Receiver, communication system, and method implemented by computer for enabling both analog and digital beamforming in communication system
View Patent ↗A method for enabling hybrid beamforming in a communication system including a transmitter being able to serve a plurality of receivers, wherein a frequency band comprises at least one subcarrier, wherein each receiver is associated to a set Cprec,k of analog precoding codewords, said method comprising: —for each receiver, computing ( 202 ) an analog precoding matrix FRF k associated to said receiver; said computation ( 202 ) comprising: /a/ for each subcarrier, performing ( 202 a ) a Singular Value Decomposition, SVD, on a channel matrix associated to said receiver and to said each subcarrier; /b/ for each subcarrier, determining a first decomposition matrix Vk(1) based on the relative SVD; /c/ determining ( 303 ) an analog precoding codeword which optimizes a first function g1(Vk(1), . . . , Vk(L), F) of Vk(1), . . . , Vk(L) and F, for a plurality of F E Cprec,k, wherein L denotes a number of subcarriers.
1. A method implemented by a computer for maximizing a sum rate of a communication system, said communication system enabling both analog and digital beamforming, said communication system including a transmitter being able to serve a plurality of receivers,
wherein each receiver among the plurality of receivers is associated to a relative set prec,k of analog precoding codewords, wherein prec,k is the set of analog precoding codewords associated to the k th receiver,
said method comprising:
for each receiver among the plurality of receivers, computing, at said receiver, an analog precoding matrix F RF,k associated to said receiver,
wherein F RF,k is the analog precoding matrix associated to the k th receiver; and
using at least one computed analog precoding matrix for processing at least one signal to transmit from the transmitter to at least one receiver;
wherein the computation of the analog precoding matrix associated to a receiver among the plurality of receivers comprises:
/a/ performing a Singular Value Decomposition, SVD, on a channel matrix associated to said receiver;
/b/ determining a first decomposition matrix V k based on the relative SVD;
characterized in that the computation of the analog precoding matrix associated to a receiver among the plurality of receivers further comprises:
/c/ determining an analog precoding codeword which maximizes a first function g 1 (V k ,F)=λ min ( V k H FF H V k ) of V k and F, for a plurality of F∈ prec,k ,
where:
A H denotes a conjugate transpose matrix of a matrix A; and
λ min (A) denotes a minimal eigenvalue of a matrix A.
2. The method according to claim 1 , wherein each receiver among the plurality of receivers is associated to a relative set comb,k of analog combining codewords,
wherein, for each receiver among the plurality of receivers and for each subcarrier among the plurality of subcarriers, a second decomposition matrix Ū k (l) is determined, based on the relative SVD performed in step /a/;
the method further comprising, for each receiver among the plurality of receivers:
computing, at said receiver, an analog combining matrix W RF,k associated to said receiver, said computation including:
determining an analog combining codeword which optimizes a second function g 2 (Ū k (1), . . . , Ū k (L),W) of Ū k (1), . . . , Ū k (L) and W, for a plurality of W∈ comb,k .
3. The method according to claim 2 , wherein the second function is:
g
2
(
U
_
k
(
1
)
,
…
,
U
_
k
(
L
)
,
W
)
=
∑
l
=
1
L
(
L
r
k
-
tr
(
WW
H
U
_
k
(
l
)
U
_
k
H
(
l
)
)
)
where:
tr(A) denotes a trace of a matrix A;
A H denotes a conjugate transpose matrix of a matrix A;
L r k is a number of receiving analog chains at said receiver;
Ū k (l) is the second decomposition matrix associated to the receiver k for a subcarrier l;
and wherein the optimization of the second function is a minimization.
4. The method according to claim 2 , wherein the number of subcarriers is equal to 1,
wherein each analog preceding; codeword F is chosen among a set of columns of a predetermined matrix having a number of rows equal to a number of antennas of the transmitter and a number of columns greater or equal than L r k , said matrix being a Discrete Fourier Transform, DFT, matrix or a matrix obtained by re-normalizing a sub-matrix extracted from a DFT matrix,
and wherein the second function g 2 (Ū k ,W) is given by:
g
2
(
U
_
k
,
W
)
=
∑
i
=
1
L
r
∑
j
=
1
L
r
(
W
(
:
,
i
)
)
H
·
U
_
k
(
:
,
j
)
2
where:
L r k is a number of receiving analog chains at said receiver;
|Q| denotes a magnitude of a complex Q;
A H denotes a conjugate transpose matrix of a matrix A; and
A(:,j) is a j-th column of a matrix A;
and wherein the optimization of the second function is a maximization.
