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

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, bi, which determines a D.C. offset adjustment to an I channel, a predistortion parameter, bq, 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 fcal 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 x12fcal, a first one of said predistortion parameters which determine said D.C. offset to a lower value than a previous b1 value equal to x1fcal, 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 fcal and the frequency 2fcal for said first set of samples equal to y1fcal and y12fcal, respectively;
• collecting a second set of samples corresponding to setting said predistortion parameter, G, to said previous G value equal to x22fcal, said first one of said predistortion parameters which determine said D.C. offset to said previous b1 value equal to x2fcal, 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 fcal and the frequency 2fcal for said second set of samples equal to y2fcal and y22fcal, 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 x32fcal, said first one of said predistortion parameters which determine said D.C. offset to a higher value than said previous b1 value equal to x3fcal, 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 fcal and the frequency 2fcal for said third set of samples equal to y3fcal and y3fcal, respectively;
• determining a subsequent value of said predistortion parameter, G, based upon a quadratic relationship between said energy level y12fcal and said value x12fcal, between said energy level y22fcal and said value x22fcal and between said energy level y32fcal and said value x32fcal;
• 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 y1fcal and said value x1fcal, between said energy level y2fcal and said value x2fcal and between said energy level y3fcal and said value x3fcal;
• 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 x42fcal, a second one of said predistortion parameters which determine said D.C. offset to a lower value than a previous b2 value equal to x4cal, 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 fcal and the frequency 2fcal for said fourth set of samples equal to y4fcal and y42fcal, respectively;
• collecting a fifth set of samples corresponding to setting predistortion parameter, K, to said previous K value equal to x52fcal, said second one of said predistortion parameters which determine said D.C. offset to said previous b2 value equal to x5cal, 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 fcal and the frequency 2fcal for said fifth set of samples equal to y5cal and y52fcal, 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 x62fcal, said second one of said predistortion parameters which determine said D.C. offset to a higher value than said previous b2 value equal to x6fcal, 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 fcal and the frequency 2fcal for said sixth set of samples equal to y6fcal and y62fcal, respectively;
• determining a subsequent value of said predistortion parameter, K, based upon a quadratic relationship between said energy level y42fcal and said value x52fcal, between said energy level y52fcal and said value x52fcal and between said energy level y62fcal and said value x62fcal;
• 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 y4cal and said value x4cal, between said energy level y5cal and said value x5cal and between said energy level y6fcal and said value x6fcal.

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, bi, which determines a D.C. offset adjustment to an I channel, a predistortion parameter, bq, 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 fcal 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 ΔG wherein G(n)−ΔG=x12fcal;
• setting said predistortion parameter, bq, equal to a previous value, bq(n), offset on the low side by the selected step value Δbq wherein bq(n)−Δbq=x1fcal;
• setting said predistortion parameter, K, equal to a previous value, K(n);
• setting said predistortion parameter, bi, equal to a previous value, bi(n);
• collecting a first set of samples of an output of said imperfect quadrature modulator and determining an energy level at the frequency fcal and the frequency 2fcal for said first set of samples equal to y1fcal and y12fcal, respectively;
• setting said predistortion parameter, G, equal to said previous value, G(n)=x22fcal;
• setting said predistortion parameter, bq, equal to said previous value, bq(n)=x22fcal;
• collecting a second set of samples of said output of said imperfect quadrature modulator and determining an energy level at the frequency fcal and the frequency 2fcal, for said second set of samples equal to y2fcal and y22fcal, respectively;
• setting said predistortion parameter, G, equal to said previous value, G(n), offset on the high side by the selected step value ΔG wherein G(n)+ΔG=x32fcal;
• setting said predistortion parameter, bq, equal to said previous value, bq(n), offset on the high side by the selected step value Δbq wherein bq(n)+Δbq=x3fcal;
• collecting a third set of samples of said output of said imperfect quadrature modulator and determining an energy level at the frequency fcal and the frequency 2fcal for said third set of samples equal to y3fcal and y32fcal, respectively;
• determining a subsequent value of said predistortion parameter, bq, equal to bq(n+1) by solving
• bq(n+1)=−b/(2a)
• where
• yifcal=a(xifcal)2+bxifcal+c for i=1,2 and 3;
• determining a subsequent value of said predistortion parameter, G, equal to G(n+1) by solving
• G(n+1)=−b/(2a)
• where
• yi2fcal=a(xi2fcal)2+bxi2fcal=c for i=1,2 and 3
• setting said predistortion parameter, G, equal to said next value, G(n+1);
• setting said predistortion parameter, bq, equal to said next value, bq(n+1);
• setting said predistortion parameter, K, equal to said previous value, K(n) offset on the low side by the selected step value ΔK wherein K(n)−ΔK=x42fcal;
• setting said predistortion parameter, bi, equal to said previous value, bi(n) offset on the low side by the selected step value Δbi wherein bi(n)−Δbi=x4fcal;
• collecting a fourth set of samples of said output of said imperfect quadrature modulator and determining an energy level at the frequency fcal and the frequency 2fcal for said fourth set of samples equal to y4fcal and y42fcal, respectively;
• setting said predistortion parameter, K, equal to said previous value, K(n)=x52fcal;
• setting said predistortion parameter, bi, equal to said previous value, bi(n)=x5fcal;
• collecting a fifth set of samples of said output of said imperfect quadrature modulator and determining an energy level at the frequency fcal and the frequency 2fcal for said fifth set of samples equal to y5fcal and y52fcal, respectively;
• setting said predistortion parameter, K, equal to said previous value, K(n), offset on the high side by the selected step value ΔK wherein K(n)+ΔK=x62fcal;
• setting said predistortion parameter, bi, equal to said previous value, bi(n), offset on the high side by the selected step value Δbi wherein bi(n)+Δbi=x6fcal;
• collecting a sixth set of samples of said output of said imperfect quadrature modulator and determining an energy level at the frequency fcal and the frequency 2fcal for said sixth set of samples equal to y6fcal and y62fcal, respectively;
• determining a subsequent value of said predistortion parameter, bi, equal to bi(n+1) by solving
• bi(n+1)=−b/(2a)
• where
• yifcal=a(xifcal)2+bxifcal+c for i=4, 5 and 6;
• and
• determining a subsequent value of said predistortion parameter, K, equal to K(n+1) by solving
• K(n+1)=−b/(2a)
• where
• yifcal=a(xifcal)2+bxi2fcal+c for i=4, 5 and 6.

