Method and apparatus for I/Q mismatch calibration of transmitter
A method for I/Q mismatch calibration of a transmitter. First, a discrete-time signal is generated. Next, a corrected signal based on the discrete-time signal and a set of correction parameters A p and B p is obtained. Next, the corrected signal is converted to an analog corrected signal. Next, I/Q modulation is applied to the analog corrected signal and outputs a modulated signal. Next, a first, second, and third desired component measures and a first, second, and third image component measures with the first, second and third sets of the correction parameters A p and B p are respectively obtained from the modulated signal. Next, a fourth and fifth set of correction parameters A p and B p are obtained based on the first, the second, and the third desired component measures as well as the first, the second, and the third image component measures. Next, a fourth desired component measure and a fourth image component measure with the fourth set of correction parameters A p and B p and a fifth desired component measure and a fifth image component measure with the fifth set of correction parameters A p and B p are obtained from the modulated signal. Finally, a final set of the correction parameters A p and B p are selected from the fourth and fifth sets of correction parameters.
1. A method for in-phase and quadrature mismatch calibration of a transmitter, comprising the following steps:
generating a discrete-time signal x[n]=x(n·T s ), wherein x(t)=e j2πf T t and f T and T s are real numbers;
obtaining a corrected signal x c [n] based on the signal x[n] and a set of correction parameters A p and B p , wherein
x c [n]=A p ·x[n]+B p ·x*[n];
converting the corrected signal x c [n] to an analog corrected signal x c (t);
applying in-phase and quadrature modulation to the analog corrected signal x c (t) and outputting a modulated signal x m (t);
obtaining a first desired component measure W (1) (f T ) and a first image component measure W (1) (−f T ) from the modulated signal x m (t) with a first set of the correction parameters A p and B p ;
obtaining a second desired component measure W (2) (f T ) and a second image component measure W (2) (−f T ) from the modulated signal x m (t) with a second set of the correction parameters A p and B p ;
obtaining a third desired component measure W (3) (f T ) and a third image component measure W (3) (−f T ) from the modulated signal x m (t) with a third set of the correction parameters A p and B p ;
obtaining a fourth and fifth set of correction parameters A p and B p based on the first, the second, and the third desired component measures as well as the first, the second, and the third image component measures;
obtaining a fourth desired component measure W (4) (f T ) and a fourth image component measure W (4) (−f T ) from the modulated signal x m (t) with the fourth set of correction parameters A p and B p ;
obtaining a fifth desired component measure W (5) (f T ) and a fifth image component measure W (5) (−f T ) from the modulated signal x m (t) with the fifth set of correction parameters A p and B p ; and
obtaining a final set of the correction parameters A p and B p from the fourth and fifth sets of correction parameters.
2. The method for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 1 , wherein the first set of correction parameters (A p , B p )=(a,0), the second set of correction parameters (A p ,B p )=(b,b), and the third set of correction parameters (A p ,B p )=(b,−b), where a and b are real numbers.
3. The method for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 2 , wherein the parameter a is 1 and the parameter b is ½.
4. The method for mismatch calibration of a transmitter as claimed in claim 1 , wherein the fourth set of correction parameters (A p ,B p ) are obtained by
A p =√{square root over (P)}−j{circumflex over (α)}√{square root over (Q)}
B p =−{circumflex over (α)}√{square root over (P)}−j√{square root over (Q)}
and the fifth set of correction parameters (A p ,B p ) are obtained by
A p =√{square root over (P)}+j{circumflex over (α)}√{square root over (Q)}
B p =−{circumflex over (α)}√{square root over (P)}+j√{square root over (Q)}
where
α
≈
α
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=
N
O
-
1
N
O
+
1
,
N
=
(
W
(
2
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(
f
T
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+
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(
2
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(
-
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3
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3
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=
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1
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f
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W
(
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.
5. The method for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 1 , wherein the final set of correction parameters (A p ,B p ) is set to be the fourth set of correction parameters if a function of W (4) (−f T ) is less than the function of W (5) (−f T ), otherwise the final set of correction parameters (A p ,B p ) is set to be the fifth set of correction parameters.
6. The method for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 5 , wherein the final set of correction parameters (A p ,B p ) is set to be the fourth set of correction parameters if a value of W (4) (−f T ) is less than a value of W (5) (−f T ), otherwise the final set of correction parameters (A p ,B p ) is set to be the fifth set of correction parameters.
7. The method for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 1 , wherein the final set of correction parameters (A p ,B p ) is set to be the fourth set of correction parameters if a function of W (4) (f T ) is greater than the function of W (5) (f T ), otherwise the final set of correction parameters (A p ,B p ) is set to be the fifth set of correction parameters.
8. The method for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 7 , wherein the final set of correction parameters (A p ,B p ) is set to be the fourth set of correction parameters if a value of W (4) (f T ) is greater than W (5) (f T ), otherwise the final set of correction parameters (A p ,B p ) is set to be the fifth set of correction parameters.
