Adaptive compensation systems for mitigating distortion due to nonlinear power amplifiers

1. A method for pre-processing a signal prior to receipt of the signal by a non-linear device (NLD) to compensate for AM-AM distortion and AM-PM distortion of the signal by the NLD, the method comprising:

generating, by at least one processor, a modified amplitude r k based on an amplitude x k derived from a digitized envelope R i,k of the signal, wherein generating the modified amplitude r k comprises estimating the inverse B of an amplitude transfer function h of the NLD obtained by an optimization of at least one parameter of B found by minimizing a measure of error between x k and h(B(x k );

generating, by the at least one processor, a scale factor c k based on the modified amplitude r k and the amplitude x k ;

generating, by the at least one processor, an AM-AM compensated signal based on the scale factor c k ;

generating, by the at least one processor, a first AM-PM phase compensation value based on the modified amplitude r k ; and

generating, by the at least one processor, an AM-AM/AM-PM compensated signal by modifying a phase of the AM-AM compensated signal based on the first AM-PM phase compensation value.

2. The method of claim 1 , wherein the signal is a complex baseband signal, and wherein a digitized representation of the signal comprises an inphasc signal component u i,k and a quadrature signal component v i,k .

3. The method of claim 2 , wherein the AM-AM compensated signal comprises an inphase signal component u p,k and a quadrature signal component v p,k , and wherein generating an AM-AM compensated signal comprises determining u p,k as the product c k ×u i,k and v p,k as the product c k ×v i,k .

4. The method of claim 1 , wherein the signal is an RF signal or an IF signal.

5. The method of claim 4 , wherein generating an AM-AM compensated signal comprises multiplying the signal by an analog representation of the scale factor c k .

6. The method of claim 1 , further comprising:

iteratively determining coefficient values of B using a gradient algorithm for minimizing error between an input amplitude x and h(B(x)), wherein B is a polynomial of degree N a ; and

terminating the iterative determination when h(B(x)) is substantially linear over a range of x.

7. The method of claim 6 , further comprising:

limiting B to a constant value A p for values of x>A th , wherein A th is a minimum value of x for which h(B(x)) is substantially equal to a saturation amplitude A s .

8. The method of claim 6 , wherein the degree N a of B is an odd number.

9. The method of claim 8 , wherein the degree N a of B is selected from the group consisting of 3, 5, 7 and 9.

10. The method of claim 6 , further comprising:

based on changes in an average value of the modified amplitude r k over a number of time intervals T I , adaptively modifying the degree N a of B.

11. The method of claim 1 , wherein generating the scale factor c k comprises determining

r

k

x

k

.

12. The method of claim 1 , wherein generating the first AM-PM phase compensation value comprises:

determining coefficient values of a polynomial φ of degree n p , the polynomial φ approximating an amplitude to phase transfer function of the NLD; and

evaluating φ(r k ), wherein φ(r k ) is equal to the first AM-PM phase compensation value.

13. The method of claim 12 , wherein generating a first AM-PM phase compensation value comprises:

estimating a nominal operating amplitude A 0,n based on an average value of the modified amplitude r k over each of a number of time intervals T I ; and

adaptively updating coefficient values of φ such that φ approximates the amplitude to phase transfer function of the NLD about the nominal operating amplitude A 0,n .

14. The method of claim 12 , wherein the degree n p of φ is selected from the group consisting of 2 and 3.

15. The method of claim 1 , comprising:

generating a second AM-PM phase compensation value by evaluating a function {circumflex over (ψ)} k (r k ), wherein {circumflex over (ψ)} k is a polynomial function of degree n q and models a phase error ψ k caused by at least one of: (1) environmentally-induced variations in an amplitude to phase transfer function of the NLD, (2) time-dependent variations in an amplitude to phase transfer function of the NLD, and (3) an unmodeled nonlinearity of the NLD, and wherein coefficient values of {circumflex over (ψ)} k are adaptively determined using a gradient algorithm for minimizing error between {circumflex over (ψ)} k and ψ k ; and

generating an AM-AM and AM-PM compensated signal by modifying a phase of the AM-AM compensated signal based on the second AM-PM phase compensation value.

16. The method of claim 1 , further comprising estimating a nominal operating amplitude A 0,n based on an average value of the modified amplitude r k over each of a number of time intervals T 1 .

17. The method of claim 1 , wherein the signal is an RF signal, further comprising generating the IF signal, and wherein generating the IF signal comprises:

coupling an input RF signal through an RF coupler, an IF down converter, and an IF bandpass filter to generate the signal; and

applying an envelope detector to generate the envelope R i,k of the signal.

