Method and apparatus for I/Q mismatch calibration in a receiver
A method for I/Q mismatch calibration in a receiver. The receiver has an I/Q correction module using parameters A p and B p . The method comprises the steps of generating an analog test signal x(t), applying I/Q demodulation to reduce the central frequency of the signal x(t) by f c Hz and outputting a demodulated signal x dem (t), converting the analog signal x dem (t) to a digital signal x dem [n], sending the signal x dem [n] into the I/Q correction module using parameters A p and B p and outputting a corrected signal w[n], obtaining two measures U 1 and U 2 of the corrected signal w[n], and updating the parameters A p and B p of the I/Q correction module respectively by a first and second function of the two measures U 1 and U 2 , and the current values of the parameters A p and B p .
1. A method for I/Q mismatch calibration in a receiver having an I/Q correction module using parameters A p and B p , the method comprising the steps of:
generating an analog test signal x(t) containing cos(2π(f c +f T )t), where f c and f T are predetermined real numbers;
applying I/Q demodulation to reduce the central frequency of the signal x(t) by f c Hz and outputting a demodulated signal x dem (t);
converting the analog signal x dem (t) to a digital signal x dem [n] with a preset sampling rate of f s Hz;
sending the signal x dem [n] into the I/Q correction module using parameters A p and B p and outputting a corrected signal w[n];
obtaining two measures U 1 and U 2 of the corrected signal w[n] where U 1 and U 2 are values indicative of the discrete-Fourier transform of w[n] corresponding to frequency +f T Hz and −f T Hz, respectively; and
updating the parameters A p and B p of the I/Q correction module respectively by a first and second function of the two measures U 1 and U 2 , and the current values of the parameters A p and B p ; wherein the initial values of A p and B p are nonzero numbers.
2. The method claimed in claim 1 , wherein the I/Q correction module implements a function:
w[n]=A p ·x dem [n]+B p ·x* dem [n],
where the superscript * refers to a complex conjugate.
3. The method claimed in claim 1 , wherein the first and second function are respectively:
A′ p =A p −μ·B* p ·U 1 ·U 2 ; and
B′ p =B p −μ·A* p ·U 1 ·U 2 ,
where A′ p and B′ p are the updated values, A p and B p are the current values, and μ is a step size parameter.
4. The method claimed in claim 1 , wherein:
f
T
=
K
M
f
s
,
where K and M are integers and the measures U 1 and U 2 are respectively obtained by:
U
1
=
1
M
∑
n
=
0
M
-
1
w
[
n
]
·
ⅇ
-
j2
π
K
M
n
;
and
U
2
=
1
M
∑
n
=
0
M
w
[
n
]
·
ⅇ
j2π
K
M
n
.
5. The method claimed in claim 1 further comprising the step of:
normalizing the updated parameters A p and B p so that the power of the corrected signal w[n] is the same as that of the digital signal x dem [n].
6. An apparatus for I/Q mismatch calibration of a receiver, comprising:
a signal generator generating an analog test signal x(t) containing cos(2π(f c +f T )t), where f c and f T are predetermined real numbers;
a demodulator applying I/Q demodulation to reduce the central frequency of the signal x(t) by f c Hz and outputting a demodulated signal x dem (t);
A/D converters converting the analog signal x dem (t) to a digital signal x dem [n] with a preset sampling rate of f s Hz;
an I/Q correction module using parameters A p and B p to compensate I/Q mismatch in the signal x dem [n] and outputting a corrected signal w[];
a dual-tone correlator outputting two measures U 1 and U 2 of the corrected signal w[n] where U 1 and U 2 are values indicative of the discrete-Fourier transform of w[n] corresponding to frequency +f T Hz and −f T Hz, respectively; and
a processor implementing the step of:
providing the parameters A p and B p with nonzero initial values; and
updating the parameters A p and B p respectively by a first and second function of the two measures U 1 and U 2 , and the current values of the parameters A p and B p .
7. The apparatus as claimed in claim 6 , wherein the processor further implements the step of:
normalizing the updated parameters A p and B p so that the power of the corrected signal w[n] is the same as that of the digital signal x dem [n].
8. The apparatus as claimed in claim 6 , wherein the first and second function are respectively:
A′ p =A p −μ·B* p ·U 1 ·U 2 ; and
B′ p =B p −μ·A* p ·U 1 ·U 2 ,
where A′ p and B′ p are the updated values, A p and B p are the current values, and μ is a preset step size parameter.
9. The apparatus as claimed in claim 6 , wherein the I/Q correction module implements a function:
w[n]=A p ·x dem [n]+B p ·x* dem [n],
where the superscript * refers to a complex conjugate.
10. The apparatus as claimed in claim 6 , wherein:
f
T
=
K
M
f
s
,
where K and M are integers and the measures U 1 and U 2 are respectively obtained by:
U
1
=
1
M
∑
n
=
0
M
-
1
w
[
n
]
·
ⅇ
-
j2
π
K
M
n
;
and
U
2
=
1
M
∑
n
=
0
M
w
[
n
]
·
ⅇ
j2π
K
M
n
.