Online power control in D2D networks
Embodiments of a method of operation of a power control coordinator to control transmission power of a plurality of Device-to-Device (D2D) pairs that co-exist with a Cellular User Equipment (CUE) that communicates with a base station of a cellular communications network comprises obtaining, for a particular time slot, delayed Network State Information (NSI) feedback from at least some of the plurality of D2D pairs. The method further comprises computing transmission powers for the D2D pairs, respectively, for the particular time slot using On-Line Convex Optimization (OCO) to solve an optimization problem that maximizes a weighted sum data rate of D2D pairs with a constraint of maximum expected interference to the base station. The method further comprises providing, to each D2D pair, an indication of the computed transmission power for the D2D pair for the particular time slot.
1. A method of operation of a power control coordinator to control transmission power of a plurality of Device-to-Device (D2D) pairs that co-exist with a Cellular User Equipment (CUE) that communicates with a base station of a cellular communications network, comprising:
obtaining, for a particular time slot, delayed Network State Information (NSI) feedback from at least some of the plurality of D2D pairs;
computing transmission powers for the D2D pairs, respectively, for the particular time slot using On-Line Convex Optimization (OCO) to solve an optimization problem that maximizes a weighted sum data rate of D2D pairs with a constraint of maximum expected interference to the base station; and
providing, to each D2D pair, an indication of the computed transmission power for the D2D pair for the particular time slot.
2. The method of claim 1 wherein obtaining the delayed NSI feedback from the at least some of the plurality of D2D pairs comprises obtaining the delayed NSI feedback from all of the plurality of D2D pairs.
3. The method of claim 2 wherein the optimization problem is:
:
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where
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|
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=
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and:
denotes the optimization problem,
p i (t) is a transmission power of a D2D transmitter of the i-th D2D pair for time slot t,
α is a defined scaling factor,
p i,min is a minimum transmission power of the D2D transmitter of the i-th D2D pair,
p i,max is a maximum transmission power of the D2D transmitter of the i-th D2D pair,
is the set of i values for the plurality of D2D pairs,
G i = [g i (t)] where g i (t) is a channel gain from the D2D transmitter of the i-th D2D pair to the base station for time slot t,
I max c is a restraint on a maximum expected interference power from the plurality of D2D pairs to the base station,
t−D is a starting time slot index,
p(t)*=[p(t)*] denotes an optimal solution to the optimization problem {tilde over (P)} t for all t, and
ƒ j,t-D (p(t−D))=w j {tilde over (R)} j,(t-D) , where w j is a weight assigned to the j-th D2D pair and:
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h
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p
j
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i
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where
h ij (t) is a channel gain from a D2D transmitter of the j-th D2D pair to a D2D receiver of the i-th D2D pair in time slot t,
I i (t) is a sum power of inter-cell interference, interference from the CUE, and noise received by the i-th D2D pair in time slot t,
Γ accounts for a gap between an actual data rate and the Shannon bound, and
h ii (t) is a channel gain from a D2D transmitter of the i-th D2D pair to a D2D receiver of the i-th D2D pair in time slot t.
4. The method of claim 1 wherein obtaining the delayed NSI feedback from the at least some of the plurality of D2D pairs comprises obtaining the delayed NSI feedback from a limited subset of the plurality of D2D pairs.
