Signal predistortion for non-linear amplifier
A method, apparatus, and computer program for modeling mathematically an effect of a plurality of factors on signal distortion caused by a non-linear amplifier are provided. First, there is computed a global model which incorporates a combined effect of the plurality of factors on signal distortion caused by the non-linear amplifier. Before applying the pre-distorted transmission signal to the non-linear amplifier, a transmission signal is pre-distorted with coefficients derived from the global model thus compensating for the signal distortion caused by the non-linear amplifier.
1. A method, comprising:
for each of a plurality of factors affecting signal distortion caused by a non-linear amplifier, creating a mathematical model for the effect of the factor, wherein the mathematical model includes a mathematical function representing an approximation of the effect of the factor;
computing a global model based on a combination of the mathematical models for each effect of the plurality of factors, wherein the global model represents mathematically a combined effect of the plurality of factors on signal distortion caused by the non-linear amplifier,
computing, during operation of the non-linear amplifier, one or more coefficients derived from the global model, wherein the coefficients are computed as a result of minimizing of a difference between an input signal representing an input of the non-linear amplifier and an output signal representing an output of the non-linear amplifier, wherein the one or more coefficients compensate for the combined effect of the plurality of factors on the signal distortion caused by the non-linear amplifier, and wherein the one or more coefficients are computed during operation of the non-linear amplifier using parameters developed during, and based on, data generated during functioning of the non-linear amplifier; and
pre-distorting a signal with coefficients derived from the global model before applying the thus pre-distorted signal to the non-linear amplifier so as to compensate for the signal distortion caused by the non-linear amplifier.
2. The method of claim 1 , wherein the minimization results in computing the coefficients by solving an equation
e= ( X*·X ) −1 ·X*y,
where e represents a set of said coefficients, X represents the input signal in a matrix form and weighted by the effect of the plurality of factors, and y represents the output signal.
3. The method of claim 2 , wherein X*·X is computed as an autocorrelation of the effect of the plurality of factors, and wherein the X*y is computed as a cross-correlation between the effect of the plurality of factors and the output signal.
4. The method of claim 1 , wherein the minimization results in computing the coefficients by solving an equation
e= ( Y*·Y ) −1 ·Y*x,
where e represents a set of said coefficients, Y represents the output signal in a matrix form and weighted by the effect of the plurality of factors, and x represents the input signal.
5. The method of claim 4 , wherein Y*·Y is computed as an autocorrelation of the effect of the plurality of factors, and wherein the Y*x is computed as a cross-correlation between the effect of the plurality of factors and the input signal.
6. The method of claim 1 , wherein said plurality of factors comprise at least one of the following: temperature, a supply voltage of the non-linear amplifier, a gate voltage of at least one transistor of the nonlinear amplifier, a drain voltage of at least one transistor of the non-linear amplifier, a collector voltage of at least one transistor of the non-linear amplifier, and a bandwidth of the signal to be predistorted.
7. The method of claim 1 , wherein an order of the polynomial function is second order or less.
8. The method of claim 1 , wherein the combined effect of said plurality of factors is normalized.
9. The method of claim 1 , wherein the number of coefficients computed is proportional to the complexity of the mathematical representation of the effect of said plurality of factors.
10. The method of claim 1 , further comprising:
forming an autocorrelation matrix describing autocorrelation properties of the predistorted signal input to the non-linear amplifier under an effect of said at least one factor;
forming a cross-correlation vector describing cross-correlation properties between the predistorted signal input to the non-linear amplifier and an output signal of the non-linear amplifier under an effect of said at least one factor; and
reducing the size of the auto-correlation matrix and the cross-correlation vector by removing at least some of their elements according to determined criterion.
11. An apparatus, comprising means configuring the apparatus to carry out the method according to claim 1 .
12. A computer program product embodied on a distribution medium readable by a computer and comprising program instructions which, when loaded into an apparatus, execute the method according to claim 1 .
