Methods and apparatuses for compensation of I/Q imbalance
Methods for compensation of imbalance between I (In-phase) and Q (Quadrature) signal paths ( 12 a, 12 b, 605 a, 605 b ) in a quadrature receiver ( 8 ) and a quadrature transmitter ( 600 ) are disclosed. In the receiver case, the imbalance is compensated for by means of post-distortion in the digital domain. In the transmitter case, the imbalance is compensated for by means of pre-distortion in the digital domain. The methods can be carried out with a relatively low computational complexity. Signal-processing devices ( 30, 610 ) for carrying out the methods are disclosed as well. The same basic internal structure may be used for the signal-processing device ( 30 ) in the receiver case as for the signal processing device ( 610 ) in the transmitter case.
1. A method for compensating an imbalance between an in-phase, I, signal path and a quadrature, Q, signal path of a quadrature receiver adapted to generate a real-valued uncompensated digital I component a(n) and a real-valued uncompensated digital Q component b(n), together forming an uncompensated complex digital signal x(n)=a(n)+jb(n), wherein j denotes an imaginary unit and n is a sequence index, the method comprising:
generating a complex compensation signal by filtering one of a(n) and jb(n) with a compensation filter having a complex-valued impulse response;
generating a first compensated complex digital signal as the sum of x(n) and the complex compensation signal; and
adaptively generating filter parameters of the compensation filter;
wherein adaptively generating filter parameters of the compensation filter involves, for each of a number of iterations, where each iteration is identified by an iteration index i:
generating filter parameters for attaining an impulse response f (i) (n), wherein f (i) (n) is a default impulse response for the first iteration, wherein i=1, and f (i) (n) is based on f (i−1) (n) and Δ (i−1) (n) for i>1, and Δ (i−1) (n) is an estimated impulse-response error of a preceding iteration;
generating the complex compensation signal, denoted e (i) (n), as e (i) (n)=f (i) (n) * w(n), wherein * denotes the convolution operator and w(n) denotes one of a(n) and jb(n);
generating the first compensated complex digital signal denoted v (i) (n), as v (i) (n)=x(n)+e (i) (n); and
generating filter parameters determining Δ (i) (n) by minimizing a cost function based on u (i) (n)=v (i) (n)+Δ (i) (n)*w(n).
2. The method according to claim 1 , wherein the impulse response f (i) (n) is on the form:
f (i) (n)=h Δ (i) (n)+jφ (k) δ(n)+jφ (i) h Δ (i) (n)+(e jφ (i) −1−jφ (i) )·(δ(n)+h Δ (i) (n)); wherein δ(n) is the unit pulse, φ (i) is a real-valued parameter and h Δ (i) (n) is a real-valued sequence.
3. The method according to claim 2 , wherein
Δ (i) (n) is on the form: Δ (i) (n)=Δ h (i) (n)+jΔ φ (i) for n belonging to a finite set of integers and Δ (i) (n)=0 outside the finite set of integers; and wherein Δ φ (i) is a real-valued parameter and Δ h (i) (n) is a real-valued sequence; and
generating filter parameters determining Δ (i) (n) comprises generating the real-valued parameter Δ φ (i) as φ (i) =φ i−1) +Δ φ (i−1) for i>1, and the real-valued sequence Δ h (i) (n) as h Δ (i) (n)=h Δ (i−1) (n)+Δ h (i−) (n) for i>1.
4. The method according to claim 1 , wherein the impulse response of the compensation filter is on the form:
h Δ (n)+jφδ(n)+jφh Δ (n)+(e jφ −1−jφ)·(δ(n)+h Δ (n)); wherein δ(n) is the unit pulse, φ is a real-valued parameter and h Δ (n) is a real-valued sequence; and
wherein adaptively generating filter parameters of the compensation filter comprises adaptively generating the real-valued parameter φ and the real-valued sequence h Δ (n).
