System and method for performing blind IQ-imbalance estimation and compensation
An IQ-imbalance of a complex receiver can be corrected by compensating the in-phase signal component and the quadrature-phase signal component produced by the complex receiver for an IQ-imbalance estimated by analyzing the in-phase signal component and the quadrature-phase signal component. A carrier signal can be received at the complex receiver. An in-phase signal component and a quadrature-phase signal component can be generated from the carrier signal. The generated in-phase signal component and the generated quadrature-phase signal component can be analyzed to estimate an IQ-imbalance. Based on the estimated IQ-imbalance, the in-phase signal component and quadrature-phase signal component can be compensated to correct the IQ-imbalance.
1. A method for correcting an IQ-imbalance of a complex receiver, comprising:
receiving an incoming carrier signal at the complex receiver and generating an in-phase (I) signal component and a quadrature-phase (Q) signal component from the carrier signal;
estimating an IQ-imbalance by analyzing the generated I signal component and the generated Q signal component; and
compensating for the IQ-imbalance by applying a function of the estimated IQ-imbalance to the generated I signal component and the generated Q signal component to produce a corrected I signal component and a corrected Q signal component;
wherein the corrected I signal component (Î) is computed according to a formula
I
^
=
I
~
(
1
-
α
2
)
-
Q
~
ɛ
2
;
and
where the corrected Q signal component ({circumflex over (Q)}) is computed according to a formula
Q
^
=
Q
~
(
1
+
α
2
)
-
I
~
ɛ
2
;
and
where Ĩ is the uncorrected I signal component, {tilde over (Q)} is the uncorrected Q signal component, α is an estimated gain imbalance, and c is an estimated phase imbalance.
2. The method of claim 1 , wherein the gain of the compensated I signal component (Î) is adjusted by multiplying the compensated I signal component (Î) by
cos
ɛ
^
2
cos
ɛ
^
and the gain of the compensated Q signal component ({circumflex over (Q)}) is adjusted by multiplying the compensated Q signal component ({circumflex over (Q)}) by
cos
ɛ
^
2
cos
ɛ
^
,
where ε is an estimated phase imbalance.
3. The method of claim 1 , wherein the IQ-imbalance is estimated in one of the following: an analog domain or a digital domain.
4. The method of claim 1 , wherein the I signal component and the Q signal component are compensated to correct the IQ-imbalance in one of the following: a digital domain or an analog domain.
5. The method of claim 1 , wherein the complex receiver comprises one of a direct conversion receiver or a low IF conversion receiver.
6. The method of claim 1 , wherein the incoming analog carrier signal comprises one of an RF signal or an FM signal.
7. The method of claim 1 , wherein the estimated IQ-imbalance is continuously or periodically updated.
8. The method of claim 1 , wherein the IQ-imbalance is at least one of a gain imbalance or a phase imbalance.
9. The method of claim 1 , wherein:
the gain imbalance α is estimated according to a formula
α
=
E
⌊
I
~
2
-
Q
~
2
⌋
E
[
I
~
2
+
Q
~
2
]
;
and
where the phase imbalance ε is estimated according to a formula
ɛ
=
E
⌊
2
I
~
·
Q
~
⌋
E
[
I
~
2
+
Q
~
2
]
;
and
where Ĩ is the uncorrected I signal component, {tilde over (Q)} is the uncorrected Q signal component, and E is a mean value function.
10. The method of claim 9 , wherein the formula
α
=
E
⌊
I
~
2
-
Q
~
2
⌋
E
[
I
~
2
+
Q
~
2
]
;
and the formula
ɛ
0
=
E
⌊
2
I
~
·
Q
~
⌋
E
[
I
~
2
+
Q
~
2
]
are applied when the gain imbalance α is smaller than 2 decibels and the phase shift error ε is smaller than 6 degrees.
11. The method of claim 1 , wherein:
the gain imbalance α is estimated according to a formula
α
=
E
⌊
I
~
2
-
Q
~
2
⌋
E
[
I
~
2
+
Q
~
2
]
;
and
where the phase imbalance ε is estimated according to a formula ε=arcsin(ε 0 ); and
where
ɛ
0
=
E
⌊
2
I
~
·
Q
~
⌋
E
[
I
~
2
+
Q
~
2
]
;
and
where Ĩ is the uncorrected I signal component and {tilde over (Q)} is the uncorrected Q signal component, and E is a mean value function.
12. The method of claim 11 , wherein the formula
α
=
E
⌊
I
~
2
-
Q
~
2
⌋
E
[
I
~
2
+
Q
~
2
]
;
and the formula ε=arcsin(ε 0 ) are applied when the gain imbalance α is smaller than 2 decibels and the phase shift error ε is larger than 6 degrees.
13. The method of claim 1 , wherein:
the gain imbalance α is estimated according to a formula
α
=
2
1
-
1
-
α
0
2
α
0
;
and
where
α
0
=
E
⌊
I
~
2
-
Q
~
2
⌋
E
[
I
~
2
+
Q
~
2
]
;
and
where the phase imbalance ε is estimated according to a formula
ɛ
=
4
+
α
2
4
-
α
2
·
ɛ
0
;
and
where
ɛ
0
=
E
⌊
2
I
~
·
Q
~
⌋
E
[
I
~
2
+
Q
~
2
]
;
and
where Ĩ is the uncorrected I signal component and {tilde over (Q)} is the uncorrected Q signal component, and E is a mean value function.
