Recursive estimation of two-dimensional processes with application to image processing

A low order quarter-plane-causal recursive model is presented to represent the class of 2-D stationary Gaussian processes with power spectra matrices factorable into a quarter-plane-causal and anti-causal parts. This model is used to develop a technique for obtaining optimal 2-D recursive estimators. The approach taken here is similar to Attasi's [8], with no commutability condition imposed on the model. Circumventing this condition allows the modeling of the 2-D processes to be achieved with fewer parameters, and enables one to find the solutions to the problems of blur and color noise which are inherent in most image degraded images. Some simulated examples illustrate these points.This research was supported in part by the U.S. Army Research Grant DAAG29-79-C-0054 and the National Science Foundation Grant ECS-8011911.     

Systems which possessg- andh- Representations

Examples are given concerning the range of applicability of recent representation results that provide a means of studying the input-output properties of nonlinear systems in terms of the familiar impulse-response concept, and which extend the concept of integral transformation to nonlinear maps. We show that such representations, which we call g- and h-representations, exist for important classes of systems governed by nonlinear integral equations. In particular, it is proved that a large class of maps that have Volterra series representations also have these representations.     

Some new results on stability robustness of two-dimensional discrete systems

In this paper, we study the problem of stability robustness of two-dimensional discrete systems in a local state-space setting. Two methods are proposed for efficient numerical evaluation of the exact complex perturbation bound . The first method combines Byers' bisection method with a three-point-pattern optimization technique to compute . The second method utilizes a direct optimization technique to find the bound. In addition, a 2-D Lyapunov approach is proposed to obtain two lower bounds of , and numerical techniques for solving the constant 2-D Lyapunov equation involved are presented. The paper is concluded with an example illustrating the main results obtained.     

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.     

Mobility Management for Hierarchical Wireless Networks

In this paper, we consider the mobility management in large, hierarchically organized multihop wireless networks. The examples of such networks range from battlefield networks, emergency disaster relief and law enforcement etc. We present a novel network addressing architecture to accommodate mobility using a Home Agent concept akin to mobile IP. We distinguish between the physical routing hierarchy (dictated by geographical relationships between nodes) and logical hierarchy of subnets in which the members move as a group (e.g., company, brigade, battalion in the battlefield). The performance of the mobility management scheme is investigated through simulation.     

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.     

On singular nonlinearH ∞ control: A state-space approach

A simple state-space approach for the four-block singular nonlinearH control problem is proposed in this paper. This approach combines a (J, J)-lossless and a class of conjugate (J, J)-expansive systems to yield a family of nonlinearH output feedback controllers. The singular nonlinearH control problem is thus transformed into a simple lossless network problem that is easy to deal with in a network-theory context.This work was supported by the National Science Council, Republic of China, under contract NSC 87-2218-E009-026.     

Distance of a complex coefficient stable polynomial from the boundary of the stability set

In this paper, the distance in the 1 2p norm from a complex coefficient polynomial to the border of its Hurwitz region is analyzed. Simplified expressions for 2p=1, 2, are also obtained.This work was supported in part by Comisión Investigaciones Cientificas de la Provincia de Buenos Aires (CIC) and Comisión Nacional de Investigaciones Cientificas y Técnicas (CONICET).     

A scalable wireless virtual LAN

This paper presents a Wireless Virtual Local Area Network (WVLAN) to support mobility in IPoverATM local area networks. Mobility is handled by a joint ATMlayer handoff for connection rerouting and MAClayer handoff for location tracking, such that the effects of mobility are localized and transparent to the higherlayer protocols. Different functions, such as Address Resolution Protocol (ARP), mobile location, and ATM connection admission are combined to reduce protocol overhead and frontend delay for connectionless packet transmission in connectionoriented ATM networks. The proposed WVLAN, through the use of ATM technology, provides a scalable wireless virtual LAN solution for IP mobile hosts.     

An algorithm for stability determination of two-dimensional delta-operator formulated discrete-time systems

The recent interest in delta-operator (or, -operator) formulated discrete-time systems (or, -systems) is due mainly to (a) their superior finite wordlength characteristics as compared to their more conventional shift-operator (or,q-operator) counterparts (or,q-systems), and (b) the possibility of a more unified treatment of both continuous- and discrete-time systems. With such advantages, design, analysis, and implementation of two-dimensional (2-D) discrete-time systems using the -operator is indeed warranted. Towards this end, the work in this paper addresses the development of an easily implementabledirect algorithm for stability checking of 2-D -system transfer function models.Indirect methods that utilize transformation techniques are not pursued since they can be numerically unreliable. In developing such an algorithm, a tabular form for stability checking of -system characteristic polynomials with complex-valued coefficients and certain quantities that may be regarded as their corresponding Schur-Cohn minors are also proposed.     

2-D harmonic retrieval using higher-order statistics

We consider the problem of estimating the harmonics of a noisy 2-D signal. The observed data is modeled as a 2-D sinusoidal signal, with either random or deterministic phases, plus additive Gaussian noise ofunknown covariance. Our method utilizes recently defined higher-order statistics, referred to as mixed-cumulants, which permit a formulation that is applicable to both the random and deterministic case. In particular, we first estimate the frequencies in each dimension using an overdetermined Yule-Walker type approach. Then, the 1-D frequencies are paired using a matching criterion. To support our theory, we examine the performance of the proposed method via simulations.     

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.     

