Method and system for multi-beam forming based on joint transceiver information

1. A method for multi-beam forming based on joint receiving and transmitting end information, and the method comprises:

a transmitting end executing geometric mean decomposition (GMD) on a channel matrix H to obtain a unitary matrix P; and

the transmitting end taking the unitary matrix P as a weight matrix of GMD beam forming, and executing multi-beam forming processing on an original transmission signal x; wherein:

the step of the transmitting end executing the GMD on the channel matrix H comprises: the transmitting end executing geometric mean decomposition on the channel matrix H: H=QRP −1 , where Q and P are unitary matrixes, a superscript −1 is a conjugate transpose operator, that is, satisfying Q −1 Q=P −1 P=I K 1 ,K 2 , where I is a unit matrix, subscripts K 1 and K 2 respectively denote numbers of rows and columns of a matrix, K 1 =K 2 K=, where K is a rank of the channel matrix H, R is an upper triangular matrix with same diagonal elements, and the diagonal elements of the upper triangular matrix are:

a

ii

=

λ

_

=

(

∏

i

=

1

K

⁢

⁢

λ

i

)

1

/

K

,

λ 1 ≧μ 2 ≧ . . . ≧λ K ≧0, λ i is a nonzero eigenvalue of a correlation matrix HH −1 , i is an integer, and 1≦i≦K;

the step of executing multi-beam forming processing on the original transmission signal x comprises: the transmitting end taking the unitary matrix P as the weight matrix to estimate a transmission weight value W GMD , W GMD =P, and executing multi-beam forming processing on the original transmission signal x according to the estimated transmission weight W GMD to acquire a beam formed transmission signal W GMD ·x, where

x

=

[

x

1

⋮

x

i

⋮

x

K

]

,

and

⁢

[

x

1

⋮

x

i

⋮

x

K

]

is an original transmission signal sequence.

2. The method of claim 1 , after the step of executing multi-beam forming processing on the original transmission signal x, the method further comprising:

the transmitting end transmitting the beam formed transmission signal W GMD ·x via the channel matrix H, wherein a transmitted signal s is: s H W ĠMD x.

3. The method of claim 2 , after the step of the transmitting end transmitting the beam formed transmission signal W GMD ·x via the channel matrix H, the method further comprising:

a receiving end receiving a signal r, r=H·W GMD ·x+n, where n is a noise;

the receiving end using a unitary matrix Q −1 to equalize the received signal r to acquire an equalized received signal

r

~

=

[

r

~

1

⋮

r

~

i

⋮

r

~

K

]

,

[

r

~

1

⋮

r

~

i

⋮

r

~

K

]

being an equalized received signal sequence, and decomposing H into K identical sub channels, and the equalized received signal on each sub channel is

r

~

i

=

λ

_

⁢

x

i

+

∑

j

>

i

K

⁢

a

ij

⁢

x

j

+

n

~

i

,

where j is an integer, 1≦j≦K, a ij is an element in the upper triangular matrix of the geometric mean decomposition, x i is an i th original transmission signal in the original transmission signal sequence, x j is a j th original transmission signal in the original transmission signal sequence, and ñ i is an i th noise in a noise sequence after equalization processing; and

recovering the transmission signal x according to the equalized received signal.

4. The method of claim 3 , wherein, in the step of recovering the transmission signal x according to the equalized received signal, a successive interference cancellation technique is used to recover the transmission signal

x

=

[

x

1

⋮

x

i

⋮

x

K

]

.

