Introduction Motivation Our Work Results Future Work

A New Power Allocation Scheme for SpectrumSharing OFDM Cognitive Radio Networks

Anubhav Singla and Mainak ChowdhuryMentor: Dr. Ajit K. Chaturvedi

BTech projectMid Term Presentation

Department of Electrical Engineering, IIT Kanpur

November 11, 2010

Introduction Motivation Our Work Results Future Work

1 Introduction

2 Existing schemes in literature

3 Our Work

4 Numerical results

5 Future Work

Introduction Motivation Our Work Results Future Work

Outline

1 Introduction

2 Existing schemes in literature

3 Our Work

4 Numerical results

5 Future Work

Introduction Motivation Our Work Results Future Work

Cognitive Radios

Opportunistic spectrum utilization by unlicensed users(Secondary Users)

Licensed users (Primary users) should not suffer much

System needs to be aware of the spectrum environment

Real time optimization of operating parameters - carrierfrequency, transmit power, etc

Introduction Motivation Our Work Results Future Work

Models of spectrum utilization

Spectrum interweave

Spectrum underlay

Spectrum overlay

In our work we consider spectrum underlay networks

Introduction Motivation Our Work Results Future Work

Models of spectrum utilization

Spectrum interweave

Spectrum underlay

Spectrum overlay

In our work we consider spectrum underlay networks

Introduction Motivation Our Work Results Future Work

Issues

Fast and Efficient Spectrum Sensing

Optimal Power Allocation Schemes

Security Issues for Primary Users

Medium Access Control

Introduction Motivation Our Work Results Future Work

Challenges in Spectrum underlay

Guarantee to primary users

Incentive for secondary users

Reasonable implementation complexity

Introduction Motivation Our Work Results Future Work

Outline

1 Introduction

2 Existing schemes in literature

3 Our Work

4 Numerical results

5 Future Work

Introduction Motivation Our Work Results Future Work

Notations used

I = {1, 2, . . . ,N} set of subcarriers

J = {1, 2, . . . ,M} set of primary users

Pi secondary user transmitter power in i th subcarrier

Ti is primary user transmitter power in i th subcarrier

Kj is the set of all subcarriers allocated to user j

Figure: Schematic representation of the OFDM channel

Introduction Motivation Our Work Results Future Work

Notations used(contd. . .)

Primary user rate Rpj =

∑i∈Kj

Rpji where

Rpji = log

(1 +

h11iTi

h12iPi + N0

)∀i ∈ Kj

Secondary user sum rate∑N

i=1 Rsi where

Rsi = log

(1 +

h22iPi

h21iTi + N0

)

21

22

12

11

Figure: Channel parameters

Introduction Motivation Our Work Results Future Work

Existing schemes in literature

No primary user protection

Interference power constraints

Primary user rate loss constraints

Introduction Motivation Our Work Results Future Work

No primary user protection

maximizeP

n∑i=1

Rsi

subject to

∑Ni=1 Pi

N≤ Pa

Pi ≥ 0 ∀ i ∈ I

Solution is a simple waterfilling scheme 1.

1[Tse and Viswanath(2005)]

Introduction Motivation Our Work Results Future Work

No primary user protection

maximizeP

n∑i=1

Rsi

subject to

∑Ni=1 Pi

N≤ Pa

Pi ≥ 0 ∀ i ∈ I

Solution is a simple waterfilling scheme 1.

1[Tse and Viswanath(2005)]

Introduction Motivation Our Work Results Future Work

Interference power constraints

maximizeP

n∑i=1

Rsi

subject to∑i∈Kj

h21iPi ≤ Γj ∀j ∈ J

∑Ni=1 Pi

N≤ Pa

Pi ≥ 0 ∀ i ∈ I

Keeps the interference to primary users down to a manageablelevel. 2

2[Wang et al.(2007)Wang, Zhao, Xiao, Zhou, and Wang]

Introduction Motivation Our Work Results Future Work

Interference power constraints

maximizeP

n∑i=1

Rsi

subject to∑i∈Kj

h21iPi ≤ Γj ∀j ∈ J

∑Ni=1 Pi

N≤ Pa

Pi ≥ 0 ∀ i ∈ I

Keeps the interference to primary users down to a manageablelevel. 2

2[Wang et al.(2007)Wang, Zhao, Xiao, Zhou, and Wang]

Introduction Motivation Our Work Results Future Work

Primary User Rate Loss constraints

maximizeP

n∑i=1

Rsi

subject to Rpj ≥ Rp0

j ∀j ∈ J∑Ni=1 Pi

N≤ Pa

Pi ≥ 0 ∀ i ∈ I

Leads to a higher secodary user rate when channel stateinformation is perfectly known 3.