CBC MACs for Arbitrary-Length Messages: The Three-Key Constructions

We suggest some simple variants of the CBC MAC that enable the efficient authentication of arbitrary-length messages. Our constructions use three keys, K1, K2, K3, to avoid unnecessary padding and MAC any message M {0,1}* using max{1, |M|/n} applications of the underlying n-bit block cipher. Our favorite construction, XCBC, works like this: if |M| is a positive multiple of n then XOR the n-bit key K2 with the last block of M and compute the CBC MAC keyed with K1; otherwise, extend Ms length to the next multiple of n by appending minimal 10 padding ( 0), XOR the n-bit key K3 with the last block of the padded message, and compute the CBC MAC keyed with K1. We prove the security of this and other constructions, giving concrete bounds on an adversarys inability to forge in terms of his inability to distinguish the block cipher from a random permutation. Our analysis exploits new ideas which simplify proofs compared with prior work.     

Controllability of the 2-D roesser model

Necessary and sufficient conditions for controllability of 2-D Roesser model are formulated. One can check controllability of 2-DRM using well-known tests for 1-D systems. Conditions are dual to the conditions for reconstructability of the system: transposed controllable 2-DRM is reconstructable. A numerical example is presented.     

An adaptive algorithm for optimizing the packet size used in wireless ARQ protocols

We develop an algorithm that allows an ARQ protocol to dynamically optimize the packet size based on estimates of the channel biterrorrate. Our algorithm is particularly useful for wireless and satellite channels where the biterrorrates tend to be relatively high and time variable. Our algorithm uses the acknowledgment history to make estimates of the channel biterrorrate, based on which the optimal packet size can be chosen. We develop a Markov chain model for the analysis of the system, under static channel conditions, and show that the algorithm can achieve close to optimal performance using a history of just 10,000 bits. We also use the Gilbert–Elliott twostate Markov channel to model dynamic channel conditions. We show, through simulation, that the algorithm performs well even under rapidly changing channel conditions. Finally, we discuss a maximum likelihood approach for choosing the packet size, which performs almost optimally but is much easier to implement.     

Solutions for H∞ Filtering of Two-Dimensional Systems

Thispaper deals with the H filtering problemfor linear discrete-time two-dimensional (2-D) systems describedby the Roesser model. It firstly establishes a version of thebounded real lemma to give a sufficient condition for quantificationof the H noise attenuation for 2-D systems.Based on the bounded real lemma, the H filteringproblem is investigated for filters of an observer-based structureor a general state equation form and the solutions are obtainedin terms of Riccati inequalities or linear matrix inequalities.The design approach is illustrated by an example of a stationaryfield in image processing.     

Characterization of subthreshold MOS mismatch in transistors for VLSI systems

MOS transistor mismatch is revisited in the context of subthreshold operation and VLSI systems. We report experimental measurements from large transistor arrays with device sizes typical for digital and analog VLSI systems (areas between 9 and 400µm²). These are fabricated at different production qualified facilities in 40-nm gate oxide,n-well andp-well, mask lithography processes. Within the small area of our test-strips (3 mm²), transistor mismatch can be classified into four categories: random variations, edge, striation, and gradient effects. The edge effect manifests itself as a dependence of the transistor current on its position with reference to the surrounding structures. Contrary to what was previously believed, edge effects extend beyond the outer most devices in the array. The striation effect exhibits itself as a position-dependent variation in transistor current following a sinusoidal oscillation in space of slowly varying frequency. The gradient effect is also a position-dependent spatial variation but of much lower frequency. When systematic effects are removed from the data, the random variations follow an inverse linear dependence on the square root of transistor area.     

β-bit serial/parallel multipliers

A generalized -bit least-significant-digit (LSD) first, serial/parallel multiplier architecture is presented with 1n wheren is the operand size. The multiplier processes both the serial input operand and the double precision product -bits per clock cycle in an LSD first, synchronous fashion. The complete two's complement double precision product requires 2n/ clock cycles. This generalized architecture creates a continuum of multipliers between traditional bit-serial/parallel multipliers (=1) and fully-parallel multipliers (=n). -bit serial/parallel multipliers allow anoptimized integrated circuit arithmetic to be designed based on a particular application's area, power, throughput, latency, and numerical precision constraints.This project was pratically funded by the UCSD-NSF I/UCR Center on Ultra-High Speed Intergrated Circuits and Systems.     

Dynamic capacity allocation and hybrid multiplexing techniques for ATM wireless LANs

We consider digital wireless multimedia LANs and timevarying traffic rates. To deal effectively with the dynamics of the timevarying traffic rates, a Traffic Monitoring Algorithm (TMA) is deployed to dynamically allocate channel capacities to the heterogeneous traffics. The TMA is implemented as a higher level protocol that dictates the capacity boundaries within two distinct framed transmission techniques: a Framed Time DomainBased (FTDB) technique and a Framed CDMA (FCDMA) technique. The performance of the TMA in the presence of the FTDB technique is compared to its performance in the presence of the FCDMA technique for some traffic scenarios. The performance metrics used for the TMAFTDB and TMAFCDMA combinations are channel capacity utilization factors, traffic rejection rates, and traffic delays. It is found that the TMAFTDB is superior to the TMAFCDMA when the speed of the transmission links is relatively low and the lengths of the transmitted messages are relatively short. As the speed of the transmission links and the length of the transmitted messages increase, the TMAFCDMA eventually outperforms the TMAFTDB.