Synthesis of an incident aperiodic tapered beam

This paper presents a technique for generating numerically an incident tapered beam of a prescribed polarization and a prescribed incidence angle by summing a finite number of propagating uniform plane waves, each constituent plane wave having its own magnitude, phase, incidence angle and polarization. Our three ad-hoc schemes for choosing the magnitude, the incidence angle and the polarization of a constituent plane wave are different from those by Braunisch et al. Our choice of the propagating plane waves corresponds to a sampling of the physical angular (/spl theta/, /spl phi/) space. This contrasts with the two-dimensional Fourier transform technique by Braunisch et al. and its Cartesian sampling of the (k/sub x/, k/sub y/) spectral plane where k/sub x/=(k/sub o/sin/spl theta/cos/spl phi/) and k/sub y/=(k/sub o/sin/spl theta/sin/spl phi/). Our technique is based on the summation of only propagating plane waves, whereas the technique by Braunisch et al. is based on the summation of both propagating and evanescent plane waves.     

On the$theta$-Coverage and Connectivity of Large Random Networks

Wireless planar networks have been used to model wireless networks in a tradition that dates back to 1961 to the work of E. N. Gilbert. Indeed the study of connected components in wireless networks was the motivation for his pioneering work that spawned the modern field of continuum percolation theory. Given that node locations in wireless networks are not known, random planar modeling can be used to provide preliminary assessments of important quantities such as range, number of neighbors, power consumption, and connectivity, and issues such as spatial reuse and capacity. In this paper, the problem of connectivity based on nearest neighbors is addressed. The exact threshold function for$theta $-coverage is found for wireless networks modeled as$n$points uniformly distributed in a unit square, with every node connecting to its$phi _n$nearest neighbors. A network is called$theta $-covered if every node, except those near the boundary, can find one of its$phi _n$nearest neighbors in any sector of angle$theta $. For all$theta in (0, 2 pi )$, if$phi _n =(1+delta ) log _ 2pi over 2pi -theta n$, it is shown that the probability of$theta $-coverage goes to one as$n$goes to infinity, for any$delta ≫0$; on the other hand, if$phi _n=(1-delta ) log _ 2pi over 2pi -theta n$, the probability of$theta $-coverage goes to zero. This sharp characterization of$theta $-coverage is used to show, via further geometric arguments, that the network will be connected with probability approaching one if$phi _n=(1+delta ) log _2 n$. Connections between these results and the performance analysis of wireless networks, especially for routing and topology control algorithms, are discussed. Digital Object Identifier 10.1109/TIT.2006.874384     

Time-frequency localisation of Shannon wavelet packets

It is well known that the 2/spl pi/ minimally supported frequency scaling function /spl phi//sup /spl alpha//(x) satisfying /spl phi//spl circ//sup /spl alpha//(/spl omega/)=/spl chi//sub (-/spl alpha/,2/spl pi/-/spl alpha/)/(/spl omega/), 0相似文献   

Compression mappings on primitive sequences over Z/(p/sup e/)

Let Z/(p/sup e/) be the integer residue ring with odd prime p/spl ges/5 and integer e/spl ges/2. For a sequence a_ over Z/(p/sup e/), there is a unique p-adic expansion a_=a_/sub 0/+a_/spl middot/p+...+a_/sub e-1//spl middot/p/sup e-1/, where each a_/sub i/ is a sequence over {0,1,...,p-1}, and can be regarded as a sequence over the finite field GF(p) naturally. Let f(x) be a primitive polynomial over Z/(p/sup e/), and G'(f(x),p/sup e/) the set of all primitive sequences generated by f(x) over Z/(p/sup e/). Set /spl phi//sub e-1/ (x/sub 0/,...,x/sub e-1/) = x/sub e-1//sup k/ + /spl eta//sub e-2,1/(x/sub 0/, x/sub 1/,...,x/sub e-2/) /spl psi//sub e-1/(x/sub 0/,...,x/sub e-1/) = x/sub e-1//sup k/ + /spl eta//sub e-2,2/(x/sub 0/,x/sub 1/,...,x/sub e-2/) where /spl eta//sub e-2,1/ and /spl eta//sub e-2,2/ are arbitrary functions of e-1 variables over GF(p) and 2/spl les/k/spl les/p-1. Then the compression mapping /spl phi//sub e-1/:{G'(f(x),p/sup e/) /spl rarr/ GF(p)/sup /spl infin// a_ /spl rarr/ /spl phi//sub e-1/(a_/sub 0/,...,a_/sub e-1/) is injective, that is, a_ = b_ if and only if /spl phi//sub e-1/(a_/sub 0/,...,a_/sub e-1/) = /spl phi//sub e-1/(b_/sub 0/,...,b_/sub e-1/) for a_,b_ /spl isin/ G'(f(x),p/sup e/). Furthermore, if f(x) is a strongly primitive polynomial over Z/(p/sup e/), then /spl phi//sub e-1/(a_/sub 0/,...,a_/sub e-1/) = /spl psi//sub e-1/(b_/sub 0/,...,b_/sub e-1/) if and only if a_ = b_ and /spl phi//sub e-1/(x/sub 0/,...,x/sub e-1/) = /spl psi//sub e-1/(x/sub 0/,...,x/sub e-1/) for a_,b_ /spl isin/ G'(f(x),p/sup e/).     

