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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
This book addresses the move towards quantum communications, in light of the recent technological developments on photonic crystals and their potential applications in systems. The authors present the state of the art on extensive quantum communications, the first part of the book being dedicated to the relevant theory; quantum gates such as Deutsch gates, Toffoli gates and Dedekind gates are reviewed with regards to their feasibility as electronic circuits and their implementation in systems, and a comparison is performed in parallel with conventional circuits such as FPGAs and DSPs. The specifics of quantum communication are also revealed through the entanglement and Bell states, and mathematical and physical aspects of quantum optical fibers and photonic crystals are considered in order to optimize the quantum transmissions. These concepts are linked with relevant, practical examples in the second part of the book, which presents six integrated applications for quantum communications.
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Seitenzahl: 255
Veröffentlichungsjahr: 2016
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Table of Contents
Cover
Dedication
Title
Copyright
Foreword
Preface
Introduction
List of Acronyms
PART 1: Theory
1 Non-linear Signal Processing
1.1. Distributions
1.2. Variance
1.3. Covariance
1.4. Stationarity
1.5. Bayes inference
1.6. Tensors in signal processing
1.7. Processing the quantum signal
2 Non-Gaussian Processes
2.1. Defining Gaussian processes
2.2. Non-Gaussian processes
2.3. Principal component analysis or Karhunen–Loève transformation
2.4. Sparse Gaussian processes
2.5. Levy process
2.6. Links with quantum communications
3 Sparse Signals and Compressed Sensing
3.1. Sparse Signals
3.2. Compressed sensing
3.3. Compressed sensing and quantum signal
4 The Fourier Transform
4.1. The Classic Fourier Transform
4.2. The Discreet Fourier Transform and the Fast Fourier Transform
4.3. The Fourier Transform and hyper-functions
4.4. Hilbert Transform
4.5. Clifford algebra and the Fourier Transform
4.6. Spinors and quantum signals
5 The Contribution of Arithmetic to Signal Processing
5.1. Gauss sums
5.2. Applications for Gauss sums
6 Riemannian Geometry and Signal Processing
6.1. Context
6.2. Riemannian varieties
6.3. Voronoi cells
6.4. Applications to Voronoi cells
PART 2: Applications
7 MIMO Systems
7.1. Introduction
7.2. A brief history of OFDM
7.3. Multi-carrier technology
7.4. OFDM technique
7.5. Generating OFDM symbols
7.6. Inter-symbol and inter-carrier interference
7.7. Cyclic prefix
7.8. Mathematical model of the OFDM system
7.9. MIMO channels
7.10. The MIMO channel model
7.11. MIMO OFDM channel model
8 Minimizing Interferences in DS–CDMA Systems
8.1. Convolutional encoding
8.2. Structure of convolutive codes
8.3. Polynomial representation
8.4. Graphic representations of convolutive codes
8.5. Decoding algorithms
8.6. Discreet Wavelet Transform (DWT)
8.7. Construction and discreet filtering
8.8. Defining the wavelet function: the place of detail
8.9. Wavelets and filter banks
8.10. Thresholding coefficients
8.11. Simulating results
9 STAP Radar
9.1. Introduction
9.2. Space–time adaptive processing (STAP)
9.3. Structure of the covariance matrix
9.4. Clutter
9.5. Optimal STAP
9.6. Performance measures
9.7. Influence of the radar’s parameters on detection
9.8. Sample matrix inversion algorithm (SMI)
9.9. Conclusion
10 Tracking Radar (Using the Dempster–Shafer Theory)
10.1. Introduction
10.2. Dempster–Shafer theory
10.3. Rules of combination
10.4. Decision rules
10.5. Digital simulation
10.6. Conclusion
11 InSAR Radar
11.1. Introduction
11.2. Coherence
11.3. System model
11.4. Inferometric phase statistics
11.5. Quantitative examples
11.6. Conclusion
12 Telecommunications Networks
12.1. Introduction
12.2. Describing the
ad hoc
simulated network’s topology
12.3. The different scenarios enacted
12.4. The statistics collected
12.5. Discussion of results
12.6. Part two: network using OLSR for routing
12.7. Conclusion
Conclusion
Bibliography
Index
End User License Agreement
List of Tables
1 Non-linear Signal Processing
Table 1.1. Devices, topics and main discoverers
9 STAP Radar
Table 9.1. Radar system parameters
10 Tracking Radar (Using the Dempster–Shafer Theory)
Table 10.1. Table of combined masses
Guide
Cover
Table of Contents
Begin Reading
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To my Mother, with my deep gratitude and affection
Series Editor
Guy Pujolle
Transitions from Digital Communications to Quantum Communications
Concepts and Prospects
Malek Benslama
Hadj Batatia
Abderraouf Messai
First published 2016 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUK
www.iste.co.uk
John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USA
www.wiley.com
© ISTE Ltd 2016
The rights of Malek Benslama, Hadj Batatia and Abderraouf Messai to be identified as the author of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Control Number: 2016940263
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-84821-925-0
Foreword
Four works dedicated entirely to satellite communications: this is the challenge set by Professor Malek Benslama of the University of Constantine, who understood that a new discipline was in the process of taking shape.
