Method for operating a digital mobile radio network with space-time block codes
View Patent ↗The invention relates to the preparation and numerical optimization of non-linear space-time block codes for application in a digital mobile radio system, with a maximum transmission diversity for “Rate 1,” transmission systems in the case of two or more transmitter antennae and with complex symbols.
1. A method for operating a digital mobile radio network with orthogonally structured space-time block transmission codes with maximum diversity n×m for a transmitting station having n transmitter antennas and a receiving station having m receiver antennas, where m and n are each an integer greater than or equal to 2, comprising:
transmitting a set of 2 l data bit vectors {right arrow over (b)}=(b 1 , b 2 , . . . b l )εB l with l bits b i ε{0,1} from the transmitting station, the data bit vectors {right arrow over (b)} being mapped by a one-to-one mapping
STM
:
B
l
→
U
(
n
)
b
⇀
→
C
(
b
⇀
)
onto a set of 2 l space-time code symbols C k , k=0, 2, . . . , 2 l −1, with each space-time code symbol C k corresponding to a unitary n×n matrix;
interpreting matrix elements c ijk , i=1, . . . n, of each of the 2 l space-time code symbols C k as space-time variables so that:
the matrix elements c ijk have corresponding signals transmitted by the n transmitter antennas, and
on transmission of one of the 2 l code symbols C k , a corresponding signal is transmitted for each of the matrix elements c ijk , the corresponding signal being transmitted from a transmitter antenna i of the n transmitter antennas, in a time interval j via a fading channel associated with the transmitter antenna i;
receiving signals transmitted in the time interval j corresponding to the matrix elements c ijk of the code symbol C k at each of the m receiver antennas of the receiving station within range of the transmitting station;
decoding a corresponding data bit vector {right arrow over (b)}εB l to be transmitted, by:
performing a reverse mapping
STM
-
1
:
U
(
n
)
→
B
l
C
(
b
→
)
→
b
→
due to an orthogonal structure of a transmission code formed by the space-time symbols C k , and
decoupling the signals transmitted by the n transmitter antennas and the corresponding matrix elements c ijk ; and
constructing the matrix elements c ijk of the space-time symbols C k as the elements of 2 l unitary n×n matrices according to the following specification:
C
k
=
(
C
11
k
c
1
n
k
⋯
c
n
1
k
c
nnk
)
=
V
(
exp
(
2
π
j
2
l
q
1
k
)
0
⋯
0
exp
2
π
j
2
l
q
1
k
)
V
-
1
where
V is any unitary complex n×n matrix,
c ijk are the generally complex matrix elements of the space-time symbol C k ,
j is an imaginary unit,
q i , where i=1, . . . , n, is any odd whole number, and
k=0, 1, . . . , 2 l −1.
2. The method according to claim 1 , wherein n is even and c ijk are real.
3. A method for operating a digital mobile radio network with orthogonally structured space-time block transmission codes with maximum diversity n×m for a transmitting station having n transmitter antennas and a receiving station having m receiver antennas, where m and n are each an integer greater than or equal to 2, comprising:
transmitting a set of 2 l data bit vectors b=(b 1 , b 2 , . . . b l )εB l with l bits b i ε{0,1} from the transmitting station, the data bit vectors b being mapped by a one-to-one mapping
STM
:
B
l
→
U
(
n
)
b
⇀
→
C
(
b
⇀
)
onto a set of 2 l space-time code symbols C k , k=0, 2, . . . , 2 l −1, with each space-time code symbol C k corresponding to a unitary n×n matrix;
interpreting matrix elements c ijk , i=1, . . . n, of each of the 2 l space-time code symbols C k as space-time variables so that:
the matrix elements c ijk have corresponding signals transmitted by the n transmitter antennas, and
on transmission of one of the 2 l code symbols C k , a corresponding signal is transmitted for each of the matrix elements c ijk , the corresponding signal being transmitted from a transmitter antenna i of the n transmitter antennas, in a time interval j via a fading channel associated with the transmitter antenna i;
receiving signals transmitted in the time interval j corresponding to the matrix elements c ijk of the code symbol C k at each of the m receiver antennas of the receiving station within range of the transmitting station;
decoding a corresponding data bit vector {right arrow over (b)}εB l to be transmitted, by:
performing a reverse mapping
SMT
-
1
:
U
(
n
)
→
B
l
C
(
b
→
)
→
b
→
due to an orthogonal structure of a transmission code formed by the space-time symbols C k , and
decoupling the signals transmitted by the n transmitter antennas and the corresponding matrix elements c ijk ; and
optimizing the matrix elements c ijk corresponding to the signals to be transmitted as elements of 2 l unitary n×n matrices C k , k=0, 2, . . . , 2 l −1, the matrix elements c ijk being optimized numerically according a specification comprising:
a) an initial set of 2 l unitary n×n initial matrices S k , k=0, 2, . . . , 2 l −1 are generated numerically at random,
b) the initial matrices S k , k=0, 2, . . . , 2 l −1 are parameterized so that each of the initial matrices has parameters,
c) a variable d ij :=d(S({right arrow over (β)} i ), S({right arrow over (β)} j ))=|det(S({right arrow over (β)} i )−S({right arrow over (β)} j ))| is selected as a measure of distance between two initial matrices S k , with {right arrow over (β)} i representing the parameters of the ith initial matrix,
d) a target functional
E
q
[
β
→
1
,
β
→
2
,
⋯
]
=
(
∑
i
<
j
2
l
[
d
(
S
(
β
→
i
)
,
S
(
β
→
j
)
)
]
)
1
q
is minimized by numerical variation of {right arrow over (β)} i , and
e) the n×n initial matrices, for which {right arrow over (β)} i was numerically varied to minimize the target functional, are selected as final n×n matrices, which correspond in each instance to a space-time symbol C k , the matrix elements of the final n×n matrices being selected as the matrix elements c ijk corresponding to the signals to be transmitted.
