System and method for I-Q imbalance correction
Systems and methods are disclosed for compensating I-Q imbalance in a wireless receiver. The receiver may employ a quadrature downconverter configured to receive an RF signal input and output an in-phase component and a quadrature component at an IF, an IF rotation block configured to downconvert the in-phase and quadrature components to baseband and an I-Q correction block configured to compensate for an I-Q imbalance in the received signal, wherein the I-Q correction block is positioned downstream from the IF rotation block in the signal path. Performing the I-Q correction after conversion to baseband may allow the compensation calculations to operate at a reduced digital rate. Similarly, digitally adjusting the gain of the signal prior to I-Q compensation may reduce the number of bits that are manipulated during the compensation process. These features may represent significant efficiencies as compared to I-Q corrections performed at IF.
1. A digital wireless receiver for receiving a data signal, wherein the receiver has a signal path comprising a quadrature downconverter configured to receive a radio frequency (RF) signal corresponding to the data signal and output an in-phase component and a quadrature component at an intermediate frequency (IF), an IF rotation block configured to downconvert the in-phase component and quadrature component to baseband and an in-phase (I)-quadrature (Q) correction block configured to compensate for a modeled I-Q imbalance in the received signal, wherein the I-Q correction block is positioned downstream from the IF rotation block in the signal path;
wherein upconversion of the data signal to IF is modeled by a matrix A and wherein the IF rotation block is configured to perform an operation corresponding to multiplication by an inverse of matrix A, matrix A −1 ;
wherein the I-Q imbalance is modeled as a matrix B and wherein the I-Q correction block is configured to perform a matrix multiplication by A −1 B −1 A.
2. The receiver of claim 1 , wherein the receiver further comprises a digital variable gain element positioned upstream from the I-Q correction block in the signal path.
3. The receiver of claim 1 , wherein the receiver further comprises analog to digital converters operating at a sample rate to digitize the in-phase component and the quadrature component produced by the quadrature downconverter and a decimator configured to provide an internal rate lower than the sample rate, wherein the I-Q correction block is positioned downstream from the decimator in the signal path.
4. The receiver of claim 3 wherein the receiver further comprises a digital variable gain element positioned upstream from the I-Q correction block in the signal path.
5. The receiver of claim 3 , wherein the I-Q correction block operates at the internal rate.
6. The receiver of claim 1 , wherein
A
-
1
B
-
1
A
=
[
c
11
c
12
c
21
c
22
]
,
where
c
11
=
cos
2
(
2
π
f
IF
n
T
in
)
-
tan
(
θ
)
sin
(
2
π
f
IF
n
T
in
)
cos
(
2
π
f
IF
n
T
in
)
+
sin
2
(
2
π
f
IF
n
T
in
)
α
cos
(
θ
)
c
12
=
-
sin
(
2
π
f
IF
n
T
in
)
cos
(
2
π
f
IF
n
T
in
)
+
tan
(
θ
)
sin
2
(
2
π
f
IF
n
T
in
)
+
sin
(
2
π
f
IF
n
T
in
)
cos
(
2
π
f
IF
n
T
in
)
α
cos
(
θ
)
c
21
=
-
sin
(
2
π
f
IF
n
T
in
)
cos
(
2
π
f
IF
n
T
in
)
-
tan
(
θ
)
cos
2
(
2
π
f
IF
n
T
in
)
+
sin
(
2
π
f
IF
n
T
in
)
cos
(
2
π
f
IF
n
T
in
)
α
cos
(
θ
)
c
22
=
sin
2
(
2
π
f
IF
n
T
in
)
+
tan
(
θ
)
sin
(
2
π
f
IF
n
T
in
)
cos
(
2
π
f
IF
n
T
in
)
+
cos
2
(
2
π
f
IF
n
T
in
)
α
cos
(
θ
)
T in is an internal digital rate of the receiver and f IF is the IF.
7. The receiver of claim 6 , further comprising a look up table holding values for c 11 , c 12 , c 21 and c 22 .
8. The receiver of claim 7 , wherein the values for the look up table are determined during calibration.
9. A method for providing in-phase (I)-quadrature (Q) imbalance compensation for a received data signal, comprising:
mixing a received radio frequency (RF) signal corresponding to the data signal with a cosine output of a local oscillator to extract an in-phase component at intermediate frequency (IF) and a sine output of the local oscillator to extract a quadrature component at IF;
applying an IF rotation to the in-phase component and the quadrature component to downconvert the in-phase component and the quadrature component to baseband; and
applying a modeled I-Q imbalance compensation to the in-phase component and the quadrature component at baseband;
wherein upconversion of the data signal to IF is modeled by a matrix A and wherein applying the IF rotation to the in-phase component and the quadrature component corresponds to multiplication by an inverse of matrix A, matrix A −1 ;
wherein the I-Q imbalance is modeled as a matrix B and wherein applying the I-Q imbalance compensation to the in-phase component and the quadrature component at baseband corresponds to matrix multiplication by A −1 B −1 A.
10. The method of claim 9 , further comprising digitally adjusting the gain of the in-phase component and the quadrature component prior to applying the I-Q imbalance compensation.
11. The method of claim 9 , further comprising downsampling the sample rate of the in-phase component and the quadrature component at IF to an internal rate lower than the sample rate prior to applying the I-Q imbalance compensation.
12. The method of claim 11 further comprising digitally adjusting the gain of the in-phase component and the quadrature component prior to applying the I-Q imbalance compensation.
13. The method of claim 11 , wherein the I-Q imbalance compensation is applied at the internal rate.
14. The method of claim 9 , wherein
A
-
1
B
-
1
A
=
[
c
11
c
12
c
21
c
22
]
,
where
c
11
=
cos
2
(
2
π
f
IF
n
T
in
)
-
tan
(
θ
)
sin
(
2
π
f
IF
n
T
in
)
cos
(
2
π
f
IF
n
T
in
)
+
sin
2
(
2
π
f
IF
n
T
in
)
α
cos
(
θ
)
c
12
=
-
sin
(
2
π
f
IF
n
T
in
)
cos
(
2
π
f
IF
n
T
in
)
+
tan
(
θ
)
sin
2
(
2
π
f
IF
n
T
in
)
+
sin
(
2
π
f
IF
n
T
in
)
cos
(
2
π
f
IF
n
T
in
)
α
cos
(
θ
)
c
21
=
-
sin
(
2
π
f
IF
n
T
in
)
cos
(
2
π
f
IF
n
T
in
)
-
tan
(
θ
)
cos
2
(
2
π
f
IF
n
T
in
)
+
sin
(
2
π
f
IF
n
T
in
)
cos
(
2
π
f
IF
n
T
in
)
α
cos
(
θ
)
c
22
=
sin
2
(
2
π
f
IF
n
T
in
)
+
tan
(
θ
)
sin
(
2
π
f
IF
n
T
in
)
cos
(
2
π
f
IF
n
T
in
)
+
cos
2
(
2
π
f
IF
n
T
in
)
α
cos
(
θ
)
T in is an internal digital rate of the receiver and f IF is the IF.
15. The method of claim 14 , further comprising storing values for c 11 , c 12 , c 21 and c 22 in a look up table.
16. The method of claim 15 , further comprising determining the values for the look up table during calibration.
17. The receiver of claim 1 , wherein the I-Q correction block is configured to perform a correction having a term corresponding to IF rotation derived from upconversion of the data signal to IF.
18. The method of claim 9 , wherein the modeled I-Q imbalance compensation has a term corresponding to the IF rotation derived from upconversion of the data signal to IF.