Method and apparatus for I/Q mismatch calibration in a receiver
A method for I/Q mismatch calibration of a receiver having an I/Q correction module with correction parameters, comprising the steps of generating a test signal containing a single tone waveform with frequency of a carrier frequency plus a predetermined frequency, applying I/Q demodulation to reduce the central frequency of the test signal and outputting a demodulated signal, converting the demodulated signal to a digital signal, obtaining measures of the digital signal respectively indicative of the frequency response of the digital signal at the plus and minus predetermined frequencies, and calculating the set of the correction parameters for the I/Q correction module based on the measures.
1. A method for I/Q mismatch calibration of a receiver having an I/Q correction module which performs x o [n]=A p ·x i [n]+B p ·x* i *[n] where x i [n] and x o [n] respectively represent the input and output signal of the I/Q correction module, the superscript * refers to a complex conjugate, and A p and B p are correction parameters, comprising the following steps:
generating a test signal x(t) containing a single tone waveform with frequency of (f c +f T ) Hz, where f c and f T are real numbers;
applying I/Q demodulation to reduce the central frequency of the test signal x(t) by f c Hz and output a demodulated signal x dem (t);
converting the demodulated signal x dem (t) to a digital signal x dem [n];
obtaining measures U 1 and U 2 of the digital signal x dem [b] where U 1 and U 2 are values indicative of the frequency response of x dem (t) at frequency +f T Hz and −f T Hz, respectively; and
calculating the set of the correction parameters A p and B p for the I/Q correction module based on the measures U 1 and U 2 .
2. The method for I/Q mismatch calibration of a receiver as claimed in claim 1 , the measure U 1 and U 2 are obtained from the coefficients of the Fourier transformation of the x dem [n] corresponding to the frequency +f T Hz and −f T Hz.
3. The method for I/Q mismatch calibration of a receiver as claimed in claim 1 , wherein the test signal x(t)=cos(2π(f c +f T )).
4. The method for I/Q mismatch calibration of a receiver as claimed in claim 1 , wherein the set of correction parameters (A p ,B p ) are obtained by
{
A
p
=
R
+
j
α
S
B
p
=
-
α
R
-
j
S
where α, R, and S are obtained based on U 1 and U 2 .
5. The method for I/Q mismatch calibration of a receiver as claimed in claim 4 , wherein α, R, and S are obtained based on
H =real( U 1 ·U 2 ),
I=imag ( U 1 ·U 2 ),
and
G=|U 1 | 2 +|U 2 | 2 .
6. The method for I/Q mismatch calibration of a receiver as claimed in claim 4 . 1 , wherein α, R, and S are obtained by
α
=
H
κ
,
where
κ
=
G
+
G
2
-
4
H
2
2
,
and
R
=
1
+
P
2
,
S
=
Q
2
·
1
+
P
2
,
where
Q
=
2
·
I
κ
·
(
1
-
α
2
)
,
P
=
1
-
(
2
·
I
κ
·
(
1
-
α
2
)
)
2
.
7. The method for I/Q mismatch calibration of a receiver as claimed in claim 4 , wherein the set of correction parameters (A p , B p ) is further normalized such that the power of the output signal of the I/Q correction module equals to that of the input signal of the I/Q correction module.
8. An apparatus for I/Q mismatch calibration of a receiver having an I/Q correction module which performs x o [n]=A p ·x i [n]+B p ·x* i [n] where x i [n] and x o [n] respectively represent the input and output signal of the I/Q correction module, the superscript * refers to a complex conjugate, and A p and B p are correction parameters, comprising:
a signal generator for generating a test signal x(t) which contains a single tone waveform with frequency of (f c +f T ) Hz, where f c and f T are real numbers;
a demodulator for applying I/Q demodulation to reduce the central frequency of the test signal x(t) by f c Hz and outputting a demodulated signal x dem (t);
A/D converters for converting the demodulated signal x dem (t) to a digital signal x dem [n];
a dual-tone correlator for obtaining measures U 1 and U 2 of the digital signal x dem [n] output from the I/Q correction module where U 1 and U 2 are values indicative of the frequency response of x dem (t) at frequency +f T Hz and −f T Hz, respectively; and
a processor for obtaining the set of the correction parameters A p and B p according to the measures U 1 and U 2 .
9. The apparatus for I/Q mismatch calibration of a receiver as claimed in claim 8 , the measure U 1 and U 2 are obtained from the coefficients of the Fourier transformation of the x dem [n] corresponding to the frequency +f T Hz and −f T Hz.
10. The apparatus for I/Q mismatch calibration of a receiver as claimed in claim 8 , wherein the test signal x(t)=cos(2π(f c +f T )).
11. The apparatus for I/Q mismatch calibration of a receiver as claimed in claim 8 , wherein the set of correction parameters (A p , B p ) are obtained by
{
A
p
=
R
+
j
α
S
B
p
=
-
α
R
-
j
S
where α, R, and S are obtained based on U 1 and U 2 .
12. The apparatus for I/Q mismatch calibration of a receiver as claimed in claim 11 , wherein α, R, and S are obtained based on
H =real( U 1 ·U 2 ),
I =imag( U 1 ·U 2 ),
and
G=|U 1 | 2 +|U 2 | 2 .
13. The apparatus for I/Q mismatch calibration of a receiver as claimed in claim 12 , wherein α, R, and S are obtained by
α
=
H
κ
,
where
κ
=
G
+
G
2
-
4
H
2
2
,
and
R
=
1
+
P
2
,
S
=
Q
2
·
1
+
P
2
,
where
Q
=
2
·
I
κ
·
(
1
-
α
2
)
,
P
=
1
-
(
2
·
I
κ
·
(
1
-
α
2
)
)
2
.
14. The apparatus for I/Q mismatch calibration of a receiver as claimed in claim 11 , wherein the set of correction parameters (A p , B p ) is further normalized such that the power of the output signal of the I/Q correction module equals to that of the input signal of the I/Q correction module.