US 8,027,396 B2Granted

Apparatus and method for transmitting and receiving a signal in a multiple input multiple output mobile communication system

AssigneesSamsung Electronics Co., Ltd., Korea Advanced Institute of Science and Technology

InventorsYoung-Ho Jung, Myeon-Kyun Cho, Jin-Gon Joung, Yong-Hoon Lee

Life of this patent

Estimating the term…

Abstract

Disclosed is an apparatus and a method for signal transmission and reception according to a pre-processing scheme in a MIMO mobile communication system. The method includes: inputting a symbol; and pre-processing the input symbol according to a pre-processing matrix corresponding to pre-processing matrix information and transmitting the pre-processed symbol through a corresponding transmission antenna, wherein the pre-processing matrix is determined in accordance with a number of transmission antennas and a rate used in the MIMO mobile communication system.

Claims8

Dependent claims

A method for transmitting a signal by a signal transmission apparatus in a Multiple Input Multiple Output (MIMO) mobile communication system, the method comprising the steps of:

inputting a symbol;
and
pre-processing the input symbol according to a pre-processing matrix corresponding to pre-processing matrix information and transmitting the pre-processed symbol through a corresponding transmission antenna,
wherein the pre-processing matrix is determined in accordance with a number of transmission antennas and a rate used in the MIMO mobile communication system, and
wherein, when the rate is 2, the number of the transmission antennas is 4, and the pre-processing matrix information includes two bits, the pre-processing matrix corresponds to one from among pre-processing matrixes defined by,
W
k
=
{
[
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
k
=
32
]
[
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
k
=
34
]
[
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
k
=
35
]
[
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
k
=
31
]
}
,
⁢
W
k
=
{
[
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
k
=
32
]
[
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
k
=
34
]
[
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
k
=
35
]
[
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
k
=
33
]
}
,
⁢
and
W
k
=
{
[
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
k
=
32
]
[
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
k
=
34
]
[
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
k
=
35
]
[
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
k
=
36
]
}
,
wherein Wk indicates the pre-processing matrix, k indicates a pre-processing matrix index, each row of each pre-processing matrix Wk is mapped to a transmission antenna index, and each column thereof is mapped to an input index of a pre-processing unit performing the pre-processing, and
wherein, when the input symbol is defined by
S
i
=
[
x
l
-
x
m
*
x
m
x
l
*
x
n
-
x
o
*
x
o
x
n
*
]
,
a final transmission symbol transmitted through a corresponding transmission antenna corresponds to one from among transmission symbols defined by
W
k
⁢
S
i
=
{
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
32
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
34
]
,
[
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
35
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
x
m
+
x
n
x
l
*
-
x
o
*
0
0
0
0
k
=
31
]
}
,
⁢
W
k
⁢
S
i
=
{
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
32
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
34
]
,
[
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
35
]
,
[
0
0
x
l
+
x
0
-
x
m
*
+
x
n
*
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
33
]
}
,
⁢
and
⁢
⁢
W
k
⁢
S
i
=
{
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
32
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
34
]
,
[
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
35
]
,
[
0
0
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
x
m
+
x
n
x
l
*
-
x
o
*
k
=
36
]
}
,
wherein Si indicates the input symbol, l≠m≠n≠o,l,m,n,o ∈ {1,2,3,4}, each row of the input symbol Si is mapped to an input index of the pre-processing unit, and each column thereof is mapped to a symbol index or another sub-carrier of the same symbol, and
each row of the final transmission symbol WkSi is mapped to a transmission antenna index, and each column thereof is mapped to the symbol index or another sub-carrier of the same symbol.

757 more elements

A method for receiving a signal by a signal reception apparatus in a Multiple Input Multiple Output (MIMO) mobile communication system, the method comprising the steps of:

