Method for Obtaining a Covariance Matrix of a Transmitting Channel in a Wireless Network
The present invention disclosed a method for obtaining a covariance matrix of a transmitting channel in a wireless network. The method comprises calculating a speculative transformation matrix, generating a covariance matrix of a receiving channel, and transforming the covariance matrix of the receiving channel into a covariance matrix of a transmitting channel using the speculative transformation matrix.
1 . A method for obtaining a covariance matrix of a transmitting channel in a wireless network, the method comprising:
calculating a speculative transformation matrix from a receiving channel;
generating a covariance matrix of the receiving channel; and
transforming the covariance matrix of the receiving channel into a covariance matrix of a transmitting channel using the speculative transformation matrix.
2 . The method of claim 1 , wherein the calculating the speculative transformation matrix comprises:
generating a plurality of arrays of steering vectors of the transmitting channel;
computing a plurality of transmitting response matrices using the plurality of steering vectors of the transmitting channel;
generating a plurality of arrays of steering vectors of the receiving channel; and
computing a plurality of receiving response matrices using the plurality of steering vector of the receiving channel.
3 . The method of claim 2 , wherein the calculating the speculative transformation matrix further comprises:
computing a cumulative transmitting response matrix using the plurality of transmitting response matrices of the transmitting channel; and
computing a cumulative receiving response matrix using the plurality of transmitting response matrices of the transmitting channel.
4 . The method of claim 3 , wherein the computing the cumulative transmitting response matrix ({tilde over (Q)} tx ) is based on the following equation:
Q
~
tx
=
[
Q
tx
(
-
φ
)
Q
tx
(
Δ
-
φ
)
⋮
Q
tx
(
(
N
a
-
1
)
Δ
-
φ
)
]
,
where i=[0, . . . , N a −1]; N a is a total number of partitions in a cell; and Q tx ((i−1)Δ−φ) is a transmitting response matrix with a direction of arrival equal to (i−1)Δ−φ.
5 . The method of claim 3 , wherein the computing the cumulative receiving response matrix ({tilde over (Q)} rx ) is based on the following equation:
Q
~
rx
=
[
Q
rx
(
-
φ
)
Q
rx
(
Δ
-
φ
)
⋮
Q
rx
(
(
N
a
-
1
)
Δ
-
φ
)
]
,
where i=[0, . . . , N a −1]; N a is a total number of partitions in a cell; and Q rx ((i−1)Δ−φ) is a receiving response matrix with a direction of arrival equal to (i−1)Δ−φ.
6 . The method of claim 3 , wherein the calculating the speculative transformation matrix comprises a step of computing C T =({tilde over (Q)} rx H {tilde over (Q)} rx ) −1 {tilde over (Q)} rx H {tilde over (Q)} tx , where C T is a speculative transformation matrix; {tilde over (Q)} tx is a cumulative transmitting response matrix; {tilde over (Q)} rx is a cumulative receiving response matrix; and (.) H is a Hermitian operator.
7 . The method of claim 1 , wherein the transforming the covariance matrix of the receiving channel into a covariance matrix of the transmitting channel is based on the following equation: R tx =R rx C T , where, C T is a speculative transformation matrix; R tx is a covariance matrix of a transmitting channel; and R rx is a covariance matrix of a receiving channel.
8 . A method for obtaining a covariance matrix of a transmitting channel in a wireless network, the method comprising:
calculating a speculative transformation matrix by generating a plurality of arrays of steering vectors of the transmitting channel, computing a plurality of transmitting response matrices, generating a plurality of arrays of steering vectors of a receiving channel, and computing a plurality of receiving response matrices;
generating a covariance matrix of a receiving channel; and
transforming the covariance matrix of the receiving channel into a covariance matrix of a transmitting channel using the following equation: R tx =R rx C T , where, C T is a speculative transformation matrix; R tx is a covariance matrix of a transmitting channel; and R rx is a covariance matrix of a receiving channel.
9 . The method of claim 8 , wherein the calculating the speculative transformation matrix comprises:
computing a cumulative transmitting response matrix using the plurality of transmitting response matrices of the transmitting channel; and
computing a cumulative receiving response matrix using the plurality of transmitting response matrices of the transmitting channel.
