Method and apparatus for determination of predistortion parameters for a quadrature modulator

• US 6,298,096 B1
• Filed: 11/19/1998
• Issued: 10/02/2001
• Est. Priority Date: 11/19/1998
• Status: Expired due to Fees

• Current Assignee: L-3 Communications Corporation (L3Harris Technologies, Inc.)
• Original Assignee: Titan (L3Harris Technologies, Inc.)
• Inventors: Burgin, George H.
• Primary Examiner(s): Chin, Stephen
• Assistant Examiner(s): JIANG, LENNY R
• Application Number:
  US09/196,361
• Time in Patent Office: 1,048 Days
• Field of Search: 375/296, 375/297, 375/285, 375/254, 330/149, 332/123
• US Class Current: 375/296
• CPC Class Codes: H03C 3/406 using a feedback loop containing mixers or demodulators
• CPC Class Codes: H03D 7/168 using a feedback loop containing mixers or demodulators
• CPC Class Codes: H03F 1/3247 using feedback acting on predistortion circuits H03F1/3264 takes precedence
• CPC Class Codes: H04L 27/368 adaptive predistortion

Abstract

A transmit modulator which uses a quadrature modulator has a predistortion block which produces a predistorted output signal. The predistortion block pre-compensates for errors introduced by the quadrature modulator based on a set of predistortion parameters. The quadrature modulator receives the output signals from the predistortion block. The quadrature modulator up-converts the I and Q channel signals and combines them. In the process, the quadrature modulator introduces errors. In calibration mode, a sinusoidal wave at frequency f_cal is applied to the input of the predistortion block and a transformer is coupled to the output of the quadrature modulator. The transformer produces a digital representation of a spectrum of the output of the quadrature modulator converted to baseband. Spurious energy produced by the quadrature modulator errors but reduced by the effect of the predistortion block is generated at f_cal and ^2*f_cal. A quadratic polynomial minimization calculator receives the output of the transformer. The quadratic polynomial minimization calculator determines a subsequent value of the predistortion parameters based upon a quadratic relationship between energies present in the digital representation of the spectrum of the output of the quadrature modulator at frequencies f_cal and 2*f_cal and the values of the previous predistortion parameters.

Claims

1. A method of determining a set of predistortion parameters for use with a quadrature modulator comprising the steps of:

(a) applying a sinusoidal wave to said quadrature modulator at a frequency f_cal;

(b) collecting a first series of sets of samples reflecting changes to the value of a first set of predistortion parameters;

(c) identifying a first series of energy values output by said quadrature modulator at said frequency f_cal and the frequency 2*f_cal, each of said series of energy values corresponding to one of said sets of samples; and

(d) determining a subsequent value of said first set of predistortion parameters based upon a quadratic relationship between the value of said first set of predistortion parameters and said first series of energy values.

2. The method of claim 1, further comprising the steps of:

(e) collecting a second series of sets of samples reflecting changes to the value of a second set of predistortion parameters;

(f) identifying a second series of energy values output by said quadrature modulator at said frequency f_cal and said frequency 2*f_cal, each of said series of energy values corresponding to one of said sets of samples; and

(g) determining a subsequent value of said second set of predistortion parameters based upon a quadratic relationship between the value of said second set of predistortion parameters and said second series of energy values.

3. The method of claim 2, wherein the steps (b)-(g) are iteratively repeated until said first and second set of predistortion parameters converge.