3[Kang et al.(2010)Kang, Garg, Liang, and Zhang]

Introduction Motivation Our Work Results Future Work

Primary User Rate Loss constraints

maximizeP

n∑i=1

Rsi

subject to Rpj ≥ Rp0

j ∀j ∈ J∑Ni=1 Pi

N≤ Pa

Pi ≥ 0 ∀ i ∈ I

Leads to a higher secodary user rate when channel stateinformation is perfectly known 3.

3[Kang et al.(2010)Kang, Garg, Liang, and Zhang]

Introduction Motivation Our Work Results Future Work

Outline

1 Introduction

2 Existing schemes in literature

3 Our Work

4 Numerical results

5 Future Work

Introduction Motivation Our Work Results Future Work

Overview

Proposed Scheme 1: Based on sum rate constraint

Proposed Scheme 2: Based on sum utility rate constraint

Analysis and numerical results

Introduction Motivation Our Work Results Future Work

Scheme 1: Sum rate constraint

maximizeP

n∑i=1

Rsi

subject to∑j∈J

Rpj ≥

∑j∈J

Rp0j = δ

∑Ni=1 Pi

N≤ Pa

Pi ≥ 0 ∀ i ∈ I

Introduction Motivation Our Work Results Future Work

Comparison of Scheme 1 with rate loss constraint

Feasible region is larger:

So, Scheme 1 leads to a secondary user rate higher than thatwith rate loss constraints

Introduction Motivation Our Work Results Future Work

Comparison of Scheme 1 with rate loss constraint

Feasible region is larger:

So, Scheme 1 leads to a secondary user rate higher than thatwith rate loss constraints

Introduction Motivation Our Work Results Future Work

Primary User centric problem formulation

OPT1 : maximizeP

∑j∈J

Rpj

subject to∑i∈I

Rsi ≥ γ∑N

i=1 Pi

N≤ Pa

Pi ≥ 0 ∀ i ∈ I

OPT2 : maximizeP

∑i∈I

Rsi

subject to∑j∈J

Rpj ≥ δ∑N

i=1 Pi

N≤ Pa

Pi ≥ 0 ∀ i ∈ I

Lemma

OPT1 and OPT2 would have the same optimal point P0 if

(i) δ in OPT2 is the optimal value of OPT1

(ii) γ in OPT1 is the optimal value of OPT2

Introduction Motivation Our Work Results Future Work

Primary User centric problem formulation

OPT1 : maximizeP

∑j∈J

Rpj

subject to∑i∈I

Rsi ≥ γ∑N

i=1 Pi

N≤ Pa

Pi ≥ 0 ∀ i ∈ I

OPT2 : maximizeP

∑i∈I

Rsi

subject to∑j∈J

Rpj ≥ δ∑N

i=1 Pi

N≤ Pa

Pi ≥ 0 ∀ i ∈ I

Lemma

OPT1 and OPT2 would have the same optimal point P0 if

(i) δ in OPT2 is the optimal value of OPT1

(ii) γ in OPT1 is the optimal value of OPT2

Introduction Motivation Our Work Results Future Work

An outline of the proof

Follows by contradiction

Strict concavity of the secondary user sum rate

Rsi = log

(1 +

h22iPi

h21iTi + N0

)Primary user rate is a decreasing function of P

Rpji = log

(1 +

h11iTi

h12iPi + N0

)

Introduction Motivation Our Work Results Future Work

Problems with Scheme 1

Note

No guarantee on the minimum rate to a primary user

In fact, the primary user rate can go to zero.

Introduction Motivation Our Work Results Future Work

Problems with Scheme 1

Note

No guarantee on the minimum rate to a primary user

In fact, the primary user rate can go to zero.

