Methods to transmit and receive for low dimensions MIMO systems
View Patent ↗Methods and apparatus are disclosed for applying successive multi-rank beamforming strategies (e.g., successive precoding strategies) for the design of precoders over a set of parallel channels. Successive beamforming is applied to a narrow band channel model and is also applied for finer quantization of a single beamforming vector (e.g., recursive beamforming). A first embodiment provides the optimal approach with high complexity. An alternative embodiment provides successive beamforming for near optimal precoding selection with medium complexity. A low complexity method for precoder selection is also provided wherein a channel representative matrix for the set of parallel channels is determined and successive beamforming on the calculated channel representative is applied.
1. A method of transmission implemented in a wireless communication system using precoding, comprising:
precoding data using a precoding matrix based on a codebook which has entries in the following form
A
(
v
1
,
v
2
,
v
3
,
…
)
=
[
v
1
,
HH
(
v
1
-
e
1
M
)
[
0
v
2
]
,
HH
(
v
1
-
e
1
M
)
[
0
HH
(
v
2
-
e
1
M
-
1
)
[
0
v
3
]
]
]
,
…
where a transmitter has M=2 antennas e 1 N =[1, 0, . . . , 0] T εC N (N=M, M−1, . . . ), C N being N-dimensional complex space, v a denotes a column vector, HH(v k −e 1 l ) is a rotation matrix that transforms vector v k to a unit vector e 1 l and v a is selected from a set V a where
V
1
=
1
2
{[1, 1] T , [1, −1] T , [1, j] T , [1, −j] T }, where j=√{square root over (−1)}, and V 2 ={e 1 l }.
2. The method of claim 1 , wherein
HH
(
w
)
=
{
I
-
2
ww
H
w
2
if
w
≠
0
I
if
w
=
0
is the house-holder transformation.
3. The method of claim 1 , wherein the precoding matrix is formed by picking one or more columns from the matrix A(v 1 , v 2 , v 3 , . . . ).
4. The method of claim 1 , wherein the precoding matrix is generated based on vector codebooks.
5. The method of claim 1 , wherein a transmission rank is determined by the transmitter.
6. The method of claim 1 , wherein a transmission rank is determined by a user equipment.
7. The method of claim 1 , wherein a scaled version of the precoding matrix is used.