Non-linear modeling of a physical system using direct optimization of look-up table values

1. A method utilizing a modeling system for producing a digital pre-distortion processing device (PDPD) for a non-linear system, comprising:

receiving, at an input of the modeling system, a physical electronic signal from said non-linear system by applying a set of input samples x(n) to said non-linear system and providing an output y(n) of said non-linear system as the physical electronic signal at the input of the modeling system;

storing non-transitory information related to the physical electronic signal in a non-volatile memory of the modeling system;

directly computing, utilizing a processor of the modeling system, parameters Φ of a non-linear system memory model for said non-linear system from the information related to said physical electronic signal, wherein said memory model comprises one or more look-up tables of said PDPD having linear interpolation and wherein said parameters Φ produce a substantially minimum mean square error; and

producing said PDPD by writing, at an output of the modeling system, said parameters Φ for storage as entries in said one or more look-up tables to a memory of said PDPD to form the processor that provides digital pre-distortion in the non-linear system;

wherein:

said parameters Φ are computed using a tri-diagonal auto correlation matrix; and

said directly computing of said parameters Φ to produce a substantially minimum mean square error comprises finding a minimum of a cost function given by:

Φ=( U T U ) −1 ·U T Y;

wherein:

Φ is a vector comprised of model parameters comprising entries for the look-up tables;

T indicates a Transpose matrix;

U is of a form:

U

=

[

0

…

0

u

0

1

-

u

0

0

…

0

0

u

1

1

-

u

1

0

0

0

…

0

⋮

⋮

0

0

…

0

0

u

N

-

1

1

-

u

N

-

1

0

]

;

u m,n =Λ(X n −mδ);

Λ is a triangular basis function;

m is a row of U;

n is a column of U; and

x n is an output of said non-linear system, given y n as an input.

2. The method of claim 1 , wherein said non-linear system has a memory length of zero.

3. The method of claim 1 , wherein said memory model comprises a dynamic memory model.

4. The method of claim 1 , wherein said non-linear system processes one or more of real signals and complex signals.

5. The method of claim 1 , wherein said mean square error is determined using one or more of a least squares algorithm, a least mean square algorithm and a recursive least squares algorithm.

6. The method of claim 1 , wherein said memory model comprises one or more of a memory polynomial model and a generalized memory polynomial model, where one or more polynomials are replaced with one or more of said look-up tables having linear interpolation, wherein said entries in said one or more look-up tables are directly calculated.

7. The method of claim 1 , wherein said non-linear system comprises one or more of a power amplifier and an inverse of a power amplifier.

8. The method of claim 1 , wherein said one or more look-up tables are used in a processor instruction to implement digital pre-distortion.

9. A modeling system apparatus for producing a digital pre-distortion processing device (PDPD) for a non-linear system, comprising:

a non-volatile memory; and

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

receive, at an input of the modeling system, a physical electronic signal from said non-linear system by applying a set of input samples x(n) to said non-linear system and providing an output y(n) of said non-linear system as the physical electronic signal at the input of the modeling system;

store non-transitory information related to the physical electronic signal in the memory;

directly compute parameters Φ of a non-linear system memory model for said non-linear system from the information related to said physical electronic signal, wherein said memory model comprises one or more look-up tables of said PDPD having linear interpolation and wherein said parameters Φ produce a substantially minimum mean square error; and

produce the PDPD by a write, at an output of the modeling system, of said parameters Φ for storage as entries in said one or more look-up tables to a memory of said PDPD to form the processor that provides digital pre-distortion in the non-linear system;

wherein said parameters Φ are computed using a tri-diagonal auto correlation matrix; and

said directly computing of said parameters Φ to produce a substantially minimum mean square error comprises finding a minimum of a cost function given by:

Φ=( U T U ) −1 ·U T Y;

wherein:

Φ is a vector comprised of model parameters comprising entries for the look-up tables;

T indicates a Transpose matrix;

U is of a form:

U

=

[

0

…

0

u

0

1

-

u

0

0

…

0

0

u

1

1

-

u

1

0

0

0

…

0

⋮

⋮

0

0

…

0

0

u

N

-

1

1

-

u

N

-

1

0

]

;

u m,n =Λ(X n −mδ);

Λ is a triangular basis function;

m is a row of U;

n is a column of U; and

x n is an output of said non-linear system, given y n as an input.

10. The apparatus of claim 9 , wherein said non-linear system has a memory length of zero.

11. The apparatus of claim 9 , wherein said memory model comprises a dynamic memory model.

12. The apparatus of claim 9 , wherein said non-linear system processes one or more of real signals and complex signals.

13. The apparatus of claim 9 , wherein said mean square error is determined using one or more of a least squares algorithm, a least mean square algorithm and a recursive least squares algorithm.

14. The apparatus of claim 9 , wherein said memory model comprises one or more of a memory polynomial model and a generalized memory polynomial model, where one or more polynomials are replaced with one or more of said look-up tables having linear interpolation, wherein said entries in said one or more look-up tables are directly calculated.

15. The apparatus of claim 9 , wherein said non-linear system comprises one or more of a power amplifier and an inverse of a power amplifier.

16. The apparatus of claim 9 , wherein said one or more look-up tables are used in a processor instruction to implement digital pre-distortion.