Communication channel optimization systems and methods in multi-user communication systems
Systems and methods of optimizing communication channels in multi-user communication systems are provided. Coding weights are determined based on communication channel state information for communication channels between a transmitter and multiple receivers. The coding weights are applied to communication signals to be transmitted from the transmitter to the receivers. Each receiver decodes received signals using inverses of the coding weights. Embodiments of the invention support multi-user MIMO (Multiple Input Multiple Output) where each receiver has fewer antennas than the transmitter, and enhance system performance if the total number of antennas at all of the receivers exceeds the number of antennas at the transmitter.
1. A method of processing signals to be transmitted to receivers on a plurality of communication channels, comprising:
determining pre-coding signal weights based on channel state information associated with the plurality of communication channels to provide proportional power allocation to the signals; and
applying the pre-coding signal weights to the signals,
wherein the pre-coding signal weights are elements of a pre-coding matrix P,
wherein determining further comprises determining the pre-coding signal weights to enhance diagonal elements of a combined communication channel matrix C=HP, where H is a matrix of the channel state information; and
wherein
P
=
[
p
11
p
12
p
21
p
22
]
,
wherein
H
=
[
h
11
h
12
h
21
h
22
]
,
and wherein determining comprises selecting the pre-coding signal weights of P such that
p
11
∝
h
11
-
h
12
h
21
h
22
;
p
22
∝
h
22
-
h
12
h
21
h
11
;
p
12
=
-
h
12
p
22
h
11
;
and
p
21
=
-
h
21
p
11
h
22
.
2. A method of processing signals transmitted to receivers on a plurality of communication channels, comprising:
at a transmitter:
determining pre-coding signal weights based on channel state information associated with the plurality of communication channels to provide proportional power allocation to the signals;
applying the pre-coding signal weights to the signals; and
transmitting weighted signals to the receivers on the plurality of communication channels;
wherein the transmitter comprises four antennas comprising two sub-groups of antennas comprising two antennas each, each sub-group of two antennas respectively associated with two sub-groups of communication channels of the plurality of communication channels, each sub-group of communication channels comprising two communication channels; and
at each of the receivers:
receiving a subset of the weighted signals over one of the sub-groups of communication channels; and
decoding the subset of the weighted signals using inverses of the pre-coding signal weights based on the channel state information associated with the one of the sub-groups of communication channels;
wherein the pre-coding signal weights are elements of a pre-coding matrix P, and wherein determining further comprises determining the pre-coding signal weights to enhance diagonal elements of a combined communication channel matrix C=HP, where H is a matrix of the channel state information; and
wherein determining the pre-coding signal weights comprises selecting the pre-coding signal weights of P such that
C
=
HP
=
[
c
11
c
12
0
0
c
21
c
22
0
0
0
0
c
33
c
34
0
0
c
43
c
44
]
,
where a group of the first two rows of C is associated with a first of the two sub-groups of communication channels, a group of the third and fourth rows of C is associated with a second of the two sub-groups of communication channels, a group of the first two columns of C is associated with a first of the two sub-groups of two antennas, and a group of the third and fourth columns of C is associated with a second of the two sub-groups of two antennas.
3. A method of processing signals to be transmitted to receivers on a plurality of communication channels, comprising:
determining pre-coding signal weights based on channel state information associated with the plurality of communication channels to provide proportional power allocation to the signals; and
applying the pre-coding signal weights to the signals,
wherein the signals comprise respective groups of signals to be transmitted to the receivers, wherein determining the pre-coding signal weights further comprises determining the pre-coding signal weights to separate the respective groups of signals,
wherein the method is implemented at a transmitter in a multi-user MIMO (Multiple Input Multiple Output) communication system that provides respective N ×N sub-MIMO channels from the transmitter to the receivers, wherein each of the groups of signals comprises N signals, and
wherein determining the pre-coding signal weights further comprises determining elements of a pre-coding matrix P such that a combined communication channel matrix C =HP has a form of U N ×N sub-matrices, diagonal elements of which are respective diagonal elements of C, and elements of C outside the N ×N sub-matrices are forced to zero.
4. The method of claim 3 , wherein the transmitter has M=4 antennas, wherein U=2, N=2,
P
=
[
p
11
p
12
p
13
p
14
p
21
p
22
p
23
p
24
p
31
p
32
p
33
p
34
p
41
p
42
p
43
p
44
]
,
H
=
[
h
11
h
12
h
13
h
14
h
21
h
22
h
23
h
24
h
31
h
32
h
33
h
34
h
41
h
42
h
43
h
44
]
,
C
=
HP
=
[
c
11
c
12
0
0
c
21
c
22
0
0
0
0
c
33
c
34
0
0
c
43
c
44
]
,
wherein determining elements of P comprises:
selecting p 31 , p 41 , p 32 , and p 42 to force c 13 =c 14 =c 23 =c 24 =0;
selecting
{
p
11
=
va
11
*
p
21
=
va
12
*
p
12
=
va
21
*
p
22
=
va
22
*
,
where v is a power normalization factor and a ij are elements of A, where
A
=
[
h
11
h
12
h
21
h
22
]
-
1
Δ
[
h
13
h
14
h
23
h
24
]
[
h
44
-
h
34
-
h
43
h
33
]
[
h
31
h
32
h
41
h
42
]
and Δ=h 33 h 44 −h 34 h 43 ;
selecting p 13 , p 23 , p 14 , and p 24 to force c 31 =c 32 =c 41 =c 42 =0; and
selecting
{
p
33
=
va
11
*
p
43
=
va
12
*
p
34
=
va
21
*
p
44
=
va
22
*
,
where a ij are elements of A, where
A
=
[
h
33
h
34
h
43
h
44
]
-
1
Δ
[
h
31
h
32
h
41
h
42
]
[
h
22
-
h
12
-
h
21
h
11
]
[
h
13
h
14
h
14
h
24
]
,
and Δ=h 11 h 22 −h 12 h 21 .