4. A method of determining a set of predistortion parameters for use in a predistortion block which drives an imperfect quadrature modulator in which a predistortion parameter, b_i, which determines a D.C. offset adjustment to an I channel, a predistortion parameter, b_q, which determines a D.C. offset adjustment to an Q channel, a predistortion parameter, K, which determines a cross talk gain between said I channel and said Q channel, and a predistortion parameter, G, which determines a gain offset adjustment between said I channel and said Q channel, the method comprising the steps of:

applying a sinusoidal wave at frequency f_cal to said predistortion block;

collecting a first set of samples of an output of said imperfect quadrature modulator corresponding to setting said predistortion parameter, G, to a lower value than a previous G value equal to x₁^2fcal, a first one of said predistortion parameters which determine said D.C. offset to a lower value than a previous b₁ value equal to x₁^fcal, setting said predistortion parameter, K, to a previous K value and a second one of said predistortion parameters which determines said D.C. offset to a previous b₂ value;

determining an energy level at the frequency f_cal and the frequency 2f_cal for said first set of samples equal to y₁^fcal and y₁^2fcal, respectively;

collecting a second set of samples corresponding to setting said predistortion parameter, G, to said previous G value equal to x₂^2fcal, said first one of said predistortion parameters which determine said D.C. offset to said previous b₁ value equal to x₂^fcal, said predistortion parameter, K, to said previous K value and said second one of said predistortion parameters which determines said D.C. offset to said previous b₂ value;

determining an energy level at the frequency f_cal and the frequency 2f_cal for said second set of samples equal to y₂^fcal and y₂^2fcal, respectively;

collecting a third set of samples corresponding to setting said predistortion parameter, G, to a higher value than said previous G value equal to x₃^2fcal, said first one of said predistortion parameters which determine said D.C. offset to a higher value than said previous b₁ value equal to x₃^fcal, said predistortion parameter, K, to said previous K value and said second one of said predistortion parameters which determines said D.C. offset to said previous b₂ value;

determining an energy level at the frequency f_cal and the frequency 2fcal for said third set of samples equal to y₃^fcal and y₃^fcal, respectively;

determining a subsequent value of said predistortion parameter, G, based upon a quadratic relationship between said energy level y₁^2fcal and said value x₁^2fcal, between said energy level y₂^2fcal and said value x₂^2fcal and between said energy level y₃^2fcal and said value x₃^2fcal;

determining a subsequent value of said first one of said predistortion parameters which determine said D.C. offset based upon a quadratic relationship between said energy level y₁^fcal and said value x₁^fcal, between said energy level y₂^fcal and said value x₂^fcal and between said energy level y₃^fcal and said value x₃^fcal;

collecting a fourth set of samples of an output of said imperfect quadrature modulator corresponding to setting said predistortion parameter, K, to a lower value than a previous K value equal to x₄^2fcal, a second one of said predistortion parameters which determine said D.C. offset to a lower value than a previous b₂ value equal to x₄^cal, setting said predistortion parameter, G, to said subsequent value thereof and said first one of said predistortion parameters which determines said D.C. offset to said subsequent value thereof;

determining an energy level at the frequency f_cal and the frequency 2f_cal for said fourth set of samples equal to y₄^fcal and y₄^2fcal, respectively;

collecting a fifth set of samples corresponding to setting predistortion parameter, K, to said previous K value equal to x₅^2fcal, said second one of said predistortion parameters which determine said D.C. offset to said previous b₂ value equal to x₅^cal, said predistortion parameter, G, to said subsequent value thereof and said first one of said predistortion parameters which determines said D.C. offset to said subsequent value thereof,

determining an energy level at the frequency f_cal and the frequency 2f_cal for said fifth set of samples equal to y₅^cal and y₅^2fcal, respectively;

collecting a sixth set of samples corresponding to setting said predistortion parameter, K, to a higher value than said previous K value equal to x₆^2fcal, said second one of said predistortion parameters which determine said D.C. offset to a higher value than said previous b₂ value equal to x₆^fcal, said predistortion parameter, G, to said subsequent value thereof and said first one of said predistortion parameters which determines said D.C. offset to said subsequent value thereof;

determining an energy level at the frequency f_cal and the frequency 2f_cal for said sixth set of samples equal to y₆^fcal and y₆^2fcal, respectively;

determining a subsequent value of said predistortion parameter, K, based upon a quadratic relationship between said energy level y₄^2fcal and said value x₅^2fcal, between said energy level y₅^2fcal and said value x₅^2fcal and between said energy level y₆^2fcal and said value x₆^2fcal; and

determining a subsequent value of said second one of said predistortion parameters which determine said D.C. offset based upon a quadratic relationship between said energy level y₄^cal and said value x₄^cal, between said energy level y₅^cal and said value x₅^cal and between said energy level y₆^fcal and said value x₆^fcal.