5. The method according to claim 2 , wherein the number of subcarriers is equal to 1, and wherein the second function g 2 (Ū k ,W) is given by:
g 2 ( Ū k ,W )=λ min ( Ū k H WW H Ū k )
where:
A H denotes a conjugate transpose matrix of a matrix A; and
λ min (A) denotes a minimal eigenvalue of a matrix A,
and wherein the optimization of the second function is a maximization.
6. The method according to claim 2 , wherein an analog combining codeword W is a column of a predetermined matrix having a number of rows equal to a number of antennas of the transmitter and a number of columns greater or equal than L r k , said matrix being relative to Discrete Fourier Transform, DFT, matrix;
wherein, in step /c/ the second function g 2 (Ū k , W) is a function of:
W
H
U
_
k
U
_
k
H
W
+
λ
min
(
Z
i
-
1
H
U
k
U
_
k
H
Z
i
-
1
)
2
-
(
W
H
U
_
k
U
_
k
H
W
-
λ
min
(
Z
i
-
1
H
U
k
U
_
k
H
Z
i
-
1
)
)
2
4
+
W
H
U
_
k
U
_
k
H
Z
i
-
1
Z
i
-
1
H
U
_
k
U
_
k
H
W
where:
Z i−1 is composed from at least one column of said predetermined matrix;
W is different from all the columns of T i−1 ;
A H denotes a conjugate transpose matrix of a matrix A; and
λ min (A) denotes a minimal eigenvalue of a matrix A,
wherein the optimization of the second function is a maximization;
and wherein step /c/ is performed iteratively for i=2 . . . L r , with C 1 =f 1 , where f 1 is a column of said predetermined matrix which maximizes a function F H V k V k h F of V k and F, for a plurality of F∈ prec,k .
7. The method according to claim 2 , the method further comprising:
for each receiver among the plurality of receivers, receiving, at the transmitter, an estimation of an equivalent user channel between the transmitter and said each receiver;
recursively computing, at the transmitter:
a first set of digital combining matrices, each digital combining matrix of said first set being associated to a receiver among the plurality of receivers, based on the received estimation of the equivalent user channel and on the computed analog combining matrices; and
a second set of digital precoding matrices, each digital precoding matrix of said second set being associated to a receiver among the plurality of receivers, based on the received estimation of the equivalent user channel and at least one digital combining matrix among the first set;
wherein the recursive computation includes:
/d/ For each receiver k among the plurality of K receivers,
Calculate:
Q
k
=
∑
l
≠
k
K
H
k
eq
F
BB
,
l
F
BB
,
l
H
(
H
k
eq
)
H
+
σ
2
W
RF
,
k
H
W
RF
,
k
where:
H k eq is the estimation of the equivalent user channel between the transmitter and said receiver k;
H eq =[(H 1 eq ) T . . . (H k eq ) T ] T ;
F BB,l is a current digital combining matrix associated to a receiver 1 ;
σ 2 is a variance of a signal noise;
W RF,k is the computed analog combining matrix associated to the receiver k;
tr(A) is the trace of a matrix A;
A H denotes a conjugate transpose matrix of a matrix A;
Update the relative digital combining matrix W BB,k according to:
W BB,k H =F BB,k H ( H k eq ) H ( H k eq F BB,k F BB,k H ( H k eq ) H +Q k ) −1
where
A −1 denotes an inverse of a matrix A;
And calculate:
M k =I+F BB,k H ( H k eq ) H Q k −1 H k eq F BB,k
where
I is a matrix identity;
/e/ Define:
F
_
=
(
(
H
eq
)
H
WMW
H
H
eq
+
tr
(
σ
2
M
W
H
RW
)
P
I
)
-
1
(
H
eq
)
H
WM
where:
W H is a block diagonal matrix whose blocks are equal to W BB,1 H , . . . , W BB,K H ;
M is a block diagonal matrix whose blocks are equal to M 1 , . . . , M K ;
R is a block diagonal matrix whose blocks are equal to W RF,1 H W RF,1 , . . . , W RF,k H W RF,K ;
P is an average total transmitting power;
Calculate the second set of digital precoding matrices from F .
