Systems and methods for updating beamforming codebooks for angle-of-arrival estimation using compressive sensing in wireless communications
A wireless communication device includes: a processing circuit configured to: receive, from an antenna array during a previous period, a first directional electromagnetic signal including beam sweeping reference symbols of a previous beam sweeping period; compute an estimated combined channel; estimate a dominant angle-of-arrival (AoA) of the first directional electromagnetic signal based on the estimated combined channel and a previous beamforming codebook including two or more beamforming vectors corresponding to different AoAs; construct an updated beamforming codebook based on the estimated dominant AoA and one or more remaining AoAs spaced apart from the estimated dominant AoA; receive, at the antenna array during a current period, a second directional electromagnetic signal including data symbols; determine a beamforming vector for data reception of the second directional electromagnetic signal based on the updated beamforming codebook; and detect the data symbols in the second directional electromagnetic signal based on the determined beamforming vector.
1. A method of updating a beamforming codebook comprising:
receiving, at an antenna array of a wireless communication device during a previous period, a first directional electromagnetic signal comprising beam sweeping reference symbols of a previous beam sweeping period;
computing, by a processing circuit of the wireless communication device, an estimated combined channel based on the received first directional electromagnetic signal;
estimating, by the processing circuit, a dominant angle-of-arrival (AoA) of the first directional electromagnetic signal based on the estimated combined channel and a previous beamforming codebook comprising two or more beamforming vectors corresponding to different angles-of-arrival; and
computing, by the processing circuit, one or more remaining angles-of-arrival spaced apart from the estimated dominant angle-of-arrival;
constructing, by the processing circuit, an updated beamforming codebook based on the estimated dominant angle-of-arrival and the one or more remaining angles-of-arrival;
receiving, at the antenna array during a current period, a second directional electromagnetic signal comprising data symbols;
determining a beamforming vector for data reception of the second directional electromagnetic signal based on the updated beamforming codebook; and
detecting, by the processing circuit, the data symbols in the second directional electromagnetic signal based on the determined beamforming vector.
2. The method of claim 1 , wherein the updated beamforming codebook consists of two beamforming vectors,
wherein the estimating the dominant AoA {tilde over (x)} 1 of the first directional electromagnetic signal comprises computing:
{tilde over (x)} 1 =∠( ĥ 2 ĥ 1 H )
where
W
1
H
Y
=
[
h
^
¯
1
h
^
¯
2
]
and
W 1 =W (1:2,1:2)∈ 2×2
where Y is the estimated combined channel, W 1 is a first beamforming vector of the beamforming codebook, 2×2 is a set of 2×2 matrices of complex values, and ĥ 1 and ĥ 2 are estimated analog channels corresponding to two antenna elements of the antenna array,
wherein the one or more remaining angles-of-arrival consists of one beamforming vector, wherein the antenna array has an even number of antenna elements, and wherein the remaining angle-of-arrival {tilde over (x)} 2 is computed in accordance with {tilde over (x)} 2 ={tilde over (x)} 1 +π, and
wherein the updated beamforming codebook W t is computed in accordance with
W
t
=
[
a
(
x
˜
1
)
H
a
(
x
˜
1
+
π
)
H
]
,
wherein a({tilde over (x)} 1 ) is an antenna response vector at the dominant AoA {tilde over (x)} 1 and a({tilde over (x)} 1 +π) is an antenna response vector at the remaining angle-of-arrival {tilde over (x)} 2 ={tilde over (x)}x 1 +π.
3. The method of claim 1 , wherein the updated beamforming codebook comprises three or more beamforming vectors.
4. The method of claim 3 , wherein the estimating the dominant AoA {tilde over (x)} 1 of the first directional electromagnetic signal comprises computing:
x
˜
1
=
arg
max
x
∈
𝒩
(
b
*
)
φ
(
x
)
H
YY
H
φ
(
x
)
φ
(
x
)
2
,
φ
(
x
¯
i
)
=
W
a
(
x
¯
i
)
∈
M
,
a
(
x
¯
i
)
=
[
e
j
0
x
¯
i
,
…
,
e
j
(
N
R
-
1
)
x
¯
i
]
T
∈
N
R
where Y is the estimated combined channel, W is the beamforming codebook, a({tilde over (x)} i ) is an antenna response vector at an i-th AoA {tilde over (x)} i , M is a number of beamforming vectors, M represents a set of vectors of complex values, the vectors having length M, N R is a number of antenna elements of the antenna array, N R represents a set of vectors of complex values, the vectors having length N R , and (b*) is a set of angles in a neighborhood around a selected search angle b*.