5. The method of claim 4 wherein the optimization problem is:
max
p
(
t
)
∑
i
=
1
N
θ
_
i
(
t
)
p
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,
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i
∈
∑
i
=
1
N
G
i
p
i
(
t
)
≤
I
max
C
,
where
θ
_
i
(
t
)
=
1
P
j
∂
f
j
,
t
-
D
(
p
(
t
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)
)
∂
p
i
(
t
-
D
)
|
p
(
t
-
D
)
=
p
(
t
-
D
)
*
and:
t denotes the optimization problem,
p i (t) is a transmission power of a D2D transmitter of the i-th D2D pair for time slot t,
α is a defined scaling factor,
p i,min is a minimum transmission power of the D2D transmitter of the i-th D2D pair,
p i,max is a maximum transmission power of the D2D transmitter of the i-th D2D pair,
is the set of i values for the plurality of D2D pairs,
G i = [g i (t)] where g i (t) is a channel gain from the D2D transmitter of the i-th D2D pair to the base station for time slot t,
I max c is a restraint on a maximum expected interference power from the plurality of D2D pairs to the base station,
t−D is a starting time slot index,
is a set of indices of the limited subset of the plurality of D2D pairs;
P j = where ∈ and =1,
p(t)*=[p(t)*] denotes an optimal solution to the optimization problem t for all t, and
ƒ j,t-D (p(t−D))=w j {tilde over (R)} j,(t-D) , where w j is a weight assigned to the j-th D2D pair and:
R
˜
i
,
t
=
log
(
∑
j
=
1
,
j
≠
i
N
p
j
(
t
)
h
i
j
(
t
)
+
I
i
(
t
)
+
Γ
p
i
(
t
)
h
i
i
(
t
)
)
-
log
(
I
i
(
t
)
)
-
∑
j
=
1
,
j
≠
1
N
h
i
j
(
t
)
p
j
(
t
)
I
i
(
t
)
where:
h ij (t) is a channel gain from a D2D transmitter of the j-th D2D pair to a D2D receiver of the i-th D2D pair in time slot t,
I i (t) is a sum power of inter-cell interference, interference from the CUE, and noise received by the i-th D2D pair in time slot t,
Γ accounts for a gap between an actual data rate and the Shannon bound, and
h ii (t) is a channel gain from a D2D transmitter of the i-th D2D pair to a D2D receiver of the i-th D2D pair in time slot t.
6. The method of claim 1 wherein the method is implemented in a network node of the cellular communications network.
7. A network node that implements a power control coordinator for controlling transmission power of a plurality of Device-to-Device (D2D) pairs that co-exist with a Cellular User Equipment (CUE) that communicates with a base station of a cellular communications network, comprising:
processing circuitry operable to cause the network node to:
obtain, for a particular time slot, delayed Network State Information (NSI) feedback from at least some of the plurality of D2D pairs;
compute transmission powers for the D2D pairs, respectively, for the particular time slot using On-Line Convex Optimization (OCO) to solve an optimization problem that maximizes a weighted sum data rate of D2D pairs with a constraint of maximum expected interference to the base station, wherein overall expected interference power from the plurality of the D 2 D pairs to the base station does not exceed a certain restraint value; and
provide, to each D2D pair, an indication of the computed transmission power for the D2D pair for the particular time slot.
8. The network node of claim 7 wherein the processing circuitry is operable to cause the network node to obtain the delayed NSI feedback from all of the plurality of D2D pairs.
9. The network node of claim 8 wherein the optimization problem is:
:
max
{
p
(
t
)
}
∑
i
=
1
N
θ
˜
i
(
t
)
p
i
(
t
)
-
α
(
p
i
(
t
)
-
p
i
(
t
-
1
)
*
)
2
s
.
t
.
p
i
,
min
≤
p
i
(
t
)
≤
p
i
,
max
,
∀
i
∈
∑
i
=
1
N
G
i
p
i
(
t
)
≤
I
max
C
,
where
θ
˜
i
(
t
)
=
∑
j
=
1
N
∂
f
j
,
t
(
p
(
t
-
D
)
)
∂
p
i
(
t
-
D
)
|
p
(
t
-
D
)
=
p
(
t
-
D
)
*
and:
denotes the optimization problem,
p i (t) is a transmission power of a D2D transmitter of the i-th D2D pair for time slot t,
α is a defined scaling factor,
p i,min is a minimum transmission power of the D2D transmitter of the i-th D2D pair,
p i,max is a maximum transmission power of the D2D transmitter of the i-th D2D pair,
is the set of i values for the plurality of D2D pairs,
G i = [g i (t)] where g i (t) is a channel gain from the D2D transmitter of the i-th D2D pair to the base station for time slot t,
I max c is a restraint on a maximum expected interference power from the plurality of D2D pairs to the base station,
t−D is a starting time slot index,
p(t)*=[p(t)*] denotes an optimal solution to the optimization problem {tilde over (P)} t for all t, and
ƒ j,t-D (p(t−D))=w j {tilde over (R)} j,(t-D) , where w j is a weight assigned to the j-th D2D pair and:
R
˜
i
,
t
=
log
(
∑
j
=
1
,
j
≠
i
N
p
j
(
t
)
h
i
j
(
t
)
+
I
i
(
t
)
+
Γ
p
i
(
t
)
h
i
i
(
t
)
)
-
log
(
I
i
(
t
)
)
-
∑
j
=
1
,
j
≠
1
N
h
i
j
(
t
)
p
j
(
t
)
I
i
(
t
)
where:
h ij (t) is a channel gain from a D2D transmitter of the j-th D2D pair to a D2D receiver of the i-th D2D pair in time slot t,
I i (t) is a sum power of inter-cell interference, interference from the CUE, and noise received by the i-th D2D pair in time slot t,
Γ accounts for a gap between an actual data rate and the Shannon bound, and
h ii (t) is a channel gain from a D2D transmitter of the i-th D2D pair to a D2D receiver of the i-th D2D pair in time slot t.
