Coding for large antenna arrays in MIMO networks
View Patent ↗A method transmits a sequence of symbols in a multiple-input multiple-output (MIMO) network including a transmitter having a set of transmit antennas and a receiver having a set of receive antennas. The sequence of symbols is represented by a vector S=[S 1 S 2 S 3 S 4 ] T of individual symbols, where T is a transpose operator. The individual symbols are transmitted as a transmit matrix S = [ S 1 - S 2 * S 1 - S 2 * S 2 S 1 * S 2 S 1 * S 3 - S 4 * - S 3 S 4 * S 4 S 3 * - S 4 - S 3 * ] , where * is a complex conjugate, and wherein each column of the matrix S represents the symbols transmitted at each transmission interval, and subscripts index the set of transmit antennas.
1. A method for transmitting a sequence of symbols S n in a multiple-input multiple-output (MIMO) network including a transmitter having a set of transmit antennas and a receiver having a set of receive antennas, comprising the steps of:
representing the sequence of symbols by a vector S=[S 1 S 2 S 3 S 4 ] T of individual symbols, where T is a transpose operator; and
using a coder transmitting the individual symbols as a transmit matrix is
S
=
[
S
1
-
S
2
*
S
1
-
S
2
*
S
2
S
1
*
S
2
S
1
*
S
3
-
S
4
*
-
S
3
S
4
*
S
4
S
3
*
-
S
4
-
S
3
*
]
,
where * is a complex conjugate, and wherein each column of the matrix S represents the symbols transmitted, and subscripts index the set of transmit antennas,
wherein the receiver has a channel matrix
H
=
[
h
1
,
1
h
1
,
2
h
1
,
3
h
1
,
4
h
2
,
1
h
2
,
2
h
2
,
3
h
2
,
4
h
3
,
1
h
3
,
2
h
3
,
3
h
4
,
4
h
4
,
1
h
4
,
2
h
4
,
3
h
3
,
4
]
,
where elements h i,j are channel coefficients from the j th transmit antenna to the i th receive antenna, wherein a received signal r is
r
=
HS
+
n
=
[
h
1
,
1
h
1
,
2
h
1
,
3
h
1
,
4
h
2
,
1
h
2
,
2
h
2
,
3
h
2
,
4
h
3
,
1
h
3
,
2
h
3
,
3
h
3
,
4
h
4
,
1
h
4
,
2
h
4
,
3
h
4
,
4
]
[
S
1
-
S
2
*
S
1
-
S
2
*
S
2
S
1
*
S
2
S
1
*
S
3
-
S
4
*
-
S
3
S
4
*
S
4
S
3
*
-
S
4
-
S
3
*
]
+
n
,
where noise n is
n
=
[
n
1
,
1
n
1
,
2
n
1
,
3
n
1
,
4
n
2
,
1
n
2
,
2
n
2
,
3
n
2
,
4
n
3
,
1
n
3
,
2
n
3
,
3
n
3
,
4
n
4
,
1
n
4
,
2
n
4
,
3
n
4
,
4
]
.
