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IEICE TRANSACTIONS on Fundamentals

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Advance publication (published online immediately after acceptance)

Volume E75-A No.12  (Publication Date:1992/12/25)

    Special Section on Networks and Mobile Communications
  • FOREWORD

    Masakazu SENGOKU  

     
    FOREWORD

      Page(s):
    1611-1612
  • Land Mobile Communication in Japan

    Tatsuo KITO  

     
    INVITED PAPER

      Page(s):
    1613-1618

    Land mobile communications in Japan have shown remarkable progress in recent years. The total number of all types of radio stations has exceeded 750 million as of March, 1992 and more than 80% of them are used for land mobile communications. The more radio telecommunications becomes popular, the more demand for communicating at any time, at any place and with anyone, intensifies. Various new land mobile systems such as digital cellular telephones have been developed and to be introduced. These new systems are designed to promote effective frequency use in order to meet the exploding demand for it. The digitalization of land mobile communication systems will be the key technology which enable to bring the new possibility in the land mobile communications.

  • TDMA Radio Link Control Techniques and Development of a Digital Cellular System

    Katsumi KOBAYASHI  Kota KINOSHITA  Hiraku MISHIMA  

     
    INVITED PAPER

      Page(s):
    1619-1624

    Digital mobile communication systems have been developed to cope with remarkable growth of the existing analog cellular telephone market. The digital cellular system needs to meet the following requirements: higher frequency efficiency, increased system capacity, new services including ISDN services, and network reliability improvements. New techniques supporting digital mobile radio sevices are presented in this paper, with special focus on TDMA radio link control. Radio channel and signalling structures are designed to achieve spectrum efficiency and flexibility. A random access scheme giving excellent access capability is shown. This paper also presents the system design and configurations of a TDMA digital cellular system based on the Japan standard, which is being developed by NTT Mobile Communications Network Inc. The system is based on the OSI model to enhance system flexibility for future services. Various techniques and devices to achieve economical and compact base stations and portable telephones are developed: multiple-carrier amplifier with extremely low distortion, facsimile/data adaptors with error free and high throughput, coherent detection with adaptive carrier tracking, and so on.

  • Technical Issues of Mobile Communication Systems for Personal Communications Services

    Takuro SATO  Takao SUZUKI  Kenji HORIGUCHI  Atsushi FUKASAWA  

     
    INVITED PAPER

      Page(s):
    1625-1633

    This paper describes a perspective on Personal Communicatoins Services (PCS) and technological trends. It takes into consideration rules pertaining to the use of PCS for mobile radio communication and countermeasures to cope with the huge increase in PCS subscribers. In this paper, PCS network structures, inter-regional roaming, microcell structure, radio access and channel access methods are also covered as PCS technologies. Furthermore, trends in domestic and international standards are also described. Although these technologies present many difficulties, we believe that they will be overcome and PCS services will be introduced in the near future.

  • On Dynamic Channel Assignment Strategies in Cellular Mobile Radio Systems

    Kazunori OKADA  Fumito KUBOTA  

     
    INVITED PAPER

      Page(s):
    1634-1641

    The rising demand for mobile communication is increasing the importance of efficient use of limited radio frequency resources. The assignment of radio channels to the cells of current cellular mobile radio systems, specifically, to each base station, has been much studied to increase efficiency in radio frequency use. Dynamic Channel Assignment (DCA) is one approach to this problem. This paper compares the basic characteristics of DCA with Fixed Channel Assignment (FCA) and describes the main DCA strategies. The most important current research topics on DCA are discussed, focusing on micro-cellular systems, which are considered indispensable in meeting the huge demand for future mobile communications.

  • On the Optimum Allotment of Frequency Resources in Mixed Cellular Layouts

    Mario FRULLONE  Paolo GRAZIOSO  Guido RIVA  

     
    PAPER

      Page(s):
    1642-1651

    The paper deals with the evaluation of channel allotment criteria in a mixed cellular environment composed by a regular grid of macrocells, plus a number of microcells deployed in the most congested areas. The optimum allotment of the resources between microcells and macrocells, which is a key issue for future personal communication systems, has to be tailored on the basis of their different functionalities. The approach is quite innovative since the analysis is carried out considering real traffic statistics, which are characterised by peaks and fluctuations resulting in uneven traffic loads on different cells. Different propagation models for macrocells and microcells have been adopted. Finally, the impact of the allotment of frequency resources to microcells and macrocells is analysed.

