Parametric compression of rank-1 analog feedback
View Patent ↗Channel state information in a closed-loop, multiple-input, multiple-output wireless networks is fed back from each mobile station to a base station by first determining a transmit covariance matrix R, and applying a singular value decomposition (SVD) R=UΣV H , where U, V are left and right singular vector matrices, Σ is a diagonal matrix with singular values. The matrix V includes column vectors V. A beamforming vector v max =[1 exp(jΦ)exp(j2Φ) . . . exp(jΦ)]/√{square root over (N)}] is approximated by the column vector V having a maximum magnitude, where Φ is a real number. Then, only the angle Φ is fed back using a phase modulation mapping of the components exp(jΦ) onto the associated subcarrier.
1. A method for feeding back channel state information (CSI) in a closed-loop (CL) multiple-input, multiple-output (MIMO) wireless networks, wherein the network includes a plurality of cells, and each cell includes a base station (BS) and a set of mobile stations (MS), wherein each BS includes a set of N antennas spaced apart by at least half a carrier wavelength λ, and wherein the N antennas are associated with N subcarriers, comprising at each MS:
determining a matrix R, wherein the matrix R is a transmit covariance matrix;
applying a singular value decomposition (SVD) to the matrix R according to
R=UΣV H ,
where U, V are left and right singular vector matrices, Σ is a diagonal matrix with singular values, the matrix V includes column vectors V, and H is a Hermitian operator;
approximating a beamforming vector v max by the column vector V having a maximum magnitude, and wherein
v max =[1exp( j Φ)exp( j 2Φ) . . . exp( j Φ)]/ √{square root over (N)}],
where an angel Φ is a real number, and j indexes N; and
feeding back, in analog form, from the MS to the BS, only the angle Φ using a phase modulation mapping of components exp(jΦ) of the vector v max onto the associated subcarrier.
2. The method of claim 1 , further comprising:
repeating the feeding back.
3. The method of claim 1 , wherein the BS includes multiple cross polarized antennas and wherein
v max =[r exp( j θ)exp( j *(0: N/ 2−1)*Φ 1 )exp( j *(0: N/ 2−1)*Φ 2 )]/√{square root over ( N (1+ r 2 )/2)},
wherein the complex value r exp(jθ) is a gain and a phase offset between two beamforming vectors mapped to one subcarrier, and wherein Φ 1 and Φ 2 are mapped to two other subcarriers.
4. The method of claim 3 , wherein the BS includes two cross polarized antennas spaced by λ/2, and further comprising:
amplitude modulating the subcarrier carrying exp(jΦ 1 ) by a real parameter c wherein the parameter c is proportional to a deviation of Φ 2 from Φ 1 and equals 1 when Φ 2 =Φ 1 .
5. The method of claim 4 , wherein
v max ≅[r exp( j θ)exp( j *(0:1)*(Φ 1 )exp( j *(0:1)*(Φ 1 +( c− 1))]/√{square root over (2+2 r 2 )},
wherein the notation (0:1) represents a sequence of integers [i, i+1, i+2, . . . , j].
6. The method of claim 1 , wherein the BS includes widely spaced clusters of antennas, and the feeding back maps c 1 exp(jΦ 1 ) and c 2 exp(jΦ 2 ) to two subcarriers, and three complex numbers α 1 α 2 α 3 correspond to the gain and the phase offset, and
V
max
≅
[
1
exp
(
j
Φ
1
)
α
1
α
1
exp
(
j
(
Φ
1
+
c
1
-
1
)
)
α
2
α
2
exp
(
j
(
Φ
2
)
)
α
3
α
3
exp
(
j
(
Φ
2
+
c
2
-
1
)
)
]
/
2
+
2
∑
i
=
1
3
α
i
2
.
7. The method of claim 1 , further comprising:
signaling to the BS whether the MS is using a compressed mode feedback.
8. The method of claim 1 , further comprising:
broadcasting, by the BS, an antenna configuration used by the BS.
9. The method of claim 8 , further comprising:
broadcasting by the BS antenna configurations of neighboring BS.
10. The method of claim 9 , wherein the feeding back is for a particular antenna configuration.
11. The method of claim 1 , wherein
exp
(
j
Φ
)
=
x
x
,
where
x=V (2: N ) H *V (1: N− 1),
and the notation (i:j) represents a sequence of integers [i, i+1, i+2, . . . , j].
12. The method of claim 1 , wherein the column vector in the matrix v having the maximum magnitude maximizes V H RV, and the components of the vector V max for the N antennas are
e jΦ i , i=1, 2, . . . , N,
and
V
H
RV
=
∑
m
∑
n
R
mn
ⅇ
j
Φ
(
m
-
n
)
=
2
Re
{
∑
k
=
0
N
-
1
S
k
ⅇ
j
Φ
k
}
,
where the notation (i:j) represents a sequence of integers [i, i+1, i+2, . . . , j], the function Re{x} is the real part of x, and
S
k
=
∑
n
R
n
+
kn
for
k
>
0
and
S
0
=
0.5
∑
n
R
nn
,
where R mn is an entry at the m th row and n th column of the matrix R.
13. The method of claim 12 , wherein Φ is maximized by taking a fast Fourier transform (FFT) of the N values of S k .
14. The method of claim 2 , wherein
exp
(
j
Φ
1
)
=
x
x
,
where
x=V (2: N/ 2) H *V (1: N/ 2−1),
where the notation (i:j) represents a sequence of integers [i, i+1, i+2, . . . , j], and
exp
(
j
Φ
2
)
=
x
x
,
where
x=V ( N/ 2+2 :N ) H *V ( N/ 2+1 :N− 1), and
the gain is
r
exp
(
j
θ
)
=
V
(
1
:
N
/
2
)
ⅇ
j
Φ
1
[
0
:
3
]
′
V
(
N
/
2
+
1
:
N
)
ⅇ
jΦ
2
[
0
:
3
]
′
,
and
r
=
sqrt
(
∑
i
=
1
N
/
2
R
ii
∑
i
=
1
N
R
ii
)
,
and the phase offset is estimated using a top right quadrant of the matrix R
R
=
[
Q
1
Q
3
Q
3
H
Q
2
]
,
which represents the cross talk between the polarizations, where Q i , i=1, 2, 3 are quadrants of the matrix R, and
exp
(
j
θ
)
=
x
x
,
where θ is the phase offset between the beamforming vectors is
x=e −jΦ 1 [0:N/2−1] Q 3 e jΦ 2 [0:N/2−1]′ .
15. The method of claim 4 , wherein
c =√{square root over (1+sin(Φ 2 −Φ 1 ))}.
16. The method of claim 1 , wherein the matrix R is a long term transmit correlation matrix R LT , which is averaged over multiple sub-carriers, and wherein the column vector V having the maximum magnitude maximizes
V
H
R
LT
H
RR
LT
V
R
LT
V
2
.