Method and system for generating candidate beamforming coefficients for transmission of data over a wireless medium
A method and system for generating a number of candidate beamforming vectors for transmission of data over a wireless medium, is provided. One implementation involves determining the number (N) of transmitter antennas; determining the number (n) of candidate beamforming vectors to be constructed as an algebraic function of N; providing a Fourier transform matrix W comprising (n+1) rows and (n+1) columns; selecting N rows from the Fourier transform matrix W; and generating an abridged matrix using the selected N rows, wherein each column of the abridged matrix is configured to be used as a candidate beamforming vector for transmission of a data signal, such that the abridged matrix comprises a N×n sub-matrix of the Fourier transform matrix W.
1. A method of generating a number of candidate beamforming vectors for transmission of data over a wireless medium in a wireless communication system, the method comprising:
determining the number (N) of transmitter antennas;
determining the number (n) of candidate beamforming vectors to be constructed as an algebraic function of N;
providing a Fourier transform matrix W comprising (n+1) rows and (n+1) columns;
selecting N rows from the Fourier transform matrix W; and
generating an abridged matrix for a codebook using the selected N rows, wherein each column of the abridged matrix is configured to be used as a candidate beamforming vector for transmission of a data signal, such that the abridged matrix comprises a N×n sub-matrix of the Fourier transform matrix W,
wherein determining the number (n) of candidate beamforming vectors to be constructed further includes determining n as n=2 [log 2 N]+2 , where [ ] is the floor operation that returns the largest integer that is no larger than the argument.
2. The method of claim 1 , wherein providing a Fourier transform matrix W comprising (n+1) rows and (n+1) columns includes determining the matrix W, wherein the (s, t) th element of matrix W is specified as [W] (s, t) =1/√(n+1)*q (s−1)(t−1) with q=e −j*2π/n+1 .
3. The method of claim 1 , wherein in selecting N rows from the Fourier transform matrix W, selected column indices in matrix W are { 1 , 2 , . . . , n} and the selected row indices in matrix W are {r 1 , r 2 , . . . , r N } where r={r 1 , r 2 , . . . , r k } is a set of integers such that:
r={t: 0≦ t<n ,trace(α t )=0},
k =( n− 1)/2, wherein N≦k,
with the trace function being defined as:
trace
(
α
)
=
∑
i
=
0
⌊
log
2
N
⌋
+
1
α
2
i
where α is a generator of a multiplicative group F(2 └log 2 N┘+2 ).
4. The method of claim 1 , wherein the Fourier transform matrix comprises a discrete Fourier transform (DFT) matrix.
5. The method of claim 1 , wherein transmission of a data signal comprises transmission of high definition video information.
6. The method of claim 1 , wherein the wireless communication system includes a wireless transmitter and a wireless receiver, the method further comprising:
the wireless transmitter and receiver cooperatively arriving at a final beamforming codebook including a predetermined set of said beamforming vectors comprising codewords for beamforming transmission of data over the wireless medium, by:
(a) maintaining an initial codebook at each of the transmitter and receiver;
(b) the transmitter transmitting a training sequence over a wireless communication channel using a specific codeword from the respective codebook;
(c) the receiver using the received training sequence to estimate the communication channel, the receiver further selecting the best codeword from its respective codebook which yields best performance under the estimated channel, and feeding back index of the selected best codeword to the transmitter;
(d) the transmitter using the index to look up its respective codebook for the best codeword;
(e) if the selected best codeword corresponds to the codeword used for transmission, indicative of convergence, then the transmitter using the best codeword to perform wireless beamforming transmission of data to the receiver, otherwise the transmitter and receiver cooperatively repeating steps (a)-(d).
7. The method of claim 1 , wherein the algebraic function comprises a floor operation.
8. The method of claim 1 , wherein the selecting of N rows is performed without numerical searching.
9. The method of claim 1 , wherein Nis less than (n+1)/2.
10. A system for generating a number of candidate beamforming vectors for transmission of data over a wireless medium, the system comprising:
a memory configured to store a plurality of candidate beamforming vectors; and
a processor for executing software configured for:
determining the number (n) of candidate beamforming vectors to be constructed as an algebraic function of a number of transmitter antennas N, wherein the algebraic function comprises a floor operation;
providing a Fourier transform matrix W comprising (n+1) rows and (n+1) columns;
selecting N rows from the Fourier transform matrix W; and
generating an abridged matrix using the selected N rows, wherein each column of the abridged matrix is configured to be used as a candidate beamforming vector for transmission of a data signal, such that the abridged matrix comprises a N×n sub-matrix of the Fourier transform matrix W.