5. A method, implemented in a MIMO (Multiple Input Multiple Output) communication system, of processing signals to be concurrently transmitted to receivers over a plurality of communication channels comprising:
determining channel state information for the plurality of communication channels;
determining a spatial coding matrix comprising a respective set of spatial coding weights for each of the receivers based on the channel state information;
applying the respective sets of spatial coding weights in the spatial coding matrix to the signals, wherein the signals comprise a plurality of groups of at least one signal to be transmitted to respective ones of the receivers; and
transmitting the signals to the receivers, wherein the spatial coding matrix F comprises elements [F (1) , F (2) , . . . F (U) ], U is an integer, and each element F (i) is the respective set of spatial coding weights for an i th one of the receivers and satisfies tr{F( (i) F (i)′ }=tr{F (i)′ F (i) }=P s , i=1,2, . . . , U, where tr{•} is a trace of a matrix, and P s is a total transmitted power of the signals;
wherein determining the spatial coding matrix comprises determining the elements F (i) of F as
F
(
i
)
=
P
s
G
^
(
i
)
′
tr
(
G
^
(
i
)
′
G
^
(
i
)
)
,
where
Ĝ (i) =Ĥ F (i)′ (Ĥ F Ĥ′ F +I N i ) −1 , i=1,2, . . . U, is a set of demodulation weights corresponding to F (i) ;
Ĥ F =[Ĥ F (1) , . . . Ĥ F (U) ];
Ĥ F (i) =(Ĥ (i) {circumflex over (F)} (i) )/√{square root over (2σ η, i 2 )} is a combined channel matrix of a virtual reverse MIMO channel from the ith receiver;
Ĥ (i)=[H (i) ]′ is a matrix of the channel state information of the virtual Reverse MIMO channel from the ith receiver;
H (i) is a matrix of the channel state information for forward MIMO channel of a plurality of channels to the ith receiver;
{square root over (F)} (i) is a spatial coding matrix of the virtual reverse MIMO channel from the ith receiver;
I N i is a unit matrix;
N i is a number of signals in the plurality of groups of at least one signal to be transmitted to the ith receiver; and
σ η, i 2 is a variance of a component of noise at the ith receiver.
6. The method of claim 5 , further comprising:
transmitting a respective set of demodulation weights Ĝ (i) to each of the receivers.
7. The method of claim 5 , wherein {circumflex over (F)} (i) = V (i) Φ (i) where
V (i) is a matrix constructed from columns of V (i) ;
V (i) is a unitary matrix resulting from a singular decomposition of the channel matrix H (i) of the forward MIMO channel to the ith receiver as {tilde over (H)} (i) =U (i) Λ (i) V (i) H , where U (i) and V (i) are unitary matrices, Λ (i) is a non-negative diagonal matrix, squares of diagonal elements of Λ (i) are equal to eigenvalues of an Ĥ (i) Ĥ (i)′ matrix, columns of U (i) are eigenvectors of the Ĥ (i) Ĥ (i)′ matrix, and columns of V (i) are also eigenvectors of the Ĥ (i) Ĥ (i)′ matrix; and
Φ (i) is a diagonal matrix having non-negative diagonal elements that determine channel power allocation and satisfy
tr
(
F
^
(
i
)
F
^
(
i
)
′
)
=
∑
k
=
1
K
ch
,
i
ϕ
k
,
k
(
i
)
2
=
P
s
,
where K ch,i is a number of spatial channels to the ith receiver.
8. The method of claim 7 , wherein the diagonal elements of Φ (i) are selected according to a criterion selected from a group consisting of:
a uniform power criterion, φ (i) k,k 2 =P s /K ch,i ;
an MMSE (Maximum Mean Squared Error) criterion,
ϕ
k
,
k
(
i
)
2
=
2
σ
η
,
i
2
[
μ
ξ
k
,
k
(
i
)
-
1
ξ
k
,
k
(
i
)
]
+
;
an MSER (Minimum Symbol-Error-Rate) criterion,
ϕ
k
,
k
(
i
)
2
=
2
σ
η
,
i
2
ξ
k
,
k
(
i
)
[
log
(
ξ
k
,
k
(
i
)
2
σ
η
,
i
2
)
-
μ
]
+
;
and
an MCIR (Maximum Capacity and Information Rate) criterion,
ϕ
k
,
k
(
i
)
2
=
(
μ
-
2
σ
η
,
i
2
ξ
k
,
k
(
i
)
)
+
,
where
(
•
)
+
=
max
(
•
,
0
)
=
1
2
(
•
+
•
)
;
ξ (i) k,k =Λ (i) k,k 2 are eigenvalues of the Ĥ (i) Ĥ (i)′ matrix, and Λ (i) k,k are diagonal elements of the Λ (i) matrix; and
μ is a factor selected to define the MMSE, MSER, and MCIR criteria.