Beamforming in a wireless communication with a partial estimation to reduce overhead
View Patent ↗A method for beamforming in a wireless communication begins by receiving a baseband signal. The method continues by receiving a feedback signal that includes a subset of angles, wherein a set of angles provide polar coordinates for a unitary matrix and wherein the subset of angles is a subset of the set of angles. The method continues by determining at least one remaining angle of the set of angles based on the subset of angles. The method continues by determining the polar coordinates for the unitary matrix. The method continues by digitally beamforming the baseband signal using the unitary matrix.
1. A method for beamforming a wireless communication, the method comprises:
receiving a baseband signal by a transmitter that includes a plurality of streams;
receiving a feedback signal by the transmitter from a receiver of the wireless communication that includes a subset of anglesψ 1 and Φ 1 , wherein a set of angles ψ 1 and Φ 1 , ψ 2 , and Φ 2 provide polar coordinates for a unitary 2×2 matrix V, wherein VV*=I and I represents an identity matrix;
determining the angles ψ 2 and Φ 2 based on the subset of angles ψ 1 and Φ 1 , wherein ψ 2 and Φ 2 are determined by solving absolute value of ψ 1 −ψ 2 =/2 and Φ 1 =Φ 2 or Φ 1 =Φ 2 +π and ψ 1 +ψ 2 =π/2;
determining the polar coordinates for the unitary matrix based on the set of angles ψ 1 and Φ 1 , ψ 2 , and Φ 2 ; and
digitally beamforming the plurality of streams of the baseband signal using the unitary matrix to produce a plurality of beamformed symbols.
2. The method of claim 1 wherein receiving the baseband signal that includes a plurality of streams includes:
encoding data to produce a stream of encoded data;
interleaving the stream of encoded data into a plurality of parallel streams of interleaved data;
constellation mapping symbols of each of the plurality of parallel streams of interleaved data to a plurality of parallel tones to produce the plurality of streams of the baseband signal; and
wherein digitally beamforming the plurality of streams of the baseband signal includes digitally beamforming each of the plurality of parallel tones using the unitary matrix to produce a plurality of beamformed symbols.
3. The method of claim 1 , wherein the unitary matrix comprises:
a plurality of polar coordinates as represented by V, wherein absolute value of each of the plurality of polar coordinates is a vector on a unit circle and each of the polar coordinates is orthogonal to at least one other of the polar coordinates such that VV*=I, where I represents an identity matrix.
4. The method of claim 3 , wherein the unitary matrix further comprises for a 2×N, wherein N is equal to the number of receiver antennas, multiple input multiple output (MIMO) wireless communication:
V
=
[
cos
ψ
1
cos
ψ
2
sin
ψ
1
ⅇ
jϕ
1
sin
ψ
2
ⅇ
jϕ
2
]
wherein ψ 1 , Φ 1 , ψ 2 , and Φ 2 represent the set of angles, wherein angles ψ 1 and Φ 1 are included in the subset of angles, wherein, ψ 2 , and Φ 2 are determined by solving absolute value of ψ 1 −ψ 2 =π/2 and Φ 1 =Φ 2 or Φ 1 =Φ 2 +π and ψ 1 +ψ 2 =π/2.