9. The method for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 1 , wherein the final set of correction parameters (A p ,B p ) is set to be the fourth set of correction parameters if a function of W (4) (−f T ) and W (4) (f T ) is less than the function of W (5) (−f T ) and W (5) (f T ), otherwise the final set of correction parameters (A p ,B p ) is set to be the fifth set of correction parameters.
10. The method for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 9 , wherein the final set of correction parameters (A p ,B p ) is set to be the fourth set of correction parameters if W (4) (−f T )/W (4) (f T ) is less than W (5) (−f T )/W (5) (f T ), otherwise the final set of correction parameters (A p ,B p ) is set to be the fifth set of correction parameters.
11. The method for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 1 , further comprising the following steps:
further adding an DC compensation parameter γ p while obtaining the corrected signal x c [n] such that
x c [n]=A p ·( x[n]+γ p )+ B p ·( x[n]+γ p )*;
obtaining a first local leakage component measure L 1 from the modulated signal x m (t) with the final set of parameters A p and B p , and the parameter γ p =ζ 1 , where ζ 1 is a real number;
obtaining a second local leakage component measure L 2 from the modulated signal x m (t) with the final set of parameters A p and B p , and the parameter γ p =ζ 2 , where ζ 2 is a real number;
obtaining a third local leakage component measure L 3 from the modulated signal x m (t) with the final set of parameters A p and B p , and the parameter γ p =jζ 1 ;
obtaining a fourth local leakage component measure L 4 from the modulated signal x m (t) with the final set of parameters A p and B p , and the parameter γ p =jζ 2 ;
obtaining a fifth local leakage component measure L 5 from the modulated signal x m (t) with the final set of parameters A p and B p , and the parameter γ p =0; and
obtaining a final DC compensation parameter γ p,final based on the first local leakage component measure L 1 , the second local leakage component measure L 2 , the third local leakage component measure L 3 , the fourth local leakage component measure L 4 and the fifth local leakage component measure L 5 .
12. The method for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 11 , wherein the final DC compensation parameter γ p,final is obtained by
γ
p
,
final
=
-
1
2
·
ζ
2
2
(
L
1
-
L
5
)
-
ζ
1
2
(
L
2
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L
5
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ζ
1
(
L
2
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L
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-
ζ
2
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L
1
-
L
5
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j
1
2
·
ζ
2
2
(
L
3
-
L
5
)
-
ζ
1
2
(
L
4
-
L
5
)
ζ
1
(
L
4
-
L
5
)
-
ζ
2
(
L
3
-
L
5
)
.
13. An apparatus for in-phase and quadrature mismatch calibration of a transmitter, comprising:
a signal generator for generating a discrete-time signal x[n]=x(n·T s ), wherein x(t)=e j2πf T t and f ▭ and T s are real numbers;
a correction module for receiving the discrete-time signal x[n] and obtaining a corrected signal x c [n] based on the test signal x[n] and a set of correction parameters A p and B p , wherein
x c [n]=A p ·x[n]+B p ·x*[n];
a first and second D/A converter converting the corrected signal x c [n] to an analog signal x c (t), wherein the first D/A converter converts the real part of the corrected signal to a real part of the analog signal, and the second D/A converter converts the imaginary part of the corrected signal to an imaginary part of the analog signal;
a modulator applying in-phase and quadrature modulation to the analog signal x c (t), and outputting a modulated signal x m (t);
a measurer configured to:
obtain a first desired component measure W (1) (f T ) and a first image component measure W (1) (−f T ) from the modulated signal x m (t) with a first set of the correction parameters A p and B p ;
obtain a second desired component measure W (2) (f T ) and a second image component measure W (2) (−f T ) from the modulated signal x m (t) with a second set of the correction parameters A p and B p ;
obtain a third desired component measure W (3) (f T ) and a third image component measure W (3) (−f T ) from the modulated signal x m (t) with a third set of the correction parameters A p and B p ;
obtain a fourth desired component measure W (4) (f T ) and a fourth image component measure W (4) (−f T ) from the modulated signal x m (t) with a fourth set of correction parameters A p and B p ; and
obtain a fifth desired component measure W (5) (f T ) and a fifth image component measure W (5) (−f T ) from the modulated signal x m (t) with a fifth set of correction parameters A p and B p ; and
a processor configured to:
obtain the fourth and fifth sets of correction parameters A p and B p based on the first, the second, and the third desired component measures as well as the first, the second, and the third image component measures; and
choose a final set of correction parameters A p and B p from the fourth and fifth sets of correction parameters.
14. The apparatus for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 13 , wherein the first set of correction parameters (A p ,B p )=(a,0), the second set of correction parameters (A p ,B p )=(b,b), and the third set of correction parameters (A p ,B p )=(b,−b), where a and b are real numbers.
15. The apparatus for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 14 , wherein the parameter a is 1 and the parameter b is ½.