4. The method according to claim 3 , wherein
a) n=2,
b) every matrix of the initial set of 2′ unitary n×n initial matrices S k is parameterized as
S= 1β 0 +i (β 1 σ 1 +β 2 σ 2 +β 3 σ 3 )={right arrow over (β)}·σ
where
the following applies for σ l :
σ
1
(
0
1
1
0
)
,
σ
2
(
0
-
j
j
0
)
,
σ
3
(
1
0
0
-
1
)
,
j is the imaginary unit, and
the real parameters β are subject to the following restriction:
∑
i
=
0
3
β
i
2
=
1
,
d ij =√{square root over (1−{right arrow over (β)} i ·{square root over (β)} j )} c)
is selected as the measure of distance between two matrices A i , A j ,
d1) {right arrow over (β)} i are parameter vectors, which are parameterized as
β
→
i
=
(
sin
Φ
i3
sin
Φ
i2
sin
Φ
i
1
cos
Φ
i3
sin
Φ
i2
sin
Φ
i
1
cos
Φ
i2
sin
Φ
i
1
cos
Φ
i
1
)
,
d2) the gradients
∂
∂
Φ
kl
d
=
-
(
∂
∂
Φ
kl
β
→
k
)
·
∑
i
≠
k
β
→
i
d
ik
are minimized numerically for all n×n initial matrices by iteration, and
e) the n×n initial matrices corresponding to the gradients that were minimized are selected as final n×n matrices.
5. The method according to claim 3 , wherein
an L m interval of the ith initial matrix in respect of all others is defined as:
d
i
m
=
∑
j
det
(
S
j
-
S
i
)
m
=
∑
j
det
(
1
-
S
j
Å
S
i
)
m
∷
=
∑
j
det
(
1
-
A
ij
)
m
,
gradients
∇
→
δ
i
d
i
m
∷
=
g
→
i
=
n
∑
j
≠
i
d
ij
n
Re
Tr
(
A
ij
-
1
B
→
ij
)
are calculated, with {right arrow over (β)} ij =−jS j † S i {right arrow over (σ)} and σ i representing corresponding Hermitian standard spin matrices,
the ith initial matrix S i is varied by an infinitesimal (unitary) rotation
S i →S i exp( j{right arrow over (σ)}·{right arrow over (δ)} i )≈ S i +j{right arrow over (δ)} i ·S i {right arrow over (σ)}, and
the gradients
∇
→
δ
i
d
i
m
∷
=
g
→
i
=
n
∑
j
≠
i
d
ij
n
Re
Tr
(
A
ij
-
1
B
→
ij
)
are calculated by iterative calculation, until they are minimized.
6. The method according to claim 3 , wherein the initial matrices S k are calculated according to the following specification:
S
k
=
(
s
11
k
s
1
nk
⋯
s
n
1
k
s
nnk
)
=
V
(
exp
(
2
π
j
2
l
q
1
k
)
0
⋯
0
exp
2
π
j
2
l
q
1
k
)
V
-
1
where
V is any unitary complex n×n matrix,
J is the imaginary unit,
S ijk are the generally complex matrix elements of S k ,
q i , where i=1, . . . , n is any odd whole number, and
k=0, 1, . . . , 2 l −1.
7. The method according to claim 3 , wherein a finite group G with dimension n and order o(G)≧2 l is mapped onto unitary n×n matrices, which are used as initial matrices S k .
