# Patent

## Title
Adaptive sample-by-sample controller for under-determined systems

## Abstract

A device and method to adapt a model in a underdetermined adaptive system that provides an output in response to an input. A controller provides parameters to the model in a transceiver system, composed of linearizers, equalizers, or estimators as a function of an error signal. The controller and the model parameters are manipulated to allow agnosticism with respect to input signals or model complexity, enabling robust operation and efficient implementation.

## Background
RELATED APPLICATION
This application claims the benefit under 35 U.S.C. 119(e) of U.S. Provisional Application Ser. No. 60/788,971 (entitled ROBUST VOLTERRA-SERIES LINEARIZATION OF TRANSMITTERS USING LOOK-UP TABLES, filed Apr. 4, 2006) and of U.S. Provisional Application Ser. No. 60/788,970 (entitled ADAPTIVE LOOK-UP BASED VOLTERRA-SERIES LINEARIZATION OF SIGNAL TRANSMITTERS, filed Apr. 4, 2006), which applications are incorporated herein by reference.


BACKGROUND
An undetermined system may have multiple or infinite solutions, in opposition to a determined system with a single unique solution. Such systems may find use in the emerging concept of applying System-on-Chip (SoC) to the case of Radio-on-Chip (software defined radio) in wireless base stations. Such systems may apply adaptive equalizers, linearizers or identifiers in either the transmitter or receiver or both.
These systems can be decomposed into a plant and model. The plant represents the physical system to be corrected (such as, but not limited to, a nonlinear transmitter) or identified and the model represents the artificial structure to be adapted to correct (through inversion) or mimic (through modeling) the plant, depending on the system architecture. The models are ideally trained (adapted) in a test or characterization mode, whereby the system is taken out of service periodically and a known test waveform applied to the system that is of similar frequency bandwidth as the plant bandwidth. However, the conflicting requirements to minimize system down-time while providing a suitable training frequency to maintain feature performance over time, precludes a characterization mode. There is a need to be able to provide adaptation with the transmission signal.
As modern radio products must support a variety of signal bandwidths, including narrow bandwidth signals, there exists the possibility for the plant bandwidth to be significantly larger than the signal bandwidth. In this case, there is insufficient information to accurately solve the system of equations characterizing the plant and the associated model—there are in effect more unknowns than equations. This scenario is described in mathematics as an under-determined system. The severity of under-determinedness increases with model complexity (model dimensionality and span—more unknowns) and excitation signal correlation (narrow bandwidth—less information).
A model solution can be found through block-based processing where data is collected in blocks, processed directly to solve for the model parameters (solution) which are then applied to the model. Other attempts to provide a model solution involve gradient methods where an error signal is processed sample-by-sample, with each outcome driving directly the model parameters towards a minimized error and ultimately the solution. When applied to solve an under-determined system, both methods can be impaired and may be sensitive to bandwidth and type of model used. While both methods of adaptation are valid, they may also lack efficiency and robustness.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of an equalizing controller for a receiver according to an example embodiment.
FIG. 2 is a block diagram of an inverse controller for a receiver according to an example embodiment.
FIG. 3 is a block diagram of a tracking controller for a built in test feature according to an example embodiment.
FIG. 4 is a block diagram of an adaptive sample-by-sample controller for an under-determined system according to an example embodiment.
FIG. 5 is a block diagram of a shared adaptive controller according to an example embodiment.
FIG. 6 is a block diagram of an example embodiment of a linearizer feature employing a single agnostic controller shared among time delayed non-linear taps according to an example embodiment.



