Power Consumption of Quasi-adiabatic Logic Gates

A computer simulation is carried out to investigate the power consumption of major quasi-adiabatic logic gates. Anomalously high dissipation is found at low clock rates. An explanation for the anomaly and a method of eliminating this are proposed. For the dissipated energy W and the clock rate f, it is found that W f C ^{1 +} as f tends to infinity, where is essentially less than unity. The mechanism of the phenomenon is identified. Rules are established that govern the power consumption of the logic gates. It is concluded that they should help one to strike a balance between power consumption and speed, to optimize power characteristics, and to predict the performance of future models made by better process technologies.     

Efficient signature generation by smart cards

We present a new public-key signature scheme and a corresponding authentication scheme that are based on discrete logarithms in a subgroup of units in _p where p is a sufficiently large prime, e.g., p 2⁵¹². A key idea is to use for the base of the discrete logarithm an integer in _p such that the order of is a sufficiently large prime q, e.g., q 2¹⁴⁰. In this way we improve the ElGamal signature scheme in the speed of the procedures for the generation and the verification of signatures and also in the bit length of signatures. We present an efficient algorithm that preprocesses the exponentiation of a random residue modulo p.European patent application 89103290.6 from February 24, 1989. U.S. patent number 4995082 of February 19, 1991.     

On the convergence rate ofs-numbers of compact Hankel operators

It is well known that the sequence ofs-numbers {s_n},n=0, 1,..., of a compact operator, and particularly a compact Hankel operator =[h _j+k –1], converges monotonically to zero. Since the (n + 1)sts-number s_n measures the error ofL (¦z¦=1) approximation, modulo an additive H function, by nth degree proper rational functions whose poles are restricted to ¦z¦ < 1, it is very important to study how fast {s _n } converges to zero. It is not difficult to see that ifh _n =O(n ^–), for some > 1, thens _n =O(n ^–). In this paper we construct, for any given sequence _n 0, a compact Hankel operator such thats _{n n} for alln.The research of C. K. Chui was supported by the SDIO/IST managed by the U.S. Army under Contract No. DAAL-03-87-K-0025, and by the NSF under Grant No. DMS-8901345. X. Li's research was supported by the SDIO/IST managed by the U.S. Army under Contract No. DAAL-03-87-K-0025. The research of J. D. Ward was supported by the NSF under Grant No. DMS-8901345.     

Performance of a joint CDMA/PRMA protocol with heavy‐tailed ON/OFF source

The performance of a joint CDMA/PRMA protocol with heavy-tailed ON/OFF source has been studied. Compared with the random access scheme, the PRMA protocol improves the system performance (such as packet loss, throughput) whether the traffic is SRD or LRD. The less bursty traffic is, the greater the improvement. The buffer design should take into account knowledge about the network traffic such as the presence or absence of the Noah effect in a typical source, especially of _on, the intensity of the Noah effect of ONperiod. The smaller _on is, the smaller the buffering gain, and the more packets will be lost. LRD has impacts on the overall system performance. The Noah effect, especially _off, the intensity of the Noah effect of OFFperiod, has significant impact on the overall system performance such as capacity, time delay, etc. As _off gets closer to 1, the traffic becomes more bursty, the system capacity is decreased and time delay is increased.     

On the distribution of characteristics in bijective mappings

Differential cryptanalysis is a method of attacking iterated mappings based on differences known as characteristics. The probability of a given characteristic is derived from the XOR tables associated with the iterated mapping. If is a mapping : Z ₂ ^m , then for each , X, Y Z ₂ ^m the XOR table for gives the number of input pairs of difference X=X+X for which gp(X)+(X)=Y.The complexity of a differential attack depends upon two properties of the XOR tables: the density of zero entries in the table, and the size of the largest entry in the table. In this paper we present the first results on the expected values of these properties for a general class of mappings . We prove that if : Z ₂ ^m Z ₂ ^m is a bijective mapping, then the expected size of the largest entry in the XOR table for is bounded by 2m, while the fraction of the XOR table that is zero approaches e ^–1/2=0.60653. We are then able to demonstrate that there are easily constructed classes of iterated mappings for which the probability of a differential-like attack succeeding is very small.The author is presently employed by the Distributed System Technology Center, Brisbane, Australia.     