performing channel estimation for an incoming signal;
and
generating pre-processing matrix information that indicates information on a pre-processing matrix to be used by a signal transmission apparatus corresponding to the signal reception apparatus in accordance with a result of the channel estimation,
wherein the pre-processing matrix is determined in accordance with a number of transmission antennas and a rate used in the MIMO mobile communication system, and
wherein, when the rate is 2, the number of the transmission antennas is 4, and the pre-processing matrix information includes two bits, the pre-processing matrix corresponds to one from among pre-processing matrixes defined by
W
k
=
{
[
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
k
=
32
]
[
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
k
=
34
]
[
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
k
=
35
]
[
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
k
=
31
]
}
,
⁢
W
k
=
{
[
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
k
=
32
]
[
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
k
=
34
]
[
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
k
=
35
]
[
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
k
=
33
]
}
,
and
W
k
=
{
[
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
k
=
32
]
[
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
k
=
34
]
[
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
k
=
35
]
[
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
k
=
36
]
}
,
wherein Wk indicates the pre-processing matrix, k indicates a pre-processing matrix index, each row of each pre-processing matrix Wk is mapped to a transmission antenna index, and each column thereof is mapped to an input index of a pre-processing unit performing the pre-processing, and
wherein, when the input symbol is defined by
S
i
=
[
x
l
-
x
m
*
x
m
x
l
*
x
n
-
x
o
*
x
o
x
n
*
]
,
a final transmission symbol transmitted through a corresponding transmission antenna corresponds to one from among transmission symbols defined by
W
k
⁢
S
i
=
{
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
32
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
34
]
,
[
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
35
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
x
m
+
x
n
x
l
*
-
x
o
*
0
0
0
0
k
=
31
]
}
,
⁢
W
k
⁢
S
i
=
{
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
32
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
34
]
,
[
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
35
]
,
[
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
33
]
}
,
and
⁢
⁢
W
k
⁢
S
i
=
{
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
32
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
34
]
,
[
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
35
]
,
[
0
0
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
x
m
+
x
n
x
l
*
-
x
o
*
k
=
36
]
}
,
wherein Si indicates the input symbol, l≠m≠n≠o,l,m,n,o ∈ {1,2,3,4}, each row of the input symbol Si is ma sed to an input index of the pre-processing unit, and each column thereof is mapped to a symbol index or another sub-carrier of the same symbol, and
each row of the final transmission symbol WkSi is mapped to a transmission antenna index, and each column thereof is mapped to the symbol index or another sub-carrier of the same symbol.

755 more elements

A signal transmission apparatus of a Multiple Input Multiple Output (MIMO) mobile communication system, the signal transmission apparatus comprising:

transmission antennas;
and
a pre-processing unit for pre-processing an input symbol according to a pre-processing matrix corresponding to pre-processing matrix information and transmitting the pre-processed symbol through a corresponding transmission antenna,
wherein the pre-processing matrix is determined in accordance with a number of the transmission antennas and a rate used in the MIMO mobile communication system, and
wherein, when the rate is 2, the number of the transmission antennas is 4, and the pre-processing matrix information includes two bits, the pre-processing matrix corresponds to one from among pre-processing matrixes defined by
W
k
=
{
[
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
k
=
32
]
[
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
k
=
34
]
[
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
k
=
35
]
[
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
k
=
31
]
}
,
⁢
W
k
=
{
[
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
k
=
32
]
[
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
k
=
34
]
[
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
k
=
35
]
[
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
k
=
33
]
}
,
⁢
and
W
k
=
{
[
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
k
=
32
]
[
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
k
=
34
]
[
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
k
=
35
]
[
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
k
=
36
]
}
,
wherein Wk indicates the pre-processing matrix, k indicates a pre-processing matrix index, each row of each pre-processing matrix Wk is mapped to a transmission antenna index and each column thereof is mapped to an input index of a pre-processing unit performing the pre-processing, and
wherein, when the input symbol is defined by
S
i
=
[
x
l
-
x
m
*
x
m
x
l
*
x
n
-
x
o
*
x
o
x
n
*
]
,
a final transmission symbol transmitted through a corresponding transmission antenna corresponds to one from among transmission symbols defined by
W
k
⁢
S
i
=
{
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
32
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
34
]
,
[
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
35
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
x
m
+
x
n
x
l
*
-
x
o
*
0
0
0
0
k
=
31
]
}
,
⁢
W
k
⁢
S
i
=
{
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
32
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
34
]
,
[
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
35
]
,
[
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
33
]
}
,
⁢
and
⁢
⁢
W
k
⁢
S
i
=
{
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
32
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
34
]
,
[
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
35
]
,
[
0
0
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
x
m
+
x
n
x
l
*
-
x
o
*
k
=
36
]
}
,
wherein Si indicates the input symbol, l≠m≠n≠o,l,m,n,o ∈ {1,2,3,4}, each row of the input symbol Si is mapped to an input index of the pre-processing unit, and each column thereof is mapped to a symbol index or another sub-carrier of the same symbol, and
each row of the final transmission symbol WkSi is mapped to a transmission antenna index, and each column thereof is mapped to the symbol index or another sub-carrier of the same symbol.

757 more elements

A signal reception apparatus of a Multiple Input Multiple Output (MIMO) mobile communication system, the signal reception apparatus comprising:

