Method and circuit arrangement for symbol decision upon the reception of a signal including a quadrature signal pair
View Patent ↗The invention relates to a method and a circuit arrangement for deciding a symbol upon the reception of a signal including or coupled with a quadrature signal pair, wherein the decision is made by means of an analysis of the metric of at least one reception point to at least one nominal point in a complex coordinate space, and the metric is analyzed in the non-Cartesian or not exclusively Cartesian complex coordinate space. The decision is made after the analysis, and during the decision process, a second most probable nominal point and a reliability of the decision are determined.
1. A method for deciding a symbol of a signal which is coupled with a quadrature signal pair, comprising
performing, using a circuit arrangement, an analysis of a metric of at least one received point related to at least one nominal point in a complex coordinate space, said analysis including an analysis of the metric based on at least a radial component and an angular component in a non-Cartesian or not completely Cartesian complex coordinate space;
making, using the circuit arrangement, a decision based on the analysis; and
determining, using the circuit arrangement, a reliability of the decision based on at least the radial component and the angular component.
2. The method according to claim 1 , wherein the decision is analyzed in a polar coordinate space, and wherein the Euclidean distance between the received point and nominal points or the values of the angle and radius projections are used as the metric between the received point and at least one nominal point.
3. The method according to claim 1 , wherein the reliability is determined based on a smallest metric from the received point to each of first and second nominal points.
4. The method according to claim 3 , wherein each of the smallest metrics to the nominal points is determined for the received symbol.
5. The method according to claim 3 , wherein the second nominal point generates the second most probable symbol for the decision.
6. The method according to claim 1 , wherein the reliability Z is determined according to
Z
=
log
(
∑
A
∈
M
1
P
[
s
=
α
|
R
]
∑
A
∈
M
0
P
[
s
=
α
|
R
]
)
wherein the sum of the conditional probabilities P[s=A|R] that the symbol a was transmitted if the symbol R is received is formed over the set MI of all transmission symbols which represent a transmitted value “1”, and wherein a corresponding sum is formed over the set MO of all transmission symbols which represent “0”.
7. The method according to claim 1 , wherein the reliability Z is determined according to
Z
=
log
(
P
[
s
=
α
1
|
R
]
P
[
s
=
α
0
|
R
]
)
wherein P[s=al|R] is the probability of the most probable transmission symbol with the transmitted value 1 and P[s=a0|R] is the probability of the most probable transmission symbol with the transmitted value 0.
8. The method according to claim 1 , wherein the reliability Z is determined according to
Z =abs[transmission]( Al−A 2)/ NF =( A 2− Al )/ NF
wherein abs is an absolute value function, Al is the smallest metric for a most probable symbol position, A2 is a second smallest metric of a second most probable symbol position, and NF is a normalization factor.
9. The method according to claim 8 , wherein the normalization factor is formed with the second smallest metric, or the sum of the metrics, or a constant.
10. A circuit arrangement for deciding a symbol of a signal coupled with a quadrature signal pair, comprising
a coordinate converter configured to convert the signal from Cartesian coordinates into non-Cartesian coordinates and
a decision device for deciding a symbol on the basis of a distance analysis of a minimal metric, based on at least a radial component and an angular component, between a reception point and two next most probable nominal points thereof, and determining a reliability of the decision based on at least the radial component and the angular component.
11. The circuit arrangement according to claim 10 , wherein the reliability Z is determined according to
Z
=
log
(
∑
A
∈
M
1
P
[
s
=
α
|
R
]
∑
A
∈
M
0
P
[
s
=
α
|
R
]
)
wherein the sum of the conditional probabilities P[s=A|R] that the symbol a was transmitted if the symbol R is received is formed over the set MI of all transmission symbols which represent a transmitted value “1”, and wherein a corresponding sum is formed over the set MO of all transmission symbols which represent “0”.
12. The circuit arrangement according to claim 10 , wherein the reliability Z is determined according to
Z
=
log
(
P
[
s
=
α
1
|
R
]
P
[
s
=
α
0
|
R
]
)
wherein P[s=ptl|R] is the probability of the most probable transmission symbol with the transmitted value 1 and P[s=a0|R] is the probability of the most probable transmission symbol with the transmitted value 0.
13. The circuit arrangement according to claim 10 , wherein the reliability Z is determined according to
Z =abs[transmission]( Al−A 2)/ NF =( A 2− Al )/ NF
wherein abs is an absolute value function, Al is the smallest metric for a most probable symbol position, A2 is a second smallest metric of a second most probable symbol position, and NF is a normalization factor.
14. The circuit arrangement according to claim 13 , wherein the normalization factor is formed with the second smallest metric, or the sum of the smallest and second smallest metrics, or a constant.