5. The method of claim 3 , wherein when the unitary matrix comprises a 3×N, wherein N is equal to the number of receiver antennas, multiple input multiple output (MIMO) wireless communication:
V
=
[
cos
ψ
1
cos
ψ
2
cos
ψ
3
sin
ψ
1
cos
θ
1
ⅇ
jϕ
21
sin
ψ
2
cos
θ
2
ⅇ
jϕ
22
sin
ψ
3
cos
θ
3
ⅇ
jϕ
23
sin
ψ
1
sin
θ
1
ⅇ
jϕ
31
sin
ψ
2
sin
θ
2
ⅇ
jϕ
32
sin
ψ
3
sin
θ
3
ⅇ
jϕ
33
]
wherein ψ 1 , ψ 2 , ψ 3 , θ 1 , θ 2 , θ 3 , Φ 21 , Φ 22 , Φ 23 , Φ 31 , Φ 32 , Φ 33 represent the set of angles, wherein ψ 1 , ψ 2 , θ 1 , θ 2 , Φ 21 , Φ 22 , and Φ 31 , are included in the subset of angles, wherein Diagonal (VV*)=1 s, and wherein ψ 3 , θ 3 , Φ 21 , Φ 23 , Φ 32 , and Φ 33 are determined by:
ψ
3
=
cos
-
1
(
1
-
cos
2
ψ
1
-
cos
2
ψ
2
)
θ
3
=
cos
-
1
(
1
-
sin
2
ψ
1
cos
2
θ
1
-
sin
2
ψ
2
cos
2
θ
2
sin
ψ
3
)
ⅇ
jϕ
23
=
-
cos
ψ
1
sin
ψ
1
cos
θ
1
ⅇ
jϕ
21
+
cos
ψ
2
sin
ψ
2
cos
θ
2
ⅇ
jϕ
22
cos
ψ
3
sin
ψ
3
cos
θ
3
ⅇ
jϕ
32
=
-
cos
ψ
1
cos
ψ
2
+
sin
ψ
1
cos
θ
1
sin
ψ
2
cos
θ
2
ⅇ
j
(
ϕ
22
-
ϕ
21
)
sin
ψ
1
sin
θ
1
sin
ψ
2
sin
θ
2
ⅇ
jϕ
31
ⅇ
jϕ
32
=
-
cos
ψ
1
cos
ψ
3
+
sin
ψ
1
cos
θ
1
sin
ψ
3
cos
θ
3
ⅇ
j
(
ϕ
23
-
ϕ
21
)
sin
ψ
1
sin
θ
1
sin
ψ
3
sin
θ
3
ⅇ
jϕ
31
.
6. The method of claim 3 , wherein when the unitary matrix comprises a 4×N, wherein N is equal to the number of receiver antennas, multiple input multiple input multiple output (MIMO) wireless communication:
V
=
[
cos
ψ
1
cos
φ
1
cos
ψ
2
cos
φ
2
cos
ψ
3
cos
φ
3
cos
ψ
4
cos
φ
4
cos
ψ
1
sin
φ
1
ⅇ
jϕ
11
cos
ψ
2
sin
φ
2
ⅇ
jϕ
12
cos
ψ
3
sin
φ
3
ⅇ
jϕ
13
cos
ψ
4
sin
φ
4
ⅇ
jϕ
14
sin
ψ
1
cos
θ
1
ⅇ
jϕ
21
sin
ψ
2
cos
θ
2
ⅇ
jϕ
22
sin
ψ
3
cos
θ
3
ⅇ
jϕ
23
sin
ψ
4
cos
θ
4
ⅇ
jϕ
24
sin
ψ
1
sin
θ
1
ⅇ
jϕ
31
sin
ψ
2
sin
θ
2
ⅇ
jϕ
32
sin
ψ
3
sin
θ
3
ⅇ
jϕ
33
sin
ψ
4
sin
θ
4
ⅇ
jϕ
34
]
wherein ψ 1 , ψ 2 , ψ 3 , ψ 4 , θ 1 , θ 2 , θ 3 , θ 4 , φ 1 , φ 2 , φ 3 , φ 4 , Φ 11 , Φ 12 , Φ 13 , Φ 14 , Φ 21 , Φ 22 , Φ 23 , Φ 24 , Φ 31 , Φ 32 , Φ 33 , Φ 34 represent the set of angles, wherein ψ 1 , ψ 2 , ψ 3 , θ 1 , θ 2 , θ 3 , φ 1 , φ 2 , φ 3 , Φ 11 , Φ 12 , Φ 13 , Φ 21 , Φ 22 , Φ 23 , Φ 31 , are the subset of angles, wherein ψ 4 , θ 4 , φ 4 , Φ 14 , Φ 24 , Φ 31 , Φ 32 , Φ 33 , Φ 34 are determined by:
ψ
4
=
cos
-
1
(
2
-
cos
2
ψ
1
-
cos
2
ψ
2
-
cos
2
ψ
3
)
φ
4
=
cos
-
1
(
1
-
cos
2
ψ
1
cos
2
φ
1
-
cos
2
ψ
2
cos
2
φ
2
-
cos
2
ψ
3
cos
2
φ
3
cos
ψ
4
)
θ
4
=
cos
-
1
(
1
-
sin
2
ψ
1
cos
2
θ
1
-
sin
2
ψ
2
cos
2
θ
2
-
sin
2
ψ
3
cos
2
θ
3
sin
ψ
4
)
ⅇ
jϕ
14
=
-
cos
2
ψ
1
sin
φ
1
cos
φ
1
ⅇ
jϕ
11
+
cos
2
ψ
2
sin
φ
2
cos
φ
2
ⅇ
jϕ
12
+
cos
2
ψ
3
sin
φ
3
cos
φ
3
ⅇ
jϕ
13
cos
2
ψ
4
sin
φ
4