13. An apparatus comprising:
at least one processor; and
at least one memory including a computer program code, wherein the at least one memory and the computer program code are configured, with the at least one processor, to cause the apparatus to:
a plurality of factors affecting signal distortion caused by a non-linear amplifier, creating a mathematical model for the effect of the factor, wherein the mathematical model includes a mathematical function representing an approximation of the effect of the factor;
compute a global model based on a combination of the mathematical models for each effect of the plurality of factors, wherein the global model represents mathematically a combined effect of the plurality of factors on signal distortion caused by the non-linear amplifier;
compute, during operation of the non-linear amplifier, one or more coefficients derived from the global model, wherein the one or more coefficients compensate for the combined effect of the plurality of factors on the signal distortion caused by the non-linear amplifier, wherein the coefficients are computed as a result of minimizing of a difference between an input signal representing an input of the non-linear amplifier and an output signal representing an output of the non-linear amplifier, and wherein the one or more coefficients are computed during operation of the non-linear amplifier using parameters developed during, and based on, data generated during functioning of the non-linear amplifier; and
pre-distort a signal with coefficients derived from the global model before applying the so pre-distorted signal to the non-linear amplifier, thus compensating for the signal distortion caused by the non-linear amplifier.
14. The apparatus of claim 13 , wherein the at least one memory and the computer program code are configured, with the at least one processor, to cause the apparatus to carry out the minimization by computing the coefficients by solving an equation
e= ( X*·X ) −1 ·X*y,
where e represents a set of said coefficients, X represents the input signal in a matrix form and weighted by the effect of the plurality of factors, and y represents the output signal.
15. The apparatus of claim 13 , wherein the at least one memory and the computer program code are configured, with the at least one processor, to cause the apparatus to compute X*·X as an autocorrelation of the effect of the plurality of factors, and wherein the X*y is computed as a cross-correlation between the effect of the plurality of factors and the output signal.
16. The apparatus of claim 13 , wherein the at least one memory and the computer program code are configured, with the at least one processor, to cause the apparatus to compute the minimization by solving an equation
e= ( Y*·Y ) −1 ·Y*x,
where e represents a set of said coefficients, Y represents the output signal in a matrix form and weighted by the effect of the plurality of factors, and x represents the input signal.
17. The apparatus of claim 16 , wherein the at least one memory and the computer program code are configured, with the at least one processor, to cause the apparatus to compute Y*·Y as an autocorrelation of the effect of the plurality of factors, and wherein the Y*x is computed as a cross-correlation between the effect of the plurality of factors and the input signal.
18. The apparatus of claim 13 , wherein said plurality of factors comprise at least one of the following: temperature, a supply voltage of the non-linear amplifier, a gate voltage of at least one transistor of the non-linear amplifier, a drain voltage of at least one transistor of the non-linear amplifier, a collector voltage of at least one transistor of the non-linear amplifier, and a bandwidth of the signal.
19. The apparatus of claim 13 , wherein the at least one memory and the computer program code are configured, with the at least one processor, to cause the apparatus to represent the combined effect of said plurality of factors as a polynomial function.
20. The apparatus of claim 19 , wherein an order of the polynomial function is second order or less.
21. The apparatus of claim 13 , wherein the at least one memory and the computer program code are configured, with the at least one processor, to cause the apparatus to normalize the combined effect of said plurality of factors normalized.
22. The apparatus of claim 13 , wherein the number of coefficients computed is proportional to the complexity of the mathematical representation of the effect of said plurality of factors.
23. The apparatus of claim 13 , wherein the at least one memory and the computer program code are configured, with the at least one processor, to cause the apparatus to:
form an autocorrelation matrix describing autocorrelation properties of the predistorted signal input to the non-linear amplifier under an effect of said at least one factor;
form a cross-correlation vector describing cross-correlation properties between the predistorted signal input to the non-linear amplifier and an output signal of the non-linear amplifier under an effect of said at least one factor; and
reduce the size of the auto-correlation matrix and the cross-correlation vector by removing at least some of their elements according to determined criterion.
24. The apparatus of claim 13 , further comprising a radio transmitter configured to provide the apparatus with radio transmission capability, wherein the non-linear amplifier is a power amplifier of the radio transmitter.