Asymptotic properties on codeword lengths of an optimal FV code for general sources

This correspondence is concerned with asymptotic properties on the codeword length of a fixed-to-variable length code (FV code) for a general source {X/sup n/}/sub n=1//sup /spl infin// with a finite or countably infinite alphabet. Suppose that for each n /spl ges/ 1 X/sup n/ is encoded to a binary codeword /spl phi//sub n/(X/sup n/) of length l(/spl phi//sub n/(X/sup n/)). Letting /spl epsiv//sub n/ denote the decoding error probability, we consider the following two criteria on FV codes: i) /spl epsiv//sub n/ = 0 for all n /spl ges/ 1 and ii) lim sup/sub n/spl rarr//spl infin///spl epsiv//sub n/ /spl les/ /spl epsiv/ for an arbitrarily given /spl epsiv/ /spl isin/ [0,1). Under criterion i), we show that, if X/sup n/ is encoded by an arbitrary prefix-free FV code asymptotically achieving the entropy, 1/nl(/spl phi//sub n/(X/sup n/)) - 1/nlog/sub 2/ 1/PX/sup n/(X/sup n/) /spl rarr/ 0 in probability as n /spl rarr/ /spl infin/ under a certain condition, where P/sub X//sup n/ denotes the probability distribution of X/sup n/. Under criterion ii), we first determine the minimum rate achieved by FV codes. Next, we show that 1/nl(/spl phi//sub n/(X/sup n/)) of an arbitrary FV code achieving the minimum rate in a certain sense has a property similar to the lossless case.     

Theory of Direct-Coupled-Cavity Filters

A new theory is presented for the design of direct-coupled-cavity filters in transmission line or waveguide. It is shown that for a specified range of parameters the insertion-loss characteristic of these filters in the case of Chebyshev equal-ripple characteristic is given very accurately by the formula P/sub 0/ / /P/sub L/ = 1+h/sup 2/T/sub n//sup 2/[/spl omega//sub 0/ / /spl omega/ sin(/spl pi/ /spl omega/ / /spl omega//sub 0/) / sin/spl theta//sub 0/'] where h defines the ripple level, T/sub n/ is the first-kind Chebyshev polynomial of degree n, /spl omega/ / /spl omega//sub 0/ is normalized frequency, and /spl theta//sub 0/' is an angle proportional to the bandwidth of a distributed lowpass prototype filter. The element values of the direct-coupled filter are related directly to the step impedances of the prototype whose values have been tabulated. The theory gives close agreement with computed data over a range of parameters as specified by a very simple formula. The design technique is convenient for practical applications.     