cos
φ
4
ⅇ
jϕ
24
=
-
cos
ψ
1
sin
ψ
1
cos
φ
1
cos
θ
1
ⅇ
jϕ
21
+
cos
ψ
2
sin
ψ
2
cos
φ
2
cos
θ
2
ⅇ
jϕ
22
+
cos
ψ
3
sin
ψ
3
cos
φ
3
cos
θ
3
ⅇ
jϕ
23
cos
ψ
4
sin
ψ
4
cos
φ
4
cos
θ
4
ⅇ
jϕ
32
=
-
cos
ψ
1
cos
ψ
2
cos
φ
1
cos
φ
2
+
cos
ψ
1
cos
ψ
2
sin
φ
1
sin
φ
2
ⅇ
j
(
ϕ
12
-
ϕ
11
)
+
sin
ψ
1
cos
θ
1
sin
ψ
2
cos
θ
2
ⅇ
j
(
ϕ
22
-
ϕ
21
)
sin
ψ
1
sin
θ
1
sin
ψ
2
sin
θ
2
ⅇ
jϕ
31
ⅇ
jϕ
33
=
-
cos
ψ
1
cos
ψ
3
cos
φ
1
cos
φ
3
+
cos
ψ
1
cos
ψ
3
sin
φ
1
sin
φ
3
ⅇ
j
(
ϕ
13
-
ϕ
11
)
+
sin
ψ
1
cos
θ
1
sin
ψ
3
cos
θ
3
ⅇ
j
(
ϕ
23
-
ϕ
21
)
sin
ψ
1
sin
θ
1
sin
ψ
3
sin
θ
3
ⅇ
jϕ
31
ⅇ
jϕ
34
=
-
cos
ψ
1
cos
ψ
4
cos
φ
1
cos
φ
4
+
cos
ψ
1
cos
ψ
4
sin
φ
1
sin
φ
4
ⅇ
j
(
ϕ
14
-
ϕ
11
)
+
sin
ψ
1
cos
θ
1
sin
ψ
4
cos
θ
4
ⅇ
j
(
ϕ
24
-
ϕ
21
)
sin
ψ
1
sin
θ
1
sin
ψ
4
sin
θ
4
ⅇ
jϕ
31
.
7. A transmit baseband processing module comprises:
an encoding module operably coupled to convert outbound data into encoded data;
a plurality of interleaving modules operably coupled to interleave the encoded data into a plurality of interleaved streams of data;
a plurality of constellation mapping modules operably coupled to map the plurality of interleaved streams of data into a plurality of streams of data symbols;
a beamforming module operably coupled to:
obtain a feedback signal that includes a subset of angles ψ 1 and Φ 1 , wherein a set of angles ψ 1 and Φ 1 , ψ 2 , and Φ 2 provide polar coordinates for a unitary 2×2 matrix V, wherein VV*=I and I represents an identity matrix;
determine the angles ψ 2 and Φ 2 based on the subset of angles ψ 1 and Φ 1 , wherein ψ 2 and Φ 2 are determined by solving absolute value of ψ 1 −ψ 2 =π/2 and Φ 1 =Φ 2 or Φ 1 =Φ 2 +π and ψ 1 +ψ 2 =π/2;
determine the polar coordinates for the unitary matrix based on the set of angles ψ 1 and Φ 1 , ψ 2 , and Φ 2 ; and
digitally beamform, using the unitary matrix having polar coordinates, the plurality of streams of data symbols into a plurality of streams of beamformed symbols; and
a plurality of inverse fast Fourier transform modules operably coupled to convert the plurality of streams of beamformed symbols into a plurality of outbound symbol streams.
8. The transmit baseband processing module of claim 7 , wherein the unitary matrix comprises:
a plurality of polar coordinates as represented by V, wherein absolute value of each of the plurality of polar coordinates is a vector on a unit circle and each of the polar coordinates is orthogonal to at least one other of the polar coordinates such that VV*=I, where I represents an identity matrix.