  • Holonic Location Registration/Paging Procedure in Microcellular Systems

    Masanori TAKETSUGU  Youichi OHTERU  

     
    PAPER

      Page(s):
    1652-1659

    A location registration/paging procedure which is free from location registration area design is proposed. Each base station (BS) broadcasts a "responsibility area", composed of its own and neighboring cells' identification (ID). A mobile station (MS) makes a new location registration request when the current BS's responsibility area does not include the MS's registered location. Each BS is allowed to decide its own responsibility area autonomously based on route information, which is composed of neighboring cells' ID and reported from MSs. Therefore, the responsibility area can be adaptively changed based on MSs' moving characteristics. Moreover, this procedure solves the problems of registration traffic concentration and excess registration request on boundary BSs.

  • Rearrangement Methods of Dynamic Channel Assignment in Cellular Mobile Systems

    Keisuke NAKANO  Masakazu SENGOKU  Toshihiko TAKAHASHI  Yoshio YAMAGUCHI  Shoji SHINODA  Takeo ABE  

     
    PAPER

      Page(s):
    1660-1666

    In mobile communication systems using Dynamic Channel Assignment, channels are possible to be rearranged so that blocking probability can be made low. The smaller the number of cells where channels are rearranged, the smaller the load on the base stations in the cells. Also, we can reduce the deterioration of communication quality caused by reassingning a new channel to a call instead of the channel already assigned. In this paper, we consider not only how to rearrange channels but also which channel should be rearranged and assigned to a new call in rearrangement, and propose very simple but effective methods for rearrangement. The ways to select a candidate channel to be rearranged and assigned to a new call in the new methods make the number of cells where a channel is rearranged smaller. We also examine the relations between characteristics and the number of cells where a channel is rearranged. Using computer simulation results, the properties of the new rearrangement methods are compared with those of the traditional methods.

  • A Proposal of a Dynamic Channel Assignment Strategy with Information of Moving Direction in Micro Cellular Systems

    Kazunori OKADA  Fumito KUBOTA  

     
    PAPER

      Page(s):
    1667-1673

    The demand for mobile communications is continuing to grow, but there is a limit on the radio frequency resources. Micro cellular systems are a strong solution to this problem. However, Forced Call Termination (FCT) and Channel Changing (CC) occur frequently in these systems because of their small cell size. This paper proposes a new Dynamic Channel Assignment (DCA) strategy which uses information of moving direction of Mobile Stations (MSs) to reduce FCT and CC. This strategy, the MD (Moving Direction) strategy, is compared with other major DCA strategies by simulating a one-dimensional service area covering a road, such as an expressway. The simulation shows that the MD strategy performs better than the other strategies with regard to FCT, CC, and carried load. FCT is an especially important factor in the quality of service. The MD strategy reduces FCT and has the largest carried load of the strategies, which means that it has the most efficient channel usage. This is an attractive characteristic of the MD strategy for micro cellular systems.

  • Performance of a Multicast Error Control Protocol Based on a Product Code Structure--Part : On Random Error Channels--

    Katsumi SAKAKIBARA  Masao KASAHARA  

     
    PAPER

      Page(s):
    1674-1683

    A multicast error control protocol proposed by Metzner is generalized and the performance of the proposed protocol on random error channels (binary symmetric channels) is analyzed. The proposed protocol adopts an encoding procedure based on a product code structure, whith enables each destined user terminal to decode the received frames with the Reddy-Robinson algorithm. As a result, the performance degradation due to the re-broadcasting of the replicas of the previously transmitted frames can be circumvented. The numerical results for the analysis and the simulation indicate that the proposed protocol yields higher throughput and less degradation of throughput with an increase of the number of destined terminals.

  • Performance of a Multicast Error Control Protocol Based on a Product Code Structure--Part : On Burst Error Channels--

    Katsumi SAKAKIBARA  Masao KASAHARA  

     
    PAPER

      Page(s):
    1684-1695

    Two types of multicast error control protocols based on a product code structure with or without interleaving are considered. The performances of these protocols are analyzed on burst error channels modeled by Gilbert's two-state Markov chain. The numerical results reveal that the interleaving does not always succeed in improving the performance of the protocol proposed in Part .