Computer-Aided Design of Three-Port Waveguide Junction Circulators

The complete performance of a lossless three-port H-plane waveguide junction loaded coaxially with various inhomogeneous ferrite cylanders has been evaluated over the waveguide bandwidth and compared with experiment. Qualitative agreement between the predicted and measured performance was generally good using only the first three modes, n=0/spl plusmn/1. It has been shown theoretically and verified experimentally that if the 4/spl pi/M/sub s/ of a homogeneous rod or the internal field is increased, the circulation frequency f/sub 0/ increases; conversely, if the pemittivity is increased, f/sub 0/ decreases. These conflicting effects are modified when the magnetization 4/spl pi/M/sub s/ and permittivity /spl epsiv/ are inhomogeneous. For example, if the 4/spl pi/M/sub s/(/spl gamma/) is small at the outer surface of the rod (with permittivity held constant), the effect on f/sub 0/ is very small; but if 4/spl pi/M/sub s/(spl gamma) approaches zero for /spl gamma/ small, then f/sub 0/ may decrease significantly. On the other hand, if /spl epsiv//sub/spl gamma//(/spl gamma/) approaches unity near the outer surface of the rod, f/sub 0/ may increase significantly; but if /spl epsiv//sub/spl gamma//(/spl gamma/) approaches unity near the center of the rod, f/sub 0/ is affected relatively little. The inhomogeneous structure has also shown that decreasing the ferrite volume may improve the performance, and high-power applications are suggested. With a conducting pin down the center of the ferrite, relative bandwidths of 40-50 percent are predicted.     

Asymptotic distribution of the number of isolated nodes in wireless ad hoc networks with Bernoulli nodes

Nodes in wireless ad hoc networks may become inactive or unavailable due to, for example, internal breakdown or being in the sleeping state. The inactive nodes cannot take part in routing/relaying, and thus may affect the connectivity. A wireless ad hoc network containing inactive nodes is then said to be connected, if each inactive node is adjacent to at least one active node and all active nodes form a connected network. This paper is the first installment of our probabilistic study of the connectivity of wireless ad hoc networks containing inactive nodes. We assume that the wireless ad hoc network consists of n nodes which are distributed independently and uniformly in a unit-area disk, and are active (or available) independently with probability p for some constant 0

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Characterization of accumulation layer capacitance for extracting data on high-/spl kappa/ gate dielectrics

A new parameter extraction technique has been outlined for high-/spl kappa/ gate dielectrics that directly yields values of the dielectric capacitance C/sub di/, the accumulation layer surface potential quotient, /spl beta//sub acc/, the flat-band voltage, the surface potential /spl phi//sub s/, the dielectric voltage, the channel doping density and the interface charge density at flat-band. The parallel capacitance, C/sub p/(=C/sub sc/+C/sub it/), was found to be an exponential function of /spl phi//sub s/ in the strong accumulation regime, for seven different high-/spl kappa/ gate dielectrics. The slope of the experimental lnC/sub p/(/spl phi//sub s/) plot, i.e., |/spl beta//sub acc/|, was found to depend strongly on the physical properties of the high-/spl kappa/ dielectric, i.e., was inversely proportional to [(/spl phi//sub b/m/sup *//m)/sup 1/2/K/C/sub di/], where /spl phi//sub b/ is the band offset, and m/sup */ is the effective tunneling mass. Extraction of /spl beta//sub acc/ represented an experimental carrier confinement index for the accumulation layer and an experimental gate-dielectric direct-tunneling current index. /spl beta//sub acc/ may also be an effective tool for monitoring the effects of post-deposition annealing/processing.     

A cone-based distributed topology-control algorithm for wireless multi-hop networks

The topology of a wireless multi-hop network can be controlled by varying the transmission power at each node. In this paper, we give a detailed analysis of a cone-based distributed topology-control (CBTC) algorithm. This algorithm does not assume that nodes have GPS information available; rather it depends only on directional information. Roughly speaking, the basic idea of the algorithm is that a node u transmits with the minimum power p/sub u,/spl alpha// required to ensure that in every cone of degree /spl alpha/ around u, there is some node that u can reach with power p/sub u,/spl alpha//. We show that taking /spl alpha/=5/spl pi//6 is a necessary and sufficient condition to guarantee that network connectivity is preserved. More precisely, if there is a path from s to t when every node communicates at maximum power then, if /spl alpha//spl les/5/spl pi//6, there is still a path in the smallest symmetric graph G/sub /spl alpha// containing all edges (u,v) such that u can communicate with v using power p/sub u,/spl alpha//. On the other hand, if /spl alpha/>5/spl pi//6, connectivity is not necessarily preserved. We also propose a set of optimizations that further reduce power consumption and prove that they retain network connectivity. Dynamic reconfiguration in the presence of failures and mobility is also discussed. Simulation results are presented to demonstrate the effectiveness of the algorithm and the optimizations.     