5. A method of determining a set of predistortion parameters for use in predistortion block which drives an imperfect quadrature modulator in which a predistortion parameter, b_i, which determines a D.C. offset adjustment to an I channel, a predistortion parameter, b_q, which determines a D.C. offset adjustment to a Q channel, a predistortion parameter, K, which determines a cross talk gain between said I channel and said Q channel, and a predistortion parameter, G, which determines a gain offset adjustment between said I channel and said Q channel, said method comprising the steps of:

applying a sinusoidal wave at frequency f_cal to said predistortion block;

setting said predistortion parameter, G, equal to a previous value, G(n), offset on the low side by the selected step value Δ

G wherein G(n)−

Δ

G=x^12fcal;

setting said predistortion parameter, b_q, equal to a previous value, b_q(n), offset on the low side by the selected step value Δ

b_q wherein b_q(n)−

Δ

b_q=x₁^fcal;

setting said predistortion parameter, K, equal to a previous value, K(n);

setting said predistortion parameter, b_i, equal to a previous value, b_i(n);

collecting a first set of samples of an output of said imperfect quadrature modulator and determining an energy level at the frequency f_cal and the frequency 2f_cal for said first set of samples equal to y₁^fcal and y₁^2fcal, respectively;

setting said predistortion parameter, G, equal to said previous value, G(n)=x₂^2fcal;

setting said predistortion parameter, b_q, equal to said previous value, b_q(n)=x₂^2fcal;

collecting a second set of samples of said output of said imperfect quadrature modulator and determining an energy level at the frequency f_cal and the frequency 2f_cal, for said second set of samples equal to y₂^fcal and y₂^2fcal, respectively;

setting said predistortion parameter, G, equal to said previous value, G(n), offset on the high side by the selected step value Δ

G wherein G(n)+Δ

G=x₃^2fcal;

setting said predistortion parameter, b_q, equal to said previous value, b_q(n), offset on the high side by the selected step value Δ

b_q wherein b_q(n)+Δ

b_q=x₃^fcal;

collecting a third set of samples of said output of said imperfect quadrature modulator and determining an energy level at the frequency f_cal and the frequency 2f_cal for said third set of samples equal to y₃^fcal and y_32fcal, respectively;

determining a subsequent value of said predistortion parameter, b_q, equal to b_q(n+1) by solving

6. The method of determining said set of predistortion parameters of claim 5, wherein said imperfect quadrature modulator is a direct conversion modulator.

7. The method of determining said set of predistortion parameters of claim 5, wherein said step of applying a sinusoidal wave at frequency f_cal to said predistortion block and said steps of collecting said first, second, third, fourth, fifth and sixth sample sets occur during a calibration mode and wherein said steps of determining said energy levels at the frequency f_cal and the frequency 2f_cal and said determining said subsequent values occur during said calibration mode or during a transmit mode.

8. The method of determining said set of predistortion parameters of claim 5, further comprising the steps of:

setting said predistortion parameter, G, equal to said next value, G(n+1);

setting said predistortion parameter, b_q, equal to said next value, b_q(n+1);

setting said predistortion parameter, K, equal to said next value, K(n+1);

setting said predistortion parameter, b_i, equal to said next value, b_i(n+1);

collecting a seventh set of samples of said output of said imperfect quadrature modulator and determining an energy level at the frequency f_cal and the frequency 2f_cal;

comparing said energy values at the frequency f_cal and the frequency 2f_cal to previously collected energy values at the frequency f_cal and the frequency 2f_cal; and

setting said previous values equal to said subsequent values and repeating said steps of collecting samples and determining said subsequent values if a difference between said energy values and said previously collected set of energy values is less than a predetermined value.