5. A method for compensating an imbalance between an in-phase, I, signal path and a quadrature, Q, signal path of a quadrature receiver adapted to generate a real-valued uncompensated digital I component a(n) and a real-valued uncompensated digital Q component b(n), together forming an uncompensated complex digital signal x(n)=a(n)+jb(n), wherein j denotes an imaginary unit and n is a sequence index, the method comprising:
for each of a number of iterations, where each iteration is identified by an iteration index i:
generating sample values of a finite-length real-valued impulse response g Δ (i) (n) that can adopt nonzero values for n in a finite set K, wherein g Δ (i) (n) is a default impulse response for the first iteration, wherein i=1, and g Δ (i) (n) is given by g Δ (i) (n)=g Δ i−-1) (n)+Δ g (i−1) (n) for i>1, and Δ g (i−1) (n) is an estimated impulse-response error of a preceding iteration;
generating a real-valued phase parameter φ (i) as a default value for the first iteration, where i=1, and as φ (i) =φ (i−1) +Δ φ (i−1) for i>1, wherein Δ φ (i−1) is an estimated phase-parameter error of the preceding iteration;
generating a first compensated complex digital signal, denoted v (i) (n), as
v
(
i
)
(
n
)
=
x
(
n
)
+
tan
(
φ
(
i
)
)
w
1
(
n
)
+
(
(
g
Δ
(
i
)
(
n
)
+
δ
(
n
)
cos
(
φ
(
i
)
)
)
-
δ
(
n
)
)
*
w
2
(
n
)
,
wherein * denotes the convolution operator, and either w 1 (n)=ja(n) and w 2 (n)=jb(n) or w 1 (n)=b(n) and w 2 (n)=a(n); and
generating the estimated impulse response error Δ g (i) (n) and the estimated phase-parameter error Δ φ (i) by minimizing a cost function based on
u
(
i
)
(
n
)
=
v
(
i
)
(
n
)
+
∑
k
∈
K
(
Δ
g
(
i
)
(
k
)
w
2
(
n
-
k
)
+
Δ
φ
(
i
)
w
1
(
n
-
k
)
)
.
6. A signal-processing device for compensating an imbalance between an in-phase, I, signal path and a quadrature, Q, signal path of a quadrature receiver, wherein the quadrature receiver is adapted to generate a real-valued uncompensated digital I component a(n) and a real-valued uncompensated digital Q component b(n), together forming an uncompensated complex digital signal x(n)=a(n)+jb(n), wherein j denotes an imaginary unit and n is a sequence index, wherein the signal-processing device is adapted to receive the uncompensated digital signal x(n) and compensate said imbalance by performing the method according to claim 1 .
7. A quadrature receiver comprising:
an in-phase, I, signal path and a quadrature, Q, signal path for generating a real-valued uncompensated digital I component a(n) and a real-valued uncompensated digital Q component b(n), together forming an uncompensated complex digital signal x(n)=a(n)+jb(n), wherein j denotes an imaginary unit and n is a sequence index; and
a signal-processing device according to claim 6 for compensating an imbalance between the I and the Q signal paths.
8. A method for compensating an imbalance between an in-phase, I, signal path and a quadrature, Q, signal path of a quadrature transmitter arranged to transmit a radio-frequency signal r a (t) representing an uncompensated complex-valued digital signal z(n)=c(n)+jd(n), wherein j denotes an imaginary unit, n is a sequence index, c(n) is an uncompensated digital I component, and d(n) is an uncompensated digital Q component, by generating a compensated complex-valued digital signal having a compensated digital I component, which is provided to the I signal path and a compensated digital Q component, which is provided to the Q signal path, the method comprising:
generating a complex compensation signal by filtering one of c(n) and jd(n) with a compensation filter having a complex-valued impulse response;
generating a first compensated complex digital signal as the sum of z(n) and the complex compensation signal; and
adaptively generating filter parameters of the compensation filter;
wherein adaptively generating filter parameters of the compensation filter involves, for each of a number of iterations, where each iteration is identified by an iteration index i:
generating filter parameters for attaining an impulse response f (i) (n), wherein f (i) (n) is a default impulse response for the first iteration, wherein i=1, and f (i) (n) is based on f (i−1) (n) and Δ (i−1) (n) for i>1, and Δ (i−1) (n) is an estimated impulse-response error of a preceding iteration;
generating the complex compensation signal denote e (i) (n), as e (i) (n)=f (i) (n)*w(n), wherein * denotes the convolution operator and w(n) denotes one of c(n) and jd(n);
generating the first compensated complex digital signal, denoted v (i) (n), as v (i) (n)=x(n)+e (i) (n); and
generating filter parameters determining Δ (i) (n) by minimizing a cost function based on a real-valued signal r BB (n), which is obtained from real downconversion of the signal r a (t).
