Recursive digital pre-distortion (DPD)

1. A digital pre-distortion method, comprising:

applying a signal to a recursive system to generate a state vector;

providing said state vector as a feedback value to said recursive system; and

applying said state vector to a second function to generate an output signal, wherein at least one of said recursive system and said second function comprise a non-linear function.

2. The method of claim 1 , wherein said recursive system is defined by a system of non-linear differential equations.

3. The method of claim 2 , wherein said system of non-linear differential equations comprises:

S ( n )= f ( S ( n− 1), x ( n )), and

y ( n )= g ( S ( n ))

where x(n) is the input signal; y(n) is the output signal; f and g are non-linear functions and S(n) is a State space signal.

4. The method of claim 3 , wherein said non-linear functions f and g are determined by a digital pre-distortion parameter estimation phase.

5. The method of claim 1 , further comprising the step of initializing said recursive system.

6. The method of claim 1 , wherein said state vector is initialized to a known initial value.

7. A digital pre-distortion system, comprising:

a memory; and

at least one hardware device, coupled to the memory, operative to:

apply a signal to a recursive system to generate a state vector;

provide said state vector as a feedback value to said recursive system; and

apply said state vector to a second function to generate an output signal, wherein at least one of said recursive system and said second function comprise a non-linear function.

8. The digital pre-distortion system of claim 7 , wherein said recursive system is defined by a system of non-linear differential equations.

9. The digital pre-distortion system of claim 8 , wherein said system of non-linear differential equations comprises:

S ( n )= f ( S ( n− 1), x ( n )), and

y ( n )= g ( S ( n ))

where x(n) is the input signal; y(n) is the output signal; f and g are non-linear functions and S(n) is a State space signal.

10. The digital pre-distortion system of claim 9 , wherein said non-linear functions f and g are determined by a digital pre-distortion parameter estimation phase.

11. The digital pre-distortion system of claim 7 , further comprising the step of initializing said recursive system.

12. The digital pre-distortion system of claim 7 , wherein said state vector is initialized to a known initial value.

13. A digital pre-distortion system, comprising:

a recursive first order system having feedback that processes an input signal x(n) to generate a state vector S(n) that is provided as a feedback value to said recursive first order system; and

a second first order system without feedback to process said state vector S(n) using a second function to generate an output signal y(n), wherein at least one of said recursive first order system and said second function comprise a non-linear function.

14. The digital pre-distortion system of claim 13 , wherein said recursive first order system is defined by a system of non-linear differential equations.

15. The digital pre-distortion system of claim 14 , wherein said system of non-linear differential equations comprises:

S ( n )= f ( S ( n− 1), x ( n )), and

y ( n )= g ( S ( n ))

where x(n) is the input signal; y(n) is the output signal; f and g are non-linear functions and S(n) is a State space signal.

16. The digital pre-distortion system of claim 15 , wherein said non-linear functions f and g are determined by a digital pre-distortion parameter estimation phase.

17. The digital pre-distortion system of claim 13 , further comprising the step of initializing said recursive first order system.

18. The digital pre-distortion system of claim 13 , wherein said state vector is initialized to a known initial value.