Quantized precoding over a set of parallel channels
View Patent ↗Methods and apparatus are disclosed for applying successive multi-rank beamforming strategies (e.g., successive preceding 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 preceding 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. An apparatus for use in precoding for data transmission over a set of parallel channels comprising:
means for determining a representative channel (H rep ) for the set of parallel channels;
means for selecting a transmission rank;
means for quantizing the representative channel using beamforming;
means for determining a precoding matrix based on the representative channel and the transmission rank; and
means for determining the representative channel for a sub-band of the set of parallel channels from a first tone, T 1 , to a second tone, T 2 , such that
H
rep
=
{
∑
i
=
T
1
T
2
H
i
*
H
i
}
1
/
2
.
2. The apparatus of claim 1 wherein the representative channel, an estimated transmitter beamforming unitary matrix (V), and a receiver beamforming unitary matrix (U) are related by the equation: H k =U k D k V k *, wherein:
H k =H rep for a k th channel in a sub-band of the set of parallel channels from a first tone, T 1 , to a second tone, T 2 ; and,
columns of V k =[v 1 v 2 . . . v Nk ] represent a plurality of eigen-vectors of the representative channel.
3. The apparatus of claim 1 comprising means for quantizing the representative channel using successive beamforming by:
quantizing a plurality of eigen-vectors of the representative channel by: quantizing a plurality of eigen-vectors of the representative channel by:
(a) quantizing a first eigen-vector;
(b) determining a rotation matrix φ({circumflex over (v)} 1 ) such that Φ( 1 ){circumflex over (v)} 1 =e 1 =[1; 0; 0; . . . ; 0];
(c) rotating the plurality of eigen-vectors by the rotation matrix to produce a new matrix; and,
(d) iteratively repeating (a)-(c) on the new matrix until all of the plurality of eigen-vectors of the representative channel are quantized.
4. The apparatus of claim 1 further comprising:
means for determining an effective rate.
5. The apparatus of claim 4 wherein the effective rate is determined using the formula
C
MRBF
=
∑
i
=
T
1
T
2
∑
p
=
1
k
log
(
1
+
SINR
p
(
i
)
)
,
wherein:
(i) SINR p is a signal-to-interference plus noise ratio of a p th stream of an i th user; and,
T 1 to T 2 are adjacent tones.
6. The apparatus of claim 1 further comprising means for quantizing the representative channel using recursive beamforming by:
(a) quantizing only a first eigen-vector v 1 using a structured codebook;
(b) determining a residual part of the first eigen-vector that lies in an orthogonal space defined by span{{circumflex over (v)} 1 ⊥ };
(c) normalizing the residual part of the first eigen-vector;
(d) determining a rotation matrix Φ({circumflex over (v)} 1 ) such that Φ({circumflex over (v)} 1 ) {circumflex over (v)} 1 =e 1 =[1; 0; 0; . . . ; 0];
(e) rotating the residual part of the first eigen-vector by the rotation matrix to produce a new matrix, wherein first elements of the new matrix are zero; and,
(d) iteratively repeating (a)-(e) on the new matrix until all of the plurality of eigen-vectors of the representative channel are quantized.
7. The apparatus of claim 1 further comprising:
means for encoding multiple codewords over multiple transmission streams using a pseudo-random scrambler and the determined precoding matrix.
8. The apparatus of claim 1 further comprising:
means for determining a channel quality index; and,
means for determining a precoding matrix based on the channel quality index.
9. The apparatus of claim 1 further comprising:
means for determining the precoding matrix using singular value decomposition.
10. The apparatus of claim 1 further comprising:
means for performing successive beamforming on the representative channel to determine the precoding matrix.
11. A non-transitory machine readable medium having program instructions stored thereon, the instructions capable of execution by a processor and defining the steps of:
determining a representative channel (H rep ) for the set of parallel channels;
selecting a transmission rank;
quantizing the representative channel using beamforming;
determining a precoding matrix based on the representative channel and the transmission rank; and
determining the representative channel for a sub-band of the set of parallel channels from a first tone, T 1 , to a second tone, T 2 , such that
H
rep
=
{
∑
i
-
T
1
T
2
H
i
*
H
i
}
1
/
2
.