9. An apparatus for determining a set of predistortion parameters for use in a predistortion block which drives an imperfect quadrature modulator in which a predistortion parameter, b_i, which determines a D.C. offset adjustment to an I channel, a predistortion parameter, b_q, which determines a D.C. offset adjustment to an Q channel, a predistortion parameter, K, which determines a cross talk gain between said I channel and said Q channel, and a predistortion parameter, G, which determines a gain offset adjustment between said I channel and said Q channel, the apparatus comprising:

means for applying a sinusoidal wave at frequency f_cal to said predistortion block;

means for collecting a first set of samples of an output of said imperfect quadrature modulator corresponding to setting said predistortion parameter, G, to a lower value than a previous G value equal to x₁^2fcal, a first one of said predistortion parameters which determine said D.C. offset to a lower value than a previous b₁ value equal to x_i^fcal, setting said predistortion parameter, K, to a previous K value and a second one of said predistortion parameters which determines said D.C. offset to a previous b₂ value;

means for determining an energy level at the frequency f_cal and the frequency 2f_cal for said first set of samples equal to y₁^fcal and y₁^2fcal, respectively;

means for collecting a second set of samples corresponding to setting said predistortion parameter, G, to said previous G value equal to x₂^2fcal, said first one of said predistortion parameters which determine said D.C. offset to said previous b₁ value equal to x₂^fcal, said predistortion parameter, K, to said previous K value and said second one of said predistortion parameters which determines said D.C. offset to said previous b₂ value;

means for determining an energy level at the frequency f_cal and the frequency 2f_cal for said second set of samples equal to y₂^fcal and y₂^2fcal, respectively;

means for collecting a third set of samples corresponding to setting said predistortion parameter, G, to a higher value than said previous G value equal to x₃^2fcal, said first one of said predistortion parameters which determine said D.C. offset to a higher value than said previous b₁ value equal to x₃^fcal, said predistortion parameter, K, to said previous K value and said second one of said predistortion parameters which determines said D.C. offset to said previous b₂ value;

means for determining an energy level at the frequency f_cal and the frequency 2f^cal for said third set of samples equal to y₃^2fcal and y₃^2fcal, respectively;

means for determining a subsequent value of said predistortion parameter, G, based upon a quadratic relationship between said energy level y₁^2fcal and said value x₁^2fcal, between said energy level y₂^2fcal and said value x₂^2fcal and between said energy level y₃^2fcal and said value x₃^2fcal;

means for determining a subsequent value of said first one of said predistortion parameters which determine said D.C. offset based upon a quadratic relationship between said energy level y₁^fcal and said value x₁^fcal, between said energy level y₂^fcal and said value x₂^fcal and between said energy level y₃^fcal and said value x₃^fcal;

means for collecting a fourth set of samples of an output of said imperfect quadrature modulator corresponding to setting said predistortion parameter, K, to a lower value than a previous K value equal to x₄^2fcal, a second one of said predistortion parameters which determine said D.C. offset to a lower value than a previous b₂ value equal to x₄^cal, setting said predistortion parameter, G, to said subsequent value thereof and said first one of said predistortion parameters which determines said D.C. offset to said subsequent value thereof;

means for determining an energy level at the frequency f_cal and the frequency 2f_cal for said fourth set of samples equal to y₄^fcal and y₄^2fcal, respectively;

means for collecting a fifth set of samples corresponding to setting predistortion parameter, K, to said previous K value equal to x₄^2fcal, said second one of said predistortion parameters which determine said D.C. offset to said previous b₂ value equal to x₄^cal, said predistortion parameter, G, to said subsequent value thereof and said first one of said predistortion parameters which determines said D.C. offset to said subsequent value thereof;

