Method and arrangement relating to telecommunications
View Patent ↗The present invention relates to a method and arrangement for providing a reliability information on information bits (bk) transmitted in a communications network, said bits constituting a transmitted vector (s) comprising elements selected by a transmitter from finite alphabet (S), wherein said transmitted vector is detected from an observed vector received symbols (y) providing a log-likelihood (L). Thus, the approximation is done by defining a number of bit terms having constant size and selecting a subset of bits and marginalizing over a selected part of said subset of bits.
1. A method for providing a reliability information on information bits (b k ) transmitted in a communications network, said bits constituting a transmitted vector (s) comprising elements selected by a transmitter from a finite alphabet (S), wherein said transmitted vector is detected from an observed vector of received symbols (y) providing a log-likelihood (L), the method comprising:
approximating said log-likelihood (L) by defining a number of bit terms having constant size and selecting a subset of bits and marginalizing over a selected part of said subset of bits, wherein said approximation comprises:
L
(
b
k
|
y
)
≈
log
(
∑
b
I
1
=
0
1
…
∑
b
I
k
-
1
=
0
1
∑
b
I
k
+
1
=
0
1
…
∑
b
I
r
=
0
1
(
max
b
I
r
+
1
,
…
,
b
I
n
t
m
μ
(
b
I
1
,
…
,
b
I
k
-
1
,
1
,
b
I
k
+
1
,
…
,
b
I
n
t
m
)
)
∑
b
I
1
=
0
1
…
∑
b
I
k
-
1
=
0
1
∑
b
I
k
+
1
=
0
1
…
∑
b
I
r
=
0
1
(
max
b
I
r
+
1
,
…
,
b
I
n
t
m
μ
(
b
I
1
,
…
,
b
I
k
-
1
,
0
,
b
I
k
+
1
,
…
,
b
I
n
t
m
)
)
)
For
k
≤
r
L
(
b
k
|
y
)
≈
log
(
∑
b
I
1
=
0
1
…
∑
b
I
r
=
0
1
(
max
b
I
r
+
1
,
…
,
b
I
k
-
1
,
b
I
k
+
1
,
…
,
b
I
n
t
m
μ
(
b
I
1
,
…
,
b
I
k
-
1
,
1
,
b
I
k
+
1
,
…
,
b
I
n
t
m
)
)
∑
b
I
1
=
0
1
…
∑
b
I
r
=
0
1
(
max
b
I
r
+
1
,
…
,
b
I
k
-
1
,
b
I
k
+
1
,
…
,
b
I
n
t
m
μ
(
b
I
1
,
…
,
b
I
b
I
k
+
1
,
…
,
b
I
n
t
m
)
)
)
For
k
>
r
,
where
μ
(
b
0
,
…
,
b
n
t
m
)
=
Δ
exp
(
-
1
N
0
y
-
Hs
(
b
0
,
…
,
b
n
t
m
)
2
)
wherein
each bit in said vector (s) is enumerated as {b k }
{
b
k
}
k
=
1
n
t
m
,
wherein n t is the number of transmit antennas and m the number of transmitted bits,
r is a fixed integer in an interval 0≦r≦n t m−1
I is an index permutation on [1, . . . , n t m] such that b 1 , b 2 , . . . , b n t m enumerate the bits in increasing order of reliability,
k is 1≦k≦n t m, and for a given k let k′ is a uniquely defined integer such that l k′ =k,
s(b 0 , . . . , b ntm ) is the vector s which corresponds to the bits {b 1 , . . . , b ntm },
H is a channel matrix of dimension n r ×n 1 , where n r number of receive and n t transmit antennas, and
N 0 is rower spectral density of noise.
2. The method of claim 1 , wherein a maximum of μ(b o , . . . , bn t m) is obtained using a linear receiver followed by clipping.
3. The method of claim 1 , wherein using a decision feed-back type receiver with optimal ordering.
4. The method of claim 2 , wherein said linear receiver uses one of a Zero Forcing (ZF) or Minimum Mean-Squared Error (MMSE).
5. The method of claim 1 , wherein said marginalizing is over r-bits considered as inferior bits.
6. The method of claim 1 , comprising a further approximation by replacing the maxima with a simple, constant complexity, estimate.
7. The method of claim 5 , wherein said estimate is obtained by one of a zero forcing receiver, or nulling and cancelling.
