Precoding and power allocation for access points in a cell-free communication system

1 . A controller for determining a precoder for a set of access points (APs) in a cell-free communication system, the set of APs comprising a first AP and a second AP, the controller comprising processing circuitry, the processing circuitry being configured to cause the controller to:

obtain a first channel estimate of a radio propagation channel between the first AP and a first user equipment (UE) included in a group of UEs served in the cell-free communication system;

obtain a second channel estimate of a radio propagation channel between the first AP and a second UE included in the group of UEs;

obtain a third channel estimate of a radio propagation channel between the second AP and the first UE;

obtain a fourth channel estimate of a radio propagation channel between the second AP and the second UE;

determine a precoder, A, for the set of APs, the precoder having a zero-forcing (ZF) precoding factor, A′, and a power allocation factor, wherein

the ZF precoding factor is determined using the obtained channel estimates,

the power allocation factor is determined by maximizing total transmission power for all user symbols to be transmitted to the UEs included in the group of UEs, one user symbol per each UE,

transmission power of each of the APs is not larger than a power constraint, and

transmission power for each of the UEs in the group of UEs is lower bounded by a scaled heuristic value; and

initiate transmission of precoded user symbols from the APs towards the UEs, wherein the user symbols are precoded according to the determined precoder.

2 . The controller of claim 1 , wherein the power allocation factor is determined by solving a linear program problem.

3 . The controller of claim 1 , wherein the power allocation factor is represented by a matrix P, wherein the matrix P is determined as P=diag {p*} 1/2 , where p* is a vector of optimal power allocation coefficients.

4 . The controller of claim 3 , wherein the total transmission power for all user symbols to be transmitted to the UEs is maximized by determining:

max

p

*

∑

i

=

1

K

p

i

,

where p i is the transmission power per user symbol for user equipment i, where i=1, . . . , K.

5 . The controller of claim 4 , wherein the ZF precoding factor is represented by a matrix A′, and wherein the matrix A′ is determined as:

A

′

=

G

ˆ

H

(

G

ˆ

⁢

G

ˆ

H

)

-

1

,

where Ĝ is a matrix representing the channel estimates.

6 . The controller of claim 5 , wherein the transmission power of AP m, where m=1, . . . , M, is denoted P m and is determined as:

P

m

=

∑

i

=

1

K

❘

"\[LeftBracketingBar]"

a

m

⁢

i

′

❘

"\[RightBracketingBar]"

2

⁢

p

i

,

where a′ mi are elements of the matrix A′.

7 . The controller of claim 5 , wherein the power constraint is denoted ρ d .

8 . The controller of claim 7 , wherein the heuristic value is denoted η and is determined as:

η

=

ρ

d

max

m

⁢

∑

i

=

1

K

⁢

❘

"\[LeftBracketingBar]"

a

m

⁢

i

′

❘

"\[RightBracketingBar]"

2

.

9 . The controller of claim 8 , wherein the linear program problem is formulated as:

max

p

f

⁡

(

p

)

=

c

T

⁢

p

subject

⁢

to

⁢

⁢

{

Dp

≤

b

,

l

i

≤

p

i

≤

u

i

,

∀

i

,

where c is a vector with K ones, where

d

ij

=

❘

"\[LeftBracketingBar]"

a

ij

′

❘

"\[RightBracketingBar]"

2

,

where b=[ρ d , . . . , ρ d ] T K×1 , where l i =α·η, and where u i =∞, ∀i.

10 . The controller of claim 1 , wherein the scaled heuristic value is a heuristic value as scaled with a factor α, where 0<α<1.

11 . The controller of claim 1 , wherein

the heuristic value is a function of the power constraint and maximum per-antenna transmit power with respect to the ZF precoding factor.

12 . A method for determining a precoder for a set of access points (APs) in a cell-free communication system, the set of Aps comprising a first AP and a second AP, the method being performed by a controller of the APs, the method comprising:

obtaining a first channel estimate of a radio propagation channel between the first AP and a first user equipment (UE) included in a group of UEs and user equipment served in the cell-free communication system;

obtaining a second channel estimate of a radio propagation channel between the first AP and a second UE included in the group of UEs;

obtaining a third channel estimate of a radio propagation channel between the second AP and the first UE;

obtaining a fourth channel estimate of a radio propagation channel between the second AP and the second UE;

determining a precoder, A, for the set of APs, the precoder having a zero-forcing, ZF, precoding factor, A′, and a power allocation factor,

wherein the ZF precoding factor is determined using the obtained channel estimates, and

wherein the power allocation factor is determined by maximizing total transmission power for all user symbols to be transmitted to the UEs included in the group of UEs, one user symbol per each UE, wherein transmission power of each of the APs is not larger than a power constraint, and wherein transmission power for each of the UEs in the group of UEs is lower bounded by a scaled heuristic value; and

initiating transmission of precoded user symbols from the APs towards the UEs, wherein the user symbols are precoded according to the determined precoder.

13 . The method of claim 12 , wherein the power allocation factor is determined by solving a linear program problem.

14 . The method of claim 12 , wherein the power allocation factor is represented by a matrix P, wherein the matrix P is determined as P=diag {p*} 1/2 , where p* is a vector of optimal power allocation coefficients.

15 . The method of claim 14 , wherein the total transmission power for all user symbols to be transmitted to the UEs is maximized by determining:

max

p

*

∑

i

=

1

K

p

i

,

where p i is the transmission power per user symbol for user equipment i, where i=1, . . . , K.

16 . The method of claim 14 , wherein the ZF precoding factor is represented by a matrix A′, and wherein the matrix A′ is determined as:

A

′

=

G

ˆ

H

(

G

ˆ

⁢

G

ˆ

H

)

-

1

,

where Ĝ is a matrix representing the channel estimates.

17 . The method of claim 16 , wherein the transmission power of AP m, where m=1, . . . , M, is denoted P m and is determined as:

P

m

=

∑

i

=

1

K

❘

"\[LeftBracketingBar]"

a

m

⁢

i

′

❘

"\[RightBracketingBar]"

2

⁢

p

i

,

where

a

m

⁢

i

′

are elements of the matrix A′.

18 . A non-transitory computer readable storage medium storing a computer program for determining a precoder for a set of access points (APs) in a cell-free communication system, the set of APs comprising a first AP and a second AP, the computer program comprising computer code which, when run on processing circuitry of a controller of the APs, causes the controller to:

obtain a first channel estimate of a radio propagation channel between the first AP and a first user equipment (UE) included in a group of UEs served in the cell-free communication system;

obtain a second channel estimate of a radio propagation channel between the first AP and a second UE included in the group of UEs;

obtain a third channel estimate of a radio propagation channel between the second AP and the first UE;

obtain a fourth channel estimate of a radio propagation channel between the second AP and the second UE;

determine a precoder, A, for the set of APs, the precoder having a zero-forcing, ZF, precoding factor, A′, and a power allocation factor, P,

wherein the ZF precoding factor is determined using the obtained channel estimates, and

wherein the power allocation factor is determined by maximizing total transmission power for all user symbols to be transmitted to the UEs included in the group of UEs, one user symbol per each UE, wherein

transmission power of each of the APs is not larger than a power constraint, and

wherein transmission power for each of the UEs in the group of UEs is lower bounded by a scaled heuristic value; and

initiate transmission of precoded user symbols from the APs towards the user equipment UEs, wherein the user symbols are precoded according to the determined precoder.