Presentation of 'A Novel Convex Power Adaptation Strategy for Multicast Communications using Random Linear Network Coding Schemes'

1. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results University of Florence Telecommunication Networks Laboratory Global Optimization Laboratory A Novel Convex Power Adaptation Strategy for Multicast Communications using Random Linear Network Coding Schemes A. Tassi, D. Marabissi, R. Fantacci, D. Di Lorenzo, M. Maischberger IEEE International Conference on Communications 2012 andrea.tassi@uniﬁ.it

2. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results Index 1. A novel formulation of the downlink power adaptation problem for multicast communications in LTE systems 2. Background and previous works 3. The Convex Power Adaptation Strategy for RLNC schemes 4. Numerical results IEEE International Conference on Communications 2012 andrea.tassi@uniﬁ.it

3. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results 1. A Novel Multicast Power Adaptation Model IEEE International Conference on Communications 2012 andrea.tassi@uniﬁ.it

4. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results Downlink radio resource allocation We focused on a TDD version of LTE: the signal is organized in a time/frequency structure (frame) in the downlink phase radio resources are split both in time and frequency domain into PRBs (7 OFDM symbols x 12 subcarriers). LTE systems (starting from Release 9) can handle both broadcast and multicast traffic flows by the MBMS framework. This work: proposes a novel convex formulation for the power adaptation problem able to take into account either the propagation conditions experienced within each MG and that all communications adopt the RLNC as error control strategy; foresees a scenario where an eNodeB sends different information flows Multicast Groups (MGs) randomly located within the cell. IEEE International Conference on Communications 2012 andrea.tassi@unifi.it

5. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results Downlink radio resource allocation We focused on a TDD version of LTE: the signal is organized in a time/frequency structure (frame) in the downlink phase radio resources are split both in time and frequency domain into PRBs (7 OFDM symbols x 12 subcarriers). LTE systems (starting from Release 9) can handle both broadcast and multicast traffic flows by the MBMS framework. This work: proposes a novel convex formulation for the power adaptation problem able to take into account either the propagation conditions experienced within each MG and that all communications adopt the RLNC as error control strategy; foresees a scenario where an eNodeB sends different information flows Multicast Groups (MGs) randomly located within the cell. IEEE International Conference on Communications 2012 andrea.tassi@unifi.it

6. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results 2. Background and Previous Works IEEE International Conference on Communications 2012 andrea.tassi@uniﬁ.it

7. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results Background and previous works The power adaptation strategies in LTE has been investigated in several works but: they usually do not take into account that the downlink communications rely on a RLNC scheme; they address network scenarios involving only Point-to-Point and not Point-to-Multipoint (P2M) communications. Our power adaptation scheme is able to lead to a fair power adaptation among each P2M downlink flow. The convex formulation provided, ensures to find a feasible solution with affordable computing efforts. IEEE International Conference on Communications 2012 andrea.tassi@unifi.it

8. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results Multicast Communication Model Linear NC coding The M = [s1; s2; . . . ; sl ] matrix is a message of l PDUs. A coded packet is obtained as: ri = M × ci , i = 1, . . . , l Linear NC decoding Whenever an UE collects l coded PDUs linearly independent it can recover the message as: M = [r1; r2; . . . ; rl ] R × [c1; c2; . . . ; cl ]−1 C−1 eNodeB MG2 MG1 MG3 MG4 Multicast network model: the eNodeB transmits to each MG a message until all members have successfully recovered it; UEs acknowledge messages with ACKs. IEEE International Conference on Communications 2012 andrea.tassi@uniﬁ.it

9. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results 3. The Convex Power Adaptation Scheme IEEE International Conference on Communications 2012 andrea.tassi@uniﬁ.it

10. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results Problem formulation (1/2) System model all resource allocation and power adaptation operations are performed on a frame-basis the downlink radio resources are modeled as a time/frequency matrix of O × S PRBs the system consists of K MGs where the b-th MG holds Wb UEs each downlink subframe holds Mb PDUs directed to the b-th MG Let ˆP be the maximum transmission power available for multicast transmissions. Transmission Power Constraint: O i=1 Pi,j ≤ ˆP ⇐⇒ O i=1 gi,j [b, t] xb,t ≤ O, (1) j = 1, . . . , S, b = 1, . . . , K, t = 1, . . . , Mk gi,j [b, t] tracks the disposition (within a frame) of each each P2M ﬂow let xb,t be the Power Scaling Factor, the t-th PRB directed to the b-th MG is transmitted with a power Pi,j = ˆP O xb,t (2) IEEE International Conference on Communications 2012 andrea.tassi@uniﬁ.it

11. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results Problem formulation (1/2) System model all resource allocation and power adaptation operations are performed on a frame-basis the downlink radio resources are modeled as a time/frequency matrix of O × S PRBs the system consists of K MGs where the b-th MG holds Wb UEs each downlink subframe holds Mb PDUs directed to the b-th MG Let ˆP be the maximum transmission power available for multicast transmissions. Transmission Power Constraint: O i=1 Pi,j ≤ ˆP ⇐⇒ O i=1 gi,j [b, t] xb,t ≤ O, (1) j = 1, . . . , S, b = 1, . . . , K, t = 1, . . . , Mk gi,j [b, t] tracks the disposition (within a frame) of each each P2M ﬂow let xb,t be the Power Scaling Factor, the t-th PRB directed to the b-th MG is transmitted with a power Pi,j = ˆP O xb,t (2) IEEE International Conference on Communications 2012 andrea.tassi@uniﬁ.it

12. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results Problem formulation (2/2) Model assumptions all the downlink communications adopt the QPSK scheme for each MG we consider the received SNRb,t of the UE characterized by the worst propagation conditions (the reference UE) The idea underlying the power adaptation: If a message is close to be successfully recovered by the UEs of a MG, it should be prioritized among the other ones. We deﬁne the Power Scaling Weight (PSW) wb,t relative to the t-th PDU directed to the b-th MG as: wb,t = 1 if 0 ≤ j < l/2 2(c−1) l j + 2 − c if j ≥ l/2 (3) where c ≥ 1 is a real value parameter such that wb,t = c when j = l. The optimization goal: the maximization of the weighted system throughput, where the weights are the PSWs. IEEE International Conference on Communications 2012 andrea.tassi@uniﬁ.it

15. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results The Convex Power Adaptation Model Concave envelope of the probability of correct reception of a PDU The function expressing the packet correct reception probability Pc(SNRb,t ) is non-concave, we define its concave envelope ˆPc(SNRb,t ) as: ˆPc(SNRb,t ) =    Pc(Z) Z SNRb,t if 0 ≤ SNRb,t ≤ Z Pc(SNRb,t ) if SNRb,t > Z We can define the Convex Power Adaptation Model (CPAM) as: min xb,t − K b=1 Mb t=1 wb,t ˆPc SNRb,t (4) O i=1 gi,j [b, t] xb,t ≤ O j = 1, . . . , S, b = 1, . . . , K, (5) t = 1, . . . , Mk IEEE International Conference on Communications 2012 andrea.tassi@unifi.it

16. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results The Convex Power Adaptation Model Concave envelope of the probability of correct reception of a PDU The function expressing the packet correct reception probability Pc(SNRb,t ) is non-concave, we define its concave envelope ˆPc(SNRb,t ) as: ˆPc(SNRb,t ) =    Pc(Z) Z SNRb,t if 0 ≤ SNRb,t ≤ Z Pc(SNRb,t ) if SNRb,t > Z We can define the Convex Power Adaptation Model (CPAM) as: min xb,t − K b=1 Mb t=1 wb,t ˆPc SNRb,t (4) O i=1 gi,j [b, t] xb,t ≤ O j = 1, . . . , S, b = 1, . . . , K, (5) t = 1, . . . , Mk IEEE International Conference on Communications 2012 andrea.tassi@unifi.it

17. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results 4. Numerical Results IEEE International Conference on Communications 2012 andrea.tassi@uniﬁ.it

18. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results The simulation parameters It has been simulated a system: 1. composed by an eNodeB and a variable number of MGs (5 ÷ 40) randomly placed within the cell; 2. where SNRb,t values are uniformly distributed between 4.5dB and 26dB; It has been compared the CPAM-S performance to the following strategies: the Fixed Allocation Strategy (FA-S) the Equalization Strategy (E-S) where each PSF (βb,t) is ﬁrstly calculated such as SNRb,t is equal to a target value1. Then the PSFs are normalized by a factor δ in order to respect the power constraint: xb,t = δ βb,t = O O i=1 gi,j [b, t] βb,t 1 To guarantee a PDU error probability less than 0.35. IEEE International Conference on Communications 2012 andrea.tassi@uniﬁ.it

19. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results Average throughput of the worst and the best MG Receiving throughput of the worst MG 8 16 32 64 128 256 512 1024 30 40 50 60 70 80 90 100 110 Generation size [Number of PDUs] Averagethroughput[Kbit/s] CPAM−S f=21B FA−S f=21B E−S f=21B CPAM−S f=42B FA−S f=42B E−S f=42B 5 MGs, PDUs of 21 or 42 Bytes long IEEE International Conference on Communications 2012 andrea.tassi@uniﬁ.it

20. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results Average throughput of the worst and the best MG Receiving throughput of the best MG 8 16 32 64 128 256 512 1024 50 60 70 80 90 100 110 120 130 140 150 160 170 Generation size [Number of PDUs] Averagethroughput[Kbit/s] CPAM−S f=21B FA−S f=21B E−S f=21B CPAM−S f=42B FA−S f=42B E−S f=42B 5 MGs, PDUs of 21 or 42 Bytes long IEEE International Conference on Communications 2012 andrea.tassi@uniﬁ.it

21. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results Overall system throughput System throughput 8 16 32 64 128 256 512 1024 200 250 300 350 400 450 500 550 600 650 700 Generation size [Number of PDUs] Overallthroughput[Kbit/s] CPAM−S f=21B FA−S f=21B E−S f=21B CPAM−S f=42B FA−S f=42B E−S f=42B 5 MGs, PDUs of 21 or 42 Bytes long IEEE International Conference on Communications 2012 andrea.tassi@uniﬁ.it

22. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results Conclusions In this work we have provided 1. a resource allocation strategy able to take into account the state of the underling RLNC-based multicast communication principle; 2. a convex formulation for the downlink power adaptation problem by a concave envelope of the packet correct reception probability function. This ensures to find always a feasible solution with affordable computing efforts. IEEE International Conference on Communications 2012 andrea.tassi@unifi.it

23. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results Thanks for your attention. IEEE International Conference on Communications 2012 andrea.tassi@uniﬁ.it

24. A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results University of Florence Telecommunication Networks Laboratory Global Optimization Laboratory A Novel Convex Power Adaptation Strategy for Multicast Communications using Random Linear Network Coding Schemes A. Tassi, D. Marabissi, R. Fantacci, D. Di Lorenzo, M. Maischberger IEEE International Conference on Communications 2012 andrea.tassi@uniﬁ.it

Presentation of 'A Novel Convex Power Adaptation Strategy for Multicast Communications using Random Linear Network Coding Schemes'

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Presentation of 'A Novel Convex Power Adaptation Strategy for Multicast Communications using Random Linear Network Coding Schemes'