12. The non-transitory machine readable medium of claim 11 wherein the representative channel, an estimated transmitter beamforming unitary matrix (V), and a receiver beamforming unitary matrix (U) are related by the equation: H k =U k D k V k *, wherein:
H k =H rep for a k th channel in a sub-band of the set of parallel channels from a first tone, T 1 , to a second tone, T 2 ; and,
columns of V k =[v 1 v 2 . . . v Nk ] represent a plurality of eigen-vectors of the representative channel.
13. The non-transitory machine readable medium of claim 11 wherein execution of the instructions quantizes the representative channel using successive beamforming by:
quantizing a plurality of eigen-vectors of the representative channel by:
(a) quantizing a first eigen-vector;
(b) determining a rotation matrix Φ({circumflex over (v)} 1 ) such that Φ( 1 ) {circumflex over (v)} 1 =e 1 =[1; 0; 0; . . . ; 0];
(c) rotating the plurality of eigen-vectors by the rotation matrix to produce a new matrix; and,
(d) iteratively repeating (a)-(c) on the new matrix until all of the plurality of eigen-vectors of the representative channel are quantized.
14. The non-transitory machine readable medium of claim 11 wherein further execution of the instructions:
determines an effective rate.
15. The non-transitory machine readable medium of claim 11 wherein execution of the instructions determines the effective rate using the formula
C
MRBF
=
∑
i
=
T
1
T
2
∑
p
=
1
k
log
(
1
+
SINR
p
(
i
)
)
,
wherein:
(i) SINR p is a signal-to-interference plus noise ratio of a p th stream of an i th user; and,
T 1 to T 2 are adjacent tones.
16. The non-transitory machine readable medium of claim 15 wherein the demodulator is a linear minimum mean square error LMMSE demodulator.
17. The non-transitory machine readable medium of claim 15 wherein the demodulator is a minimum mean square error—successive interference cancellation MMSE-SIC demodulator.
18. The non-transitory machine readable medium of claim 15 wherein the demodulator is a QR-maximum likelihood detection QR-MLD demodulator.
19. The non-transitory machine readable medium of claim 11 wherein execution of the instructions further comprises:
quantizing the representative channel using recursive beamforming by quantizing a plurality of eigen-vectors of the representative channel by quantizing a plurality of eigen-vectors of the representative channel by:
(a) quantizing only a first eigen-vector v 1 using a structured codebook;
(b) determining a residual part of the first eigen-vector that lies in an orthogonal space defined by span{{circumflex over (v)} 1 195 };
(c) normalizing the residual part of the first eigen-vector;
(d) determining a rotation matrix Φ({circumflex over (v)} 1 ) such that Φ({circumflex over (v)} 1 ) {circumflex over (v)} 1 =e 1 =[1; 0; 0; . . . ; 0];
(e) rotating the residual part of the first eigen-vector by the rotation matrix to produce a new matrix, wherein first elements of the new matrix are zero; and,
(d) iteratively repeating (a)-(e) on the new matrix until all of the plurality of eigen-vectors of the representative channel are quantized.
20. The non-transitory machine readable medium of claim 11 wherein execution of the instructions further comprises:
encoding, using the determined precoding matrix, multiple codewords over multiple transmission streams using a pseudo-random scrambler.
21. The non-transitory machine readable medium of claim 11 wherein further execution of the instructions:
determines a channel quality index; and,
determines a precoding matrix based on the channel quality index.
22. The non-transitory machine readable medium of claim 11 wherein further execution of the instructions:
determines the precoding matrix using singular value decomposition.
23. The non-transitory machine readable medium of claim 11 wherein further execution of the instructions:
successively beamforms the representative channel to determine the precoding matrix.