He demonstrated this by organizing the first international symposium on Electromagnetism, Satellites and Cryptography at Jijel in June 2005. The success of congress, surprising for a first-time event, shows that there was a need to gather, in a single place, specialists with skills that are sometimes very removed from one another. The 140 papers accepted concerned systems for electromagnetic systems as well as circuit and antennae engineering and cryptography, which is very often based on pure mathematics. A synergy between these disciplines is necessary to develop the new field of activity that is satellite communication.
The emergence of new disciplines of this type has already taken place before: for electromagnetic compatibility, it was as necessary to know electrical engineering for “driven modes” and “choppers” as electromagnetics (“radiating modes”) and to be able to define specific experimental protocols. Further back in time, we saw the emergence of computing which, at the start, lay in the field of electronics and was able, over time, to become independent.
Professor Benslama has the outlook and open-mindedness indispensable for bringing to fruition the synthesis between the skills that coexist in satellite telecommunications. I have known him for 28 years and for me it is a real pleasure to remember all these years of close acquaintance. There has not been a year in which we have not had an opportunity to see one another. For 15 years he worked on the interaction between acoustic waves and semi-conductors. He specialized in resolving piezoelectric equations (Rayleigh waves, creeping waves, etc.), and at the same time was interested in theoretical physics. A doctoral thesis in engineering and then a state thesis crowned his professional achievements. Notably, his examination committee included Jeannine Henaf, then Chief Engineer for the National Center for Telecommunications studies. He was already interested in telecommunications, but also, with the presence of Michel Planat, responsible for research at CNRS, in the difficult problem of synchronizing oscillators.
It is with Planat that he created the path that would lead to quantum cryptography. He made this transformation over 10 years, thus moving without any apparent difficulty from Maxwell’s equations to Galois groups. He is now therefore one of the people most likely to dominate all those diverse disciplines that form satellite telecommunications.
I wish, with all my friendly admiration, that these four volumes are with a warm welcome from students and teachers alike.
Henri BAUDRAND
Professor Emeritus
ENSEEIHT
Preface
This book follows on from two other books published by ISTE [BEN 15a, BEN 15b]. I would like to express my respect and gratitude for this publishing house, which makes a decisive contribution to the publishing and distribution of French-speaking scientific authors. I could not forget Professor Guy Pujolle, Director of the Networks and Telecommunications Series, in which this book is published. I am infinitely grateful to him.
The idea of transitions from the digital to the quantum field came to me during my stay at Besancon LPMO under the direction of Michel Planat. The discussions that I had with Planat encouraged me to move in the direction of fundamental scientific research. Initially, I met Michel Planat at Toulouse when I defended my state doctorate, which concerned the evolution of surface waves in piezoelectric materials. He suggested that I move towards the non-linear domain in terms of propagation. This then opened the way for me towards solitons in the first instance and then to chaos. Planat was then working on synchronizing surface wave oscillators; he ended by finding an interesting correlation with number theory. This opened the way for formalizing synchronization concepts. Subsequently, his work took a formal, mathematical orientation with the investigation of decoherence phenomena. The quantum aspect was becoming prevalent, and processing tools were drawn from higher math (Galois groups, Lie algebra, non-commutative geometry, etc.). All my respect, admiration and regards go to him.
The act of formalizing concepts is not unique to engineers, as the need for feasibility and practice means that any excessive theorizing has been avoided. Only the evolution of technology requires us to make a theoretical effort to explain, understand and justify this evolution. This book is a contribution to this effort. To this end, we have focused on linking the relevant, practical application to each concept.
Malek BENSLAMA
May 2016
Introduction
Progress recently demonstrated in crystal photonics and nanotechnologies suggests that communications will imminently drift towards quantum communications. An ever-increasing demand for bandwidth and very high speed in digital communications has made research into new systems necessary to be able to meet these requirements. Parallel with purely technological research, and with a view to adaptation, it has become necessary to rethink the very foundations of signal processing [CHO 04, GUP 05, CHA 05].