5. A transmitting device for supporting multi-beam forming based on joint receiving and transmitting end information, which comprises:

a geometric mean decomposition module, which is configured to: execute geometric mean decomposition (GMD) on a channel matrix H to obtain a unitary matrix P;

a beam forming processing module, which is configured to: take the unitary matrix P as a weight matrix of GMD beam forming, and execute multi-beam forming processing on an original transmission signal x; and

a transmitting module, which is configured to: transmit a beam formed transmission signal via the channel matrix H; wherein:

the geometric mean decomposition module is configured to execute GMD on the channel matrix H according to a following way: executing the geometric mean decomposition on the channel matrix H: H=QRP −1 , where Q and P are unitary matrixes, a superscript −1 is a conjugate transpose operator, that is, satisfying Q −1 Q=P −1 P=I K 1 ,K 2 , where I is a unit matrix, subscripts K 1 and K 2 respectively denote numbers of rows and columns of a matrix, K 1 =K 2 K=, where K is a rank of the channel matrix H, R is an upper triangular matrix with same diagonal elements, and the diagonal elements of the upper triangular matrix are:

a

ii

=

λ

_

=

(

∏

i

=

1

K

⁢

⁢

λ

i

)

1

/

K

,

λ 1 ≧λ 2 ≧ . . . ≧λ K ≧0, λ i is a nonzero eigenvalue of a correlation matrix HH −1 , i is an integer, and 1≦i≦K;

the beam forming processing module is configured to execute multi-beam forming processing on the original transmission signal according to a following way: taking the unitary matrix P as the weight matrix to estimate a transmission weight W GMD , W GMD =P, and executing multi-beam forming processing on the original transmission signal x according to the estimated transmission weight W GMD to acquire a beam formed transmission signal W GMD ·x, where

x

=

[

x

1

⋮

x

i

⋮

x

K

]

,

and

⁢

[

x

1

⋮

x

i

⋮

x

K

]

is an original transmission signal sequence.

6. The transmitting device of claim 5 , wherein:

the transmitting module is configured to transmit the beam formed transmission signal W GMD ·x via the channel matrix H, wherein a transmitted signal s is: s H W ĠMD x.

7. A receiving device for supporting multi-beam forming based on joint receiving and transmitting end information, which comprises:

a receiving module, which is configured to: receive a signal r, r=H·W GMD ·x+n, where n is a noise; wherein H is a channel matrix, x is an original transmission signal, W GMD is a transmission weight, W GMD =P; P is a unitary matrix, geometric mean decomposition is executed on the channel matrix H: H=QRP −1 , where Q is the unitary matrix; a superscript −1 is a conjugate transpose operator, that is, satisfying Q −1 Q=P −1 P=I K 1 ,K 2 , where I is a unit matrix, the subscripts K 1 and K 2 respectively denote numbers of rows and columns of a matrix, K 1 =K 2 K=, where K is a rank of the channel matrix H, R is an upper triangular matrix with same diagonal elements, and the diagonal elements of the upper triangular matrix are:

a

ii

=

λ

_

=

(

∏

i

=

1

K

⁢

⁢

λ

i

)

1

/

K

,

λ 1 ≧λ 2 ≧ . . . ≧λ K ≧0, λ i is a nonzero eigenvalue of a correlation matrix HH −1 , i is an integer, and 1≦i≦K;

an equalization processing module, which is configured to: use a unitary matrix Q −1 to equalize the received signal r to acquire an equalized received signal

r

~

=

[

r

~

1

⋮

r

~

i

⋮

r

~

K

]

,

[

r

~

1

⋮

r

~

i

⋮

r

~

K

]

is an equalized received signal sequence, decompose H into K identical sub channels, and the equalized received signal on each sub-channel is

r

~

i

=

λ

_

⁢

x

i

+

∑

j

>

i

K

⁢

a

ij

⁢

x

j

+

n

~

i

,

ñ i , where j is an integer, 1≦j≦K, a ij is an element in the upper triangular matrix of the geometric mean decomposition, x i is an i th original transmission signal in the original transmission signal sequence, x j is a i th original transmission signal in the original transmission signal sequence, and ñ i is an i th noise in a noise sequence after equalization processing; and

a signal recovering module, which is configured to: recover the transmission signal x according to the equalized received signal.

8. The receiving device of claim 7 , wherein, the signal recovering module is configured to use a successive interference cancellation technique to recover the transmission signal

x

=

[

x

1

⋮

x

i

⋮

x

K

]

.