means for determining an energy level at the frequency f_cal and the frequency 2f_cal for said fifth set of samples equal to y₅^cal and y₅^2fcal, respectively;

means for collecting a sixth set of samples corresponding to setting said predistortion parameter, K, to a higher value than said previous K value equal to x₆^2fcal, said second one of said predistortion parameters which determine said D.C. offset to a higher value than said previous b₂ value equal to x₆^fcal, said predistortion parameter, G, to said subsequent value thereof and said first one of said predistortion parameters which determines said D.C. offset to said subsequent value thereof;

determining an energy level at the frequency f_cal and the frequency 2f_cal for said sixth set of samples equal to y₆^fcal and y₆^2fcal, respectively;

determining a subsequent value of said predistortion parameter, K, based upon a quadratic relationship between said energy level y₄^2fcal and said value x₄^2fcal, between said energy level y₅^2fcal and said value x₅^2fcal and between said energy level y₆^2fcal and said value x₆^2fcal; and

determining a subsequent value of said second one of said predistortion parameters which determine said D.C. offset based upon a quadratic relationship between said energy level y₄^cal and said value x₄^cal, between said energy level y₅^cal and said value x₅^cal and between said energy level y₆^fcal and said value x₆^fcal.

10. A transmit modulator comprising:

a predistortion block producing a predistorted output signal comprising;

a D.C. offset compensation summer which determines a D.C. offset adjustment to an I channel based upon a predistortion parameter, b_i;

a D.C. offset compensation summer which determines a D.C. offset adjustment to an Q channel based upon a predistortion parameter, b_q;

<

a cross talk amplifier which determines a cross talk gain between said I channel and said Q channel based upon a predistortion parameter, K; and

a gain compensation amplifier which determines a gain offset adjustment between said I channel and said Q channel based upon a predistortion parameter, G;

an imperfect quadrature modulator coupled to said predistortion block and receiving said predistorted output signal and producing a modulated signal;

a transformer coupled to said imperfect quadrature modulator and receiving said modulated signal and producing a digital representation of a spectrum of said modulated signal;

a quadratic polynomial minimization calculator which determines a subsequent value of said predistortion parameters, b_i, b_q, K and G based upon a quadratic relationship between energies present in said digital representation of said spectrum of said modulated signal and the values of said predistortion parameter b_i, b_q, K and G.

11. The transmit modulator of claim 10 wherein said quadratic polynomial minimization calculator contains a series of processes that when executed perform the steps of:

collecting a first set of samples of an output of said imperfect quadrature modulator corresponding to setting said predistortion parameter, G, to a lower value than a previous G value equal to x₁^2fcal, a first one of said predistortion parameters which determine a D.C. offset to a lower value than a previous b₁ value equal to x₁^fcal, setting said predistortion parameter, K, to a previous K value and a second one of said predistortion parameters which determines a D.C. offset to a previous b₂ value;

determining an energy level at the frequency f_cal and the frequency 2f_cal for said first set of samples equal to y₁^{fcal and y}₁^2fcal, respectively;

collecting a second set of samples corresponding to setting said predistortion parameter, G, to said previous G value equal to x₂^2fcal, said first one of said predistortion parameters which determine said D.C. offset to said previous b₁ value equal to x₂^fcal, said predistortion parameter, K, to said previous K value and said second one of said predistortion parameters which determines said D.C. offset to said previous b₂ value;

determining an energy level at the frequency f_cal and the frequency 2f_cal for said second set of samples equal to y₂^fcal and y₂^2fcal, respectively;

collecting a third set of samples corresponding to setting said predistortion parameter, G, to a higher value than said previous G value equal to x₃^2fcal, said first one of said predistortion parameters which determine said D.C. offset to a higher value than said previous b₁ value equal to x₃^fcal, said predistortion parameter, K, to said previous K value and said second one of said predistortion parameters which determines a D.C. offset to said previous b₂ value;