8. A method for operating a digital mobile radio network with orthogonally structured space-time block transmission codes with maximum diversity n×m for a transmitting station having n transmitter antennas and a receiving station having m receiver antennas, where m and n are each an integer greater than or equal to 2, comprising:
transmitting a set of 2 l data bit vectors b=(b 1 , b 2 , . . . b l )εB l with l bits b i ε{0,1} from the transmitting station, the data bit vectors b being mapped by a one-to-one mapping
STM
:
B
l
→
U
(
n
)
b
⇀
→
C
(
b
⇀
)
onto a set of 2 l space-time code symbols C k , k=0, 2, . . . , 2 l −1, with each space-time code symbol C k corresponding to a unitary n×n matrix;
interpreting matrix elements c ijk , i=1, . . . n, of each of the 2 l space-time code symbols C k as space-time variables so that:
the matrix elements c ijk have corresponding signals transmitted by the n transmitter antennas, and
on transmission of one of the 2 l code symbols C k , a corresponding signal is transmitted for each of the matrix elements c ijk , the corresponding signal being transmitted from a transmitter antenna i of the n transmitter antennas, in a time interval j via a fading channel associated with the transmitter antenna i;
receiving signals transmitted in the time interval j corresponding to the matrix elements c ijk of the code symbol C k at each of the m receiver antennas of the receiving station within range of the transmitting station;
decoding a corresponding data bit vector {right arrow over (b)}εB l to be transmitted, by:
performing a reverse mapping
SMT
-
1
:
U
(
n
)
→
B
l
C
(
b
→
)
→
b
→
due to an orthogonal structure of a transmission code formed by the space-time symbols C k , and
decoupling the signals transmitted by the n transmitter antennas and the corresponding matrix elements c ijk ; and
constructing the matrix elements c ijk of the space-time symbols C k as the elements of 2 l unitary n×n matrices according to the following specification:
a) a first hypersphere with a radius r is constructed numerically around any first code symbol C 1 of the code symbols C k . so that a quantity of all code symbols C k is determined, the first hypersphere following hypersphere properties comprising:
S r ={C′|det ( C′−C i )= r }, which results from calculating
r
=
det
(
C
-
C
′
)
=
det
(
1
-
C
1
Å
C
′
)
=
det
(
1
-
exp
(
j
σ
→
β
→
)
)
=
∏
i
=
1
n
(
1
-
exp
(
λ
i
)
)
,
where λ i are eigenvalues of j{right arrow over (σ)}{right arrow over (β)},
b) on the first hypersphere, a second code symbol C 2 of the code symbols C k is selected, around which a second hypersphere is constructed following the hypersphere properties, and
c) a further code symbol C 3 is produced at a point of intersection of the first and second hyperspheres around the code symbols C 1 , C 2 , and
d) further hyperspheres are iteratively constructed around the further code symbol following the hypershere properties around the further code symbol following the hypersphere properties, until a full set of 2 l code symbols C k is constructed and represented in each instance by a unitary n×n matrix.
9. A base station, comprising:
a storage unit, containing an association table, wherein
the association stores an association of individual bit vectors with space-time code symbols, and
the association table is in the form of a matrix that contains the matrix elements c ijk association of individual bit vectors with space-time symbols association matrix elements c ijk used in one of the methods according to any claims 1 - 8 .
10. A mobile station, comprising:
a storage unit, containing an association table, wherein
the association stores an association of individual bit vectors with space-time code symbols, and
the association table is in the form of a matrix that contains the matrix elements c ijk association of individual bit vectors with space-time symbols association matrix elements c ijk used in one of the methods according to any claims 1 - 8 .
11. A computer readable storage medium storing a program to control a processor to perform a method for operating a digital mobile radio network with orthogonally structured space-time block transmission codes with maximum diversity n×m for a transmitting station having n transmitter antennas and a receiving station having m receiver antennas, where m and n are each an integer greater than or equal to 2, comprising:
transmitting a set of 2 data bit vectors {right arrow over (b)}=(b 1 , b 2 , . . . b l ) E B l with l bits b i ε{0,1} from the transmitting station, the data bit vectors b being mapped by a one-to-one mapping
STM
:
B
l
→
U
(
n
)
b
⇀
→
C
(
b
⇀
)
onto a set of 2 l space-time code symbols C k , k=0, 2, . . . , 2 l −1, with each space-time code symbol C k corresponding to a unitary n×n matrix;
interpreting matrix elements c ijk , i=1, . . . n, of each of the 2 l space-time code symbols C k as space-time variables so that:
the matrix elements c ijk have corresponding signals transmitted by the n transmitter antennas, and
on transmission of one of the 2 l code symbols C k , a corresponding signal is transmitted for each of the matrix elements c ijk , the corresponding signal being transmitted from a transmitter antenna i of the n transmitter antennas, in a time interval j via a fading channel associated with the transmitter antenna i;
receiving signals transmitted in the time interval j corresponding to the matrix elements c ijk of the code symbol C k at each of the m receiver antennas of the receiving station within range of the transmitting station;
decoding a corresponding data bit vector {right arrow over (b)}εB l to be transmitted, by:
performing a reverse mapping
SMT
-
1
:
U
(
n
)
→
B
l
C
(
b
→
)
→
b
→
due to an orthogonal structure of a transmission code formed by the space-time symbols C k , and
decoupling the signals transmitted by the n transmitter antennas and the corresponding matrix elements c ijk ; and
constructing the matrix elements c ijk of the space-time symbols C k as the elements of 2 l unitary n×n matrices according to the following specification:
C
k
=
(
C
11
k
c
1
nk
⋯
c
n
1
k
c
nnk
)
=
V
(
exp
(
2
π
j
2
l
q
1
k
)
0
⋯
0
exp
2
πj
2
l
q
1
k
)
V
-
1
where
V is any unitary complex n×n matrix,
c ijk are the generally complex matrix elements of the space-time symbol C k ,
j is an imaginary unit,
q i , where i=1, . . . , n, is any odd whole number, and
k=0, 1, . . . , 2 l −1.