18. A method for pre-processing a signal prior to receipt of the signal by a non-linear device (NLD) to compensate for AM-AM distortion and AM-PM distortion of the signal by the NLD, the method comprising:

compensating, by at least one processor, an AM-AM distortion of the signal based on a scale factor

r

k

x

k

,

wherein x k is an amplitude derived from a digitized envelope R i,k of the signal, and wherein r k is a modified amplitude determined by a function B(x k ), wherein B is a polynomial function of degree N a and an inverse function of an amplitude transfer function h of the NLD; and

compensating, by at least one processor, an AM-PM distortion of the signal based on a first AM-PM phase compensation value determined by a function φ(r k ), wherein φ is a polynomial of degree n p approximating the amplitude to phase transfer function of the NLD about a nominal operating amplitude A 0,n of r k .

19. The method of claim 18 , comprising adaptively modifying the degree N a of B based on changes in an average value of the modified amplitude r k over a number of time intervals T I .

20. The method of claim 18 , comprising generating a second AM-PM phase compensation value determined by a function {circumflex over (ψ)} k (r k ), wherein {circumflex over (ψ)} k is a polynomial function of degree n q and models a phase error ψ k caused by at least one of: (1) environmentally-induced variations in an amplitude to phase transfer function of the NLD, (2) time-dependent variations in an amplitude to phase transfer function of the NLD, and (3) an unmodeled nonlinearity of the NLD, and wherein coefficient values of {circumflex over (ψ)} k are adaptively determined using a gradient algorithm for minimizing error between {circumflex over (ψ)} k and ψ k ; and

compensating, by at least one processor, the AM-PM distortion of the signal based on the second AM-PM phase compensation value.

21. A system, comprising:

a non-linear electronic signal processing device for processing an input signal, wherein the non-linear electronic signal processing device has a non-linear transfer function; and

a pre-processor in communication with the non-linear electronic signal processing device, wherein the pre-processor receives a signal, processes the received signal, and outputs the processed signal to an input of the non-linear electronic signal processing device, wherein the pre-processor comprises at least one processor programmed to:

generate a modified amplitude r k based on an amplitude x k derived from a digitized envelope R i,k of the signal, wherein generating a modified amplitude r k comprises estimating the inverse B of an amplitude transfer function h of the NLD obtained by an optimization of at least one par der of B found by minimizing a measure of error between x k and h(B(x k ));

generate a scale factor c k based on the modified amplitude r k and the amplitude x k ;

generate an AM-AM compensated signal based on the scale factor c k ;

generate a first AM-PM phase compensation value based on the modified amplitude r k ; and

generate an AM-AM and AM-PM compensated signal by modifying a phase of the AM-AM compensated signal based on the first AM-PM phase compensation value.

22. The system of claim 21 , wherein the least one processor is further programmed to:

store function B, wherein the function B is a polynomial function of degree N a ; and

evaluate B(x k ), wherein B(x k )=r k .

23. The system of claim 22 , wherein the degree N a of B is an odd number.

24. The system of claim 23 , wherein the degree N a of B is selected from the group consisting of 3, 5, 7 and 9.

25. The system of claim 22 , wherein the degree N a of B is based on changes in an average value of the modified amplitude r k over a number of time intervals T I .

26. The system of claim 21 , wherein the least one processor is further programmed to:

store a polynomial φ of degree n p , the polynomial φ approximating an amplitude to phase transfer function of the non-linear electronic signal processing device; and

evaluate φ(r k ), wherein φ(r k ) is equal to the first AM-PM phase compensation value.

27. The system of claim 26 , wherein the at least one processor is further programmed to:

estimate a nominal operating amplitude A 0,n based on an average value of the modified amplitude r k over each of a number of time intervals T 1 ; and

adaptively update coefficient values of φ such that φ approximates the amplitude to phase transfer function of the NLD about the nominal operating amplitude A 0,n .

28. The system of claim 26 , wherein the degree n p of φ is selected from the group consisting of 2 and 3.

29. The system of claim 21 , wherein the at least one processor is further programmed to:

generate a second AM-PM phase compensation value by evaluating a function {circumflex over (ψ)} k (r k ), wherein {circumflex over (ψ)} k is a polynomial function of degree n q and models a phase error ψ k caused by at least one of: (1) environmentally-induced variations in an amplitude to phase transfer function of the non-linear electronic signal processing device, (2) time-dependent variations in an amplitude to phase transfer function of the non-linear electronic signal processing device, and (3) an unmodeled nonlinearity of the non-linear electronic signal processing device, and wherein coefficient values of {circumflex over (ψ)} k are adaptively determined using a gradient algorithm for minimizing error between {circumflex over (ψ)} k and ψ k ; and

generate the AM-AM and AM-PM compensated signal by modifying the phase of the AM-AM compensated signal based on the second AM-PM phase compensation value.

30. The system of claim 21 , wherein the non-linear electronic signal processing device is a power amplifier.

31. The system of claim 21 , wherein the non-linear electronic signal processing device comprises a cascade of multiple signal processing devices.

32. The system of claim 31 , wherein at least one of the cascade of multiple signal processing devices is a power amplifier.