Low-power low-voltage CMOS A/D sigma-delta modulator for bio-potential signals driven by a single-phase scheme

Since the 1970's, the analog switches in switched-capacitor (SC) circuits are operated by nonoverlapping bi-phase control signals (/spl phi//sub 1/, /spl phi//sub 2/). The nonoverlapping of these two phases is essential for successful SC operation since, a capacitor inside an SC circuit can discharge if two switches, driven by /spl phi//sub 1/ and /spl phi//sub 2/, are turned on simultaneously. Moreover, since 1983, two additional phases are generally used in many SC circuits, which consist of advanced versions of /spl phi//sub 1/ and /spl phi//sub 2/. These two additional phases overcome the problem of signal-dependent charge injection. This paper presents a low-power and low-voltage analog-to-digital (A/D) interface module for biomedical applications. This module provides an A/D conversion based on a mixed clock-boosting/switched-opamp (CB/SO) second-order sigma-delta (/spl Sigma//spl Delta/) modulator, capable of interfacing with several different types electrical signals existing in the human body, only by re-programming the output digital filter. The proposed /spl Sigma//spl Delta/ architecture employs a novel single-phase scheme technique, which improves the dynamic performance and highly reduces the clocking circuitry complexity, substrate noise and area. Simulated results demonstrate that the signal integrity can be preserved by exploring the gap between the high conductance region of pMOS and nMOS switches at low power-supply voltages and the fast clock transitions that exist in advanced CMOS technologies. The mixed CB/SO architecture together with the overall distortion reduction resulting from using the proposed single-phase scheme, result that the dynamic range of the modulator is pushed closer to the theoretical limit of an ideal second-order /spl Sigma//spl Delta/ modulator.     

Cyclic codes over GR(4/sup m/) which are also cyclic over /spl Zopf//sub 4/

Let GR(4/sup m/) be the Galois ring of characteristic 4 and cardinality 4/sup m/, and /spl alpha/_={/spl alpha//sub 0/,/spl alpha//sub 1/,...,/spl alpha//sub m-1/} be a basis of GR(4/sup m/) over /spl Zopf//sub 4/ when we regard GR(4/sup m/) as a free /spl Zopf//sub 4/-module of rank m. Define the map d/sub /spl alpha/_/ from GR(4/sup m/)[z]/(z/sup n/-1) into /spl Zopf//sub 4/[z]/(z/sup mn/-1) by d/spl alpha/_(a(z))=/spl Sigma//sub i=0//sup m-1//spl Sigma//sub j=0//sup n-1/a/sub ij/z/sup mj+i/ where a(z)=/spl Sigma//sub j=0//sup n-1/a/sub j/z/sup j/ and a/sub j/=/spl Sigma//sub i=0//sup m-1/a/sub ij//spl alpha//sub i/, a/sub ij//spl isin//spl Zopf//sub 4/. Then, for any linear code C of length n over GR(4/sup m/), its image d/sub /spl alpha/_/(C) is a /spl Zopf//sub 4/-linear code of length mn. In this article, for n and m being odd integers, it is determined all pairs (/spl alpha/_,C) such that d/sub /spl alpha/_/(C) is /spl Zopf//sub 4/-cyclic, where /spl alpha/_ is a basis of GR(4/sup m/) over /spl Zopf//sub 4/, and C is a cyclic code of length n over GR(4/sup m/).     