5. The method of claim 4 , wherein the selected search angle b* is selected in accordance with:
b
*
=
arg
max
m
y
¯
m
y
¯
m
H
,
where
Y
=
[
y
_
1
⋮
y
_
M
]
,
where m is an m-th beamforming vector among the M beamforming vectors.
6. The method of claim 4 , wherein the selected search angle b* is selected in accordance with an estimated dominant angle-of-arrival of a third directional electromagnetic signal received in a previous beam sweeping period.
7. The method of claim 4 , wherein the set of angles in the neighborhood (b*) around the selected search angle b* is computed by:
( b *)={ x:x=b*+Δl,l=−N, . . . , 0, . . . N}
where N controls a number of angles in (b*) to 2N+1 and where Δ is an angular resolution of the angles in (b*).
8. The method of claim 3 , wherein a number of antenna elements N R in the antenna array is an integer multiple of a number of beamforming vectors M in the updated beamforming codebook, and
wherein the one or more remaining angles-of-arrival {tilde over (x)} i are computed in accordance with:
x
˜
i
=
x
˜
1
+
2
π
M
(
i
-
1
)
,
i
=
2
,
…
,
M
where {tilde over (x)} 1 is the estimated dominant angle-of-arrival of the first directional electromagnetic signal.
9. The method of claim 3 , wherein a number of antenna elements N R in the antenna array is not an integer multiple of a number of beamforming vectors M in the updated beamforming codebook, and
wherein the one or more remaining angles-of-arrival are selected from a constraint set of angles l({tilde over (x)} 1 ), where
I
(
x
˜
1
)
=
{
x
:
x
=
x
˜
1
+
2
π
N
R
n
,
n
=
0
,
…
,
N
R
-
1
}
.
10. The method of claim 1 , wherein the determining the beamforming vector for data reception of the second directional electromagnetic signal comprises selecting the beamforming vector for data reception from the updated beamforming codebook without performing channel estimation.
11. The method of claim 1 , wherein the determining the beamforming vector for data reception of the second directional electromagnetic signal comprises explicitly calculating the beamforming vector based on a channel estimation on the second directional electromagnetic signal and based on the updated beamforming codebook.
12. A wireless communication device configured to update a beamforming codebook, the wireless communication device comprising:
an antenna array;
a processing circuit configured to receive signals from the antenna array and configured to:
receive, at the antenna array during a previous period, a first directional electromagnetic signal comprising beam sweeping reference symbols of a previous beam sweeping period;
compute an estimated combined channel based on the received first directional electromagnetic signal;
estimate a dominant angle-of-arrival (AoA) of the first directional electromagnetic signal based on the estimated combined channel and a previous beamforming codebook comprising two or more beamforming vectors corresponding to different angles-of-arrival;
compute one or more remaining angles-of-arrival spaced apart from the estimated dominant angle-of-arrival;
construct an updated beamforming codebook based on the estimated dominant angle-of-arrival and the one or more remaining angles-of-arrival;
receive, at the antenna array during a current period, a second directional electromagnetic signal comprising data symbols;
determine a beamforming vector for data reception of the second directional electromagnetic signal based on the updated beamforming codebook; and
detect the data symbols in the second directional electromagnetic signal based on the determined beamforming vector.