Introduction Motivation Our Work Results Future Work

Scheme 2: A sum utility rate constraint

maximizeP

n∑i=1

Rsi

subject to∑j∈J

logRpj ≥

∑j∈J

logRp0j∑N

i=1 Pi

N≤ Pa

Pi ≥ 0 ∀ i ∈ I

where log(x) has been chosen to be the utility function.

Question

Does this scheme have a guarantee?

Introduction Motivation Our Work Results Future Work

Scheme 2: A sum utility rate constraint

maximizeP

n∑i=1

Rsi

subject to∑j∈J

logRpj ≥

∑j∈J

logRp0j∑N

i=1 Pi

N≤ Pa

Pi ≥ 0 ∀ i ∈ I

where log(x) has been chosen to be the utility function.

Question

Does this scheme have a guarantee?

Introduction Motivation Our Work Results Future Work

A trivial guarantee from this scheme

Lemma

There exists δ0 > 0 such that

Rpj > δ0 ∀j ∈ J

Proof.

We have∑

j∈J logRpj > δ

Power bounded implies each term bounded

logRpj > M (M > −∞)

δ0 = eM > 0

Introduction Motivation Our Work Results Future Work

Outline

1 Introduction

2 Existing schemes in literature

3 Our Work

4 Numerical results

5 Future Work

Introduction Motivation Our Work Results Future Work

Numerical Results

The following parameters reflect those used in a paper 4

N = 128 sub-carriers

4 PUs, 32 sub-carriers per user

Channel gains: h22 = 1, h12 = 0.1, h21 = 0.1, h11 varying

PU Transmit Power T = 10dB

Noise N0 = 1

4[Kang et al.(2010)Kang, Garg, Liang, and Zhang]

Introduction Motivation Our Work Results Future Work

Comparison of different schemes

−10 −5 0 5 10 15 200

0.5

1

1.5

2

2.5

3

Transmit Power Constraint, Pa(dB)

Tra

nsm

issio

n r

ate

of

SU

Inteference

Rate Loss

Scheme 1: Σ Rate

Scheme 2: Σ log(Rate)

Figure: Secondary User sum rate for different schemes.

Proposed schemes allow higher SU sum rate.

Introduction Motivation Our Work Results Future Work

PU Rate Protection

−10 −5 0 5 10 15 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Transmit Power Constraint, Pa(dB)

Min

imum

tra

nsm

issio

n r

ate

of P

Us

Scheme 1: Σ rate

Scheme 2: Σ log(rate)

Figure: Minimum primary user rate for two proposed schemes

Scheme 2 doesn’t allow any PU rate to go to zero

Introduction Motivation Our Work Results Future Work

Simulation results for two users

−10 −5 0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

3

3.5

4

Transmit Power Constraint, Pa(dB)

Tra

nsm

issio

n r

ate

of

SU

Inteference

Rate Loss

Scheme 1: Σ Rate

Scheme 2: Σ log(Rate)

Figure: Optimal secondary user sum rate for 2 primary users

Introduction Motivation Our Work Results Future Work

Outline

1 Introduction

2 Existing schemes in literature

3 Our Work

4 Numerical results

5 Future Work

Introduction Motivation Our Work Results Future Work

Future Work

Analytical explanations for the observed simulationperformance

Implementation of a better optimization algorithm

Introduction Motivation Our Work Results Future Work

Acknowledgements

We would like to thank Dr. Ajit K. Chaturvedi for providing helpfulinsights and able guidance to our investigations.

Introduction Motivation Our Work Results Future Work

References I

X. Kang, H. Garg, Y.-C. Liang, and R. Zhang.Optimal power allocation for ofdm-based cognitive radio withnew primary transmission protection criteria.Wireless Communications, IEEE Transactions on, 9(6):2066–2075, 2010.ISSN 1536-1276.doi: 10.1109/TWC.2010.06.090912.

D. Tse and P. Viswanath.Fundamentals of wireless communication.Cambridge Univ Pr, 2005.ISBN 0521845270.

Introduction Motivation Our Work Results Future Work

References II

P. Wang, M. Zhao, L. Xiao, S. Zhou, and J. Wang.Power allocation in ofdm-based cognitive radio systems.In Global Telecommunications Conference, 2007. GLOBECOM’07. IEEE, pages 4061 –4065, 2007.doi: 10.1109/GLOCOM.2007.772.

Introduction Motivation Our Work Results Future Work

Questions?

Thank you for your attention.