a pre-processing information generator for generating pre-processing matrix information that indicates information on a pre-processing matrix to be used by a signal transmission apparatus corresponding to the signal reception apparatus in accordance with a result of channel estimation for an incoming signal,
wherein the pre-processing matrix is determined in accordance with a number of transmission antennas and a rate used in the MIMO mobile communication system, and
wherein, when the rate is 2, the number of the transmission antennas is 4, and the pre-processing matrix information includes two bits, the pre-processing matrix corresponds to one from among pre-processing matrixes defined by
W
k
=
{
[
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
k
=
32
]
⁡
[
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
k
=
34
]
⁡
[
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
k
=
35
]
⁡
[
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
k
=
31
]
}
,
⁢
W
k
=
{
[
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
k
=
32
]
⁡
[
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
k
=
34
]
⁡
[
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
k
=
35
]
⁡
[
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
k
=
33
]
}
,
⁢
and
W
k
=
{
[
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
k
=
32
]
⁡
[
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
k
=
34
]
⁡
[
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
k
=
35
]
⁡
[
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
k
=
36
]
}
,
wherein Wk indicates the pre-processing matrix, k indicates a pre-processing matrix index, each row of each pre-processing matrix Wk is mapped to a transmission antenna index and each column thereof is mapped to an input index of a pre-processing unit performing the pre-processing, and
wherein, when the input symbol is defined by
S
i
=
[
x
l
-
x
m
*
x
m
x
l
*
x
n
-
x
o
*
x
o
x
n
*
]
,
a final transmission symbol transmitted through a corresponding transmission antenna corresponds to one from among transmission symbols defined by
W
k
⁢
S
i
=
{
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
32
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
34
]
,
[
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
35
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
x
m
+
x
n
x
l
*
-
x
o
*
0
0
0
0
k
=
31
]
}
,
⁢
W
k
⁢
S
i
=
{
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
32
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
34
]
,
[
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
35
]
,
[
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
33
]
}
,
and
W
k
⁢
S
i
=
{
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
32
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
34
]
,
[
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
35
]
,
[
0
0
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
x
m
+
x
n
x
l
*
-
x
o
*
k
=
36
]
}
,
wherein Si indicates the input symbol, l≠m≠n≠o,l,m,n,o ∈ {1,2,3,4}, each row of the input symbol Si is mapped to an input index of the pre-processing unit, and each column thereof is mapped to a symbol index or another sub-carrier of the same symbol, and
each row of the final transmission symbol WkSi is mapped to a transmission antenna index, and each column thereof is mapped to the symbol index or another sub-carrier of the same symbol.

761 more elements

Dependencies are inferred from the claim text.

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Abstract

A method for transmitting a signal by a signal transmission apparatus in a Multiple Input Multiple Output (MIMO) mobile communication system, the method comprising the steps of:

inputting a symbol;
and
pre-processing the input symbol according to a pre-processing matrix corresponding to pre-processing matrix information and transmitting the pre-processed symbol through a corresponding transmission antenna,
wherein the pre-processing matrix is determined in accordance with a number of transmission antennas and a rate used in the MIMO mobile communication system, and
wherein, when the rate is 2, the number of the transmission antennas is 4, and the pre-processing matrix information includes two bits, the pre-processing matrix corresponds to one from among pre-processing matrixes defined by,
W
k
=
{
[
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
k
=
32
]
[
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
k
=
34
]
[
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
k
=
35
]
[
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
k
=
31
]
}
,
⁢
W
k
=
{
[
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
k
=
32
]
[
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
k
=
34
]
[
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
k
=
35
]
[
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
k
=
33
]
}
,
⁢
and
W
k
=
{
[
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
k
=
32
]
[
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
k
=
34
]
[
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
k
=
35
]
[
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
k
=
36
]
}
,
wherein Wk indicates the pre-processing matrix, k indicates a pre-processing matrix index, each row of each pre-processing matrix Wk is mapped to a transmission antenna index, and each column thereof is mapped to an input index of a pre-processing unit performing the pre-processing, and
wherein, when the input symbol is defined by
S
i
=
[
x
l
-
x
m
*
x
m
x
l
*
x
n
-
x
o
*
x
o
x
n
*
]
,
a final transmission symbol transmitted through a corresponding transmission antenna corresponds to one from among transmission symbols defined by
W
k
⁢
S
i
=
{
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
32
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
34
]
,
[
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
35
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
x
m
+
x
n
x
l
*
-
x
o
*
0
0
0
0
k
=
31
]
}
,
⁢
W
k
⁢
S
i
=
{
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
32
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
34
]
,
[
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
35
]
,
[
0
0
x
l
+
x
0
-
x
m
*
+
x
n
*
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
33
]
}
,
⁢
and
⁢
⁢
W
k
⁢
S
i
=
{
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
0
0
k
=
32
]
,
[
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
34
]
,
[
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
0
0
x
m
+
x
n
x
l
*
-
x
o
*
k
=
35
]
,
[
0
0
0
0
x
l
+
x
o
-
x
m
*
+
x
n
*
x
m
+
x
n
x
l
*
-
x
o
*
k
=
36
]
}
,
wherein Si indicates the input symbol, l≠m≠n≠o,l,m,n,o ∈ {1,2,3,4}, each row of the input symbol Si is mapped to an input index of the pre-processing unit, and each column thereof is mapped to a symbol index or another sub-carrier of the same symbol, and
each row of the final transmission symbol WkSi is mapped to a transmission antenna index, and each column thereof is mapped to the symbol index or another sub-carrier of the same symbol.

757 more elements