Bandpass predistortion method and apparatus for radio transmission

1. A method of predistorting a complex baseband signal x having an in-phase component I and a quadrature component Q, said method comprising the steps of:

sampling the complex baseband signal x to obtain k samples I k of the in-phase component and k samples Q k of the quadrature component;

for each of the obtained samples determining a respective distortion factor D k ={(atanh (Cx k ))/Cx k }e 31 jΦ k , where Φ k =(πx k tanh (Cx k ))/6, x k is the magnitude of the sample k, and C is a scaling factor;

multiplying each of the samples I k of the in-phase component and each of the samples Q k of the quadrature component by its respective distortion factor D k to obtain a predistorted in-phase component sample and a predistorted quadrature component sample; and

combining the predistorted in-phase component samples and the predistorted quadrature component samples to provide a predistorted combined signal.

2. A method as claimed in claim 1 , wherein for each of the k samples the respective distortion factor D k is determined by:

determining the magnitude I k of each of the k samples of the in-phase component and the magnitude Q k of each of the k samples of the quadrature component;

for each of the k pairs of corresponding samples of the in-phase component and the quadrature component, determining a respective value of x k =(I k 2 +Q k 2 ) 1/2 ; and for each value of x k , determining a value of tanh (Cx k ) and a value of (atanh (Cx k ))/Cx k .

3. A method as claimed in claim 2 , wherein for each value of x k the value of tanh (Cx k ) is determined from a lookup table.

4. A method as claimed in claim 2 , wherein for each value of x k the value of atanh (Cx k )/Cx k is determined from a lookup table.

5. A method as claimed in claim 2 , wherein for each of the k pairs of corresponding samples the respective value of x k is determined by:

detecting the maximum value of I k and Q k by determining the larger of I k and Q k ;

detecting the minimum value of I k and Q k by determining the smaller of I k and Q k ;

calculating a value y k =½ {(the detected minimum value)÷(the detected maximum value)} 2 ; and

calculating a value of (I k 2 +Q k 2 ) 1/2 as a function of y k .

6. A method as claimed in claim 5 , wherein the value of (I k 2 +Q k 2 ) is calculated as (the detected maximum value)×{(1+y k )/2+½(1+y k −y k 2 +y k 3 −y k 4 +y k 5 −y k 6 )}.

7. A method of generating an envelope predistorted radio frequency signal, said method comprising the steps of:

providing an envelope modulated signal including a complex baseband signal x having an in-phase component I and a quadrature component Q;

sampling the complex baseband signal x to obtain k samples I k of the in-phase component and k samples Q k of the quadrature component;

for each of the obtained samples determining a respective distortion factor D k ={(atanh (Cx k ))/Cx}e −jΦ k , where Φ k =(πx k tanh (Cx k))/ 6, x k is the magnitude of the sample k, and C is a scaling factor;

multiplying each of the samples I k of the in-phase component and each of the samples Q k of the quadrature component by its respective distortion factor D k to obtain a predistorted in-phase component sample and a predistorted quadrature component sample;

combining the predistorted in-phase component samples and the predistorted quadrature component samples to provide a predistorted combined signal;

up-converting the predistorted combined signal to provide a radio frequency signal; and

applying the radio frequency signal to a power amplifier have hyperbolic tangent distortion.

8. A method as claimed in claim 7 , wherein for each of the k samples the respective distortion factor D k is determined by:

determining the magnitude I k of each of the k samples of the in-phase component and the magnitude Q k of each of the k samples of the quadrature component;

for each of the k pairs of corresponding samples of the in-phase component and the quadrature component, determining a respective value of x k =(I k 2 +Q k 2 ) 1/2 ; and

for each value of x k , determining a value of tanh (Cx k ) and a value of (atanh (Cx k ))/Cx k .

9. A method as claimed in claim 8 , wherein for each value of x k the value of tanh (Cx k ) is determined from a lookup table.

10. A method as claimed in claim 8 , wherein for each value of the x k the value of atanh (Cx k )/x k is determined from a lookup table.

11. A method as claimed in claim 8 , wherein for each of the k pairs of corresponding samples the respective value of x k is determined by:

detecting the maximum value of I k and Q k by determining the larger of I k and Q k ;

detecting the minimum value of I k and Q k by determining the smaller of I k and Q k ;

calculating a value y k =/½ {(the detected minimum value)÷(the detected maximum value)} 2 ;

calculating a value of (I k 2 +Q k 2 ) 1/2 as a function of y k .

12. A method as claimed in claim 11 , wherein the value of (I k 2 +Q k 2 ) is calculated as (the detected maximum value)×{(1+y k )/2+½(1+y k −y k 2 +y k 3 −y k 4 +y k 5 −y k 6 )}.

13. A method as claimed in claim 7 , further comprising the step of:

transmitting the radio frequency signal.

14. A method as claimed in claim 7 , wherein the scaling factor C is based on a comparison of the envelope of the complex baseband signal x and the envelope of the radio frequency signal.