DETAILED DESCRIPTION
In the following description, reference is made to the accompanying drawings that form a part hereof, and in which is shown by way of illustration specific embodiments which may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention, and it is to be understood that other embodiments may be utilized and that structural, logical and electrical changes may be made without departing from the scope of the present invention. The following description of example embodiments is, therefore, not to be taken in a limited sense, and the scope of the present invention is defined by the appended claims.
The functions or algorithms described herein may be implemented in software or a combination of software and human implemented procedures in one embodiment. The software may consist of computer executable instructions stored on computer readable media such as memory or other type of storage devices. Further, such functions correspond to modules, which are software, hardware, firmware or any combination thereof. Multiple functions are performed in one or more modules as desired, and the embodiments described are merely examples. The software may be executed on a FPGA, ASIC, digital signal processor, microprocessor, or other type of processor operating on a computer system, such as a personal computer, server or other computer system.
The performance of the sample-by-sample adaptive processes is sensitive to the degree of under-determinedness and so is strongly dependent on the correlation properties of the excitation signal. Highly correlated excitation leads to: (1) poor convergence rates (poor tracking ability), (2) parameter drift (leading to eventual overflow in fixed point implementations), (3) excess error (suboptimal solution) in the case of systems requiring complex model structures, and (4) excess error in cases of plant over-modeling (an issue for any generalized model structure). These issues are of especial relevance in the adaptive linearization and equalization of modern transceivers where the trend is towards higher sample rates (higher signal correlation) and higher efficiency structures exhibiting increased nonlinearity and memory (more complicated models).
Several adaptive system architectures are described and make use of sample-by-sample controller for under-determined systems. Enhancements of sample-by-sample adaptive systems applied to under-determined systems are described. Specifically, they involve: (1) pre-conditioning of the adaptive process inputs, (2) constraining of the adaptive elements, and (3) modifying the internal mechanics of adaptation. Unlike other methods, one or more embodiments described may achieve improved adaptation performance in an under-determined system without alteration of the input/controlled signal, while remaining bandwidth- and model-agnostic.
FIGS. 1, 2 and 3 are block diagrams of various controllers in adaptive system architectures. In FIG. 1, a post-inverse modeling architecture 100 is illustrated and may be applied in a receiver for post-equalization or linearization for example. The receiver is represented by plant 110 which receives an input signal and provides an output to a model and controller 120, which provides an output signal. The output signal is combined with the input signal at summer 130 to provide an error signal back to the model and controller 120. Further details of the model and controller 120 for each of FIGS. 1, 2 and 3 are shown in FIG. 4.
In FIG. 2, inverse control as could applied in a transmitter for pre-equalization or pre-linearization (pre-distortion) is illustrated. In this architecture 200, an input signal is provided to a model and controller 210, which is coupled to plant 220. Plant 220 provides an output which is combined with the input at summer 230 which generates an error signal provided to the model and controller 210.
In FIG. 3, system identification as could be applied for BIST (Built In Self Test) features is illustrated. In this architecture 300, an input signal is provided to a plant 310 and model and controller 320. Outputs of the plant 310 and model and controller 320 are combined at summer 330, and an error signal is provided to model and controller 320. While the architectures 100 and 300 are realized through classic adaptive filter theory, architecture 200 is not, rather being realized through inverse control theory. In architecture 200 the model and controller 210 does not require the model output, un, to properly adapt.
A sample-by-sample controller device 400 for under-determined systems is depicted in FIG. 4. Through the proper application of signaling, a controller 410 can be applied in any of the architectures depicted in FIGS. 1, 2 and 3, and likely others. The controller 410 works to evolve model parameters, W at 415 such that after a convergence period, an error signal, en at 420, is minimized, and the system of equations describing the model-plant architecture 430 has been solved.
As indicated in FIG. 4, signals for adaptation (xn or un and en) may be preconditioned at 440 and 450 respectively before being applied in the adaptation process of controller 410. Although not shown in FIG. 4, the feedback signal, yn, may also be preconditioned in certain embodiments. The preconditioning may provide decorrelation, and a consequent improvement of the sample-by-sample adaptation performance. In certain cases, system complexity can be reduced through the application of the pre-conditioner to either the reference or error signal rather than both. Examples of possible decorrelating pre-conditioners include fixed whitening filters, transforms, adaptive prediction filters, or self whitening systems.
The adaptive process applies the updated model parameters, W at 415, to the model 430. These parameters typically consist of complex coefficients of adaptive elements spanning both time and dynamic range. Parameter drift can be countered by allowing for the current model parameters to influence the adaptation process. This can be accomplished through two techniques: 1) manipulation of the individual model parameters, or 2) constraining a set of the model parameters across a dimension (e.g. at a given time offset or dynamic range level) as represented in a parameter control block 460. The former technique involves manipulation in such a manner as to counter drift or to introduce decorrelating virtual noise across the full system bandwidth. An example of such manipulation would be a variant of a leakage technique. The latter technique involves application of a macro constraint to a group of parameters, such as a set of parameters corresponding to an instance of a dimension, restricting the solution space (effectively reducing the number of unknowns) and reducing vulnerability to parameter drift. The fixing or restriction of the root mean square (RMS) value of a single or multiple taps of an adaptive filter through the application of an adaptive controller would fall under this technique. Thus, the parameter control 460 is coupled to the controller 410 to control parameters provided to the model 430 by controller 410.
In various embodiments, a generic adaptive sample-by-sample controller structure may be insensitive to system architecture, model complexity, and input signal. Such a controller can therefore be applied to service any number of features in a System-on-Chip (SoC) product, regardless of their nature, enabling the efficiency of a single shared adaptation engine.
FIG. 5 at 500 depicts an example embodiment of an agnostic controller 510 applied as a single shared resource in a transceiver. Agnostic controller 510 in one embodiment is a shared generic adaptive controller with parameter control as previously described. Controller 510 may provide service to several distinct features, such as a linearizer 515, equalizer 520 and system identifier 525. A signal set selector 530 operates to provide signals to the controller 510 corresponding to those used for providing service to such features. Such signals generally include outputs from each of the features, referred to as feature input signals, as well as an input signal to the linearizer 515. The signal set selector 530 may also provide outputs from an analog feedback receiver 535 that receives output from an analog transmitter 540, and from an analog receiver 545. Signal set selector 530 may also include one or more preconditioners to decorrelate such input signals. Depending on the implementation, error generation can be performed either within the set selector or within the generic controller.
FIG. 6 depicts an example embodiment of a linearizer feature 600 employing a single agnostic controller 610 shared among time delayed non-linear taps 615, 620 and 625. Time delays may be provided by a tapped delay line 630. Controller 610 is a generic adaptive sample-by-sample controller that can be shared across a dimension within feature model 600. In one embodiment, the linearizer feature 600 provides linearization for a non-linear transmitter 635. An error signal for the generic controller 610 may be provided by summing, at 640, the output of the transmitter 635 with a propagation delay compensated, at 645, input signal.
One or more embodiments described may exhibit one or more of the following characteristics. Adaptation may be signal agnostic and system (architecture and model) agnostic. Residual error may be reduced, and robustness improved in the case of complex and over modeled systems. Adaptive signal paths alone may be manipulated to achieve improved adaptation performance leaving the transmission signal untouched. One or more embodiments may provide improved immunity to numerical quantization effects.
Further, implementation of some embodiments may be very efficient. Using a sample-by-sample solution, blocks of data need not be processed. Methods can be applied once to adaptive paths of multiple controllers. Compatibility with modular architectures with shared adaptation circuitry, and model/signal agnosticism allows a single adaptive engine to service filters and linearizers, as well as across taps and model dimensions.
Various embodiments described may be applied to improve the performance, efficiency and size of signal transmitters in different fields such as, but not limited to, RF transmission, Hi-Fi audio, Hi-Fi video, optical transmission and, generally, in systems where high-quality of electrical/electro-mechanical/electro-optical/electro-magnetic signal transformation has to be achieved.
Specifically, the adaptation methods described may be applied in Volterra series power amplifier linearization which may be used in cellular radios of various standards such as for example CDMA, WiMax and UMTS. Future applications may include 4G/LTE radio development and include applications in observation receiver linearization and equalization, receiver linearization and equalization, BIST, and system with transceiver diversity including Digitally Convertible Radio and/or power combining features.
The Abstract is provided to comply with 37 C.F.R. §1.72(b) to allow the reader to quickly ascertain the nature and gist of the technical disclosure. The Abstract is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims.

