Omni-directional and low-correlated pre-coding broadcast beamforming

1. A method comprising:

determining system parameters for a device configured to wirelessly transmit one or more broadcast signals via a plurality of antennas;

computing a plurality of beamforming weight vectors based on the system parameters such that all of the beamforming weight vectors have omni-directional characteristics and such that correlation between beamforming weight vectors is relatively low; and

applying respective ones of the plurality of beamforming weight vectors to corresponding contiguous groups of subcarrier signals being associated with the one or more broadcast signals to produce beamformed transmit signals for transmission via the plurality of antennas.

2. The method of claim 1 , wherein determining system parameters comprises determining the number of the plurality of antennas, the spacing of the antennas, the geometry of the antennas, the number of transmit sectors, and the center carrier frequency of the one or more broadcast signals.

3. The method of claim 1 , wherein computing the plurality of beamforming weight vectors comprises computing beamforming weight vectors for a uniform linear antenna array.

4. The method of claim 1 , wherein computing the plurality of beamforming weight vectors comprises computing beamforming weight vectors for a uniform circular antenna array.

5. The method of claim 1 , wherein computing comprises computing the plurality of beamforming weight vectors so as to smooth the magnitude of signals from application of the beamforming weight vectors at boundaries of the contiguous groups of subcarriers.

6. The method of claim 1 , wherein computing the plurality of beamforming weight vectors comprises computing:

w

i

=

1

M

⁡

[

exp

⁡

(

jβ

i

,

1

)

exp

⁡

(

jβ

i

,

2

)

…

exp

⁡

(

jβ

i

,

M

)

]

T

where w i is the i th beamforming weight vector for i=1 to M, M is the number of antennas of the device, exp( ) is an exponential function, and β i,M are angles between zero and 2 π.

7. The method of claim 6 , wherein computing the plurality of beamforming weight vectors to achieve their omni-directional characteristics comprises computing the plurality of beamforming weight vectors such that:

ab

⁢

⁢

s

⁡

(

w

i

H

⁢

A

⁡

(

θ

k

⁢

⁢

1

,

λ

DL

)

)

ab

⁢

⁢

s

⁡

(

w

i

H

⁢

A

⁡

(

θ

k

⁢

⁢

2

,

λ

DL

)

)

≥

p

r

where abs( ) is the absolute value function, A(θ k1 ,λ DL ) and A(θ k2 ,λ DL ) are array steering vectors, θ k1 and θ k2 are transmission angles in a sector, λ DL is the wavelength of the broadcast signals, and p r is a power ratio selected to form an omni-directional beam within a given sector.

8. The method of claim 7 , wherein computing the plurality of beamforming weight vectors comprises computing the plurality of beamforming weight vectors subject to the constraint that abs(w i1 H w i2 ) is relatively small for i 1 ≠i 2 .

9. An apparatus comprising:

a plurality of antennas;

a transmitter configured to transmit signals via respective ones of the plurality of antennas;

a controller coupled to the transmitter and configured to:

compute a plurality of beamforming weight vectors based on system parameters such that all of the beamforming weight vectors have omni-directional characteristics and such that correlation between beamforming weight vectors is relatively low; and

apply respective ones of the plurality of beamforming weight vectors to corresponding contiguous groups of subcarrier signals being associated with one or more broadcast signals to produce beamformed transmit signals by the transmitter via the plurality of antennas.

10. The apparatus of claim 9 , wherein the plurality of antennas are configured as a uniform linear antenna array, and wherein the controller is further configured to compute the beamforming weight vectors for the uniform linear antenna array.

11. The apparatus of claim 9 , wherein the plurality of antennas are configured as a uniform circular antenna array, and wherein the controller is further configured to compute the beamforming weight vectors for the uniform circular antenna array.

12. The apparatus of claim 9 , wherein the controller is configured to compute the plurality of beamforming weight vectors so as to smooth the magnitude of signals resulting from application of the beamforming weight vectors at boundaries of the contiguous groups of subcarriers.

13. One or more tangible non-transitory computer readable media encoded with instructions for execution and when executed operable to:

compute a plurality of beamforming weight vectors based on system parameters associated with a device configured to wirelessly transmit one or more broadcast signals via a plurality of antennas such that all of the beamforming weight vectors have omni-directional characteristics and such that correlation between beamforming weight vectors is relatively low; and

apply respective ones of the plurality of beamforming weight vectors to corresponding contiguous groups of subcarrier signals being associated with the one or more broadcast signals to produce beamformed transmit signals for transmission via the plurality of antennas.

14. The non-transitory computer readable media of claim 13 , wherein the instructions operable to compute the plurality of beamforming weight vectors is based on system parameters comprising the number of the antennas, the spacing of the antennas, the geometry of the antennas, the number of transmit sectors, and the center carrier frequency of the one or more broadcast signals.

15. The non-transitory computer readable media of claim 13 , wherein the instructions operable to compute the plurality of beamforming weight vectors comprise instructions operable to compute the beamforming weight vectors for a uniform linear antenna array.

16. The non-transitory computer readable media of claim 13 , wherein the instructions operable to compute the plurality of beamforming weight vectors comprise instructions operable to compute the beamforming weight vectors for a uniform circular antenna array.

17. The non-transitory computer readable media of claim 13 , wherein the instructions operable to compute the plurality of beamforming weight vectors comprise instructions operable to compute the plurality of beamforming weight vectors so as to smooth the magnitude of signals resulting from application of the beamforming weight vectors at boundaries of the contiguous groups of subcarriers.

18. The apparatus of claim 9 , wherein the system parameters comprise a number of the plurality of antennas, spacing of the antennas, geometry of the antennas, a number of transmit sectors, and a center carrier frequency of the one or more broadcast signals.

19. The apparatus of claim 9 , wherein the controller is configured to compute the plurality of beamforming weight vectors by computing:

w

i

=

1

M

⁡

[

exp

⁡

(

jβ

i

,

1

)

exp

⁡

(

jβ

i

,

2

)

…

exp

⁡

(

jβ

i

,

M

)

]

T

where w i is the i th beamforming weight vector for i=1 to M, M is the number of antennas of the device, exp( ) is an exponential function, and β i,M are angles between zero and 2π.

20. The non-transitory computer readable media of claim 13 , wherein the instructions operable to compute comprise instructions operable to compute the plurality of beamforming weight vectors by computing:

w

i

=

1

M

⁡

[

exp

⁡

(

jβ

i

,

1

)

exp

⁡

(

jβ

i

,

2

)

…

exp

⁡

(

jβ

i

,

M

)

]

T

where w i is the i th beamforming weight vector for i=1 to M, M is the number of antennas of the device, exp( ) is an exponential function, and β i,M are angles between zero and 2 π.