  • Bit Error Probability and Throughput Performance of Time Spread PPM/CDMA Systems

    Xuping ZHOU  Ikuo OKA  Chikato FUJIWARA  

     
    PAPER

      Page(s):
    1696-1701

    A model for time spread-pulse position modulation (TS-PPM)/code division multiple access (CDMA) systems is presented. A TS signal is produced by a TS-filter, whose characteristic is a pseudonoise sequence in frequency domain. The error probability performance is analyzed and compared with those of on-off keying (OOK) and binary phase shift keying (BPSK). It is shown that at the same transmission speed TS-PPM is superior to TS-OOK and TS-BPSK due to the dramatic decrease of multiple access interference. The throughput of the network is analyzed, and its relation to the length of pseudonoise sequence and the packet length is also discussed.

  • Voice Communication Connection Control in Digital Public Land Mobile Networks

    Masami YABUSAKI  Kouji YAMAMOTO  Shinji UEBAYASHI  Hiroshi NAKAMURA  

     
    PAPER

      Page(s):
    1702-1709

    This paper describes voice communication connection controls in digital public land mobile networks (D-PLMNs). Voice communications in the D-PLMNs are carried at about 10 kbit/s over narrow-band TDMA channels with highly efficient cellular voice encoding schemes. Extensive research is being carried on half-rate voice encoding schemes that will effectively double radio resources. We first outline the configuration of voice communication connection between a cellular phone in the D-PLMN and a telephone in a fixed network, and we describe the optimum position for the CODECs that transform cellular voice codes to the conventional voice codes used in the fixed network, and vice versa. Then we propose a CODEC-bypassed communication control scheme that improves the quality of voice communication between cellular phones. And we propose a cellular voice code negotiation scheme in the D-PLMN which supports different cellular voice encoding schemes. We also propose an efficient channel reassignment scheme for effectively assigning TDMA channels to voice calls with two different bitrates (full-rate and half-rate), and we analyze this scheme's traffic capability. Finally, we describe a dual-tone multiple-frequency (DTMF) signal transmission scheme and estimate the number of DTMF signal senders required in the D-PLMN.

  • A Parallel Collision Resolution Algorithm for Mobile Systems

    Shigeru SHIMAMOTO  Noriaki HAGIYA  Jaidev KANIYIL  Yoshikuni ONOZATO  

     
    PAPER

      Page(s):
    1710-1719

    For the connection request procedure in mobile communication systems, a previous study had shown that the 3-channel systems provide the haighest maximum of stable per channel throughput. In this paper, we propose and study a new algorithm, called the Parallel Collision Resolution Algorithm, which can be implemented in a Q-channel connection request environment, where Q3. For the implementation, the channels are arranged in R groups, where R is a positive integer. The collision resolution scheme distributes the collided messages over all the groups so that throughput and delay measures can be improved. At any point in time, there can be a maximum of R collision resolution schemes operational irrespective of the channel or the group number over which collisions occurred. The performance measures are estimated by computer simulation. Under the new algorithm, almost the same level of the perchannel stable throughput measure of a 3-channel network can be achieved in networks for which Q3. This feature allows freedom to the network designer to employ a higher number of connection request channels without forfeiting high channel utilization rates. When Q is an integral multiple of 3, the maximum stable per channel throughput level achieved can be the same as that achieved by the 3 channel system, if the grouping of channels is such that each group consists of 3 channels. When Q is not an integral multiple of 3, the intuitive strategy of organizing the channels in such a way that Q/3 groups consist of 3 channels each and one group consists of (Q mod 3) channels, may result in much degraded performance. It is found that, if the channels are so organised that no group is composed of (Q mod 3) channels, the performance levels can be substantially enhanced. Also, under the new algorithm, the delay measure is significantly improved, particularly in schemes like the mobile satellite systems with high propagation delays. We conclude that the new scheme presents a promising collision resolution methodology for connection request procedures.

  • Layered Self-Organizing Packet Radio Networks

    Akira ISHIDA  Jae-Gyu YOO  Miki YAMAMOTO  Hiromi OKADA  Yoshikazu TEZUKA  

     
    PAPER

      Page(s):
    1720-1726

    In this paper, we propose a new network organizing method for packet radio networks, a layered self-organizing method. In the layered self-organizing network, whole service area is divided into multiple sub-areas and one base station is settled in each sub-area. Communication links are settled in shorter time than the conventional self-organizing method. We evaluate the network organizing performance of the method by using simulations.