determining an energy level at the frequency f_cal and the frequency 2f_cal for said third set of samples equal to y₃^fcal and y₃^2fcal, respectively;

determining a subsequent value of said predistortion parameter, G, based upon a quadratic relationship between said energy level y₁^2fcal and said value x₁^2fcal, between said energy level y₂^2fcal and said value x₂^2fcal and between said energy level y₃^2fcal and said value x₃^2fcal;

determining a subsequent value of said first one of said predistortion parameters which determine said D.C. offset based upon a quadratic relationship between said energy level y₁^fcal and said value x₁^fcal, between said energy level y₂^fcal and said value x₂^fcal and between said energy level y₃^fcal and said value x₃^fcal;

collecting a fourth set of samples of an output of said imperfect quadrature modulator corresponding to setting said predistortion parameter, K, to a lower value than a previous K value equal to x₄^2fcal, a second one of said predistortion parameters which determine said D.C. offset to a lower value than a previous b₂ value equal to x₄^cal, setting said predistortion parameter, G, to said subsequent value thereof and said first one of said predistortion parameters which determines a D.C. offset to said subsequent value thereof;

determining an energy level at the frequency f_cal and the frequency 2f_cal for said fourth set of samples equal to y₄^fcal and y₄^2fcal, respectively;

collecting a fifth set of samples corresponding to setting predistortion parameter, K, to said previous K value equal to x₄^2fcal, said second one of said predistortion parameters which determine said D.C. offset to said previous b₂ value equal to x₄^cal, said predistortion parameter, G, to said subsequent value thereof and said first one of said predistortion parameters which determines a D.C. offset to said subsequent value thereof;

determining an energy level at the frequency f_cal and the frequency 2f_cal for said fifth set of samples equal to y₅^cal and y₅^2fcal, respectively;

collecting a sixth set of samples corresponding to setting said predistortion parameter, K, to a higher value than said previous K value equal to x₆^2fcal, said second one of said predistortion parameters which determine said D.C. offset to a higher value than said previous b₂ value equal to x₆^fcal, said predistortion parameter, G, to said subsequent value thereof and said first one of said predistortion parameters which determines a D.C. offset to said subsequent value thereof;

determining an energy level at the frequency f_cal and the frequency 2f_cal for said sixth set of samples equal to y₆^fcal and y₆^2fcal, respectively;

determining a subsequent value of said predistortion parameter, K, based upon a quadratic relationship between said energy level y₄^2fcal and said value x₄^2fcal, between said energy level y₅^2fcal and said value x₅^2fcal and between said energy level y₆^2fcal and said value x₆^2fcal; and

determining a subsequent value of said second one of said predistortion parameters which determine said D.C. offset based upon a quadratic relationship between said energy level y₄^cal and said value x₄^cal, between said energy level y₅^cal and said value x₅^cal and between said energy level y₆^fcal and said value x₆^fcal.

12. A programmed storage device storing a series of process that when executed perform a method of determining a set of predistortion parameters for use in a predistortion block which drives an imperfect quadrature modulator in which a predistortion parameter, b_i, which determines a D.C. offset adjustment to an I channel, a predistortion parameter, b_q, which determines a D.C. offset adjustment to an Q channel, a predistortion parameter, K, which determines a cross talk gain between said I channel and said Q channel, and a predistortion parameter, G, which determines a gain offset adjustment between said I channel and said Q channel, the method comprising the steps of:

applying a sinusoidal wave at frequency f_cal to said predistortion block;

collecting a first set of samples of an output of said imperfect quadrature modulator corresponding to setting said predistortion parameter, G, to a lower value than a previous G value equal to x₁^2fcal a first one of said predistortion parameters which determine said D.C. offset to a lower value than a previous b₁ value equal to x₁^fcal, setting said predistortion parameter, K, to a previous K value and a second one of said predistortion parameters which determines said D.C. offset to a previous b₂ value;

