After more than 80 years of using a regulatory environment that is characterized principally by frequency and, to a lesser extent, spatial division to avoid interference, UWB introduces the significantly different concepts of spectrum underlay and ‘detect and avoid’ (DAA). Both of these concepts are somewhat experimental and clearly evolving over time. It is reasonable to expect that regulations governing UWB around the world may change somewhat over the next few years as we learn more about what does and does not work well in the UWB experiment.

Additionally, regulators are looking to see which applications the industry will choose to deploy UWB for. Some applications are potentially problematic from an interference perspective and others are relatively inert. The choices that UWB manufacturers and implementers make about applications will have an effect on the regulatory environment. If the industry elects to deploy a greater number of problematic applications than was estimated during the regulatory hearings, this will be of material interest to regulators and may cause them to introduce regulatory limits to discourage that deployment. The conscientiousness that the UWB industry shows in its efforts to avoid interference to incumbents will also influence how generous regulators are toward UWB interests in later rounds. As an example, if the UWB industry pushes uncoded and minimally coded video heavily in the crowded lower frequencies, it may be necessary for the regulators to issue more stringent rules to protect the incumbent services.

When a new technology is established as a standard, it gains a degree of validation. Standardization is a statement that the industry has largely consolidated its opinion around an approach for a new technology. This is important from a market-development perspective because it sets the technology onto a path of broad recognition and acceptance. Many people believe that when the standard is completed, the work of coordination in the market is done and the market will develop on its own from there.

The development of the standard is usually the first and most public of a series of activities designed to coordinate the market evolution. The work in the standards body is only meaningful when it is properly coupled with work done in special-interest groups (SIGs). These organizations insure interoperability, establish terms for access to intellectual property, manage brands, speak on behalf of the industry and generally take responsibility for the ongoing management of the market. It is not uncommon for special-interest groups to take an existing standard that has multiple modes or options, which may have been included to obtain political support for the standard, and whittle those down to the essentials. While participation in the standardization process is undoubtedly important to a company developing UWB products, participation in the SIG is at least equally so.

There is no set process through which the industry decides to structure a SIG. As a rule of thumb, a SIG is created when the industry perceives the need to coordinate the activities of manufacturers.

When a property is owned by a single person or entity, it is the responsibility of that person to maintain the property in good condition. If he or she fails to do so, it is entirely to his or her own disadvantage. The value of the property will decline. Likewise, any profit that may be derived is solely to the benefit of the property owner. The owner is therefore motivated to manage the property in a manner that optimizes its profitability.

If a property is communally owned and the individuals are not closely associated with one another, the incentives change. The individuals involved will each attempt to maximize their own personal profit from the property while attempting to minimize their contribution to the upkeep and maintenance. The property becomes overused, while at the same time maintenance is neglected. The value of the property goes into a downward spiral. This behaviour is known in regulatory circles as ‘the tragedy of the commons’ and is frequently used to describe potential risks of unlicensed spectrum. More specifically, this describes spectrum wherein anybody is able to build devices which operate without the enforcement mechanisms that manage use.

Ultra-wideband spectrum saturation

Ultra-wideband is an unlicensed spectrum of this type. Ultra-wideband is somewhat different in considering spectrum saturation than longer-range technologies. The fact that its power is so strictly limited reduces the number of devices that might cause interference to UWB as well as the number of devices that it might interfere.

System identification, as a particular process of statistical inference, exploits two types of information. The first is experiment; the other, called a priori, is known before making any measurements. In a wide sense, the a priori information concerns the system itself and signals entering the system. Elements of the information are, for example:

• the nature of the signals, which may be random or nonrandom, white or correlated, stationary or not, their distributions can be known in full or partially (up to some parameters) or completely unknown,

• general information about the system, which can be, for example, continuous or discrete in the time domain, stationary or not,

• the structure of the system, which can be of the Hammerstein or Wiener type, or other,

• the knowledge about subsystems, that is, about nonlinear characteristics and linear dynamics.

In other words, the a priori information is related to the theory of the phenomena taking place in the system (a real physical process) or can be interpreted as a hypothesis (if so, results of the identification should be necessarily validated) or can be abstract in nature.

This book deals with systems consisting of nonlinear memoryless and linear dynamic subsystems, for example, Hammerstein and Wiener systems and other related structures.

