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A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results
University of FlorenceTelecommunication Networks Laboratory
Global Optimization Laboratory
A Novel Convex Power Adaptation Strategy forMulticast Communications using Random Linear
Network Coding Schemes
A. Tassi, D. Marabissi, R. Fantacci, D. Di Lorenzo, M. Maischberger
IEEE International Conference on Communications 2012 [email protected]
A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results
Index
1. A novel formulation of the downlink power adaptationproblem for multicast communications in LTE systems
2. Background and previous works
3. The Convex Power Adaptation Strategy for RLNCschemes
4. Numerical results
IEEE International Conference on Communications 2012 [email protected]
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 [email protected]
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 andfrequency domain into PRBs (7 OFDM symbols x 12 subcarriers).
LTE systems (starting from Release 9) can handle both broadcast andmulticast traffic flows by the MBMS framework.
This work:
proposes a novel convex formulation for the power adaptationproblem able to take into account either the propagationconditions experienced within each MG and that allcommunications adopt the RLNC as error control strategy;
foresees a scenario where an eNodeB sends different informationflows Multicast Groups (MGs) randomly located within the cell.
IEEE International Conference on Communications 2012 [email protected]
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 andfrequency domain into PRBs (7 OFDM symbols x 12 subcarriers).
LTE systems (starting from Release 9) can handle both broadcast andmulticast traffic flows by the MBMS framework.
This work:
proposes a novel convex formulation for the power adaptationproblem able to take into account either the propagationconditions experienced within each MG and that allcommunications adopt the RLNC as error control strategy;
foresees a scenario where an eNodeB sends different informationflows Multicast Groups (MGs) randomly located within the cell.
IEEE International Conference on Communications 2012 [email protected]
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 [email protected]
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 severalworks but:
they usually do not take into account that the downlinkcommunications rely on a RLNC scheme;
they address network scenarios involving only Point-to-Point and notPoint-to-Multipoint (P2M) communications.
Our power adaptation scheme is able to lead to a fair poweradaptation among each P2M downlink flow. The convexformulation provided, ensures to find a feasible solution withaffordable computing efforts.
IEEE International Conference on Communications 2012 [email protected]
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 amessage of l PDUs. A coded packet isobtained as:
ri = M× ci , i = 1, . . . , l
Linear NC decoding
Whenever an UE collects l coded PDUslinearly independent it can recover themessage as:
M = [r1; r2; . . . ; rl ]︸ ︷︷ ︸R
× [c1; c2; . . . ; cl ]−1︸ ︷︷ ︸
C−1
eNodeB
MG2
MG1
MG3
MG4
Multicast network model:
the eNodeB transmits to eachMG a message until all membershave successfully recovered it;
UEs acknowledge messages withACKs.
IEEE International Conference on Communications 2012 [email protected]
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 [email protected]
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 ona frame-basis
the downlink radio resources are modeled as a time/frequency matrix ofO × 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 P̂ be the maximum transmission power available for multicast transmissions.
Transmission Power Constraint:O∑i=1
Pi,j ≤ P̂ ⇐⇒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 aframe) of each each P2M flow
let xb,t be the Power Scaling Factor, thet-th PRB directed to the b-th MG istransmitted with a power
Pi,j =P̂
Oxb,t (2)
IEEE International Conference on Communications 2012 [email protected]
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 ona frame-basis
the downlink radio resources are modeled as a time/frequency matrix ofO × 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 P̂ be the maximum transmission power available for multicast transmissions.