11. The system of claim 10 , wherein the memory is contained within a wireless beamforming transceiver.
12. The system of claim 10 , wherein determining the number (n) of candidate beamforming vectors to be constructed further includes determining n as n=2 └log 2 N┘+2 −1, where └ ┘ is the floor operation that returns the largest integer that is no larger than the argument.
13. The system of claim 12 , wherein providing a Fourier transform matrix W comprising (n+1)rows and (n+1) columns includes determining the matrix W, wherein the (s,t) th element of matrix W is specified as
[
W
]
(
s
,
t
)
=
1
n
+
1
q
(
s
-
1
)
(
t
-
1
)
with
q
=
e
-
j
2
π
n
+
1
.
14. The system of claim 13 , wherein in selecting N rows from the Fourier transform matrix W, selected column indices in matrix W are {1,2, . . . , n} and the selected row indices in matrix W are {r 1 , r 2 , . . . , r N } where r={r 1 , r 2 , . . . , r k } is a set of integers such that:
r={t: 0≦ t<n ,trace(α t )=0},
k =( n− 1)/2, wherein N≦k,
with the trace function being defined as:
trace
(
α
)
=
∑
i
=
0
⌊
log
2
N
⌋
+
1
α
2
i
where α is a generator of a multiplicative group F(2 └log 2 N┘+2 ).
15. The system of claim 10 , wherein the Fourier transform matrix comprises a discrete Fourier transform (DFT) matrix.
16. The system of claim 10 , wherein transmission of a data signal comprises transmission of high definition video information.
17. A wireless communication system, comprising:
a wireless transmitter and a wireless receiver, configured for beamforming communication over a wireless medium;
the transmitter and the receiver each including a codebook in a memory therein, each codebook including a number of candidate beamforming vectors for transmission of data over a wireless medium;
wherein each codebook is generated by:
determining the number (N) of transmitter antennas;
determining the number (n) of candidate beamforming vectors to be constructed as an algebraic function of N, wherein the algebraic function comprises a floor operation;
providing a Fourier transform matrix W comprising (n+1) rows and (n+1) columns;
selecting N rows from the Fourier transform matrix W; and
generating an abridged matrix using the selected N rows, wherein each column of the abridged matrix is configured to be used as a candidate beamforming vector for transmission of a data signal, such that the abridged matrix comprises a N×n sub-matrix of the Fourier transform matrix W.
18. The system of claim 17 , wherein determining the number (n) of candidate beamforming vectors to be constructed further includes determining n as n=2 └log 2 N┘+2 −1, where └ ┘ is the floor operation that returns the largest integer that is no larger than the argument.
19. The system of claim 18 , wherein providing a Fourier transform matrix W comprising (n+1) rows and (n+1) columns includes determining the matrix W, wherein the (s,t) th element of matrix W is specified as
[
W
]
(
s
,
t
)
=
1
n
+
1
q
(
s
-
1
)
(
t
-
1
)
with
q
=
e
-
j
2
π
n
+
1
.
20. The system of claim 19 , wherein in selecting N rows from the Fourier transform matrix W, selected column indices in matrix W are {1,2, . . . , n} and the selected row indices in matrix W are {r 1 , r 2 , . . . , r N } where r={r 1 , r 2 , . . . , r k } is a set of integers such that:
r={t: 0≦ t<n ,trace(α t )=0},
k =( n− 1)/2, wherein N≦k,
with the trace function being defined as:
trace
(
α
)
=
∑
i
=
0
⌊
log
2
N
⌋
+
1
α
2
i
where α is a generator of a multiplicative group F(2 └log 2 N┘+2 ).
21. The system of claim 17 , wherein the Fourier transform matrix comprises a discrete Fourier transform (DFT) matrix.
22. The system of claim 17 , wherein transmission of a data signal comprises transmission of high definition video information.
23. A wireless communication system, comprising:
a wireless receiver, configured for receiving beamforming communication over a wireless medium;
the receiver each including a codebook in a memory therein, the codebook including a number of candidate beamforming vectors for transmission of data over a wireless medium;
wherein each codebook is generated by:
determining the number (N) of transmitter antennas;
determining the number (n) of candidate beamforming vectors to be constructed as an algebraic function of N, wherein the algebraic function comprises a floor operation;
providing a Fourier transform matrix W comprising (n+1) rows and (n+1) columns;
selecting N rows from the Fourier transform matrix W; and
generating an abridged matrix using the selected N rows, wherein each column of the abridged matrix is configured to be used as a candidate beamforming vector for transmission of a data signal, such that the abridged matrix comprises a N×n sub-matrix of the Fourier transform matrix W.