9. The transmit baseband processing module of claim 8 , wherein the unitary matrix further comprises for a 2×N, wherein N is equal to the number of receiver antennas, multiple input multiple output (MIMO) wireless communication:
V
=
[
cos
ψ
1
cos
ψ
2
sin
ψ
1
ⅇ
jϕ
1
sin
ψ
2
ⅇ
jϕ
2
]
wherein ψ 1 , Φ 1 , ψ 2 , and Φ 2 represent the set of angles, wherein angles ψ 1 and Φ 1 are included in the subset of angles, wherein, ψ 2 , and Φ 2 are determined by solving absolute value of ψ 1 −ψ 2 =π/2 and Φ 1 =Φ 2 or Φ 1 =Φ 2 +π and ψ 1 +ψ 2 =π/2.
10. The transmit baseband processing module of claim 8 , wherein the unitary matrix further comprises for a 3×N, wherein N is equal to the number of receiver antennas, multiple input multiple output (MIMO) wireless communication:
V
=
[
cos
ψ
1
cos
ψ
2
cos
ψ
3
sin
ψ
1
cos
θ
1
ⅇ
jϕ
21
sin
ψ
2
cos
θ
2
ⅇ
jϕ
22
sin
ψ
3
cos
θ
3
ⅇ
jϕ
23
sin
ψ
1
sin
θ
1
ⅇ
jϕ
31
sin
ψ
2
sin
θ
2
ⅇ
jϕ
32
sin
ψ
3
sin
θ
3
ⅇ
jϕ
33
]
wherein ψ 1 , ψ 2 , ψ 3 , θ 1 , θ 2 , θ 3 , Φ 21 , Φ 22 , Φ 23 , Φ 31 , Φ 32 , Φ 33 represent the set of angles, wherein ψ 1 , ψ 2 , θ 1 , θ 2 , Φ 21 , Φ 22 , and Φ 31 , are included in the subset of angles, wherein (VV*)=1 s, and wherein ψ 3 , θ 3 , Φ 21 , Φ 23 , Φ 32 , and Φ 33 are determined by:
ψ
3
=
cos
-
1
(
1
-
cos
2
ψ
1
-
cos
2
ψ
2
)
θ
3
=
cos
-
1
(
1
-
sin
2
ψ
1
cos
2
θ
1
-
sin
2
ψ
2
cos
2
θ
2
sin
ψ
3
)
ⅇ
jϕ
23
=
-
cos
ψ
1
sin
ψ
1
cos
θ
1
ⅇ
jϕ
21
+
cos
ψ
2
sin
ψ
2
cos
θ
2
ⅇ
jϕ
22
cos
ψ
3
sin
ψ
3
cos
θ
3
ⅇ
jϕ
32
=
-
cos
ψ
1
cos
ψ
2
+
sin
ψ
1
cos
θ
1
sin
ψ
2
cos
θ
2
ⅇ
j
(
ϕ
22
-
ϕ
21
)
sin
ψ
1
sin
θ
1
sin
ψ
2
sin
θ
2
ⅇ
jϕ
31
ⅇ
jϕ
32
=
-
cos
ψ
1
cos
ψ
3
+
sin
ψ
1
cos
θ
1
sin
ψ
3
cos
θ
3
ⅇ
j
(
ϕ
23
-
ϕ
21
)
sin
ψ
1
sin
θ
1
sin
ψ
3
sin
θ
3
ⅇ
jϕ
31
.
