Transmission apparatus, reception apparatus, transmission method, reception method, and method for generating multi-dimensional constellations
View Patent ↗The present invention relates to digital data communication and provides an efficient method for generating multi-dimensional constellations for digital data modulation with a high degree of modulation diversity, a method for transmitting and receiving data on the basis of such constellations, and a corresponding apparatus. This is achieved by considering only multi-dimensional rotation matrices with all elements on the diagonal having the same first absolute value and all other elements having the same second absolute value. In this manner, multi-dimensional rotation matrices can be generated having only a single independent parameter and a structure that is as regular as possible. The independent parameter can be configured in order to minimize the error probability for various constellation sizes.
1. A transmission apparatus for transmitting a block of data over a plurality of transmission channels, the transmission apparatus comprising:
a modulator operable to generate one of a plurality of rotated constellation points in accordance with the block of data to be transmitted, each of the plurality of rotated constellation points having N components;
a mapper operable to separate and map each of the N components of the generated rotated constellation point to a different one of a plurality of complex symbols; and
a transmitter operable to transmit each of the complex symbols at a different time and/or at a different frequency, wherein
the plurality of rotated constellation points are obtained by applying an orthogonal transformation to each of a plurality of initial constellation points having N components so as to increase a reception robustness under fading conditions,
N is a multiple of four,
the orthogonal transformation has one of (i) an N-by-N matrix representation with absolute values of all elements on a main diagonal equal to a first value, and with absolute values of all elements not on the main diagonal equal to a non-zero second value, and (ii) a matrix representation obtained by permuting rows and/or columns in an N-by-N matrix representation with absolute values of all elements on a main diagonal equal to a first value, and with absolute values of all elements not on the main diagonal equal to a non-zero second value, and
when each of the N-by-N matrix representations is denoted by R,
R
=
(
s
1
,
1
a
s
1
,
2
b
…
s
1
,
N
b
s
2
,
1
b
s
2
,
2
a
⋮
⋮
⋱
s
N
-
1
,
N
b
s
N
,
1
b
…
s
N
,
N
-
1
b
s
N
,
N
a
)
a and b denote real parameters,
each sign value s i,j satisfies
s i,j ε{−1,+1}, and
s i,i s i,j =−s j,i s j,j for all i≠j , and
the real parameters a and b satisfy
a 2 +( N− 1) b 2 =1.
2. A reception apparatus for receiving a block of data over a plurality of transmission channels, the reception apparatus comprising:
a receiver operable to receive a plurality of received complex symbols at a different time and/or at a different frequency, one of a plurality of rotated constellation points being generated in accordance with the block of data, each of the plurality of rotated constellation points having N components, each of the N components of the generated rotated constellation point being separated and mapped to a different one of a plurality of transmitted complex symbols, each of the plurality of the transmitted complex symbols being transmitted at a different time and/or at a different frequency, the plurality of the received complex signals being obtained by receiving the plurality of the transmitted complex signals; and
a demodulator operable to demodulate N components obtained from the plurality of received complex symbols based on a rotated constellation, wherein
the plurality of rotated constellation points are obtained by applying an orthogonal transformation to each of a plurality of initial constellation points having N components so as to increase a reception robustness under fading conditions,
N is a multiple of four, and
the orthogonal transformation has one of (i) an N-by-N matrix representation with absolute values of all elements on a main diagonal equal to a first value, and with absolute values of all elements not on the main diagonal equal to a non-zero second value, and (ii) a matrix representation obtained by permuting rows and/or columns in an N-by-N matrix representation with absolute values of all elements on a main diagonal equal to a first value, and with absolute values of all elements not on the main diagonal equal to a non-zero second value, and
when each of the N-by-N matrix representations is denoted by R,
R
=
(
s
1
,
1
a
s
1
,
2
b
…
s
1
,
N
b
s
2
,
1
b
s
2
,
2
a
⋮
⋮
⋱
s
N
-
1
,
N
b
s
N
,
1
b
…
s
N
,
N
-
1
b
s
N
,
N
a
)
a and b denote real parameters,
each sign value s i,j satisfies
s i,j ε{−1,+1}, and
s i,i s i,j =−s j,i s j,j for all i≠j , and
the real parameters a and b satisfy
a 2 +( N− 1) b 2 =1.
