Pre-distortion architecture for compensating non-linear effects
View Patent ↗An input signal is pre-distorted to reduce distortion resulting from subsequent signal amplification. Frequency-dependent pre-distortion is preferably implemented in combination with frequency-independent pre-distortion, where the frequency-dependent pre-distortion is generated by expanding the derivative of a product of a pre-distortion function and the input signal and then relaxing constraints on the pre-distortion function and/or on frequency-dependent filtering associated with the frequency-dependent pre-distortion. In one implementation, four different frequency-dependent pre-distortion signals are generated for the expansion using up to four different pre-distortion functions and up to four different frequency-dependent filters.
1. A method for reducing distortion in an output signal by applying pre-distortion to an input signal to generate a pre-distorted signal, such that, when the pre-distorted signal is applied to a non-linear system to generate the output signal, the pre-distortion reduces the distortion in the output signal, wherein the pre-distorted signal is generated by:
(a) generating a first frequency-dependent pre-distortion signal corresponding to a product of (i) a derivative of a first pre-distortion function and (ii) the input signal;
(b) generating a second frequency-dependent pre-distortion signal corresponding to a product of (i) a derivative of a second pre-distortion function and (ii) the input signal;
(c) generating a third frequency-dependent pre-distortion signal corresponding to a product of (i) a third pre-distortion function and (ii) a derivative of the input signal;
(d) generating a fourth frequency-dependent pre-distortion signal corresponding to a product of (i) a fourth pre-distortion function and (ii) the derivative of the input signal; and
(e) generating the pre-distorted signal based on a combination of the first, second, third, and fourth frequency-dependent pre-distortion signals.
2. The invention of claim 1 , further comprising:
(f) applying the pre-distorted signal to the non-linear system to generate the output signal.
3. The invention of claim 2 , wherein the non-linear system comprises an amplifier that generates the output signal.
4. The invention of claim 1 , wherein at least one of the first and second pre-distortion functions is different from both of the third and fourth pre-distortion functions.
5. The invention of claim 4 , wherein each of the first and second pre-distortion functions is different from both of the third and fourth pre-distortion functions.
6. The invention of claim 1 , wherein:
step (a) comprises applying a first filter function to generate the first frequency-dependent pre-distortion signal;
step (b) comprises applying a second filter function to generate the second frequency-dependent pre-distortion signal;
step (c) comprises applying a third filter function to generate the third frequency-dependent pre-distortion signal; and
step (d) comprises applying a fourth filter function to generate the fourth frequency-dependent pre-distortion signal.
7. The invention of claim 6 , wherein the first, second, third, and fourth filter functions are frequency-dependent functions.
8. The invention of claim 6 , wherein at least one of the first and second filter functions is different from both of the third and fourth filter functions.
9. The invention of claim 8 , wherein each of the first and second filter functions is different from both of the third and fourth filter functions.
10. The invention of claim 1 , further comprising:
(f) generating a frequency-independent pre-distortion signal corresponding to a product of (i) a fifth pre-distortion function and (ii) the input signal, wherein step (e) comprises generating the pre-distorted signal based on the first, second, third, and fourth frequency-dependent pre-distortion signals and the frequency-independent pre-distortion signal.
11. The invention of claim 1 , wherein the pre-distorted signal is generated according to:
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where:
x[n] is the input signal;
x pd [n′] is the pre-distorted signal;
a[n] is the power of the input signal;
d 0 is a synchronization delay;
x[n−d 0 ] is a delayed version of the input signal;
ƒ 11 (·), ƒ 12 (·), ƒ 21 (·), ƒ 22 (·) are the first, second, third, and fourth pre-distortion functions;
ƒ 0 (·) is a fifth pre-distortion function used to generate a frequency-independent pre-distortion signal;
h d [·] is a differentiating filter function;
h B1 [·], h B2 [·], h B3 [·], h B4 [·] are frequency-dependent filter functions;
“·” represents complex multiplication; and
“*” represents convolution.
12. The invention of claim 11 , wherein at least one of:
ƒ 11 is different from both ƒ 21 and ƒ 22 ;
ƒ 12 is different from both ƒ 21 and ƒ 22 ;
h B1 is different from both h B3 and h B4 ; and
h B2 is different from both h B3 and h B4 .