16. The apparatus for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 13 , wherein the fourth set of correction parameters (A p ,B p ) are obtained by
A p =√{square root over (P)}−j{circumflex over (α)}√{square root over (Q)}
B p =−{circumflex over (α)}√{square root over (P)}−j√{square root over (Q)}
and the fifth set of correction parameters (A p ,B p ) are obtained by
A p =√{square root over (P)}+j{circumflex over (α)}√{square root over (Q)}
B p =−{circumflex over (α)}√{square root over (P)}+j√{square root over (Q)}
where
α
≈
α
^
=
N
/
O
-
1
N
/
O
+
1
,
N
=
(
W
(
2
)
(
f
T
)
+
W
(
2
)
(
-
f
T
)
)
/
2
,
O
=
(
W
(
3
)
(
f
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+
W
(
3
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(
-
f
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2
,
Q
=
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2
-
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(
1
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1
+
ρ
(
1
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)
(
α
^
2
-
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P
=
1
-
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,
ρ
(
1
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=
W
(
1
)
(
-
f
T
)
W
(
1
)
(
f
T
)
.
17. The apparatus for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 13 , wherein the final set of correction parameters (A p ,B p ) is set to be the fourth set of correction parameters if a function of W (4) (−f T ) is less than the function of W (5) (−f T ), otherwise the final set of correction parameters (A p ,B p ) is set to be the fifth set of correction parameters.
18. The apparatus for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 17 , wherein the final set of correction parameters (A p ,B p ) is set to be the fourth set of correction parameters if a value of W (4) (−f T ) is less than a value of W (5) (−f T ), otherwise the final set of correction parameters (A p ,B p ) is set to be the fifth set of correction parameters.
19. The apparatus for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 13 , wherein the final set of correction parameters (A p ,B p ) is set to be the fourth set of correction parameters if a function of W (4) (−f T ) is greater than the function of W (5) (f T ), otherwise the final set of correction parameters (A p ,B p ) is set to be the fifth set of correction parameters.
20. The apparatus for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 19 , wherein the final set of correction parameters (A p ,B p ) is set to be the fourth set of correction parameters if a value of W (4) (f T ) is greater than a value of W (5) (f T ), otherwise the final set of correction parameters (A p ,B p ) is set to be the fifth set of correction parameters.
21. The apparatus for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 13 , wherein the final set of correction parameters (A p ,B p ) is set to be the fourth set of correction parameters if a function of W (4) (−f T ) and W (4) (f T ) is less than the function of W (5) (−f T ) and W (5) (f T ), otherwise the final set of correction parameters (A p ,B p ) is set to be the fifth set of correction parameters.
22. The apparatus for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 21 , wherein the final set of correction parameters (A p ,B p ) is set to be the fourth set of correction parameters if W (4) (−f T )/W (4) (f T ) is less than W (5) (−f T )/W (5) (f T ), otherwise the final set of correction parameters (A p ,B p ) is set to be the fifth set of correction parameters.
23. The apparatus for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 13 , wherein the processor further configured to:
further add an DC compensation parameter γ p while obtaining the corrected signal x c [n] such that
x c [n]=A p ·( x[n]+γ p )+ B p ·( x[n]+γ p )*;
obtain a first local leakage component measure L 1 from the modulated signal x m (t) with the final set of parameters A p and B p , and the parameter γ p =ζ 1 , where ζ 1 is a real number;
obtain a second local leakage component measure L 2 from the modulated signal x m (t) with the final set of parameters A p and B p , and the parameter γ p ζ 2 , where ζ 2 is a real number;
obtain a third local leakage component measure L 3 from the modulated signal x m (t) with the final set of parameters A p and B p , and the parameter γ p =jζ 1 ;
obtain a fourth local leakage component measure L 4 from the modulated signal x m (t) with the final set of parameters A p and B p , and the parameter γ p =jζ 2 ;
obtain a fifth local leakage component measure L 5 from the modulated signal x m (t) with the final set of parameters A p and B p , and the parameter γ p =0; and
obtain a final DC compensation parameter γ p,final based on the first local leakage component measure L 1 , the second local leakage component measure L 2 , the third local leakage component measure L 3 , the fourth local leakage component measure L 4 and the fifth local leakage component measure L 5 .
24. The apparatus for in-phase and quadrature mismatch calibration of a transmitter as claimed in claim 23 , wherein the final DC compensation parameter γ p,final is obtained by
γ
p
,
final
=
-
1
2
·
ζ
2
2
(
L
1
-
L
5
)
-
ζ
1
2
(
L
2
-
L
5
)
ζ
1
(
L
2
-
L
5
)
-
ζ
2
(
L
1
-
L
5
)
-
j
1
2
·
ζ
2
2
(
L
3
-
L
5
)
-
ζ
1
2
(
L
4
-
L
5
)
ζ
1
(
L
4
-
L
5
)
-
ζ
2
(
L
3
-
L
5
)
.