8. The method of claim 1 , wherein a bit ordering, I, is obtained by groping bits into symbols and choosing a symbol ordering, , according to a brute-force enumeration of all possible orderings:
*
=
arg
max
𝒥
cond
(
H
_
𝒥
)
,
H
_
𝒥
=
[
h
𝒥
r
/
m
+
1
,
…
,
h
𝒥
n
t
]
.
Eq
.
1
where cond(.) refers to a condition number of a matrix.
9. The method of claim 8 , wherein the bit ordering I is then obtained from by identifying to which symbol a particular bit is mapped.
10. The method of claim 8 , wherein is chosen by:
i. Letting =[ ] and c =[1, . . . , 2n t ];
ii. Computing γ=diag{( H T H ) −1 } wherein i is the index of the largest element of γ;
iii. Setting :=[ , i c ];
iv. Removing the ith column from H;
v. Removing the ith element of c ; and
vi. If H is empty, terminating otherwise repeating from step ii.
11. The method of claim 8 , wherein Eq. 1 is approximated where is the index vector obtained by sorting diag{( H T H ) −1 }.
12. The method of claim 1 , comprising penalty factors that correspond to a priori information on the bits that constitute s.
13. The method according to claim 1 , wherein said network comprises a number of transmit and receive antennas, being one of Multiple-Input, Multiple-Output (MIMO).
14. A communications network infrastructure arrangement comprising a computational device for providing a reliability information on transmitted information bits (b k ), said bits constituting a transmitted vector (s) comprising elements selected by a transmitter from a finite alphabet (S), wherein said transmitted vector is detected from an observed vector of received symbols (y) providing a log-likelihood (L),
wherein said device comprises a unit for detecting the transmitted vector from an observed vector of received symbols, (y), a processing unit for applying approximation by defining a number of bit terms having constant size, a selector means for selecting a subset of bits and calculation means for marginalizing over a selected part of the subset of the bits, wherein said approximation comprises:
L
(
b
k
|
y
)
≈
log
(
∑
b
I
1
=
0
1
…
∑
b
I
k
-
1
=
0
1
∑
b
I
k
+
1
=
0
1
…
∑
b
I
r
=
0
1
(
max
b
I
r
+
1
,
…
,
b
I
n
t
m
μ
(
b
I
1
,
…
,
b
I
k
-
1
,
1
,
b
I
k
+
1
,
…
,
b
I
n
t
m
)
)
∑
b
I
1
=
0
1
…
∑
b
I
k
-
1
=
0
1
∑
b
I
k
+
1
=
0
1
…
∑
b
I
r
=
0
1
(
max
b
I
r
+
1
,
…
,
b
I
n
t
m
μ
(
b
I
1
,
…
,
b
I
k
-
1
,
0
,
b
I
k
+
1
,
…
,
b
I
n
t
m
)
)
)
For
k
≤
r
L
(
b
k
|
y
)
≈
log
(
∑
b
I
1
=
0
1
…
∑
b
I
r
=
0
1
(
max
b
I
r
+
1
,
…
,
b
I
k
-
1
,
b
I
k
+
1
,
…
,
b
I
n
t
m
μ
(
b
I
1
,
…
,
b
I
k
-
1
,
1
,
b
I
k
+
1
,
…
,
b
I
n
t
m
)
)
∑
b
I
1
=
0
1
…
∑
b
I
r
=
0
1
(
max
b
I
r
+
1
,
…
,
b
I
k
-
1
,
b
I
k
+
1
,
…
,
b
I
n
t
m
μ
(
b
I
1
,
…
,
b
I
b
I
k
+
1
,
…
,
b
I
n
t
m
)
)
)
For
k
>
r
,
where
μ
(
b
0
,
…
,
b
n
t
m
)
=
Δ
exp
(
-
1
N
0
y
-
Hs
(
b
0
,
…
,
b
n
t
m
)
2
)
wherein
each bit in said vector (s) is enumerated as {b k }
{
b
k
}
k
=
1
n
t
m
,
wherein n t is the number of transmit antennas and m the number of transmitted bits,
r is a fixed integer in an interval 0≦r≦n t m−1
I is an index permutation on [1, . . . , n t m] such that b 1 , b 2 , . . . , b n t m enumerate the bits in increasing order of reliability,
k is 1≦k≦n t m, and for a given k let k′ is a uniquely defined integer such that l k′ =k,
s(b 0 , . . . , b ntm ) is the vector s which corresponds to the bits {b 1 , . . . , b ntm },
H is a channel matrix of dimension n r ×n t , where n r number of receive and n t transmit antennas, and
N 0 is power spectral density of noise.
