RSPSR,i , one of which is an increasing function ofγi and another is a decreasing function of γi , so RS,i canachieve its maximization when

(1 − α)γi RSTPT ,i = (1 − α)(1 − γi)RSPSR,i (10)

.


ModelProtocol


It can be inferred from the definition of SU’s utility function thatui is an increasing function of Ri .Moreover, Ri is the minimum of (1 − α)γiRSTPT ,i and(1 − α)(1 − γi)RSPSR,i , one of which is an increasing function ofγi and another is a decreasing function of γi , so RS,i canachieve its maximization when

(1 − α)γi RSTPT ,i = (1 − α)(1 − γi)RSPSR,i (10)

.Then we have

γ∗i =

RSPSR,i

RSPSR,i + RSTPT ,i(11)


ModelProtocol



ModelProtocol


For ci ,

∂ui

∂ci=

wsbRi∑j 6=i

j∈S cj

(∑

j∈S cj)2 (12)

where b denotes 11+wx

.


ModelProtocol


For ci ,

∂ui

∂ci=

wsbRi∑j 6=i

j∈S cj

(∑

j∈S cj)2 (12)

where b denotes 11+wx

.And

∂2ui

∂2ci= −

2wsbRi∑j 6=i

j∈S cj∑

j∈S cj

3

< 0 (13)

which indicates that the first order is an decreasing function ofci .


ModelProtocol



ModelProtocol


So, if we let ∂ui∂ci

= 0, and suppose k SUs are chosen, we canget the optimal

c∗i = wsb(k − 1)(

∑

j∈S

1Rj

− k − 1Ri

)/(∑

j∈S

1Rj

)2 (14)

under conditionsj 6=i∑

j∈S

cj < bwsRi (15)

and√

bwsRisumj 6=ij∈Scj − sumj 6=i

j∈Scj < c̄ (16)

where

c̄ > wsb(k − 1)(∑

j∈S

1Rj

− k − 1maxi∈S Ri

)/(∑

j∈S

1Rj

)2 (17)

.by Team10 Haobing Wang Ren Mao Fei Ye Li Li Improved Utility-Based Cooperative Cognitive Radio Networks

ModelProtocol

Maximizing PU’s Utility


ModelProtocol


By substituting the value of c∗i into the function of PU’s utility,

we can get

UP =wP

1 + e−a(RP(α,β,S)−Ro)+

bws(k − 1)∑

i∈S1Ri

(18)

.


ModelProtocol



we can get

UP =wP


bws(k − 1)∑

i∈S1Ri

(18)

.UP is an increasing function of RP(α, β, S), and similar to themethod of finding γ∗

i and c∗i , we can get that

β∗ =RPSPR(S)

RPSPR(S) + RPTST (S)(19)


ModelProtocol



we can get

UP =wP


bws(k − 1)∑

i∈S1Ri

(18)

.UP is an increasing function of RP(α, β, S), and similar to themethod of finding γ∗

i and c∗i , we can get that

β∗ =RPSPR(S)

RPSPR(S) + RPTST (S)(19)

α∗ = [aRo − ln (A − 2B +

√A2 − 4AB

2B)]/A (20)

where A = awpRSTPT ,i(S)RSPSR,i (S)/(RSTPT ,i(S) + RSPSR,i(S))

and B = bws(k − 1)/∑

( 1RSTPT ,i (S) + 1

RSPSR,i (S)), and B should be

less than A/4.by Team10 Haobing Wang Ren Mao Fei Ye Li Li Improved Utility-Based Cooperative Cognitive Radio Networks

ModelProtocol

Selection of SUs


ModelProtocol

Selection of SUs

1 α∗ = α∗(S), β∗ = β∗(S)


ModelProtocol

Selection of SUs

1 α∗ = α∗(S), β∗ = β∗(S)

2 We should select proper S to make UP as large aspossible.


ModelProtocol

Selection of SUs

1 α∗ = α∗(S), β∗ = β∗(S)


3 Thus, S∗ = arg maxS U∗P(S)


ModelProtocol

Selection of SUs

1 α∗ = α∗(S), β∗ = β∗(S)



In our report, we use two kinds of selecting methods: traversaland greedy algorithm.


ModelProtocol

Selection of SUs

1 α∗ = α∗(S), β∗ = β∗(S)



In our report, we use two kinds of selecting methods: traversaland greedy algorithm.And the complexity of each method is: O(t) = 2k andO(g) = k2.


ModelProtocol

Selection of SUs


ModelProtocol

Selection of SUs

The flow chart of greedy algorithm is as below:


ScenarioResults

Part III

Simulation


ScenarioResults

Scenario

In simulation, we consider one pair of PU with six groups ofSUs.

Gain: All the channel gain h are set as GaussianDistribution.

Power: No = 0.1, PP = 1 and 0 < PsPP

< 1

Rate-weight: ws = 0.15, wP = 0.3, wx = 1.2

PU’s required data rate Ro = 3.6


ScenarioResults

Select Method Compare

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.31

0.32

0.33

0.34

0.35

0.36

0.37

0.38

0.39

0.4

Ps/Pp

Up

Sub−optimalOptimal

Figure: Comparison of selecting method

The Comparison between two selecting methods.


ScenarioResults

Alpha-Beta

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Ps/Pp

alph

a,be

ta

alphabeta

Figure: Optimal Alpha Beta

While Ps changes from 0 to Pp, the choosing of parameteralpha and beta also changes.


ScenarioResults

Utility

Figure: Utility over Ps/Pp

When we increase the ratio of Ps over Pp, the utility of both PUand SUs become greater.


ScenarioResults

Optimal Gamma

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−4

−3

−2

−1

0

1

2

3

4

5

6x 10

−3

gama

Util

ity

Ui

Figure: Ui over gamma

Use different values of gamma, observe how Ui changes.


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