Motivation Our work

A Family of Power Allocation Schemes AchievingHigh Secondary User Rates in Spectrum Sharing

OFDM Cognitive Radio

Mainak Chowdhury

IIT Kanpur, StanfordJoint work with: Anubhav Singla (IIT Kanpur, Stanford) and

Ajit K. Chaturvedi (IIT Kanpur)

IEEE Globecom 2012

Motivation Our work

1 Motivation

2 Our work

Motivation Our work

Outline

1 Motivation

2 Our work

Motivation Our work

The secondary user power allocation problem

maximizeP

n∑i=1

Rsi

subject to

∑Ni=1 Pi

N≤ Pa

Pi ≥ 0 ∀ i ∈ I

Motivation Our work

The feasible region

1.5 2.0 2.5 3.0 3.5 4.0Rate of PU 1

1.5

2.0

2.5

3.0

3.5

4.0

Rat

eof

PU

2

SU power constr Pa = 40

SU power constr Pa = 20

Motivation Our work

Observations

Solution is simple “water filling”

No protection to primary users, limited only by secondary userpower

Motivation Our work

Protecting primary users

maximizeP

n∑i=1

Rsi

subject to∑i∈Kj

h21iPi≤ Γj ∀j ∈ J

∑Ni=1 Pi

N≤ Pa

Pi ≥ 0 ∀ i ∈ I

Motivation Our work

Some Points

Keeps interference to primary users(PU) under control

But what about PU rate?

It turns out that knowledge of CSI can be exploited to get higherSU rates with guarantees on PU rates.

Motivation Our work

Some Points

Keeps interference to primary users(PU) under control

But what about PU rate?

It turns out that knowledge of CSI can be exploited to get higherSU rates with guarantees on PU rates.

Motivation Our work

Rate Loss Constraints

maximizeP

n∑i=1

Rsi

subject to Rpj ≥ Rp0

j ∀j ∈ J∑Ni=1 Pi

N≤ Pa

Pi ≥ 0 ∀ i ∈ I

Motivation Our work

Feasible region

1.5 2.0 2.5 3.0 3.5 4.0Rate of PU 1

1.5

2.0

2.5

3.0

3.5

4.0

Rat

eof

PU

2

SU power constr onlyRate Loss Constraints

Motivation Our work

Comments

Uses CSI to get better SU rates, with same guarantees to PU

Is this the best that we can achieve?

Motivation Our work

Outline

1 Motivation

2 Our work

Motivation Our work

Summary

Utilize the CSI to obtain still higher SU rates

Efficient algorithm to solve the optimization problem

Proof of global optimality

Rate Loss Constraints is a limiting case in our scheme

Motivation Our work

Utilize CSI to obtain higher SU rates

General scheme:

maximizeP

n∑i=1

Rsi

subject to∑j∈J

Uj(Rpj )≥ δ

∑Ni=1 Pi

N≤ Pa

Pi ≥ 0 ∀ i ∈ I

δ in the above can be taken as

δ =∑j∈J

Uj(Rp0j )

Motivation Our work

Feasible regions under different utility functions

1.5 2.0 2.5 3.0 3.5 4.0Rate of PU 1

1.5

2.0

2.5

3.0

3.5

4.0

Rat

eof

PU

2

SU power constr onlyUj(x) = log(x)

Uj(x) = xRp0j

Rate Loss Constraints

Uj(x) =(x/Rp0j )

−19

−19

Motivation Our work

Sample solution using different PU protection criteria

−10 −5 0 5 10 15 200

0.5

1

1.5

2

2.5

3

3.5

SumLogRate50

SumRate50

RateLoss50

IP50

Motivation Our work

Schematic of algorithm to solve the optimization problem

Primal Optimization Problem

t 1, T 1

Φ 1( t 1,

T 1)

λ, μ

P 1

Prim

al D

ecom

posi

tion

Dua

l Dec

ompo

sitio

n

λ, μ

PM

λ, μ

P 2

t 2, T 2

Φ 2( t 2,

T 2)

tK , TK

ΦK ( tK , T

K )

λ, μ

P N-M

+1 λ, μ

PN

λ, μ

P N-M

+2λ, μ

P M+1 λ, μ

P2M

λ, μ

P M+2

N – 1D Problems

K – Sub-Problems

Figure : K is number of PUs, N is number of subcarriers

Motivation Our work

Proof of global optimality

We show that in solving our problem, we are essentially achieving aglobal optimum from the point of view of PUs.

Motivation Our work

Proof of global optimality (contd.)

Considermaximize

P

∑j∈J

Uj(Rpj )

subject to∑i∈I

Rsi ≥ γ

∑Ni=1 Pi

N≤ Pa

Pi ≥ 0 ∀ i ∈ IHere γ is the optimal SU sum rate obtained from our problem.We have shown that the same power allocation solves both theproblems.

Motivation Our work

Limiting case: Rate Loss

Take

Ukj (x) =

(x

Rp0j

)1−k

1− k

Then as k →∞ we have the rate loss constraints