3. A transmission method for transmitting a block of data over a plurality of transmission channels, the transmission method comprising the steps of:
generating one of a plurality of rotated constellation points in accordance with the block of data to be transmitted, each of the plurality of rotated constellation points having N components;
separating and mapping each of the N components of the generated rotated constellation point to a different one of a plurality of complex symbols; and
transmitting each of the complex symbols at a different time and/or at a different frequency, wherein
the plurality of rotated constellation points are obtained by applying an orthogonal transformation to each of a plurality of initial constellation points having N components so as to increase a reception robustness under fading conditions,
N is a multiple of four, and
the orthogonal transformation has one of (i) an N-by-N matrix representation with absolute values of all elements on a main diagonal equal to a first value, and with absolute values of all elements not on the main diagonal equal to a non-zero second value, and (ii) a matrix representation obtained by permuting rows and/or columns in an N-by-N matrix representation with absolute values of all elements on a main diagonal equal to a first value, and with absolute values of all elements not on the main diagonal equal to a non-zero second value, and
when each of the N-by-N matrix representations is denoted by R,
R
=
(
s
1
,
1
a
s
1
,
2
b
…
s
1
,
N
b
s
2
,
1
b
s
2
,
2
a
⋮
⋮
⋱
s
N
-
1
,
N
b
s
N
,
1
b
…
s
N
,
N
-
1
b
s
N
,
N
a
)
a and b denote real parameters,
each sign value s i,j satisfies
s i,j ε{−1,+1}, and
s i,i s i,j =−s j,i s j,j for all i≠j , and
the real parameters a and b satisfy
a 2 +( N− 1) b 2 =1.
4. A reception method for receiving a block of data over a plurality of transmission channels, the reception method comprising the steps of:
receiving a plurality of received complex symbols at a different time and/or at a different frequency, one of a plurality of rotated constellation points being generated in accordance with the block of data, each of the plurality of rotated constellation points having N components, each of the N components of the generated rotated constellation point being separated and mapped to a different one of a plurality of transmitted complex symbols, each of the plurality of the transmitted complex symbols being transmitted at a different time and/or at a different frequency, the plurality of the received complex signals being obtained by receiving the plurality of the transmitted complex signals;
demodulating N components obtained from the plurality of received complex symbols based on a rotated constellation, wherein
the plurality of rotated constellation points are obtained by applying an orthogonal transformation to each of a plurality of initial constellation points having N components so as to increase a robustness under fading conditions,
N is a multiple of four, and
the orthogonal transformation has one of (i) an N-by-N matrix representation with absolute values of all elements on a main diagonal equal to a first value, and with absolute values of all elements not on the main diagonal equal to a non-zero second value, and (ii) a matrix representation obtained by permuting rows and/or columns in an N-by-N matrix representation with absolute values of all elements on a main diagonal equal to a first value, and with absolute values of all elements not on the main diagonal equal to a non-zero second value, and
when each of the N-by-N matrix representations is denoted by R,
R
=
(
s
1
,
1
a
s
1
,
2
b
…
s
1
,
N
b
s
2
,
1
b
s
2
,
2
a
⋮
⋮
⋱
s
N
-
1
,
N
b
s
N
,
1
b
…
s
N
,
N
-
1
b
s
N
,
N
a
)
a and b denote real parameters,
each sign value s i,j satisfies
s i,j ε{−1,+1}, and
s i,i s i,j =−s j,i s j,j for all i≠j , and
the real parameters a and b satisfy
a 2 +( N− 1) b 2 =1.
5. A generation method for generating an N-dimensional rotated constellation for a digital modulation scheme in a data communication system, the generation method comprising the steps of:
receiving a plurality of vectors of an N-dimensional vector space; and
obtaining constellation points of the N-dimensional rotated constellation by applying an orthogonal transformation to the plurality of vectors received, each of the constellation points having N components, each of the N components being separated and mapped to a different one of a plurality of complex symbols, each of the plurality of complex symbols being transmitted at a different time and/or at a different frequency, wherein
the orthogonal transformation is adapted for increasing a minimum number of different values in components of any two distinct N-dimensional rotated constellation points relative to a minimum number of different values in components of any two distinct vectors received, and
the orthogonal transformation has one of (i) an N-by-N matrix representation, N being a multiple of four, with absolute values of all elements on a main diagonal equal to a first value, and with absolute values of all elements not on the main diagonal equal to a non-zero second value, and (ii) a matrix representation obtained by permuting rows and/or columns in an N-by-N matrix representation with absolute values of all elements on a main diagonal equal to a first value, and with absolute values of all elements not on the main diagonal equal to a non-zero second value, and
when each of the N-by-N matrix representations is denoted by R,
R
=
(
s
1
,
1
a
s
1
,
2
b
…
s
1
,
N
b
s
2
,
1
b
s
2
,
2
a
⋮
⋮
⋱
s
N
-
1
,
N
b
s
N
,
1
b
…
s
N
,
N
-
1
b
s
N
,
N
a
)
a and b denote real parameters,
each sign value s i,j satisfies
s i,j ε{−1,+1}, and
s i,i s i,j =−s j,i s j,j for all i≠j , and
the real parameters a and b satisfy
a 2 +( N− 1) b 2 =1.