13. The wireless communication device of claim 12 , wherein the updated beamforming codebook consists of two beamforming vectors,
wherein the processing circuit is configured to estimate the dominant AoA {tilde over (x)} 1 of the first directional electromagnetic signal by computing:
{tilde over (x)} 1 =∠( ĥ 2 ĥ 1 H )
where
W
1
H
Y
=
[
h
^
_
1
h
^
_
2
]
and
W 1 =W (1:2,1:2)∈ 2×2
where Y is the estimated combined channel, W 1 is a first beamforming vector of the beamforming codebook, 2×2 is a set of 2×2 matrices of complex values, and ĥ 1 and ĥ 2 are estimated analog channels corresponding to two antenna elements of the antenna array,
wherein the one or more remaining angles-of-arrival consists of one beamforming vector, wherein the antenna array has an even number of antenna elements, and wherein the remaining angle-of-arrival {tilde over (x)} 2 is computed in accordance with {tilde over (x)} 2 ={tilde over (x)} 1 +π, and
wherein the updated beamforming codebook W t is computed in accordance with
W
t
=
[
a
(
x
˜
1
)
H
a
(
x
˜
1
+
π
)
H
]
,
wherein a({tilde over (x)} 1 ) is an antenna response vector at the dominant AoA {tilde over (x)} 1 and a({tilde over (x)} 1 +π) is an antenna response vector at the remaining angle-of-arrival {tilde over (x)} 2 ={tilde over (x)} 1 +π.
14. The wireless communication device of claim 12 , wherein the updated beamforming codebook comprises three or more beamforming vectors.
15. The wireless communication device of claim 14 , wherein the processing circuit is configured to estimate the dominant AoA {tilde over (x)} 1 of the first directional electromagnetic signal by computing:
x
˜
1
=
arg
max
x
∈
𝒩
(
b
*
)
φ
(
x
)
H
YY
H
φ
(
x
)
φ
(
x
)
2
,
φ
(
x
¯
i
)
=
Wa
(
x
¯
i
)
∈
𝒞
M
,
a
(
x
¯
i
)
=
[
e
j
0
x
_
i
,
…
,
e
j
(
N
R
-
1
)
x
¯
i
]
T
∈
𝒞
N
R
where Y is the estimated combined channel, W is the beamforming codebook, a({tilde over (x)} i ) is an antenna response vector at an i-th AoA {tilde over (x)} i , M is a number of beamforming vectors, M represents a set of vectors of complex values, the vectors having length M, N R is a number of antenna elements of the antenna array, N R represents a set of vectors of complex values, the vectors having length N R , and (b*) is a set of angles in a neighborhood around a selected search angle b*.
16. The wireless communication device of claim 15 , wherein the processing circuit is configured to select the selected search angle b* in accordance with:
b
*
=
arg
max
m
y
_
m
y
_
m
H
,
where
Y
=
[
y
_
1
⋮
y
_
M
]
,
where m is an m-th beamforming vector among the M beamforming vectors.
17. The wireless communication device of claim 15 , wherein the processing circuit is configured to select the selected search angle b* in accordance with an estimated dominant angle-of-arrival of a third directional electromagnetic signal received in a previous beam sweeping period.
18. The wireless communication device of claim 15 , wherein the processing circuit is configured to compute the set of angles in the neighborhood (b*) around the selected search angle b* by:
( b *)={ x:x=b*+Δl,l=−N, . . . , 0, . . . N}
where N controls a number of angles in (b*) to 2N+1 and where Δ is an angular resolution of the angles in (b*).
19. The wireless communication device of claim 14 , wherein a number of antenna elements N R in the antenna array is an integer multiple of a number of beamforming vectors M in the updated beamforming codebook, and
wherein the one or more remaining angles-of-arrival {tilde over (x)} i are computed in accordance with:
x
˜
i
=
x
˜
1
+
2
π
M
(
i
-
1
)
,
i
=
2
,
…
,
M
where {tilde over (x)} 1 is the estimated dominant angle-of-arrival of the first directional electromagnetic signal.
20. The wireless communication device of claim 14 , wherein a number of antenna elements N R in the antenna array is not an integer multiple of a number of beamforming vectors M in the updated beamforming codebook, and
wherein the one or more remaining angles-of-arrival are selected from a constraint set of angles l({tilde over (x)} 1 ), where
I
(
x
˜
1
)
=
{
x
:
x
=
x
˜
1
+
2
π
N
R
n
,
n
=
0
,
…
,
N
R
-
1
}
.
21. The wireless communication device of claim 12 , wherein the processing circuit is configured to determine the beamforming vector for data reception of the second directional electromagnetic signal by selecting the beamforming vector for data reception from the updated beamforming codebook without performing channel estimation.
22. The wireless communication device of claim 12 , wherein the determining the beamforming vector for data reception of the second directional electromagnetic signal comprises explicitly calculating the beamforming vector based on a channel estimation on the second directional electromagnetic signal and based on the updated beamforming codebook.