Transmission Power Constraint:O∑i=1
Pi,j ≤ P̂ ⇐⇒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 aframe) of each each P2M flow
let xb,t be the Power Scaling Factor, thet-th PRB directed to the b-th MG istransmitted with a power
Pi,j =P̂
Oxb,t (2)
IEEE International Conference on Communications 2012 [email protected]
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 bythe worst propagation conditions (the reference UE)
The idea underlying the power adaptation: If a message is close to be successfullyrecovered 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 tothe b-th MG as:
wb,t =
{1 if 0 ≤ j < dl/2e2(c−1)
lj + 2− c if j ≥ dl/2e (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 [email protected]
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 bythe worst propagation conditions (the reference UE)
The idea underlying the power adaptation: If a message is close to be successfullyrecovered 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 tothe b-th MG as:
wb,t =
{1 if 0 ≤ j < dl/2e2(c−1)
lj + 2− c if j ≥ dl/2e (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 [email protected]
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 bythe worst propagation conditions (the reference UE)
The idea underlying the power adaptation: If a message is close to be successfullyrecovered 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 tothe b-th MG as:
wb,t =
{1 if 0 ≤ j < dl/2e2(c−1)
lj + 2− c if j ≥ dl/2e (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 [email protected]
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 correctreception probability Pc(SNRb,t) isnon-concave, we define its concaveenvelope P̂c(SNRb,t) as:
P̂c(SNRb,t ) =
Pc(Z)
ZSNRb,t if 0 ≤ SNRb,t ≤ Z
Pc(SNRb,t ) if SNRb,t > Z
We can define the Convex Power Adaptation Model (CPAM) as:
minxb,t
(−
K∑b=1
Mb∑t=1
wb,t P̂c(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 [email protected]
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 correctreception probability Pc(SNRb,t) isnon-concave, we define its concaveenvelope P̂c(SNRb,t) as:
P̂c(SNRb,t ) =
Pc(Z)
ZSNRb,t if 0 ≤ SNRb,t ≤ Z
Pc(SNRb,t ) if SNRb,t > Z
We can define the Convex Power Adaptation Model (CPAM) as:
minxb,t
(−
K∑b=1
Mb∑t=1
wb,t P̂c(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 [email protected]
A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results
4. Numerical Results
IEEE International Conference on Communications 2012 [email protected]
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 followingstrategies:
the Fixed Allocation Strategy (FA-S)the Equalization Strategy (E-S) where each PSF (βb,t) is firstlycalculated such as SNRb,t is equal to a target value1. Then the PSFsare 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
1To guarantee a PDU error probability less than 0.35.IEEE International Conference on Communications 2012 [email protected]
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 102430
40
50
60
70
80
90
100
110
Generation size [Number of PDUs]
Ave
rage
thro
ughp
ut [K
bit/s
]
CPAM−Sf=21B FA−Sf=21B E−Sf=21B CPAM−Sf=42B FA−Sf=42B E−Sf=42B
5 MGs, PDUs of 21 or 42 Bytes longIEEE International Conference on Communications 2012 [email protected]
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 10245060708090
100110120130140150160170
Generation size [Number of PDUs]
Ave
rage
thro
ughp
ut [K
bit/s
]
CPAM−Sf=21B FA−Sf=21B E−Sf=21B CPAM−Sf=42B FA−Sf=42B E−Sf=42B
5 MGs, PDUs of 21 or 42 Bytes longIEEE International Conference on Communications 2012 [email protected]
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 1024200
250
300
350
400
450
500
550
600
650
700
Generation size [Number of PDUs]
Ove
rall
thro
ughp
ut [K
bit/s
]
CPAM−Sf=21B FA−Sf=21B E−Sf=21B CPAM−Sf=42B FA−Sf=42B E−Sf=42B
5 MGs, PDUs of 21 or 42 Bytes longIEEE International Conference on Communications 2012 [email protected]
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 ofthe underling RLNC-based multicast communication principle;
2. a convex formulation for the downlink power adaptation problem bya concave envelope of the packet correct reception probabilityfunction. This ensures to find always a feasible solution withaffordable computing efforts.
IEEE International Conference on Communications 2012 [email protected]
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 [email protected]
A Novel Multicast Power Adaptation Model Background and previous works The CPAM scheme Numerical results
University of FlorenceTelecommunication Networks Laboratory
Global Optimization Laboratory
A Novel Convex Power Adaptation Strategy forMulticast Communications using Random Linear
Network Coding Schemes
A. Tassi, D. Marabissi, R. Fantacci, D. Di Lorenzo, M. Maischberger
IEEE International Conference on Communications 2012 [email protected]
