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

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

Motivation Our work Motivation 1 Our work 2

Motivation Our work Outline Motivation 1 Our work 2

Motivation Our work The secondary user power allocation problem n � R s maximize i P i =1 � N i =1 P i subject to ≤ P a N P i ≥ 0 ∀ i ∈ I

Motivation Our work The feasible region 4 . 0 3 . 5 3 . 0 Rate of PU 2 2 . 5 2 . 0 SU power constr P a = 40 SU power constr P a = 20 1 . 5 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 Rate of PU 1

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

Motivation Our work Protecting primary users n � R s maximize i P i =1 � subject to h 21 i P i ≤ Γ j ∀ j ∈ J i ∈K j � N i =1 P i ≤ P a N P i ≥ 0 ∀ i ∈ I

Motivation Our work Some Points Keeps interference to primary users(PU) under control But what about PU rate?

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.

Motivation Our work Rate Loss Constraints n � R s maximize i P i =1 R p j ≥ R p 0 subject to ∀ j ∈ J j � N i =1 P i ≤ P a N P i ≥ 0 ∀ i ∈ I

Motivation Our work Feasible region 4 . 0 3 . 5 3 . 0 Rate of PU 2 2 . 5 2 . 0 SU power constr only Rate Loss Constraints 1 . 5 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 Rate of PU 1

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 Motivation 1 Our work 2

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: n � R s maximize i P i =1 � U j ( R p subject to j ) ≥ δ j ∈J � N i =1 P i ≤ P a N P i ≥ 0 ∀ i ∈ I δ in the above can be taken as � U j ( R p 0 δ = j ) j ∈J

Motivation Our work Feasible regions under different utility functions 4 . 0 3 . 5 3 . 0 Rate of PU 2 2 . 5 SU power constr only U j ( x ) = log ( x ) x U j ( x ) = R p 0 j 2 . 0 Rate Loss Constraints − 19 U j ( x ) = ( x/R p 0 j ) − 19 1 . 5 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 Rate of PU 1

Motivation Our work Sample solution using different PU protection criteria 3.5 3 SumLogRate50 SumRate50 RateLoss50 2.5 IP50 2 1.5 1 0.5 0 −10 −5 0 5 10 15 20

Motivation Our work Schematic of algorithm to solve the optimization problem Primal Optimization Problem Primal Decomposition Φ K ( t K , T K ) Φ 1 ( t 1 , T 1 ) Φ 2 ( t 2 , T 2 ) t 1 , T 1 t 2 , T 2 t K , T K K – Sub-Problems Dual Decomposition P M P 2M P N λ , μ λ , μ λ , μ λ , μ λ , μ λ , μ P N-M+1 P N-M+2 P M+1 P M+2 P 1 P 2 λ , μ λ , μ λ , μ N – 1D 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 a global optimum from the point of view of PUs.

Motivation Our work Proof of global optimality (contd.) Consider � U j ( R p maximize j ) P j ∈J � R s subject to i ≥ γ i ∈I � N i =1 P i ≤ P a N P i ≥ 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.

Motivation Our work Limiting case: Rate Loss Take � 1 − k � x R p 0 U k j j ( x ) = 1 − k Then as k → ∞ we have the rate loss constraints