8. A method implemented by a computer for maximizing a sum rate of a communication system, said communication system enabling both analog and digital beamforming, said communication system including a transmitter being able to serve a plurality of receivers,
wherein each receiver among the plurality of receivers is associated to a relative set prec,k of analog precoding codewords, wherein prec,k is the set of analog precoding codewords associated to the k th receiver,
wherein each analog precoding codeword F is a column of a predetermined matrix having a number of rows equal to a number of antennas of the transmitter and a number of columns greater or equal than L r k , said matrix being a Discrete Fourier Transform, DFT, matrix or a matrix obtained by re-normalizing a sub-matrix extracted from a DFT matrix;
said method comprising:
for each receiver among the plurality of receivers, computing, at said receiver, an analog precoding matrix F RF,k associated to said receiver, wherein F RF,k is the analog precoding matrix associated to the receiver; and
using at least one computed analog precoding matrix for processing at least one signal to transmit from the transmitter to at least one receiver;
wherein the computation of the analog precoding matrix associated to a receiver among the plurality of receivers comprises:
/a/ performing a Singular Value Decomposition, SVD, on a channel matrix associated to said receiver;
/b/ determining a first decomposition matrix V k based on the relative SVD;
characterized in that the computation of the analog precoding matrix associated to a receiver among the plurality of receivers further comprises:
/c/ determining an analog precoding codeword which maximizes a first function g 1 ( V k ,F) of V k and F, said first function being function of:
F
H
V
_
k
V
_
k
H
F
+
λ
min
(
C
i
-
1
H
V
_
k
V
_
k
H
C
i
-
1
)
2
-
(
F
H
V
_
k
V
_
k
H
F
-
λ
min
(
C
i
-
1
H
V
_
k
V
_
k
H
C
i
-
1
)
)
2
4
+
F
H
V
_
k
V
_
k
H
C
i
-
1
C
i
-
1
H
V
_
k
V
_
k
H
F
where:
C i−1 is composed from at least one column of said predetermined matrix;
F is different from all the columns of C i−1 ;
A H denotes a conjugate transpose matrix of a matrix A; and
λ min (A) denotes a minimal eigenvalue of a matrix A;
wherein /c/ is performed iteratively for i=2 . . . L r , with C 1 =f 1 , where f 1 is column of said predetermined matrix which maximizes a function F H V k V k H F of V k and F, for a plurality of F∈ prec,k .
9. The method according to claim 8 , wherein each receiver among the plurality of receivers is associated to a relative set comb,k of analog combining codewords,
wherein, for each receiver among the plurality of receivers and for each subcarrier among the plurality of subcarriers, a second decomposition matrix Ū k (l) is determined, based on the relative SVD performed in step /a/;
the method further comprising, for each receiver among the plurality of receivers:
computing, at said receiver, an analog combining matrix W RF,k associated to said receiver, said computation including:
determining an analog combining codeword which optimizes a second function g 2 (Ū k (1), . . . , Ū k (L),W) of Ū k (1), . . . , Ū k (L) and W, for a plurality of W∈ comb,k .
10. A receiver configured to receive data from a transmitter able to serve a plurality of receivers, in a communication system enabling both analog and digital beamforming,
said receiver being associated to a set prec,k of analog precoding codewords,
said receiver comprising a circuit for maximizing a sum rate of the communication system, said maximization including a computation of an analog precoding matrix F RF,k ,
wherein the computation of the analog precoding matrix comprises:
/a/ performing a Singular Value Decomposition, SVD, on a channel matrix;
/b/ determining a first decomposition matrix V k based on said SVD; and
characterized in that the computation of the analog precoding matrix associated to a receiver among the plurality of receivers further comprises:
/c/ determining an analog precoding codeword which maximizes a first function g 1 (V k ,F)=λ min ( V k H FF H V k ) of V k and F, for a plurality of F∈ prec,k ,
where:
A H denotes a conjugate transpose matrix of a matrix A; and
λ min (A) denotes a minimal eigenvalue of a matrix A.