13. The invention of claim 11 , wherein:
ƒ 11 is different from both ƒ 21 and ƒ 22 ;
ƒ 12 is different from both ƒ 21 and ƒ 22 ;
h B1 is different from both h B3 and h B4 ; and
h B2 is different from both h B3 and h B4 .
14. Apparatus for reducing distortion in an output signal by applying pre-distortion to an input signal to generate a pre-distorted signal, such that, when the pre-distorted signal is applied to a non-linear system to generate the output signal, the pre-distortion reduces the distortion in the output signal, wherein apparatus comprises:
a first signal path configured to generate a first frequency-dependent pre-distortion signal corresponding to a product of (i) a derivative of a first pre-distortion function and (ii) the input signal;
a second signal path configured to generate a second frequency-dependent pre-distortion signal corresponding to a product of (i) a derivative of a second pre-distortion function and (ii) the input signal;
a third signal path configured to generate a third frequency-dependent pre-distortion signal corresponding to a product of (i) a third pre-distortion function and (ii) a derivative of the input signal;
a fourth signal path configured to generate a fourth frequency-dependent pre-distortion signal corresponding to a product of (i) a fourth pre-distortion function and (ii) the derivative of the input signal; and
a summer configured to generate the pre-distorted signal based on the first, second, third, and fourth frequency-dependent pre-distortion signals.
15. The invention of claim 14 , further comprising the non-linear system.
16. The invention of claim 15 , wherein the non-linear system comprises an amplifier configured to generate the output signal.
17. The invention of claim 14 , wherein:
the first, second, third, and fourth pre-distortion functions are implemented using lookup tables; and
each derivative is generated by applying a differentiating filter.
18. The invention of claim 14 , wherein at least one of the first and second pre-distortion functions is different from both of the third and fourth pre-distortion functions.
19. The invention of claim 14 , wherein:
the first signal path comprises a first filter configured to apply a first filter function to generate the first frequency-dependent pre-distortion signal;
the second signal path comprises a second filter configured to apply a second filter function to generate the second frequency-dependent pre-distortion signal;
the third signal path comprises a third filter configured to apply a third filter function to generate the third frequency-dependent pre-distortion signal; and
the fourth signal path comprises a fourth filter configured to apply a fourth filter function to generate the fourth frequency-dependent pre-distortion signal.
20. The invention of claim 19 , wherein the first, second, third, and fourth filter functions are frequency-dependent functions.
21. The invention of claim 19 , wherein at least one of the first and second filter functions is different from both of the third and fourth filter functions.
22. The invention of claim 14 , further comprising:
a frequency-independent signal path configured to generate a frequency-independent pre-distortion signal corresponding to a product of (i) a frequency-independent pre-distortion function and (ii) the input signal, wherein the summer is configured to generate the pre-distorted signal based on the first, second, third, and fourth frequency-dependent pre-distortion signals and the frequency-independent pre-distortion signal.
23. The invention of claim 14 , wherein the pre-distorted signal is generated according to:
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where:
x[n] is the input signal;
x pd [n′] is the pre-distorted signal;
a[n] is the power of the input signal generated by a power detector;
d 0 is a synchronization delay applied by a delay block;
x[n−d 0 ] is a delayed version of the input signal;
ƒ 11 (·), ƒ 12 (·), ƒ 21 (·), ƒ 22 (·) are the first, second, third, and fourth pre-distortion functions;
ƒ 0 (·) is a fifth pre-distortion function used in a frequency-independent signal path to generate a frequency-independent pre-distortion signal;
h d [·] is a differentiating filter function;
h B1 [·], h B2 [·], h B3 [·], h B4 [·] are frequency-dependent filter functions;
“·” represents complex multiplication; and
“*” represents convolution.
24. The invention of claim 23 , wherein at least one of:
ƒ 11 is different from both ƒ 21 and ƒ 22 ;
ƒ 12 is different from both ƒ 21 and ƒ 22 ;
h B1 is different from both h B3 and h B4 ; and
h B2 is different from both h B3 and h B4 .
25. The invention of claim 14 , wherein each derivative corresponds to differentiation with respect to time.
26. The invention of claim 1 , wherein each derivative corresponds to differentiation with respect to time.