The first thought that came to mind is the following: what are the practical references available in the literature to justify the benefit of studying this transition, as well as the future developments that have been announced? Three distinct domains will be considered: advances in signal processing, in digital communications and finally those that relate to quantum communications. In fact, it seemed imperative to us to justify the benefit of this study on the basis of practical advances to show the reader that these transitions are not merely a figment of our imaginations but a tangible reality [VAN 05, CHE 07, BAS 08, PIE 14, KAT 06, HUN 10].
To process a signal very thoroughly and completely, some characteristics must be provided, without which any processing can only be approximate [KAN 09]. Classical techniques have become less important in the face of new considerations based on new concepts [AKY 11]. It is mainly signals resulting from RMN, from tomography and the neurosciences [THA 13] that have created this new problem. Thus, it has been necessary to discuss sparse signals [MAR 12, ZHA 13] and neurofuzzy signals.
Two signal characteristics should be considered – electric and photonic signals [DEU 04]. In the interests of a homogeneous study it seems useful for us to explore ways to reconcile particle and waves types [FRI 14]. This is a difficult challenge if we dwell on formal concepts; however, experimentally convincing results allow us to hope for a transition [IAF96, ELD01, SZU 13]. It is always tempting to examine these transitions in terms of continuity, which it too restrictive. We will, however, try to take inspiration from the example of the distributions, then the hyper functions that have resolved the continuity handicap and then the differentiability handicap and from the example of Lebesque integration, which has resolved the convergence problem for Riemann or Stieljes integrals [CHU 94, CHU 95a, CHU 95b, SAB 85].
The most sensible way to study the digital to quantum transition consists of relying on published experimental results [DIM 13]. What at first appears to be a figment of the imagination becomes plausible. Two of the most significant examples are superconductivity [OBA 13] and new materials [BRU 14a, BRU 14b], as well as graphene. A third example is provided by Kaspard Klug’s theory in virology [SHO 10] which has found an application in entanglements across the quadrangle, the Fano triangle and the icosahedron, which has enabled an important evolution towards the study of Voronoi cells with a direct application for network covers [COQ 01].
Here, an initial evolution consisted of researching new forms of Fourier transform in which information was not only confined to amplitude, but the phase could provide some aspects of information. To do this, the Fourier transform has evolved into hyper-functions such as the Riemann zeta function or Hardy transforms. On the other hand, the Shannon sampling theorem on which the sampling was based was no longer adequate for weak samples. In fact, the Shannon theorem resulted in a full matrix, whereas a random matrix carrying several zeros enabled the initial signal to be found, as long as the matrix had a certain rank. This gave rise to compressed sensing.
The signal/noise ratio, which is found in information theory formulas, as it has been established since Shannon [SHA 48, SHA 49], is a fundamental element for defining the communications’ quality.
It has been shown that the signal to noise ratio, so important in information theory, becomes moot for digital communications where symbols modulate the carrier solutions of differential linear equations with polynomial coefficients. On the other hand, new algebraic techniques for estimation enable demodulation according to Fliess [FLI 07].
The possibility that there are links between information theory and quantum mechanics has been examined by various authors [BRI 59, BRU 01, GRE 00].
The principals brought into question are conveyed by works on signal non-stationarity and the generalized Gaussian as shown by [VAR 89]. This has opened the way for signal processing by principal component analysis or Karhunen–Loeve transformation. Gaussian processes have thereafter been processed in the form of Levy processes and sparse Gaussian processes. The links with quantum communications therefore appeared naturally. These links were then accentuated by new developments obtained from geometry via Clifford algebra, which is a natural extension of the analysis and processing of two dimensional signals such as images. In this way, the quaternion signal and the quaternion phase, the signal and the monogenic phase are constructed in geometric algebra or Clifford algebra [TOD 14].
In Geometric Algebra for Computer Graphics, John Vince notes that geometric algebra has a natural affinity with Clifford algebra [VIN 08]. This brings us to a natural transition from Clifford algebra to non-Euclidian geometry. He also states the reasons why geometric algebra only emerged in the 21st Century, even though it was discovered in the 19th Century. The works of Clifford and Hestenes were authoritative, leading to Grassmann’s work.
David Hestenes’ works start with the compliant model that was used in 5D Minkowski space. Applications are numerous in quantum mechanics, in electrodynamics and, in what concerns us, in graphic computing [HES 84]. A remarkable work by the same author tackled spinors [HES 67].