9. The method according to claim 8 , further comprising generating a signal q BB (n) corresponding to a signal that would have resulted from real downconversion of a radio-frequency signal generated by inputting the signal z(t) to a quadrature transmitter having no imbalance between the I and Q signal paths, wherein the cost function is based on a difference between r BB (n) and q BB (n) based on an L 2 norm or L ∞ norm of the difference.
10. The method according to claim 8 , wherein the impulse response f (i) (n) is on the form:
f (i) (n)=h Δ (i) (n)+jφ (k) δ(n)+jφ (i) h Δ (i) (n)+(e jφ (i) −1−jφ (i) )·(δ(n)+h Δ (i) (n)); wherein δ(n) is the unit pulse, φ (i) is a real-valued parameter and h Δ (i) (n) is a real-valued sequence.
11. The method according to claim 10 , wherein Δ (i) (n) is on the form: Δ (i) (n)=Δ h (i) (n)+jΔ φ (i) for n belonging to a finite set of integers and Δ (i) (n)=0 outside the finite set of integers; and wherein Δ φ (i) is a real-valued parameter and Δ h (i) (n) is a real-valued sequence; and wherein generating filter parameters determining Δ (i) (n) comprises generating the real-valued parameter Δ φ (i) as φ (i) =φ i−1) +Δ φ (i−1) for i>1, and the real-valued sequence Δ h (i) (n) as h Δ (i) (n)=h Δ (i−1) (n)+Δ h (i−1) (n) for i>1.
12. The method according to claim 8 , wherein the impulse response of the compensation filter is on the form:
h Δ (n)+jφδ(n)+jφh Δ (n)+(e jφ −1−jφ)·(δ(n)+h Δ (n)); wherein δ(n) is the unit pulse, φ is a real-valued parameter and h Δ (n) is a real-valued sequence; and
wherein adaptively generating filter parameters of the compensation filter comprises adaptively generating the real-valued parameter φ and the real-valued sequence h Δ (n).
13. A signal-processing device for compensating an imbalance between an in-phase, I, signal path and a quadrature, Q, signal path of a quadrature transmitter for transmitting a radio-frequency signal r a (t) representing an uncompensated complex-valued digital signal z(n)=c(n)+jd(n), wherein j denotes an imaginary unit, n is a sequence index, c(n) is an uncompensated digital I component, and d(n) is an uncompensated digital Q component, wherein the signal processing device is adapted to receive the uncompensated complex-valued digital signal z(n) and generate a compensated digital I component, to be provided to the I signal path, and a compensated digital Q component, to be provided to the Q signal path, by performing the method according to claim 8 for compensating the imbalance.
14. A quadrature transmitter for transmitting a radio-frequency signal r a (t) representing an uncompensated complex-valued digital signal z(n)=c(n)+jd(n), comprising:
an in-phase, I, signal path and a quadrature, Q, signal path arranged to receive a compensated digital I component and a compensated digital Q component, respectively, for generating the radio-frequency signal r a (t); and
a signal-processing device according to claim 13 for compensating an imbalance between the I and the Q signal paths.
15. An electronic apparatus comprising the quadrature receiver according to claim 7 .
16. A non-transitory computer readable medium having stored thereon a computer program product comprising computer program code means for executing the method according to claim 1 when the computer program code means are run by an electronic device having computer capabilities.
17. An electronic apparatus comprising the quadrature transmitter according to claim 14 .
18. A non-transitory computer readable medium having stored thereon a computer program product comprising computer program code means for executing the method according to claim 5 when the computer program code means are run by an electronic device having computer capabilities.
19. A non-transitory computer readable medium having stored thereon a computer program product comprising computer program code means for executing the method according to claim 8 when the computer program code means are run by an electronic device having computer capabilities.