Grammar-based lossless universal refinement source coding

A sequence y=(y/sub 1/,...,y/sub n/) is said to be a coarsening of a given finite-alphabet source sequence x=(x/sub 1/,...,x/sub n/) if, for some function /spl phi/, y/sub i/=/spl phi/(x/sub i/) (i=1,...,n). In lossless refinement source coding, it is assumed that the decoder already possesses a coarsening y of a given source sequence x. It is the job of the lossless refinement source encoder to furnish the decoder with a binary codeword B(x|y) which the decoder can employ in combination with y to obtain x. We present a natural grammar-based approach for finding the binary codeword B(x|y) in two steps. In the first step of the grammar-based approach, the encoder furnishes the decoder with O(/spl radic/nlog/sub 2/n) code bits at the beginning of B(x|y) which tell the decoder how to build a context-free grammar G/sub y/ which represents y. The encoder possesses a context-free grammar G/sub x/ which represents x; in the second step of the grammar-based approach, the encoder furnishes the decoder with code bits in the rest of B(x|y) which tell the decoder how to build G/sub x/ from G/sub y/. We prove that our grammar-based lossless refinement source coding scheme is universal in the sense that its maximal redundancy per sample is O(1/log/sub 2/n) for n source samples, with respect to any finite-state lossless refinement source coding scheme. As a by-product, we provide a useful notion of the conditional entropy H(G/sub x/|G/sub y/) of the grammar G/sub x/ given the grammar G/sub y/, which is approximately equal to the length of the codeword B(x|y).     

Physics-based mathematical conditioning of the MOSFET surface potential equation

The traditional form of the implicit equation for the surface potential (/spl phi//sub s/) in metal-oxide-semiconductor field-effect transistors (MOSFETs) works well except near the flatband point /spl phi//sub s/=0 where it is both unphysical and ill-conditioned mathematically. This represents a significant difficulty for recent surface potential-based models, which require /spl phi//sub s/ evaluation from the accumulation to the strong inversion region. Detailed physical analysis combined with two-dimensional numerical simulations is used to develop a physics-based well-conditioned version of the surface potential equation.     

On the filtering problem for stationary random /spl Zopf//sup 2/-fields

It is shown that whenever a stationary random field (Z/sub n,m/)/sub n,m/spl isin/z/ is given by a Borel function f:/spl Ropf//sup z/ /spl times/ /spl Ropf//sup z/ /spl rarr/ /spl Ropf/ of two stationary processes (X/sub n/)/sub n/spl isin/z/ and (Y/sub m/)/sub m/spl isin/z/ i.e., then (Z/sub n, m/) = (f((X/sub n+k/)/sub k/spl epsi/z/, (Y/sub m + /spl lscr// )/sub /spl lscr/ /spl epsi/z/)) under a mild first coordinate univalence assumption on f, the process (X/sub n/)/sub n/spl isin/z/ is measurable with respect to (Z/sub n,m/)/sub n,m/spl epsi/z/ whenever the process (Y/sub m/)/sub m/spl isin/z/ is ergodic. The notion of universal filtering property of an ergodic stationary process is introduced, and then using ergodic theory methods it is shown that an ergodic stationary process has this property if and only if the centralizer of the dynamical system canonically associated with the process does not contain a nontrivial compact subgroup.     

RF HBT oscillators with low-phase noise and high-power performance utilizing a (/spl lambda//4/spl plusmn//spl delta/) open-stubs resonator

This paper presents a new type of transmission-line resonator and its application to RF (microwave and millimeter-wave) heterojunction bipolar transistor (HBT) oscillators. The resonator is a parallel combination of two open stubs having length of /spl lambda//4/spl plusmn//spl delta/(/spl delta//spl Lt//spl lambda/), where /spl lambda/ is a wavelength at a resonant frequency. The most important feature of this resonator is that the coupling coefficient (/spl beta//sub C/) can be controlled by changing /spl delta/ while maintaining unloaded Q-factor (Q/sub u/) constant. Choosing a small value of /spl delta/ allows us to reduce /spl beta//sub C/ or equivalently to increase loaded Q-factor (Q/sub L/). Since coupling elements such as capacitors or electromagnetic gaps are not needed, /spl beta//sub C/ and Q/sub L/ can be precisely controlled based on mature lithography technology. This feature of the resonator proves useful in reducing phase noise and also in enhancing output power of microwave oscillators. The proposed resonator is applied to 18-GHz and 38-GHz HBT oscillators, leading to the phase noise of -96-dBc/Hz at 100-kHz offset with 10.3-dBm output power (18-GHz oscillator) and -104-dBc/Hz at 1-MHz offset with 11.9 dBm (38-GHz oscillator). These performances are comparable to or better than state-of-the-art values for GaAs- or InP-based planar-circuit fundamental-frequency oscillators at the same frequency bands.     

