3GPP's Long Term Evolution (LTE) represents the one of the most valuable alternatives to offer a wireless broadband access in fully mobile network context. In particular LTE is able to manage several communication flows characterized by different QoS constrains. This paper deals with a network topology where the mobile users are clustered in Multicast Groups and the base station broadcasts a different traffic flow to each cluster. In order to improve the network throughput on a per-user basis, all communications rely on a Random Linear Network Coding (RLNC) scheme. A key aspect in the QoS management is represented by the power adaptation strategy in use. This paper proposes a novel convex formulation to the power adaptation problem for the downlink phase taking into account the specific RLNC scheme adopted by each communication flow. By the proposed convex formalization, an optimal solution of the problem can be early found in real time. Moreover, the proposed power adaptation strategy shows good performance for what concern throughput and fairness among the users when compared with other alternatives.

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
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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
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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

13. 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

14. 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