Non-linear modeling of a physical system using look-up table with polynomial interpolation
First Claim
1. A digital pre-distortion (DPD) system, comprising:
- a digital signal processor configured to evaluate a non-linear function for a complex input value, comprising;
a memory configured to store at least one look-up table with polynomial interpolation that represents said non-linear function, wherein entries in said look-up table comprise polynomial coefficients of at least degree two for different segments of said non-linear function, said polynomial coefficients configured to provide at least one of a rectangular or triangular basis function for each segment of said non-linear function;
at least one processor, coupled to the memory, operative to;
obtain a point from said look-tip table that is near a magnitude of said complex input value; and
generate a complex output value by evaluating said polynomial coefficients at said point to perform a Taylor Series expansion from said point.
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Abstract
Methods and apparatus are provided for non-linear modeling of a physical system using look-up tables with polynomial interpolation. A non-linear function is evaluated for a complex input value by obtaining at least one look-up table with polynomial interpolation that represents the non-linear function, wherein entries in the look-up table comprise polynomial coefficients of at least degree two for different segments of the non-linear function; obtaining a point from the look-up table that is near a magnitude of the complex input value; and generating a complex output value by evaluating the polynomial coefficients at the point to perform a Taylor Series expansion from said point. The non-linear function characterizes, for example, a power amplifier or an inverse of a power amplifier and the look-up tables can be used, for example, to implement digital pre-distortion.
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Citations
20 Claims
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1. A digital pre-distortion (DPD) system, comprising:
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a digital signal processor configured to evaluate a non-linear function for a complex input value, comprising; a memory configured to store at least one look-up table with polynomial interpolation that represents said non-linear function, wherein entries in said look-up table comprise polynomial coefficients of at least degree two for different segments of said non-linear function, said polynomial coefficients configured to provide at least one of a rectangular or triangular basis function for each segment of said non-linear function; at least one processor, coupled to the memory, operative to; obtain a point from said look-tip table that is near a magnitude of said complex input value; and generate a complex output value by evaluating said polynomial coefficients at said point to perform a Taylor Series expansion from said point. - View Dependent Claims (3, 4, 5, 6, 7, 8, 9, 10)
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2. A digital pre-distortion (DPD) system, comprising:
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a digital signal processor configured to evaluate a non-linear function for a complex input value, comprising; a memory configured to store at least one look-up table with polynomial interpolation that represents said non-linear function, wherein entries in said look-up table comprise polynomial coefficients of at least degree two for different segments of said non-linear function; at least one processor, coupled to the memory, operative to; obtain a point from said look-tip table that is near a magnitude of said complex input value; and generate a complex output value by evaluating said polynomial coefficients at said point to perform a Taylor Series expansion from said point, wherein values in said look-up table are configured to be obtained using a direct optimization technique that obtains physical data for said non-linear function by applying a set of complex input samples x(n) to said non-linear function and measuring a complex output y(n) of said non-linear function and directly computes parameters φ
of a memory model for said non-linear function from said physical data, said memory model comprises one or more look-up tables having polynomial interpolation, and said parameters φ
produce a substantially minimum mean square error, said parameters φ
are provided for storage as entries in said one or more look-up tables.
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11. A power amplifier, comprising:
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a digital signal processor that evaluates a non-linear function for a complex input value, comprising; a memory configured to store storing at least one look-up table with polynomial interpolation that represents said non-linear function, wherein entries in said look-up table comprise polynomial coefficients of at least degree two for different segments of said non-linear function, said polynomial coefficients configured to provide at least one of a rectangular or triangular basis function for each segment of said non-linear function; and at least one processor, coupled to the memory, operative to; obtain a point from said look-tip table that is near a magnitude of said complex input value; and generate a complex output value by evaluating said polynomial coefficients at said point to perform a Taylor Series expansion from said point. - View Dependent Claims (13, 14, 15, 16, 17, 18, 19, 20)
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12. A power amplifier, comprising:
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a digital signal processor that evaluates a non-linear function for a complex input value, comprising; a memory configured to store at least one look-up table-with polynomial interpolation that represents said non-linear function, wherein entries in said look-up table comprise polynomial coefficients of at least degree two for different segments of said non-linear function; and at least one processor, coupled to the memory, operative to; obtain a point from said look-tip table that is near a magnitude of said complex input value; and generate a complex output-value by evaluating said polynomial coefficients at said point to perform a Taylor Series expansion from said point, wherein values in said look-up table are configured to be obtained using a direct optimization technique that obtains physical data for said non-linear function by applying a set of complex input samples x(n) to said non-linear function and measuring a complex output y(n) of said non-linear function and directly computes parameters φ
of a memory model for said non-linear function from said physical data, said memory model comprises one or more look-up tables having polynomial interpolation, and said parameters φ
produce a substantially minimum mean square error, said parameters φ
are provided for storage as entries in said one or more look-up tables.
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Specification