Complementary beamforming methods and apparatuses

1. A method comprising:

providing a smart antenna;

determining at least one signal operatively configured for subspace complementary beamforming (SCBF) in a wireless communication system;

generating the at least one signal such that the signal is operatively configured to cause said smart antenna to perform said SCBF and to transmit at least one complementary beam; and

determining the at least one signal using a Steering Matrix: A=[α(θ 1 ) α(θ 2 ) . . . α(θ k )], wherein α(θ k ) represents a steering vector of user k;

wherein:

if W=A*B, where B is a non-singular K-by-K matrix, then using a complementary beamforming matrix of

W

c

=

k

0

⁢

C

0

N

⁡

[

u

K

+

1

u

K

+

2

…

u

N

]

wherein C 0 =Nc 0 is the level of the main lobe, k 0 is the scaling factor and u l is the l-th column vector of U; otherwise using a complementary beamforming matrix of

W

c

=

k

0

⁢

C

0

N

⁡

[

u

_

1

u

_

2

…

u

_

N

-

K

]

wherein ū 1 is the l-th left singular vector of the matrix

(Σ l=K+1 N ũ 1 ũ 1 H )UΛ c = UΛV H , where A*=Ũ{tilde over (Λ)}{tilde over (V)} H is assumed and a scattering channel

H*=Ũ{tilde over (Λ)}{tilde over (V)} H is assumed.

2. A method according to claim 1 wherein the step of determining the at least one signal comprises at least one of: modifying a weight matrix to operatively support said SCBF; expanding a size of the weight matrix to operatively support said SCBF.

3. A method according to claim 1 , further comprising determining the at least one signal using a Downlink Beamforming Matrix: W=UΛV H .

4. A method according to claim 1 , wherein it is assumed that 2K<N,

W a =(WA*)=U a Λ a V a H , and

W

c

=

k

0

⁢

C

0

N

⁡

[

u

a

,

r

+

1

u

a

,

r

+

2

…

u

a

,

N

]

;

and

wherein r is rank of W a .

5. A method comprising:

providing a smart antenna;

determining at least one signal operatively configured for complementary superposition beamforming (CSBF) in a wireless communication system;

generating the at least one signal such that the signal is operatively configured to cause said smart antenna to perform said CSBF and to transmit at least one complementary beam, and

determining the at least one signal using a downlink beamforming matrix:

{tilde over (W)}=└w 1 . . . w k−1 {tilde over (w)} k w k+1 . . . w k ┘, where {tilde over (w)} k =p 0 w k +W c p and p is complex conjugate transpose of the l-th row of W c ,

p

0

=

w

k

,

l

*



w

k

,

l



is normalized complex conjugate of the l-th element of w k ,

where W c =√{square root over ( c 0 [u K+1 ,u K+2 , . . . , u N ])},

c 0 is a scalar, K=the number of users, N=the number of antennas and u l is the l-th vector of U.

6. A method comprising:

providing a smart antenna;

determining at least one signal operatively configured for complementary superposition beamforming (CSBF) in a wireless communication system;

generating the at least one signal such that the signal is operatively configured to cause said smart antenna to perform said CSBF and to transmit at least one complementary beam, and

determining the at least one signal using: {tilde over (W)}=[w 1 w 2 . . . w k W c p]

wherein:

p is complex conjugate transpose of the l-th row of W c ,

W c =√{square root over ( c 0 [u K+1 ,u K+2 , . . . , u N ])},

c 0 is a scalar, K=the number of users, N=the number of antennas and u l is the l-th column vector of U.

7. A method according to claim 6 wherein said step of determining the at least one signal comprises using a null-generation technique that is configured to generate L nulls at angles θ 1 , θ 2 , . . . θ L at a beam.

8. A method according to claim 6 wherein said step of determining said at least one signal uses: A=[α(θ 1 ) α(θ 2 ) . . . α(θ L )].

9. A method according to claim 6 wherein said step of determining the at least one signal uses a vector: w=(l−P s )w where P s =A*(A T A*) −1 A T , and in scattering channel P s =H*(H T A*) −1 H T .

10. A method according to claim 6 wherein said step of determining the at least one signal uses a null-widening technique that is configured to produce at least one null at a vicinity of selected angles.

11. A method according to claim 6 wherein said step of determining the at least one signal comprises selectively modifying a steering matrix to:

A=└{tilde over (α)}(θ 1 ) {tilde over (α)}(θ 2 ) . . . {tilde over (α)}(θ K )┘, wherein {tilde over (α)}(θ K )=└α(θ k −Δθ 1 ) α(θ k ) α(θ k +Δθ r )┘.

12. A method according to claim 6 wherein said step of determining the at least one signal comprises establishing at least two nulls such that a rank of A is less than N.

13. A method according to claim 6 wherein said step of determining the at least one signal uses adaptive control of a complementary beam level.

14. A method according to claim 6 wherein said step of determining the at least one signal, in a non-zero angular channel, comprises selectively reducing a complementary beam level.

15. A method according to claim 6 wherein said step of determining the at least one signal, for delay spread channels, comprises selectively reducing a complementary beam level.

16. A method according to claim 6 wherein said step of determining the at least one signal, in free space, comprises selectively increasing the complementary beam level.