11. The receiver according to claim 10 , said receiver being further associated to a relative set comb,k of analog combining codewords,
wherein for each subcarrier among the plurality of subcarriers, a second decomposition matrix Ū k (l) is determined, based on said SVD;
said receiver further comprising a circuit for computing an analog combining matrix W RF,k , said computation including:
determining an analog combining codeword which optimizes a second function g 2 (Ū k (1), . . . , Ū k (L),W) of Ū k (1), . . . , Ū k (L) and W, for a plurality of W∈ comb,k .
12. A communication system enabling both analog and digital beamforming, said system comprising a transmitter being able to serve a plurality of receivers, wherein each receiver is configured to receive data from said transmitter,
said receiver being associated to a set prec,k of analog preceding codewords,
said receiver comprising a circuit for maximizing a sum rate of the communication system, said maximization including a computation of an analog precoding matrix F RF,k ,
wherein the computation of the analog precoding matrix comprises:
/a/ performing a Singular Value Decomposition, SVD, on a channel matrix:
/b/ determining a first decomposition matrix V k based on said SVD; and
characterized in that the computation of the analog precoding matrix associated to a receiver among the plurality of receivers further comprises:
/c/ determining an analog precoding, codeword which maximizes a first function g 1 ( V k , F)=λ min ( V k H FF H V k ) of V k and F, for a plurality of F∈ prec,k ,
where:
A H denotes a conjugate transpose matrix of a matrix A; and
λ min (A) denotes a minimal eigenvalue of a matrix A.
13. A computer program product, comprising instructions for performing a method implemented by a computer for maximizing a sum rate of a communication system, said communication system enabling both analog and digital beamforming, said communication system including a transmitter being able to serve a plurality of receivers,
wherein each receiver among the plurality of receivers is associated to a relative set prec,k of analog precoding codewords wherein prec,k is the set of analog precoding codewords associated to the k th receiver,
said method comprising:
for each receiver among the plurality of receivers, computing, at said receiver, an analog precoding matrix F RF,k associated to said receiver,
wherein F RF,k is the analog precoding matrix associated to the k th receiver; and
using at least one computed analog precoding matrix for processing at least one signal to transmit from the transmitter to at least one receiver;
wherein the computation of the analog precoding matrix associated to a receiver among the plurality of receivers comprises:
/a/ performing a Singular Value Decomposition, SVD, on a channel matrix associated to said receiver;
/b/ determining a first decomposition matrix V k based on the relative SVD;
characterized in that the computation of the analog precoding matrix associated to a receiver among the plurality of receivers further comprises:
/c/ determining an analog precoding codeword which maximizes a first function g 1 ( V k , F)=λ min ( V k H FF H V k ) of V k and F, for a plurality of F∈ prec,k ,
where:
A H denotes a conjugate transpose matrix of a matrix A; and
λ min (A) denotes a minimal eigenvalue of a matrix A.
14. A computer program product, comprising instructions for performing a method implemented by a computer for maximizing a sum rate of a communication system, said communication system enabling both analog and digital beamforming, said communication system including a transmitter being able to serve a plurality of receivers,
wherein each receiver among the plurality of receivers is associated to a relative set prec,k of analog precoding codewords, wherein prec,k is the set of analog precoding codewords associated to the k th receiver,
said method comprising:
for each receiver among the plurality of receivers, computing, at said receiver, an analog precoding matrix F RF,k associated to said receiver,
wherein F RF,k is the analog precoding matrix associated to the k th receiver; and
using at least one computed analog precoding matrix for processing at least one signal to transmit from the transmitter to at least one receiver;
wherein the computation of the analog precoding matrix associated to a receiver among the plurality of receivers comprises:
/a/ performing a Singular Value Decomposition, SVD, on a channel matrix associated to said receiver;
/b/ determining a first decomposition matrix V k based on the relative SVD;
characterized in that the computation of the analog precoding matrix associated to a receiver among the plurality of receivers further comprises:
/c/ determining an analog precoding codeword which maximizes a first function g 1 ( V k , F)=λ min ( V k H FF H V k ) of V k and F, for a plurality of F∈ prec,k ,
where:
A H denotes a conjugate transpose matrix of a matrix A; and
λ min (A) denotes a minimal eigenvalue of a matrix A.