15. Apparatus for predistorting a complex baseband signal x having an in-phase component I and a quadrature component Q, said apparatus comprising:

a sampling circuit for sampling the complex baseband signal x to provide k samples I k of the in-phase component and k samples Q k of the quadrature component;

a distortion determining circuit for determining for each of the provided samples a respective distortion factor D k ={(atanh (Cx k ))/Cx k }e 31 jΦ k , where Φ k =(πx k tanh (Cx k ))/6, x k ))/is the magnitude of the sample k, and C is a scaling factor;

a first multiplier for multiplying each of the samples I k of the in-phase component and each of the samples Q k of the quadrature component by its respective distortion factor D k to obtain a predistorted in-phase component sample and a predistorted quadrature component sample; and

a summing circuit for combining the predistorted in-phase component samples and the predistorted quadrature component samples to provide a predistorted combined signal.

16. Apparatus as claimed in claim 15 , wherein said distortion determining circuit comprises:

a first calculation circuit for determining for each of the k pairs of corresponding samples of the in-phase component and the quadrature component, a respective value of x k =(I k 2 +Q k 2 ) 1/2 ; and

a second calculation circuit for determining for each value of x k a value of tanh (Cx k ) and a value of (atanh (Cx k ))/Cx k .

17. Apparatus as claimed in claim 16 , wherein said second calculation circuit includes a plurality of lookup tables.

18. Apparatus as claimed in claim 16 , wherein said first calculation circuit comprises:

first means for detecting the maximum value of I k and Q k by determining the larger of I k and Q k ;

second means for detecting the minimum value of I k and Q k by determining the smaller of I k and Q k ;

third means for calculating a value of y k =½ {(the detected minimum value)÷(the detected maximum value)} 2 ; and

fourth means for calculating a value if (I k 2 +Q k 2 ) 1/2 as a function of y k .

19. Apparatus as claimed in claim 16 , wherein said first calculating circuit calculates the value of (I k 2 +Q k 2 ) 1/2 as (the detected maximum value)×{(1+y k )/2+½(1+y k −y k 2 +y k 3 −y k 4 +y k 5 −y k 6 )}.

20. Apparatus as claimed in claim 15 , wherein said sampling circuit, said distortion determining circuit, said first and second multipliers, and said summing circuit comprise a gate array.

21. Apparatus as claimed in claim 20 , wherein said gate array is a field programmable gate array.

22. Apparatus for generating an envelope predistorted radio frequency signal, said apparatus comprising:

a source of an envelope modulated signal including a complex baseband signal x having an in-phase component I and a quadrature component Q;

a sampling circuit for sampling the baseband signal x to provide k samples I k of the in-phase component and k samples Q k of the quadrature component;

a distortion determining circuit for determining for each of the provided samples a respective distortion factor D k ={(atanh (Cx k ))/Cx k }e 31 jΦ k , where k =(πx k tanh (Cx k ))/6, x k is the magnitude of the sample k, and C is a scaling factor;

a first multiplier for multiplying each of the samples I k of the in-phase component and each of the samples Q k of the quadrature component by its respective distortion factor D k to obtain a predistorted in-phase component sample and a predistorted quadrature component sample;

a summing circuit for combining the predistorted in-phase component samples and the predistorted quadrature component samples to provide a predistorted combined signal;

an up-converter for up-converting the predistorted combined signal to provide a radio frequency signal; and

a power amplifier having hyperbolic tangent distortion for amplifying the radio frequency signal while canceling the predistortion therein.

23. Apparatus as claimed in claim 22 , wherein said distortion determining circuit comprises:

a first calculation circuit for determining for each of the k pairs of corresponding samples of the in-phase component and the quadrature component, a respective value of x k =(I k 2 +Q k 2 ) 1/2 ; and

a second calculation circuit for determining for each value of x k a value of (tanh (Cx k ) and a value of atanh (Cx k ))/Cx k .

24. Apparatus as claimed in claim 23 , wherein said second calculation circuit includes a plurality of lookup table.

25. Apparatus as claimed in claim 23 , wherein said first calculation circuit comprises:

first means for detecting the maximum value of I k and Q k by determining the larger of I k and Q k ;

second means for detecting the minimum value of I k and Q k by determining the smaller of I k and Q k ;

third means for calculating a value of y k =½ {(the detected minimum value)=(the detected maximum value)} 2 ; and

fourth means for calculating a value if (I k 2 +Q k 2 ) 1/2 as a function of y k .

26. Apparatus as claimed in claim 23 , wherein said first calculation circuit calculates the value of (I k 2 +Q k 2 ) 1/2 as (the detected maximum value)×{(1+y k )/2+½(1+y k −y k 2 +y k 3 −y k 4 +y k 5 −y k 6 )}.

27. Apparatus as claimed in claim 22 , wherein said sampling circuit, said distortion determining circuit, said first and second multipliers, and said summing circuit comprise a gate array.

28. Apparatus as claimed in claim 27 , wherein said gate array is a field programmable gate array.

29. Apparatus as claimed in claim 22 , further comprising a circuit for providing the scaling factor C based on a comparison of the envelope of the complex baseband signal x and the envelope of the radio frequency signal.