In this chapter, we discuss the problem of identification of a class of semiparametric block-oriented systems. This class of block-oriented systems can be restricted to a parameterization that includes a finite-dimensional parameter and nonlinear characteristics that run through a nonparametric class of mostly univariate functions. The parametric part of a semiparametric model defines characteristics of linear dynamical subsystems and low-dimensional projections of multivariate nonlinearities. The nonparametric part of the model comprises all static nonlinearities defined by functions of a single variable. A general methodology for identifying semiparametric block-oriented systems is developed. This includes a semiparametric version of least squares and a direct method using the concept of the average derivative of a regression function. These general approaches are applied in cases of semiparametric versions of Wiener, Hammerstein, and parallel systems. Section 14.2 gives examples of semiparametric block-oriented systems. This includes the multivariate version of Hammerstein and Wiener systems. In Section 14.3, we give a general approach to semiparametric inference. Section 14.4 is devoted to an important case study concerning the semiparametric Wiener system. Sections 14.5 and 14.6 provide similar considerations for semiparametric Hammerstein and parallel systems. In Section 14.7, we derive direct estimation methods for semiparametric nonlinear systems.

Introduction

In all of the preceding chapters, we have examined various fully nonparametric block-oriented systems.

Thus far we have examined block-oriented systems of the cascade form, namely the Hammerstein and Wiener systems. The main tool that was used to recover the characteristics of the systems was based on the theory of nonparametric regression and correlation analysis. In this chapter, we show that this approach can be successfully extended to a class of block-oriented systems of the series-parallel form as well as systems with nonlinear dynamics. The latter case includes generalized Hammerstein and Wiener models as well as the sandwich system. We highlight some of these systems and present identification algorithms that can use various nonparametric regression estimates. In particular, Section 12.1 develops nonparametric algorithms for parallel, series-parallel, and generalized nonlinear block-oriented systems. Section 12.2 is devoted to a new class of nonlinear systems with nonlinear dynamics. This includes the important sandwich system as a special case.

Series-parallel, block-oriented systems

The cascade nonlinear systems presented in the previous chapters define the fundamental building blocks for defining general models of series-parallel forms. Together, all of these models may create a useful class of structures for modeling various physical processes. The choice of a particular model depends crucially on physical constraints and needs.

In this section, we present a number of nonlinear models of series-parallel forms for which we can relatively easily develop identification algorithms based on the regression approach used throughout the book.

In all of the preceding chapters, we have examined the identification problem for block-oriented systems of various forms, that are characterized by a one-dimensional input process. In numerous applications, we confront the problem of identifying a system that has multiple inputs and multiple interconnecting signals. The theory and practical algorithms for identification of multivariate linear systems have been thoroughly examined in the literature [332]. On the other hand, the theory of identification of multivariate nonlinear systems has been far less explored. This is mainly due to the mathematical and computational difficulties appearing in multivariate problems. In this chapter, we examine some selected multivariate nonlinear models that are natural generalizations of the previously introduced block-oriented connections. An apparent curse of dimensionality that takes place in high-dimensional estimation problems forces us to focus on low-dimensional counterparts of the classical block-oriented structures. In particular, we examine a class of additive models, which provides a parsimonious representation for multivariate systems. Indeed, we show that the additive systems provide simple and interpretable structures, which also give a reasonable trade-off between the systematic modeling error and the estimation error of an identification algorithm. The theory of finding an optimal additive model is examined.

Multivariate nonparametric regression

As in all of the previous chapters, we will make use of the notion of a regression function.

The aim of this book is to show that the nonparametric regression can be applied successfully to nonlinear system identification. It gathers what has been done in the area so far and presents main ideas, results, and some new recent developments.

The study of nonparametric regression estimation began with works published by Cencov, Watson, and Nadaraya in the 1960s. The history of nonparametric regression in system identification began about ten years later. Such methods have been applied to the identification of composite systems consisting of nonlinear memoryless systems and linear dynamic ones. Therefore, the approach is strictly connected with so-called block-oriented methods developed since Narendra and Gallman's work published in 1966. Hammerstein and Wiener structures are most popular and have received the greatest attention in numerous applications. Fundamental for nonparametric methods is the observation that the unknown characteristic of the nonlinear subsystem or its inverse can be represented as regression functions.

In terms of the a priori information, standard identification methods and algorithms work when it is parametric, that is, when our knowledge about the system is rather large; for example, when we know that the nonlinear subsystem has a polynomial characteristic. In this book, the information is much smaller, nonparametric. The mentioned characteristic can be, for example, any integrable or bounded or, even, any Borel function.