## Claims

1. A device for adapting a model in an adaptive system that provides a nonlinear radio transmitter output in response to an input with bandwidth variations, the device comprising:
a controller that provides model parameters to the model in the adaptive system as a function of an error signal; and
a parameter control coupled to the controller that controls which set of parameters from multiple sets of parameters, is provided to the model by the controller as a function of bandwidth of the input signal.

2. The device of claim 1 wherein the parameter control counters parameter drift.

3. The device of claim 2 wherein the parameter control manipulates individual filter parameters.

4. The device of claim 3 wherein the parameter control counters drift or introduces virtual noise across a system bandwidth to counter parameter drift.

5. The device of claim 2 wherein the parameter control constrains a set of filter parameters across a dimension of a given time offset or dynamic range level.

6. The device of claim 5 wherein the parameter control applies a macro constraint to a group of parameters.

7. The device of claim 6 wherein the group of parameters corresponds to an instance of a dimension and a solution space is restricted.

8. The device of claim 6 wherein the parameter control maintains a fixed root mean square value of a single or multiple taps of a Volterra series filter/linearizer over time, over dynamic range or over time and dynamic range.

9. The device of claim 1 and further comprising:
an analog receiver to receive transmitted signals and provide a feedback signal; and
one or more preconditioners coupled to the controller that decorrelates one or more of the error signal, input and feedback signal.

10. The device of claim 9 wherein the preconditioners include at least one of a fixed whitening filter, an adaptive prediction filter, or a self whitening system.

11. A method comprising:
providing model parameters to a model in an adaptive system for a nonlinear radio transmitter as a function of an error signal;
controlling parameters provided to the model to counter parameter drift as a function of a dynamic bandwidth range of an input signal; and
transmitting an output radio signal.

12. The method of claim 11 and further comprising decorrelating one or more of the error signal and input signal.

13. The method of claim 12 wherein decorrelating includes providing at least one of a fixed whitening filter, an adaptive prediction filter, or a self whitening system.

14. The method of claim 11 wherein controlling the model parameters comprises evolving the model parameters using a sample-by-sample adaptation.