Method and apparatus for I/Q imbalance calibration of a transmitter system

1. A method for I/Q imbalance calibration of a transmitter, comprising the steps of:

initializing parameters A p , B p and γ p ;

estimating a loop delay factor L;

generating a test signal x[n]=x(n·T S ), wherein x(t)=e jω T t and ω T is a preset radian frequency and T S is sampling interval;

generating a compensated signal x com [n] by compensating the test signal x[n] according to a first function with parameters A p , B p and γ p ;

converting the compensated signal x com [n] to an analog signal x com (t);

applying I/Q modulation to the analog signal x com (t) and outputting a modulated signal x mod (t);

obtaining a characteristic signal x c (t) of the modulated signal x mod (t);

obtaining a sampled characteristic signal x S [n] by sampling the characteristic signal x c (t) and obtaining statistics U 1 and U 2 of the sampled characteristic signal x S [n], where U 1 and U 2 are values indicative of the frequency response of x c (t) at radian frequency ω T and 2ω T , respectively; and

updating the parameters A p , B p and γ p respectively by one of the second functions, the loop delay factor L, the statistics U 1 and U 2 , and the current values of the parameters A p , B p and γ p .

2. The method as claimed in claim 1 , wherein the step of estimating the loop delay factor further comprises the steps of:

generating a test signal x′[n]=cos(ω T nT S )+γ T which is a discrete-time signal and γ T is a predetermined number;

converting the test signal x′[n] to an analog signal x′(t);

applying I/Q modulation to the analog signal x′(t) and outputting a modulated signal x′ mod (t);

obtaining a characteristic signal x′ c (t) of the modulated signal x′ mod (t);

obtaining a sampled characteristic signal x′ S [n] by sampling the characteristic signal x′ c (t) and obtaining a statistics v of the sampled characteristic signal x′ S [n], where V is a value indicative of the frequency response of x′ c (t) at radian frequency ω T ; and

estimating the loop delay factor L based on the statistics V.

3. The method as claimed in claim 2 , wherein the statistics V is obtained by taking FFT of the sampled characteristic signal x′ S [n].

4. The method as claimed in claim 3 , wherein the estimated loop delay factor L is V/|V|.

5. The method as claimed in claim 2 , wherein the characteristic signal is derived by taking the square of an envelope of the modulated signal.

6. The method as claimed in claim 1 , wherein the first function is x com [n]=A p ·x[n]+B p ·x*[n]−γ p .

7. The method as claimed in claim 1 , wherein the statistics U 1 and U 2 are obtained by taking FFT of the sampled characteristic signal x S [n].

8. The method as claimed in claim 1 , wherein the parameters A p , B p and γ p are updated by the steps of:

computing the updated A p based on the current A p and B p , the loop delay factor L, and the statistic U 2 ;

computing the updated B p based on the current A p and B p , the loop delay factor L, and the statistic U 2 ; and

computing the updated γ p based on the current γ p , the loop delay factor L, and the statistic U 1 .

9. The method as claimed in claim 1 , wherein the second functions for updating the parameters A p , B p and γ p are:

A′ p =A p −μ·B p ·U* 2 ·L·L;

B′ p =B p −μ·A p ·U 2 ·( L·L )*; and

γ′ p =γ p +μ·U 1 ·L*;

where A′ p , B′ p and γ′ p are the updated values, A p , B p and γ p are the current values, and μ is a preset step size parameter.

10. The method as claimed in claim 1 , wherein the characteristic signal is derived by taking the square of an envelope of the modulated signal.

11. An apparatus for I/Q imbalance calibration in a transmitter comprising:

a discrete-time signal generator generating a first test signal x 1 [n]=cos(ω T nT S )+γ T , where ω T is a preset radian frequency, T S is a predetermined sampling interval, and γ T is a predetermined number, in an estimation phase, and generating a second test signal x 2 [n]=e jω T nT S in a calibration phase which follows the estimation phase;

a correction module receiving the test signal from the signal generator, compensating the test signal according to a first function with parameters A p , B p and γ p to produce a compensated signal;

a first and second D/A converter converting the compensated signal to an analog signal, wherein the first D/A converter converts the real part of the compensated signal to the real part of the analog signal, and the second D/A converter converts the imaginary part of the compensated signal to the imaginary part of the analog signal;

a modulator applying I/Q modulation to the analog signal, and outputting a modulated signal;

a detector obtaining a characteristic signal of the modulated signal;

an A/D converter converting the characteristic signal to a sampled characteristic signal; and

a processor implementing the steps of:

initializing the parameters A p , B p and γ p ;

obtaining a statistic V based on the sampled characteristic signal in the estimation phase, where V is a value indicative of the frequency response of x′ c (t) at radian frequency ω T ;

estimating a loop delay factor L based on the statistic V in the estimation phase;

obtaining statistics U 1 and U 2 based on the sampled characteristic signal in the calibration phase, where U 1 and U 2 are values indicative of the frequency response of x c (t) at radian frequency ω T and 2ω T , respectively; and

updating the parameters A p , B p and γ p based on the loop delay factor L, the statistics U 1 and U 2 , and the current values of the parameters A p , B p and γ p in the calibration phase.

12. The apparatus as claimed in claim 11 , wherein the statistics V are obtained by taking FFT of the sampled characteristic signal in the estimation phase.

13. The apparatus as claimed in claim 11 , wherein the loop delay factor L is V/|V|.

14. The apparatus as claimed in claim 11 , wherein the first function is x com [n]=A p ·x[n]+B p ·x*[n]−γ p , where x[n] and x com [n] denote the test signal and the compensated signal, respectively, and x[n]=x 1 [n] in the estimation phase, x[n]=x 2 [n] in the calibration phase.

15. The apparatus as claimed in claim 11 , wherein the statistics U 1 and U 2 are obtained by taking FFT of the sampled characteristic signal in the calibration phase.

16. The apparatus as claimed in claim 11 , wherein the processor updates the parameters A p , B p and γ p by the steps of:

computing the updated A p based on the current A p and B p , the loop delay factor L, and the statistic U 2 ;

computing the updated B p based on the current A p and B p , the loop delay factor L, and the statistic U 2 ; and

computing the updated γ p based on the current γ p , the loop delay factor L, and the statistic U 1 .

17. The apparatus as claimed in claim 16 , wherein the processor updates the parameters A p , B p and γ p by the equations:

A′ p =A p −μ·B p ·U* 2 ·L·L;

B′ p =B p −μ·A p ·U 2 ·( L·L )*; and

γ′ p =γ p +μ·U 1 ·L*

where A′ p , B′ p and γ′ p are the updated values, A p , B p and γ p are the current values, and μ is a preset step size parameter.

18. The apparatus as claimed in claim 11 , wherein the characteristic signal is derived by taking the square of an envelope of the modulated signal.