For programmers interested in genetic algorithms (GA), a wide variety of tools is available for systems such as MAPLE and Mathematica, which has resulted in GAIGEN [FON 06]. Practical applications for refining the coprocessor based on Clifford algebra have been created by [FRA 13]. The opening towards higher algebras has thus been demonstrated.
Dorst and Manne give a calculation framework for geometric applications. Their calculation elements are sub-spaces. They specify that the base elements for the calculation are sub-spaces oriented from higher dimensions called “blades” [DOR 01].
The first definition of geometric algebra is introduced – it is an outer product. In this way, the outer product of vectors a1, a2, …. ak is antisymmetric, associative and linear in these arguments. It is written: a1⊄a2⊄…k and called blade k. The algebraic geometry, however, remains a Euclidian geometry.
Our book will begin with a chapter on non-linear signal processing, with a brief reminder of Gumbel’s work on probability distributions. We will not expand on the variance and covariance, which have been discussed enough in the literature. On the contrary, we will set out a reflection on stationarity and Bayes inference, which still constitute an element of research. For us, they are an important introductory aspect of tensors in signal processing, which we will extend to quantum signal processing. The second chapter will tackle non-Gaussian processes. We will give elements of information on principle component analysis, sparse Gaussian processes and generalizations to Levy processes. The links with quantum communications are also given.
The third chapter is devoted to sparse signals and to compressed sensing, a relatively new domain that merits our attention. The density of the results obtained and their applications in LiFi and WiFi networks, leads us to assemble all the information in a specific work that we will propose to our readers next. The fourth chapter hinges on the Fourier transform and is fairly traditional in its formulation. We have judged it useful to include it to reveal the current and future extensions in Clifford algebra and quantum spinors. The fifth chapter relates to the contribution of arithmetic to signal processing and to Gauss Sums in particular. In fact, it seemed interesting to us to refine the notion of the Abelian group in formulating Fourier transforms. The geometric aspect has not been concealed in this text; it will be tackled in the sixth chapter, with an extension towards Voronoi cells.
There are six integrated applications in this text. The first application relates to MIMO systems; it will highlight the notions of distributions, variance, covariance and stationarity. The second application includes elements relating to wavelets, which are much studied in signal processing. The third and fifth applications tackle adaptive radar and SAR radar respectively. Still with radar in mind, we have considered it useful to reveal the belief functions that are the counterpart to probability in signal processing. Finally, a relevant application for geometry is given via the networks.
List of Acronyms
Ad hoc
Wireless network infrastructure
ACK
ACKnowledgement
AOD
Ad hoc On Demand Distance Vector
ARQ
Automatic repeat request
Bcoh
Channel coherence band
BER
Bit Error Ratio
BF
Belief
BGP
Border gateway protocol
BW
Bandwidth
CCA
Clear Channel Detection
CDMA
Code Division Multiple Access
CEF
Clearing Code
CNR
Clutter to Noise Ratio
CMOS
Complementary Metal Oxide Semiconductor
CP
Cyclic prefix
CRC
Cyclic Redundancy Check
CSMA
Carrier Sense Multiple Access
CSMA/CA
CSMA with Collision Avoidance
CSMA/CD
CSMA with Collision Detection
CTS
Clear to Send
DAB
Digital audio broadcasting,
DCF
Distributed Coordination Function
DFP
Direct Form Processing
DFT
Discrete Fourier Transform
DIFS
Distributed Inter Frame Space
DOF
Degree Of Freedom
DS–CDMA
Direct sequence code division multiple access
DSDV
Destination Sequenced Distance Vector
DSSS
Direct Sequence Spread Spectrum
DSP
Digital Signal Processor
DST
Dempster–Shafer theory
DWT
Digital Wavelet Transform
EDCF
Enhanced DCF
EIFS
Extended IFS
FDM
Frequency division multiplexing
FDMA
Frequency Division Multiple Access
FEC
Forward Error Correction
FFT
Fast Fourier transform
FHSS
Frequency Hopping Spread Spectrum
FIFO
First Input First Output
FM
Frequency modulation,
FPGA
Field-programmable gate array,
GAF
Geographic Adaptive Fidelity
GMTI
Ground Moving Target Indicator
GSR
Global State Routing
HDTV
High Definition Television
ICI
Inter-carrier interference
IDFT
Inverse Digital Fourier Transform
IEEE
Institute of Electrical and Electronics Engineers
IF
Improvement factor
IFS