further comprising:
setting a received signal
r
=
[
r
1
,
1
r
1
,
2
r
1
,
3
r
1
,
4
r
2
,
1
r
2
,
2
r
2
,
3
r
2
,
4
r
3
,
1
r
3
,
2
r
3
,
3
r
3
,
4
r
4
,
1
r
4
,
2
r
4
,
3
r
4
,
4
]
,
and the first symbol S 1 is
[
r
1
,
1
r
1
,
2
*
r
1
,
3
r
1
,
4
*
]
[
h
1
,
1
*
h
1
,
2
h
1
,
1
*
h
1
,
2
]
+
[
r
2
,
1
r
2
,
2
*
r
2
,
3
r
2
,
4
*
]
[
h
2
,
1
*
h
2
,
2
h
2
,
1
*
h
2
,
2
]
=
2
(
h
1
,
1
2
+
h
1
,
2
2
+
h
2
,
1
2
+
h
2
,
2
2
)
S
1
*
+
n
1
′
the second symbol S 2 is
[
r
1
,
1
r
1
,
2
*
r
1
,
3
r
1
,
4
*
]
[
h
1
,
2
*
-
h
1
,
1
h
1
,
2
*
-
h
1
,
1
]
+
[
r
2
,
1
r
2
,
2
*
r
2
,
3
r
2
,
4
*
]
[
h
2
,
2
*
-
h
2
,
1
h
2
,
2
*
-
h
2
,
1
]
=
2
(
h
1
,
1
2
+
h
1
,
2
2
+
h
2
,
1
2
+
h
2
,
2
2
)
S
2
+
n
2
′
the third symbol S 3 is
[
r
3
,
1
r
3
,
2
*
r
3
,
3
r
3
,
4
*
]
[
h
3
,
3
*
h
3
,
4
-
h
3
,
3
*
-
h
3
,
4
]
+
[
r
4
,
1
r
4
,
2
*
r
4
,
3
r
4
,
4
*
]
[
h
4
,
3
*
h
4
,
4
-
h
4
,
3
*
-
h
4
,
4
]
=
2
(
h
3
,
3
2
+
h
3
,
4
2
+
h
4
,
3
2
+
h
4
,
4
2
)
S
3
+
n
3
′
.
2. The method of claim 1 , wherein the columns are transmitted as a stream of symbols before any feedback from a receiver is expected.
3. The method of claim 1 , further comprising:
detecting and decoding after all columns of symbols have been received at a receiver.
4. The method of claim 1 , wherein the sequence of symbols is
S=[S 1 S 2 S 3 S 5 S 6 S 7 S 8 ], and the transmit matrix is
S
=
[
S
1
-
S
2
*
S
5
-
S
6
*
S
2
S
1
*
S
7
-
S
8
*
S
3
-
S
4
*
S
6
S
5
*
S
4
S
3
*
S
8
S
7
*
❘
S
1
-
S
2
*
S
5
-
S
6
*
S
2
S
1
*
-
S
7
S
8
*
-
S
3
S
4
*
S
6
S
5
*
-
S
4
-
S
3
*
-
S
8
-
S
7
*
]
,
and the received signal is
r
=
HS
+
n
=
[
h
1
,
1
h
1
,
2
h
1
,
3
h
1
,
4
h
2
,
1
h
2
,
2
h
2
,
3
h
2
,
4
h
3
,
1
h
3
,
2
h
3
,
3
h
3
,
4
h
4
,
1
h
4
,
2
h
4
,
3
h
4
,
4
]
[
S
1
-
S
2
*
S
5
-
S
6
*
S
2
S
1
*
S
7
-
S
8
*
S
3
-
S
4
*
S
6
S
5
*
S
4
S
3
*
S
8
S
7
*
❘
S
1
-
S
2
*
S
5
-
S
6
*
S
2
S
1
*
-
S
7
S
8
*
-
S
3
S
4
*
S
6
S
5
*
-
S
4
-
S
3
*
-
S
8
-
S
7
*
]
+
n
′
where noise is
n
=
[
n
1
,
1
n
1
,
2
n
1
,
3
n
1
,
4
n
1
,
5
n
1
,
6
n
1
,
7
n
1
,
8
n
2
,
1
n
2
,
2
n
2
,
3
n
2
,
4
n
2
,
5
n
2
,
6
n
2
,
7
n
2
,
8
n
3
,
1
n
3
,
2
n
3
,
3
n
3
,
4
n
3
,
5
n
3
,
6
n
3
,
7
n
3
,
8
n
4
,
1
n
4
,
2
n
4
,
3
n
4
,
4
n
4
,
5
n
4
,
6
n
4
,
7
n
4
,
8
]
.
5. The method of claim 1 , wherein each successive column is transmited at each transmission interval.
6. The method of claim 1 , wherein each successive column is transmitted on adjacent sub-carriers using space-frequency block coding.