BV/sub CEO/--BV/sub CBO/ separation and sharpness of breakdown in high-speed bipolar transistors

The effect of secondary impact ionization by the noninitiating carrier on the near avalanche behavior of high-speed n-p-n bipolar transistors is studied. We show that secondary collector ionization by generated holes traveling back toward the base layer significantly reduces BV/sub CBO/ if the hole ionization coefficient is higher than that of electrons [/spl beta//sub p/(E)>/spl alpha//sub n/(E)]: positive feedback associated with a strong secondary ionization sharpens the breakdown characteristic by speeding up carrier multiplication and decreases separation between the open-base collector-emitter (BV/sub CEO/) and the open-emitter base-collector (BV/sub CBO/) breakdown voltages. The effect of secondary ionization on the BV/sub CEO/-BV/sub CBO/ separation has not previously been described. Multiplication coefficient comparisons for representative InP, GaAs, and Si collectors indicate all structures can sustain low-current above BV/sub CEO/ operation from a transport (nonthermal) point of view, although the different degrees of secondary ionization in various semiconductors lead to fundamental differences when InP is compared to GaAs and Si since for the latter materials /spl beta//sub p/(E)相似文献   

A new binary sequence family with low correlation and large size

For odd n=2l+1 and an integer /spl rho/ with 1/spl les//spl rho//spl les/l, a new family S/sub o/(/spl rho/) of binary sequences of period 2/sup n/-1 is constructed. For a given /spl rho/, S/sub o/(/spl rho/) has maximum correlation 1+2/sup n+2/spl rho/-1/2/, family size 2/sup n/spl rho//, and maximum linear span n(n+1)/2. Similarly, a new family of S/sub e/(/spl rho/) of binary sequences of period 2/sup n/-1 is also presented for even n=2l and an integer /spl rho/ with 1/spl les//spl rho/相似文献   

Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information

This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal f/spl isin/C/sup N/ and a randomly chosen set of frequencies /spl Omega/. Is it possible to reconstruct f from the partial knowledge of its Fourier coefficients on the set /spl Omega/? A typical result of this paper is as follows. Suppose that f is a superposition of |T| spikes f(t)=/spl sigma//sub /spl tau//spl isin/T/f(/spl tau/)/spl delta/(t-/spl tau/) obeying |T|/spl les/C/sub M//spl middot/(log N)/sup -1/ /spl middot/ |/spl Omega/| for some constant C/sub M/>0. We do not know the locations of the spikes nor their amplitudes. Then with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the /spl lscr//sub 1/ minimization problem. In short, exact recovery may be obtained by solving a convex optimization problem. We give numerical values for C/sub M/ which depend on the desired probability of success. Our result may be interpreted as a novel kind of nonlinear sampling theorem. In effect, it says that any signal made out of |T| spikes may be recovered by convex programming from almost every set of frequencies of size O(|T|/spl middot/logN). Moreover, this is nearly optimal in the sense that any method succeeding with probability 1-O(N/sup -M/) would in general require a number of frequency samples at least proportional to |T|/spl middot/logN. The methodology extends to a variety of other situations and higher dimensions. For example, we show how one can reconstruct a piecewise constant (one- or two-dimensional) object from incomplete frequency samples - provided that the number of jumps (discontinuities) obeys the condition above - by minimizing other convex functionals such as the total variation of f.     

Functional classification in Hilbert spaces

Let X be a random variable taking values in a separable Hilbert space X, with label Y/spl isin/{0,1}. We establish universal weak consistency of a nearest neighbor-type classifier based on n independent copies (X/sub i/,Y/sub i/) of the pair (X,Y), extending the classical result of Stone to infinite-dimensional Hilbert spaces. Under a mild condition on the distribution of X, we also prove strong consistency. We reduce the infinite dimension of X by considering only the first d coefficients of a Fourier series expansion of each X/sub i/, and then we perform k-nearest neighbor classification in /spl Ropf//sup d/. Both the dimension and the number of neighbors are automatically selected from the data using a simple data-splitting device. An application of this technique to a signal discrimination problem involving speech recordings is presented.