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, bi, which determines a D.C. offset adjustment to an I channel, a predistortion parameter, bq, 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 fcal 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 x12fcal, a first one of said predistortion parameters which determine said D.C. offset to a lower value than a previous b1 value equal to xifcal, 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 fcal and the frequency 2fcal for said first set of samples equal to y1fcal and y12fcal, respectively;
• means for collecting a second set of samples corresponding to setting said predistortion parameter, G, to said previous G value equal to x22fcal, said first one of said predistortion parameters which determine said D.C. offset to said previous b1 value equal to x2fcal, 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 fcal and the frequency 2fcal for said second set of samples equal to y2fcal and y22fcal, 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 x32fcal, said first one of said predistortion parameters which determine said D.C. offset to a higher value than said previous b1 value equal to x3fcal, 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 fcal and the frequency 2fcal for said third set of samples equal to y32fcal and y32fcal, respectively;
• means for determining a subsequent value of said predistortion parameter, G, based upon a quadratic relationship between said energy level y12fcal and said value x12fcal, between said energy level y22fcal and said value x22fcal and between said energy level y32fcal and said value x32fcal;
• 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 y1fcal and said value x1fcal, between said energy level y2fcal and said value x2fcal and between said energy level y3fcal and said value x3fcal;
• 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 x42fcal, a second one of said predistortion parameters which determine said D.C. offset to a lower value than a previous b2 value equal to x4cal, 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 fcal and the frequency 2fcal for said fourth set of samples equal to y4fcal and y42fcal, respectively;
• means for collecting a fifth set of samples corresponding to setting predistortion parameter, K, to said previous K value equal to x42fcal, said second one of said predistortion parameters which determine said D.C. offset to said previous b2 value equal to x4cal, 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 fcal and the frequency 2fcal for said fifth set of samples equal to y5cal and y52fcal, 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 x62fcal, said second one of said predistortion parameters which determine said D.C. offset to a higher value than said previous b2 value equal to x6fcal, 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 fcal and the frequency 2fcal for said sixth set of samples equal to y6fcal and y62fcal, respectively;
• determining a subsequent value of said predistortion parameter, K, based upon a quadratic relationship between said energy level y42fcal and said value x42fcal, between said energy level y52fcal and said value x52fcal and between said energy level y62fcal and said value x62fcal;
• 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 y4cal and said value x4cal, between said energy level y5cal and said value x5cal and between said energy level y6fcal and said value x6fcal.

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, bi;
• a D.C. offset compensation summer which determines a D.C. offset adjustment to an Q channel based upon a predistortion parameter, bq;
• <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, bi, bq, 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 bi, bq, K and G.

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, bi, which determines a D.C. offset adjustment to an I channel, a predistortion parameter, bq, 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 fcal 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 x12fcal a first one of said predistortion parameters which determine said D.C. offset to a lower value than a previous b1 value equal to x1fcal, 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 fcal and the frequency 2fcal for said first set of samples equal to y1fcal and y12fcal, respectively;
• collecting a second set of samples corresponding to setting said predistortion parameter, G, to said previous G value equal to x22fcal, said first one of said predistortion parameters which determine said D.C. offset to said previous b1 value equal to x2fcal, 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 fcal and the frequency 2fcal for said second set of samples equal to y2fcal and y22fcal, 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 x32fcal, said first one of said predistortion parameters which determine said D.C. offset to a higher value than said previous b1 value equal to x3fcal, 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 fcal and the frequency 2fcal for said third set of samples equal to y3fcal and y32fcal, respectively;
• determining a subsequent value of said predistortion parameter, G, based upon a quadratic relationship between said energy level y12fcal and said value x12fcal, between said energy level y22fcal and said value x22fcal and between said energy level y32fcal and said value x32fcal;
• 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 y1fcal and said value x1fcal, between said energy level y2fcal and said value x2fcal and between said energy level y3fcal and said value x3fcal;
• 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 x42fcal, a second one of said predistortion parameters which determine said D.C. offset to a lower value than a previous b2 value equal to x4cal, 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 fcal and the frequency 2fcal for said fourth set of samples equal to y4fcal and y42fcal, respectively;
• collecting a fifth set of samples corresponding to setting predistortion parameter, K, to said previous K value equal to x42fcal, said second one of said predistortion parameters which determine said D.C. offset to said previous b2 value equal to x4cal, 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 fcal and the frequency 2fcal for said fifth set of samples equal to y5cal and y52fcal, 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 x62fcal, said second one of said predistortion parameters which determine said D.C. offset to a higher value than said previous b2 value equal to x6fcal, 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 fcal and the frequency 2fcal for said sixth set of samples equal to y6fcal and y62fcal, respectively;
• determining a subsequent value of said predistortion parameter, K, based upon a quadratic relationship between said energy level y42fcal and said value x42fcal, between said energy level y52fcal and said value x52fcal and between said energy level y62fcal and said value x62fcal;
• 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 y4cal and said value x4cal, between said energy level y5cal and said value x5cal and between said energy level y6fcal and said value x6fcal.