Multi-band digital compensator for a non-linear system
A pre-distorter that both accurately compensates for the non-linearities of a radio frequency transmit chain, and that imposes as few computation requirements in terms of arithmetic operations, uses a diverse set of real-valued signals that are derived from separate band signals that make up the input signal. The derived real signals are passed through configurable non-linear transformations, which may be adapted during operation, and which may be efficiently implemented using lookup tables. The outputs of the non-linear transformations serve as gain terms for a set of complex signals, which are functions of the input, and which are summed to compute the pre-distorted signal. A small set of the complex signals and derived real signals may be selected for a particular system to match the classes of non-linearities exhibited by the system, thereby providing further computational savings, and reducing complexity of adapting the pre-distortion through adapting of the non-linear transformations.
1. A method for compensation for a distortion comprising:
receiving a first signal;
maintaining values in a storage for a data structure with a plurality of data sections, each data section encoding a different non-linear function of a plurality of non-linear functions and being accessible according to a sample value of a derived signal of a plurality of derived signals to yield a corresponding value of the non-linear function encoded by the data section;
processing the first signal, including computing successive sample values of a plurality of transformed signals and successive sample values of the plurality of derived signals from sample values of the first signal;
for each sample value of a plurality of sample values of the first signal,
for each data section of the data structure, accessing the data section to yield a value of the non-linear function represented by said section according to a corresponding sample value of a derived signal of the plurality of derived signals,
for each of the transformed signals, computing a corresponding gain for said transformed signal according to a corresponding subset of the values of the non-linear functions, and
computing a sample value of a second signal from sample values of the transformed signals and the corresponding gains for the transformed signals; and
using the second signal to compensate for the distortion.
2. The method of claim 1 , further comprising:
monitoring a fourth signal that depends on a combination of the first signal and the second signal; and
updating the values in the storage to reduce a degree of non-linearity in a transformation from the first signal to the fourth signal.
3. The method of claim 2 , wherein updating the values in the storage comprises incrementally updating said values.
4. The method of claim 3 , wherein incrementally updating the values comprises applying a gradient updating procedure.
5. The method of claim 2 , wherein updating the values in the storage includes determining values of a plurality of adaptation parameters, where each adaptation parameter of at least some adaptation parameters of the plurality of adaptation values is associated with a one of the non-linear functions.
6. The method of claim 5 , wherein each adaptation parameters is associated with a corresponding kernel, and the non-linear function associated with said adaptation parameter is representable as a weighted combination of kernels, the kernels being weighted by values of respective adaptation parameters of the plurality of adaptation parameters.
7. The method of claim 6 , where the corresponding kernel is zero outside a corresponding range of argument values of the non-linear function associated with the adaptation parameter.
8. The method of claim 7 , wherein the kernel has the form a piecewise linear function in the corresponding range of argument values.
9. The method of claim 6 , wherein variation of a value of a single adaptation parameter modifies at most one of the non-linear functions, and for said function, modifies said function over only a restricted range of argument values.
10. The method of claim 2 , updating the values in the storage includes determining values of a plurality of adaption parameters for values of monitored signals including the fourth signal, the determining including at least one of the following:
direct inversion of a Gramian determined from the monitored signals accumulated during a sampling interval;
inversion of a Gramian determined using a decaying averaging of contributions from batches of the monitored signals;
coordinate descent, wherein at each iteration of the coordinate descent, only some fewer than all of the adaptation parameters are updated; and
stochastic gradient updating of the adaptation parameters by iteratively randomly selecting time samples of monitored signals.
11. The method of claim 10 , wherein the inversion of the Gramian includes inversion of a combination of the Gramian and a regularization term.
12. The method of claim 10 , wherein each iteration of the coordinate descent updates only one of the values of the adaptation parameters.
13. The method of claim 1 , wherein using the second signal to compensate for the distortion comprises combining the first signal with the second signal to form a predistorted signal, and providing the predistorted signal as an input to a non-linear component, an output of the non-linear component comprising a third signal.
14. The method of claim 13 , further comprising:
monitoring a fourth signal that depends on the third signal; and
updating the values in the storage to reduce a degree of non-linearity in a transformation from the first signal to the third signal.
15. The method of claim 14 , wherein the non-linear component comprises a non-linear radio-frequency power amplifier, and monitoring the fourth signal comprises monitoring an output of the power amplifier.
16. The method of claim 1 , wherein the first signal has a first signal bandwidth, and some or all of the transformed signals have bandwidths greater than the first signal bandwidth.
17. The method of claim 16 , wherein at least some of the transformed signals comprise non-linear functions of the first signal representing distortion components of the first signal.
18. The method of claim 16 , wherein the first signal comprises a plurality of sub-band signals within the first signal bandwidth, and wherein at least some of the transformed signals comprise non-linear combinations of the sub-band signals.
19. The method of claim 1 , wherein each data section comprises values encoding a corresponding piecewise linear function, and wherein accessing the data section to yield the value of the non-linear function according to the corresponding sample value of a derived signal comprises selecting a particular value encoding the piecewise linear function to compute the value of the non-linear function.
20. The method of claim 19 , wherein accessing the data section to yield the value of the non-linear function according to the corresponding sample of a derived signal comprises selecting two particular values encoding a linear section of the piecewise linear function to compute the value of the non-linear function.