Symmetry relations in multidimensional Fourier transform pairs

A relation between the types of symmetries that exist in signal and Fourier transform domain representations is derived for continuous as well as discrete domain signals. The symmetry is expressed by a set of parameters, and the relations derived in this paper will help to find the parameters of a symmetry in the signal or transform domain resulting from a given symmetry in the transform or signal domain respectively. A duality among the relations governing the conversion of the parameters of symmetry in the two domains is also brought to light. The application of the relations is illustrated by a number of two-dimensional examples.Notation R the set of real numbers - R ^m R × R × ... × R m-dimensional real vector space - continuous domain real vector - L {¦ – _i , i = 1,2,..., m} - m-dimensional frequency vector - W { – _i ,i=1,2,..., m} - m-dimensional normalized frequency vector - _P {¦ – _i , i=1,2,...,m} - g(ol) g (₁,₂,..., _m ) continuous domain signal - () ( _{1 2},..., _m )=G (j ₁,j ₂,..., j _m ) Fourier transform ofg (ol) - (A,b,,,) parameters ofT- symmetry - N the set of integers - N ^m N × N × ... × N m-dimensional integer vector spacem-dimensional lattice - h(n) h (n ₁,.,n _m ) discrete domain signal - H() Fourier transform ofh (n) - v ₁,v ₂,..., v_m m sample-direction and interval vectors - V (v ₁ v ₂ ...v _m ) sampling basis matrix - [x]^* complex conjugate ofx - detA determinant ofA - X {x¦ – x _i , i=1,2,..., m} - A ^–t [A ^–1] ^t ,t stands for transpose This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant A-7739 to M. N. S. Swamy and in part by Tennessee Technological University under its Faculty Research support program to P. K. Rajan.     

Geometric properties of nonlinear networks containing capacitor-only cutsets and/or inductor-only loops. Part I: Conservation laws

This paper is the first in a two part sequence which studies nonlinear networks, containing capacitor-only cutsets and/or inductor-only loops from the geometric coordinate-free point of view of differentiable manifolds. Given such a nonlinear networkN, with °₀ equal to the sum of the number of independent capacitor-only cutsets and the number of independent inductor-only loops, we establish the following: (i) circuit theoretic sufficient conditions to guarantee that the set ⁰, of equilibrium points is a ₀-dimensional submanifold of the state space ofN; (ii) circuit theoretic sufficient conditions for the condition thatN has ₀ independent conservation laws and hence that through each point of the state space ofN, there passes a codimension ₀ invariant submanifold ^* of the network dynamics; (iii) circuit theoretic sufficient conditions to guarantee that the manifolds ^* and ⁰ intersect transversely.This work was supported by the Natural Sciences and Engineering Research Council of Canada, under Grant Number A7113, and by scholarships from the Natural Sciences and Engineering Research Council of Canada and the Ontario Provincial Government.     

Bilateral polynomial matrix equations in two indeterminates

Two special cases of the bilateral 2-D polynomial matrix equationDU +VN=C whenC=I andC=I with being a -stable 2-D polynomial, which are related respectively to deadbeat and asymptotic control problems of 2-D systems, are first considered. By generalizing the concepts of factor coprimeness, zero coprimeness and zero skew primeness in the 2-D polynomial ring to the ring of causal -stable 2-D rational functions, a constructive solution of these two problems mentioned is proposed. Based on these results, we derive a solvability condition for the bilateral equiation whereC is a general 2-D polynomial matrix. The general solutions are investigated as well.     

Gaussian radial basis functions and inner product spaces

An approximation result is given concerning Gaussian radial basis functions in a general inner product space. Applications are described concerning the classification of the elements of disjoint sets of signals, and also the approximation of continuous real functions defined on all of ⁿ using radial basis function (RBF) networks. More specifically, it is shown that an important large class of classification problems involving signals can be solved using a structure consisting of only a generalized RBF network followed by a quantizer. It is also shown that Gaussian radial basis functions defined on ⁿ can uniformly approximate arbitrarily well over all of ⁿ any continuous real functionalf on ⁿ that meets the condition that |f(x)|0 as x.     

On the robustness of stability for uncertain large-scale systems subjected to multiple time delays

The robustness problem of stability for large-scale uncertain systems with a class of multiple time delays is addressed in this paper. By applying the complex Lyapunov stability theorem, the matrix measure techniques, and norm inequalities, a new approach for solving a general case of the above problem is proposed. Several robust stability conditions, delay-dependent or delay-independent, are derived to guarantee the asymptotic stability and exponential stability of the uncertain large-scale time-delay systems. Moreover, these obtained results can also be applied to the stabilization design.Notation real number field - complex number field - x x=(x ₁,x ₂,...,x _n ) ^T R ⁿ - x ^T transpose of vectorx - x* complex conjugate transpose of vectorx - Re(·) real part of (·) - x norm of vectorx; x=(x*x)^1/2 - A ^T transpose of matrixA - A* complex conjugate transpose of matrixA - ¯(·) maximal absolute value of eigenvalue of matrixA - (A) matrix measure of matrixA; (A)=¯((A + A*)/2) - A induced norm of matrix A; A=[¯(A*A)]^1/2 - ¦a_ij ¦ absolute value of element a_ij - ¦ A¦ {¦a_ij¦} for matrix A={a_ij} - A >B a_ij > b_ij for alli andj where A={a_ij} andB={b_ij} - z complex number - ¯z complex conjugate ofz Supported by National Science Council, Taiwan, Republic of China, Grant NSC83-0404-E006-001.     

On the design of feedback controllers to achieve prescribed initial value constraints

The problem of designing a stabilizing compensator for a control system to achieve prescribed initial value constraints ⁽ⁱ⁾(0⁺)=y_i is considered. Indeed, modulo certain technical conditions, such a compensator exists if and only if y_i=0;i= 0,1,...,rp +rt –2; whererp is the relative degree of the plant andrt is the relative degree of the system input. This theorem is derived and a complete parameterization of the set of compensators that achieve the prescribed design constraints is formulated.This research was supported in part by NSF Grant No. 921106.     