15. The arrangement of claim 14 , further comprising a linear receiver followed by clipping.
16. The arrangement of claim 14 , further comprising a decision feed-back type receiver with optimal ordering.
17. The arrangement of claim 15 , wherein said linear receiver uses one of a Zero Forcing (ZF) or Minimum Mean-Squared Error (MMSE).
18. A communications device comprising a processing unit handling communication data and communication control information, a memory unit, an interface unit, a communication unit with a respective connecting interface and transmit receive antennas, an arrangement for providing a reliability information on transmitted information bits (b k ), which constitute a transmitted vector (s) detected from an observed vector of received symbols (y) providing a log-likelihood (L),
wherein said communication unit being operatively arranged to detect the transmitted vector from an observed vector of received symbols, (y), said processing unit being operatively arranged for applying approximation by defining a number of bit terms having constant size, a selector means for selecting a subset of bits and calculation means for marginalizing over a selected part of the subset of the bits, wherein said approximation comprises:
L
(
b
k
|
y
)
≈
log
(
∑
b
I
1
=
0
1
…
∑
b
I
k
-
1
=
0
1
∑
b
I
k
+
1
=
0
1
…
∑
b
I
r
=
0
1
(
max
b
I
r
+
1
,
…
,
b
I
n
t
m
μ
(
b
I
1
,
…
,
b
I
k
-
1
,
1
,
b
I
k
+
1
,
…
,
b
I
n
t
m
)
)
∑
b
I
1
=
0
1
…
∑
b
I
k
-
1
=
0
1
∑
b
I
k
+
1
=
0
1
…
∑
b
I
r
=
0
1
(
max
b
I
r
+
1
,
…
,
b
I
n
t
m
μ
(
b
I
1
,
…
,
b
I
k
-
1
,
0
,
b
I
k
+
1
,
…
,
b
I
n
t
m
)
)
)
For
k
≤
r
L
(
b
k
|
y
)
≈
log
(
∑
b
I
1
=
0
1
…
∑
b
I
r
=
0
1
(
max
b
I
r
+
1
,
…
,
b
I
k
-
1
,
b
I
k
+
1
,
…
,
b
I
n
t
m
μ
(
b
I
1
,
…
,
b
I
k
-
1
,
1
,
b
I
k
+
1
,
…
,
b
I
n
t
m
)
)
∑
b
I
1
=
0
1
…
∑
b
I
r
=
0
1
(
max
b
I
r
+
1
,
…
,
b
I
k
-
1
,
b
I
k
+
1
,
…
,
b
I
n
t
m
μ
(
b
I
1
,
…
,
b
I
b
I
k
+
1
,
…
,
b
I
n
t
m
)
)
)
For
k
>
r
,
where
μ
(
b
0
,
…
,
b
n
t
m
)
=
Δ
exp
(
-
1
N
0
y
-
Hs
(
b
0
,
…
,
b
n
t
m
)
2
)
wherein
each bit in said vector (s) is enumerated as {b k }
{
b
k
}
k
=
1
n
t
m
,
wherein n t is the number of transmit antennas and m the number of transmitted bits,
r is a fixed integer in an interval 0≦r≦n t m−1
I is an index permutation on [1, . . . , n t m] such that b 1 , b 2 , . . . , b n t m enumerate the bits in increasing order of reliability,
k is 1≦k≦n t m, and for a given k let k′ is a uniquely defined integer such that l k′ =k,
s(b 0 , . . . , b ntm ) is the vector s which corresponds to the bits {b 1 , . . . , b ntm },
H is a channel matrix of dimension n r ×n t , where n r number of receive and n t transmit antennas, and
N 0 is power spectral density of noise.
19. The communications device of claim 18 , further comprising a linear receiver followed by clipping.
20. The communications device of claim 18 , further comprising a decision feed-back type receiver with optimal ordering.
21. The communications device of claim 19 , wherein said linear receiver uses one of a Zero Forcing (ZF) or Minimum Mean-Squared Error (MMSE).