determining an energy level at the frequency f_cal and the frequency 2f_cal for said first set of samples equal to y₁^fcal and y₁^2fcal, respectively;

collecting a second set of samples corresponding to setting said predistortion parameter, G, to said previous G value equal to x₂^2fcal, said first one of said predistortion parameters which determine said D.C. offset to said previous b₁ value equal to x₂^fcal, said predistortion parameter, K, to said previous K value and said second one of said predistortion parameters which determines said D.C. offset to said previous b₂ value;

determining an energy level at the frequency f_cal and the frequency 2f_cal for said second set of samples equal to y₂^fcal and y₂^2fcal, respectively;

collecting a third set of samples corresponding to setting said predistortion parameter, G, to a higher value than said previous G value equal to x₃^2fcal, said first one of said predistortion parameters which determine said D.C. offset to a higher value than said previous b₁ value equal to x₃^fcal, said predistortion parameter, K, to said previous K value and said second one of said predistortion parameters which determines said D.C. offset to said previous b₂ value;

determining an energy level at the frequency f_cal and the frequency 2f_cal for said third set of samples equal to y₃^fcal and y₃^2fcal, respectively;

determining a subsequent value of said predistortion parameter, G, based upon a quadratic relationship between said energy level y₁^2fcal and said value x₁^2fcal, between said energy level y₂^2fcal and said value x₂^2fcal and between said energy level y₃^2fcal and said value x₃^2fcal;

determining a subsequent value of said first one of said predistortion parameters which determine said D.C. offset based upon a quadratic relationship between said energy level y₁^fcal and said value x₁^fcal, between said energy level y₂^fcal and said value x₂^fcal and between said energy level y₃^fcal and said value x₃^fcal;

collecting a fourth set of samples of an output of said imperfect quadrature modulator corresponding to setting said predistortion parameter, K, to a lower value than a previous K value equal to x₄^2fcal, a second one of said predistortion parameters which determine said D.C. offset to a lower value than a previous b₂ value equal to x₄^cal, setting said predistortion parameter, G, to said subsequent value thereof and said first one of said predistortion parameters which determines said D.C. offset to said subsequent value thereof;

determining an energy level at the frequency f_cal and the frequency 2f_cal for said fourth set of samples equal to y₄^fcal and y₄^2fcal, respectively;

collecting a fifth set of samples corresponding to setting predistortion parameter, K, to said previous K value equal to x₄^2fcal, said second one of said predistortion parameters which determine said D.C. offset to said previous b₂ value equal to x₄^cal, said predistortion parameter, G, to said subsequent value thereof and said first one of said predistortion parameters which determines said D.C. offset to said subsequent value thereof;

determining an energy level at the frequency f_cal and the frequency 2f_cal for said fifth set of samples equal to y₅^cal and y₅^2fcal, respectively;

collecting a sixth set of samples corresponding to setting said predistortion parameter, K, to a higher value than said previous K value equal to x₆^2fcal, said second one of said predistortion parameters which determine said D.C. offset to a higher value than said previous b₂ value equal to x₆^fcal, said predistortion parameter, G, to said subsequent value thereof and said first one of said predistortion parameters which determines said D.C. offset to said subsequent value thereof;

determining an energy level at the frequency f_cal and the frequency 2f_cal for said sixth set of samples equal to y₆^fcal and y₆^2fcal, respectively;

determining a subsequent value of said predistortion parameter, K, based upon a quadratic relationship between said energy level y₄^2fcal and said value x₄^2fcal, between said energy level y₅^2fcal and said value x₅^2fcal and between said energy level y₆^2fcal and said value x₆^2fcal; and

determining a subsequent value of said second one of said predistortion parameters which determine said D.C. offset based upon a quadratic relationship between said energy level y₄^cal and said value x₄^cal, between said energy level y₅^cal and said value x₅^cal and between said energy level y₆^fcal and said value x₆^fcal.