14. The method of claim 13 , wherein the formula
α
=
2
1
-
1
-
α
0
2
α
0
and the formula
ɛ
0
=
E
⌊
2
I
~
·
Q
~
⌋
E
[
I
~
2
+
Q
~
2
]
are applied when the gain imbalance α is larger than 2 decibels and the phase shift error ε is smaller than 6 degrees.
15. The method of claim 1 , wherein:
the gain imbalance α is estimated according to a formula
α
=
2
1
-
1
-
α
0
2
α
0
;
and
where
α
0
=
E
⌊
I
~
2
-
Q
~
2
⌋
E
[
I
~
2
+
Q
~
2
]
;
and
where the phase imbalance ε is estimated according to a formula
ɛ
=
arcsin
(
4
+
α
0
2
4
-
α
0
2
·
ɛ
0
)
;
and
where
ɛ
0
=
E
⌊
2
I
~
·
Q
~
⌋
E
[
I
~
2
+
Q
~
2
]
;
and
where Ĩ is the uncorrected I signal component and {tilde over (Q)} is the uncorrected Q signal component, and E is a mean value function.
16. A method for correcting an IQ-imbalance of a complex receiver, comprising:
receiving an incoming carrier signal at the complex receiver and generating an in-phase (I) signal component and a quadrature-phase (Q) signal component from the carrier signal;
estimating an IQ-imbalance by analyzing the generated I signal component and the generated Q signal component; and
compensating for the IQ-imbalance by applying a function of the estimated IQ-imbalance to the generated I signal component and the generated Q signal component to produce a corrected I signal component and a corrected Q signal component;
wherein the corrected I signal component (Î) and the corrected Q signal component ({circumflex over (Q)}) are estimated according to a formula
(
I
^
Q
^
)
=
(
1
-
tan
ɛ
2
-
tan
ɛ
2
1
)
·
(
I
^
α
Q
^
α
)
;
and
where
I
^
α
=
1
1
+
α
2
·
I
~
;
and
where
Q
^
α
=
1
1
-
α
2
·
Q
~
;
and
where Ĩ is the uncorrected I signal component, {tilde over (Q)} is the uncorrected Q signal component, α is an estimated gain imbalance, and ε is an estimated phase imbalance.
17. The method of claim 16 , wherein:
the gain imbalance α is estimated according to a formula
α
=
E
⌊
I
~
2
-
Q
~
2
⌋
E
[
I
~
2
+
Q
~
2
]
;
and
where the phase imbalance ε is estimated according to a formula
ɛ
=
E
⌊
2
I
~
·
Q
~
⌋
E
[
I
~
2
+
Q
~
2
]
;
and
where Ĩ is the uncorrected I signal component, {tilde over (Q)} is the uncorrected Q signal component, and E is a mean value function.
18. The method of claim 16 , wherein:
the gain imbalance α is estimated according to a formula
α
=
E
⌊
I
~
2
-
Q
~
2
⌋
E
[
I
~
2
+
Q
~
2
]
;
and
where the phase imbalance ε is estimated according to a formula ε=arcsin(ε 0 ); and
where
ɛ
0
=
E
⌊
2
I
~
·
Q
~
⌋
E
[
I
~
2
+
Q
~
2
]
and
where Ĩ is the uncorrected I signal component and {tilde over (Q)} is the uncorrected Q signal component, and E is a mean value function.
19. The method of claim 16 , wherein:
the gain imbalance α is estimated according to a formula
α
=
2
1
-
1
-
α
0
2
α
0
;
and
where
α
0
=
E
⌊
I
~
2
-
Q
~
2
⌋
E
[
I
~
2
+
Q
~
2
]
;
and
where the phase imbalance ε is estimated according to a formula
ɛ
=
4
+
α
2
4
-
α
2
·
ɛ
0
;
and
where
ɛ
0
=
E
⌊
2
I
~
·
Q
~
⌋
E
[
I
~
2
+
Q
~
2
]
;
and
where Ĩ is the uncorrected I signal component and {tilde over (Q)} is the uncorrected Q signal component, and E is a mean value function.
20. The method of claim 16 , wherein:
the gain imbalance α is estimated according to a formula
α
=
2
1
-
1
-
α
0
2
α
0
;
and
where
α
0
=
E
⌊
I
~
2
-
Q
~
2
⌋
E
[
I
~
2
+
Q
~
2
]
;
and
where the phase imbalance ε is estimated according to a formula
ɛ
=
arcsin
(
4
+
α
0
2
4
-
α
0
2
·
ɛ
0
)
;
and
where
ɛ
0
=
E
⌊
2
I
~
·
Q
~
⌋
E
[
I
~
2
+
Q
~
2
]
;
and
where Ĩ is the uncorrected I signal component and {tilde over (Q)} is the uncorrected Q signal component, and E is a mean value function.