11. The transmit baseband processing module of claim 8 , wherein the unitary matrix further comprises for a 4×N, wherein N is equal to the number of receiver antennas, multiple input multiple output (MIMO) wireless communication:
V
=
[
cos
ψ
1
cos
φ
1
cos
ψ
2
cos
φ
2
cos
ψ
3
cos
φ
3
cos
ψ
4
cos
φ
4
cos
ψ
1
sin
φ
1
ⅇ
jϕ
11
cos
ψ
2
sin
φ
2
ⅇ
jϕ
12
cos
ψ
3
sin
φ
3
ⅇ
jϕ
13
cos
ψ
4
sin
φ
4
ⅇ
jϕ
14
sin
ψ
1
cos
θ
1
ⅇ
jϕ
21
sin
ψ
2
cos
θ
2
ⅇ
jϕ
22
sin
ψ
3
cos
θ
3
ⅇ
jϕ
23
sin
ψ
4
cos
θ
4
ⅇ
jϕ
24
sin
ψ
1
sin
θ
1
ⅇ
jϕ
31
sin
ψ
2
sin
θ
2
ⅇ
jϕ
32
sin
ψ
3
sin
θ
3
ⅇ
jϕ
33
sin
ψ
4
sin
θ
4
ⅇ
jϕ
34
]
wherein ψ 1 , ψ 2 , ψ 3 , ψ 4 , θ 1 , θ 2 , θ 3 , θ 4 , φ 1 , φ 2 , φ 3 , φ 4 , Φ 11 , Φ 12 , Φ 13 , Φ 14 , Φ 21 , Φ 22 , Φ 23 , Φ 24 , Φ 31 , Φ 32 , θ 33 , Φ 34 represent the set of angles, wherein ψ 1 , ψ 2 , ψ 3 , θ 1 , θ 2 , θ 3 , φ 1 , φ 2 , φ 3 , Φ 11 , Φ 12 , Φ 13 , Φ 21 , Φ 22 , Φ 23 , Φ 31 , are the subset of angles, wherein ψ 4 , θ 4 , φ 4 , Φ 14 , Φ 24 , Φ 31 , Φ 32 , Φ 33 , Φ 34 are determined by:
ψ
4
=
cos
-
1
(
2
-
cos
2
ψ
1
-
cos
2
ψ
2
-
cos
2
ψ
3
)
φ
4
=
cos
-
1
(
1
-
cos
2
ψ
1
cos
2
φ
1
-
cos
2
ψ
2
cos
2
φ
2
-
cos
2
ψ
3
cos
2
φ
3
cos
ψ
4
)
θ
4
=
cos
-
1
(
1
-
sin
2
ψ
1
cos
2
θ
1
-
sin
2
ψ
2
cos
2
θ
2
-
sin
2
ψ
3
cos
2
θ
3
sin
ψ
4
)
ⅇ
jϕ
14
=
-
cos
2
ψ
1
sin
φ
1
cos
φ
1
ⅇ
jϕ
11
+
cos
2
ψ
2
sin
φ
2
cos
φ
2
ⅇ
jϕ
12
+
cos
2
ψ
3
sin
φ
3
cos
φ
3
ⅇ
jϕ
13
cos
2
ψ
4
sin
φ
4
cos
φ
4
ⅇ
jϕ
24
=
-
cos
ψ
1
sin
ψ
1
cos
φ
1
cos
θ
1
ⅇ
jϕ
21
+
cos
ψ
2
sin
ψ
2
cos
φ
2
cos
θ
2
ⅇ
jϕ
22
+
cos
ψ
3
sin
ψ
3
cos
φ
3
cos
θ
3
ⅇ
jϕ
23
cos
ψ
4
sin
ψ
4
cos
φ
4
cos
θ
4
ⅇ
jϕ
32
=
-
cos
ψ
1
cos
ψ
2
cos
φ
1
cos
φ
2
+
cos
ψ
1
cos
ψ
2
sin
φ
1
sin
φ
2
ⅇ
j
(
ϕ
12
-
ϕ
11
)
+
sin
ψ
1
cos
θ
1
sin
ψ
2
cos
θ
2
ⅇ
j
(
ϕ
22
-
ϕ
21
)
sin
ψ
1
sin
θ
1
sin
ψ
2
sin
θ
2
ⅇ
jϕ
31
ⅇ
jϕ
33
=
-
cos
ψ
1
cos
ψ
3
cos
φ
1
cos
φ
3
+
cos
ψ
1
cos
ψ
3
sin
φ
1
sin
φ
3
ⅇ
j
(
ϕ
13
-
ϕ
11
)
+
sin
ψ
1
cos
θ
1
sin
ψ
3
cos
θ
3
ⅇ
j
(
ϕ
23
-
ϕ
21
)
sin
ψ
1
sin
θ
1
sin
ψ
3
sin
θ
3
ⅇ
jϕ
31
ⅇ
jϕ
34
=
-
cos
ψ
1
cos
ψ
4
cos
φ
1
cos
φ
4
+
cos
ψ
1
cos
ψ
4
sin
φ
1
sin
φ
4
ⅇ
j
(
ϕ
14
-
ϕ
11
)
+
sin
ψ
1
cos
θ
1
sin
ψ
4
cos
θ
4
ⅇ
j
(
ϕ
24
-
ϕ
21
)
sin
ψ
1
sin
θ
1
sin
ψ
4
sin
θ
4
ⅇ
jϕ
31
.