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.

Description:
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, u n , 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, e n  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 (x n  or u n  and e n ) 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, y n , 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.