10 . The method of claim 9 , wherein the computing the cumulative transmitting response matrix ({tilde over (Q)} tx ) is based on the following equation:
Q
~
tx
=
[
Q
tx
(
-
φ
)
Q
tx
(
Δ
-
φ
)
⋮
Q
tx
(
(
N
a
-
1
)
Δ
-
φ
)
]
,
where i=[0, . . . , N a −1]; N a is a total number of partitions in a cell; and Q tx ((i−1)Δ−φ) is a transmitting response matrix with a direction of arrival equal to (i−1)Δ−φ.
11 . The method of claim 9 , wherein the computing the cumulative receiving response matrix ({tilde over (Q)} rx ) is based on the following equation:
Q
~
rx
=
[
Q
rx
(
-
φ
)
Q
rx
(
Δ
-
φ
)
⋮
Q
rx
(
(
N
a
-
1
)
Δ
-
φ
)
]
,
where i=[0, . . . , N a −1]; N a is a total number of partitions in a cell; and Q rx ((i−1)Δ−φ) is a receiving response matrix with a direction of arrival equal to (i−1)Δ−φ.
12 . The method of claim 9 , wherein the calculating the speculative transformation matrix comprises a step of computing C T =({tilde over (Q)} rx H {tilde over (Q)} rx ) −1 {tilde over (Q)} rx H {tilde over (Q)} tx , where C T is a speculative transformation matrix; {tilde over (Q)} tx is a cumulative transmitting response matrix; {tilde over (Q)} rx is a cumulative receiving response matrix; and (.) H is a Hermitian operator.
13 . A method for transforming a covariance matrix of a receiving channel into a covariance matrix of a transmitting channel in a wireless network employing frequency division duplex, the method comprising:
calculating a speculative transformation matrix from a receiving channel;
generating a covariance matrix of the receiving channel; and
transforming the covariance matrix of the receiving channel into a covariance matrix of a transmitting channel using the speculative transformation matrix.
14 . The method of claim 13 , wherein the calculating the speculative transformation matrix comprises:
generating a plurality of arrays of steering vectors of the transmitting channel;
computing a plurality of transmitting response matrices using the plurality of steering vectors of the transmitting channel;
generating a plurality of arrays of steering vectors of the receiving channel; and
computing a plurality of receiving response matrices using the plurality of steering vector of the receiving channel.
15 . The method of claim 14 , wherein the calculating the speculative transformation matrix further comprises:
computing a cumulative transmitting response matrix using the plurality of transmitting response matrices of the transmitting channel; and
computing a cumulative receiving response matrix using the plurality of transmitting response matrices of the transmitting channel.
16 . The method of claim 15 , wherein the computing the cumulative transmitting response matrix ({tilde over (Q)} tx ) is based on the following equation:
Q
~
tx
=
[
Q
tx
(
-
φ
)
Q
tx
(
Δ
-
φ
)
⋮
Q
tx
(
(
N
a
-
1
)
Δ
-
φ
)
]
,
where i=[0, . . . , N a −1]; N a is a total number of partitions in a cell; and Q tx ((i−1)Δ−φ) is a transmitting response matrix with a direction of arrival equal to (i−1)Δ−φ.
17 . The method of claim 15 , wherein the computing the cumulative receiving response matrix ({tilde over (Q)} rx ) is based on the following equation:
Q
~
rx
=
[
Q
rx
(
-
φ
)
Q
rx
(
Δ
-
φ
)
⋮
Q
rx
(
(
N
a
-
1
)
Δ
-
φ
)
]
,
where i=[0, . . . , N a −1]; N a is a total number of partitions in a cell; and Q rx ((i−1)Δ−φ) is a receiving response matrix with a direction of arrival equal to (i−1)Δ−φ.
18 . The method of claim 15 , wherein the calculating the speculative transformation matrix comprises a step of computing C T =({tilde over (Q)} rx H {tilde over (Q)} rx ) −1 {tilde over (Q)} rx H {tilde over (Q)} tx , where C T is a speculative transformation matrix; {tilde over (Q)} tx is a cumulative transmitting response matrix; {tilde over (Q)} rx is a cumulative receiving response matrix; and (.) H is a Hermitian operator.
19 . The method of claim 13 , wherein the transforming the covariance matrix of the receiving channel into a covariance matrix of the transmitting channel is based on the following equation: R tx =R rx C T , where, C T is a speculative transformation matrix; R tx is a covariance matrix of a transmitting channel; and R rx is a covariance matrix of a receiving channel.