The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

It is shown that, particularly for terrestrial cellular telephony, the interference-suppression feature of CDMA (code division multiple access) can result in a many-fold increase in capacity over analog and even over competing digital techniques. A single-cell system, such as a hubbed satellite network, is addressed, and the basic expression for capacity is developed. The corresponding expressions for a multiple-cell system are derived. and the distribution on the number of users supportable per cell is determined. It is concluded that properly augmented and power-controlled multiple-cell CDMA promises a quantum increase in current cellular capacity. >

On the capacity of a cellular CDMA system

The ever-increasing demand for higher data rates in wireless communications in the face of limited or underutilized spectral resources has motivated the introduction of cognitive radio. Traditionally, licensed spectrum is allocated over relatively long time periods and is intended to be used only by licensees. Various measurements of spectrum utilization have shown substantial unused resources in frequency, time, and space [1], [2]. The concept behind cognitive radio is to exploit these underutilized spectral resources by reusing unused spectrum in an opportunistic manner [3], [4]. The phrase cognitive radio is usually attributed to Mitola [4], but the idea of using learning and sensing machines to probe the radio spectrum was envisioned several decades earlier (cf., [5]).

Spectrum Sensing for Cognitive Radio : State-of-the-Art and Recent Advances

Cyclostationarity: half a century of research

Spectrum sensing is the very task upon which the entire operation of cognitive radio rests. For cognitive radio to fulfill the potential it offers to solve the spectrum underutilization problem and do so in a reliable and computationally feasible manner, we require a spectrum sensor that detects spectrum holes (i.e., underutilized subbands of the radio spectrum), provides high spectral-resolution capability, estimates the average power in each subband of the spectrum, and identifies the unknown directions of interfering signals. Cyclostationarity is another desirable property that could be used for signal detection and classification. The multitaper method (MTM) for nonparametric spectral estimation accomplishes these tasks accurately, effectively, robustly, and in a computationally feasible manner. The objectives of this paper are to present: 1) tutorial exposition of the MTM, which is expandable to perform space-time processing and time-frequency analysis; 2) cyclostationarity, viewed from the Loeve and Fourier perspectives; and 3) experimental results, using Advanced Television Systems Committee digital television and generic land mobile radio signals, followed by a discussion of the effects of Rayleigh fading.

/pdf/spectrum-sensing-for-cognitive-radio-1nggwiu43v.pdf

Spectrum Sensing for Cognitive Radio

Spectral analysis with nonuniform frequency resolution of nonstationary stochastic processes is addressed. The frequency-warping operation aimed at increasing the frequency resolution is shown to modify the nonstationarity kind of the analyzed process. Specifically, in several cases of interest, the frequency-warped process is shown to belong to the recently introduced class of the spectrally correlated processes. Spectral correlation density estimation is performed by frequency smoothing the periodogram along curves in the bifrequency plane instead of lines with unit slopes as in the case of wide-sense stationary and almost-cyclostationary processes. Application to cyclic spectral analysis of the GPS-L1 signal is considered.

On spectral analysis with nonuniform frequency resolution of nonstationary stochastic processes

In this paper, the effects of multipath Doppler channels on the very recently introduced generalized almost-cyclostationary signals are analyzed. Multipath Doppler channels generate several replicas of the input signal, each characterized by a different complex amplitude, delay, time-scaling factor, and Doppler shift. It is shown that such channels can be modeled as linear almost-periodically time-variant or as linear time-variant systems, depending on the length of the collect time adopted in the measurements.

Generalized almost-cyclostationary signals on multipath Doppler channels

A recently proposed cyclostationarity exploiting, i.e., spectral-correlation based, method for estimating the channel parameters needs a long integration time to obtain a sufficient level of noise and interference suppression in weak-signal case. The paper overcomes such a limitation by adopting a noncoherent data processing, i.e., by segmenting data and averaging the estimates obtained from each segment. The appropriate length of the temporal segment is determined as a compromise between computation time and estimate accuracy. It is shown that the noncoherent data processing can work well also when the accuracy in knowledge of the cycle frequency (i.e., the parameter characterizing the cyclostationarity) is not sufficient to assure an acceptable performance level with a coherent data processing. >

Spectral-correlation based estimation of channel parameters by noncoherent data processing

In this paper, the linear almost-periodically time-variant (LAPTV) filtering of generalized almost-cyclostationary (GACS) signals is considered in the fraction-of-time probability framework. It is shown that in general GACS signals, when processed by LAPTV filters, deliver output signals with zero power.

Linear almost-periodically time-variant filtering of generalized almost-cyclostationary signals

The class of the second-order oscillatory almost-cyclostationary processes is characterized. These processes have autocorrelation function which is the superposition of amplitude- and angle-modulated complex sinewaves, where the modulating functions, referred to as evolutionary cyclic autocorrelation functions, depend on both time and lag parameter. This class of processes includes that of the almost-cyclostationary processes. The problem of statistical function measurements is addressed for the special case of amplitude-modulated time-warped almost-cyclostationary processes. These processes are shown to be a suitable model for the electrocardiogram.

/pdf/on-characterization-and-application-of-oscillatory-almost-2f7jeuhj41.pdf

On characterization and application of oscillatory almost-cyclostationary processes

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Antonio Napolitano

Author Tools

Chat about Author