10. The network node of claim 7 wherein the processing circuitry is operable to cause the network node to obtain the delayed NSI feedback from a limited subset of the plurality of D2D pairs.
11. The network node of claim 10 wherein the optimization problem is:
t
:
max
p
(
t
)
∑
i
=
1
N
θ
_
i
(
t
)
p
i
(
t
)
-
α
(
p
i
(
t
)
-
p
(
t
-
1
)
*
)
2
s
.
t
.
p
i
,
min
≤
p
i
(
t
)
≤
p
i
,
max
,
∀
i
∈
,
∑
i
=
1
N
G
i
p
i
(
t
)
≤
I
max
C
,
where
θ
_
i
(
t
)
=
1
P
j
∂
f
j
,
t
-
D
(
p
(
t
-
D
)
)
∂
p
i
(
t
-
D
)
|
p
(
t
-
D
)
=
p
(
t
-
D
)
*
and:
t denotes the optimization problem,
p i (t) is a transmission power of a D2D transmitter of the i-th D2D pair for time slot t,
α is a defined scaling factor,
p i,min is a minimum transmission power of the D2D transmitter of the i-th D2D pair,
p i,max is a maximum transmission power of the D2D transmitter of the i-th D2D pair,
is the set of i values for the plurality of D2D pairs,
G i = [g i (t)] where g i (t) is a channel gain from the D2D transmitter of the i-th D2D pair to the base station for time slot t,
I max c is a restraint on a maximum expected interference power from the plurality of D2D pairs to the base station,
t−D is a starting time slot index,
is a set of indices of the limited subset of the plurality of D2D pairs;
P j = where ∈ and =1,
p(t)*=[p(t)*] denotes an optimal solution to the optimization problem t for all t, and
ƒ j,t-D (p(t−D))=w j {tilde over (R)} j,(t-D) , where w j is a weight assigned to the j-th D2D pair and:
R
˜
i
,
t
=
log
(
∑
j
=
1
,
j
≠
i
N
p
j
(
t
)
h
i
j
(
t
)
+
I
i
(
t
)
+
Γ
p
i
(
t
)
h
i
i
(
t
)
)
-
log
(
I
i
(
t
)
)
-
∑
j
=
1
,
j
≠
1
N
h
i
j
(
t
)
p
j
(
t
)
I
i
(
t
)
where:
h ij (t) is a channel gain from a D2D transmitter of the j-th D2D pair to a D2D receiver of the i-th D2D pair in time slot t,
I i (t) is a sum power of inter-cell interference, interference from the CUE, and noise received by the i-th D2D pair in time slot t,
Γ accounts for a gap between an actual data rate and the Shannon bound, and
h ii (t) is a channel gain from a D2D transmitter of the i-th D2D pair to a D2D receiver of the i-th D2D pair in time slot t.
12. A network node that implements a power control coordinator for controlling transmission power of a plurality of Device-to-Device pairs that co-exist with a Cellular User Equipment (CUE) that communicates with a base station for a cellular communications network, the network node adapted to:
obtain, for a particular time slot, delayed Network State Information (NSI) feedback from at least some of a plurality of Device-to-Device (D2D) pairs;
compute transmission powers for the D2D pairs, respectively, for the particular time slot using On-Line Convex Optimization (OCO) to solve an optimization problem that maximizes a weighted sum data rate of D2D pairs with a constraint of maximum expected interference to the base station, wherein overall expected interference power from the plurality of the D 2 D pairs to the base station does not exceed a certain restraint value; and
provide, to each D2D pair, an indication of the computed transmission power for the D2D pair for the particular time slot.
13. The method of claim 1 wherein:
the delayed NSI feedback includes information of a sum power of inter-cell interference, interference from the CUE, and noise received by the at least some of the plurality of D2D pairs in the particular time slot; and
the computing transmission powers for the D2D pairs are based on the delayed NSI feedback.