A Family of Power Allocation Schemes Achieving High Secondary User - - PowerPoint PPT Presentation

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Dec 11, 2022 535 likes •767 views

Motivation Our work A Family of Power Allocation Schemes Achieving High Secondary User Rates in Spectrum Sharing OFDM Cognitive Radio Mainak Chowdhury IIT Kanpur, Stanford Joint work with: Anubhav Singla (IIT Kanpur, Stanford) and Ajit K.

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Motivation Our work

A Family of Power Allocation Schemes Achieving High Secondary User Rates in Spectrum Sharing OFDM Cognitive Radio

Mainak Chowdhury IIT Kanpur, Stanford Joint work with: Anubhav Singla (IIT Kanpur, Stanford) and Ajit K. Chaturvedi (IIT Kanpur) IEEE Globecom 2012

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Motivation Our work

1

Motivation

2

Our work

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Motivation Our work

Outline

1

Motivation

2

Our work

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Motivation Our work

The secondary user power allocation problem

maximize

P n

Rs

i

subject to N

i=1 Pi

N ≤ Pa Pi ≥ 0 ∀ i ∈ I

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Motivation Our work

The feasible region

1.5 2.0 2.5 3.0 3.5 4.0 Rate of PU 1 1.5 2.0 2.5 3.0 3.5 4.0 Rate of PU 2

SU power constr Pa = 40 SU power constr Pa = 20

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Motivation Our work

Observations

Solution is simple “water filling” No protection to primary users, limited only by secondary user power

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Motivation Our work

Protecting primary users

maximize

P n

Rs

i

subject to

i∈Kj

h21iPi≤ Γj ∀j ∈ J N

i=1 Pi

N ≤ Pa Pi ≥ 0 ∀ i ∈ I

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Motivation Our work

Some Points

Keeps interference to primary users(PU) under control But what about PU rate?

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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 higher SU rates with guarantees on PU rates.

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Motivation Our work

Rate Loss Constraints

maximize

P n

Rs

i

subject to Rp

j ≥ Rp0 j

∀j ∈ J N

i=1 Pi

N ≤ Pa Pi ≥ 0 ∀ i ∈ I

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Motivation Our work

Feasible region

1.5 2.0 2.5 3.0 3.5 4.0 Rate of PU 1 1.5 2.0 2.5 3.0 3.5 4.0 Rate of PU 2

SU power constr only Rate Loss Constraints

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Motivation Our work

Comments

Uses CSI to get better SU rates, with same guarantees to PU Is this the best that we can achieve?

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Motivation Our work

Outline

1

Motivation

2

Our work

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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

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Motivation Our work

Utilize CSI to obtain higher SU rates

General scheme: maximize

P n

Rs

i

subject to

j∈J

Uj(Rp

j )≥ δ

N

i=1 Pi

N ≤ Pa Pi ≥ 0 ∀ i ∈ I δ in the above can be taken as δ =

j∈J

Uj(Rp0

j )

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Motivation Our work

Feasible regions under different utility functions

1.5 2.0 2.5 3.0 3.5 4.0 Rate of PU 1 1.5 2.0 2.5 3.0 3.5 4.0 Rate of PU 2

SU power constr only Uj(x) = log(x) Uj(x) =

x Rp0

Rate Loss Constraints Uj(x) = (x/Rp0

j ) −19

−19

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Motivation Our work

Sample solution using different PU protection criteria

−10 −5 5 10 15 20 0.5 1 1.5 2 2.5 3 3.5 SumLogRate50 SumRate50 RateLoss50 IP50

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Motivation Our work

Schematic of algorithm to solve the optimization problem

Primal Optimization Problem t1, T1 Φ1( t1, T1) λ, μ P1 Primal Decomposition Dual Decomposition λ, μ PM λ, μ P2 t2, T2 Φ2( t2, T2) tK, TK ΦK( tK, TK) λ, μ PN-M+1 λ, μ PN λ, μ PN-M+2 λ, μ PM+1 λ, μ P2M λ, μ PM+2 N – 1D Problems K – Sub-Problems

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

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Motivation Our work

Proof of global optimality

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

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Motivation Our work

Proof of global optimality (contd.)

Consider maximize

P

j∈J

Uj(Rp

j )

subject to

i∈I

Rs

i ≥ γ

N

i=1 Pi

N ≤ Pa Pi ≥ 0 ∀ i ∈ I Here γ is the optimal SU sum rate obtained from our problem. We have shown that the same power allocation solves both the problems.