A 70-MHz Continuous-Time CMOS Band-Pass ΣΔ Modulator for GSM Receivers

A 70-MHz continuous-time CMOS band-pass modulator for GSM receivers is presented. Impulse-invariant-transformation is used to transform a discrete-time loop-filter transfer function into continuous-time. The continuous-time loop-filter is implemented using a transconductor-capacitor (G _m -C) filter. A latched-type comparator and a true-single-phase-clock (TSPC) D flip-flop are used as the quantizer of the modulator. Implemented in a MOSIS HP 0.5-m CMOS technology, the chip area is 857 m × 420 m, and the total power consumption is 39 mW. At a supply voltage of 2.5 V, the maximum SNDR is measured to be 42 dB, which corresponds to a resolution of 7 bits.     

Higher-order terms in asymptotic expansion for information loss in quantized random processes

Uniform quantization of random vectors onto -grids ⁿ is considered. Higherorder terms in asymptotic expansions for the entropy of the -quantized random vector and for the loss of the mutual information between two random vectors under such quantization as 0+are obtained. The coefficients in these asymptotics are explicitly calculated for Gaussian distributed vectors. Taken for initial segments of stationary Gaussian sequences, these factors have limit average values per unit of time. For such sequences governed by state-space equations, computation of these average values is reduced to solutions of algebraic matrix Riccati and Lyapunov equations.Work supported by the Australian Research Council grant A 4970 2246.     

The discrete Einstein relation

In this paper the connection between massM, resistance and commute time for random walks on graphs is further explored, and the relation=2M · is proved. An extension of the result is made to multigraphs, which are an extension of the graph concept where a black box is treated like an edge.     

Input-output systems whose transmission operators furnish nearly best approximations to a given map

Let {S(A):A A}, whereA is a subset of an infinite-dimensional normed linear spaceL, be a class of general nonlinear input-output systems that are governed by operator equations relating the input, state, and output, all of which are in extended spaces. IfQ is a given operator from a specified set ¯D _i, of inputs into the space of outputs ¯H ₀, the problem we consider is to find, for a given >0, a parameterA A such that the transmission operatorR(A ) ofS(A ) furnishes a nearly best (or -best) approximation toQ from allR(A),A A. Here the distance betweenQ andR(A) is defined as the supremum of distances betweenQz andR(A)z taken over allz ¯D _i. In Theorems 2 through 5 we show that ifS(A) is normal (Definition 2),A satisfies some mild requirement andL contains a fundamental sequence, then establishingA A reduces to minimizing a certain continuous functional on a compact subset ofR ⁿ, and thus can be carried out by conventional methods. The applications of results are illustrated by the example of a model-matching problem for a nonlinear system, and of optimal tracking.     

Systematic Width-and-Length Dependent CMOS Transistor Mismatch Characterization and Simulation

This paper presents a methodology for characterizing the random component of transistor mismatch in CMOS technologies. The methodology is based on the design of a special purpose chip which allows automatic characterization of arrays of NMOS and PMOS transistors of different sizes. Up to 30 different transistor sizes were implemented in the same chip, with varying transistors width W and length L. A simple strong inversion large signal transistor model is considered, and a new five parameters MOS mismatch model is introduced. The current mismatch between two identical transistors is characterized by the mismatch in their respective current gain factors /, V _TO threshold voltages , bulk threshold parameters , and two components for the mobility degradation parameter mismatch ₀ and _e. These two components modulate the mismatch contribution differently, depending on whether the transistors are biased in ohmic or in saturation region. Using this five parameter mismatch model, an extraordinary fit between experimental and computed mismatch is obtained, including minimum length (1 m) transistors for both ohmic and saturation regions. Standard deviations for these five parameters are obtained as well as their respective correlation coefficients, and are fitted to two dimensional surfaces f(W, L) so that their values can be predicted as a function of transistor sizes. These functions are used in an electrical circuit simulator (Hspice) to predict transistor mismatch. Measured and simulated data are in excellent agreement.     

Digital Modulator with Bandpass Delta-Sigma Modulator

A digital quadrature modulator with a bandpass -modulator is presented that interpolates orthogonal input carriers by 16 and performs a digital quadrature modulation at carrier frequencies f_s/4, –f_s/4 (f_s is the sampling frequency). After quadrature modulation, the signal is converted into an analogue IF signal using a bandpass modulator and a 1-bit D/A converter. The die area of the chip is 5.2 mm² (0.13 m CMOS technology). The total power consumption is 139 mW at 1.5 V with a clock frequency of 700 MHz (D/A converter full-scale output current 11.5 mA).     

Order selection statistical test for nonstationary AR models

A new statistical test for selecting the order of a nonstationary AR modelyk is presented based on the predictive least-squares principle. This test is of the same order as the accumulated cost function _n = _k=1 ⁿ ( _k ^* – _k )²;i.e., ^* wherey _k ^* is the predictive least-square estimate. It is constructed to show how many times the integrated AR processy _k is differenced in order to obtain a stationary AR process given that the exact order of the process is unknown.