  • Special Section on the 1992 IEICE Fall Conference
  • FOREWORD

    Takao ASANO  

     
    FOREWORD

      Page(s):
    1727-1727
  • A Scheduling Method Using Boolean Equations in High-Level Synthesis

    Toshiaki MIYAZAKI  

     
    LETTER

      Page(s):
    1728-1731

    This paper describes two algorithms based on Boolean formulations aimed at solving scheduling, the main subtask of data path synthesis. Using the first algorithm, all possible scheduling solutions can be obtained under a time constraint, something that cannot be accomplished with other available systems. The second algorithm produces feasible solutions without increasing the complexity of the problem. The effectiveness of the algorithms is confirmed through experimental studies.

  • Hierarchical Timing Analyzer for Multiple Phase Clocked Designs

    Hiromi ISHIKAWA  Masanori IMAI  Junko KOBARA  Shinichi MURAI  

     
    LETTER

      Page(s):
    1732-1735

    The objective of this work is to demonstrate a new hierarchical timing analysis technique for multi-phase clocked designs with feedback loops including level sensitive latches. By using this technique, large synchronous designs can be analyzed accurately without loop breaking.

  • A Realization of Type 1 Mutator Using CCIIs and Its Application to Impedance Simulation

    Masami HIGASHIMURA  

     
    LETTER

      Page(s):
    1736-1738

    This paper proposes a new circuit configuration for realizing a type 1 mutator using two current conveyor (CCIIs) and a network with a suitable current transfer function. The advantage of the proposed circuit configuration is that any impedance functions which are proportional to the realizable current transfer function can be simulated.

  • Efficient Design of N-D Hyperspherically Symmetric FIR Filters

    Todor COOKLEV  Akinori NISHIHARA  

     
    LETTER

      Page(s):
    1739-1742

    The design of N-dimensional (N-D) FIR filters requires in general an enormous computational effort. One of the most successful methods for design and implementation is the McClellan transformation. In this paper a numerically simple technique for determining the coefficients of the transformation is suggested. This appears to be the simplest available method for the design of N-D hyperspherically symmetric FIR filters with excellent symmetry.

  • Chaotic Behavior in Ferroelectrics

    Ikuo SUZUKI  Minoru MURAKAMI  Masaki MAEDA  

     
    LETTER

      Page(s):
    1743-1746

    Chaotic behavior in a series resonance circuit with a ferroelectric triglycine sulfate (TGS) crystal was observed just below the ferroelectric phase transition temperature. We have analyzed the nonlinear responses by applying external electric fields to the crystal. The computer simulation was made for the modified forroelectric hysteresis loops to realize the experimental results. The fractal correlation dimension was determined to be ν=1.8 in the chaotic phase.

  • Chaotic Phenomena in the Maxwell-Bloch Equation with Time Delay

    Keiji KONISHI  Yoshiaki SHIRAO  Hiroaki KAWABATA  Masaya HIRATA  Toshikuni NAGAHARA  Yoshio INAGAKI  

     
    LETTER

      Page(s):
    1747-1750

    One model of a laser is a set of differential equations called the Maxwell-Bloch equations. Actually, in a physical system, causing a chaotic behavior is very difficult. However the chaotic behavior can be observed easily in the system which has a mirror to feedback the delayed output.

  • Discussion on a Method to Generalize the Computerized Test Based on the Analysis of Learners' Image Structure to Computer System

    Takako AKAKURA  Keizo NAGAOKA  

     
    LETTER

      Page(s):
    1751-1754

    In this letter authors discussed on the strategy to apply computerized tests on learners who have negative attitude to computerized tests. First, learners' image to computer system was measured by semantic differential method (SD method). It was revealed that the image of computer systems was made up of four factors of subjective evaluation (Es), objective evaluation (Eo), potency (P) and activity (A). Learners who have negative attitude to computerized test were revealed to have negative image on (Es) and (A) factors, while on the other hand have rather positive image on (Eo) and (P) factors. Then authors developed the feedback record charts laying stress on (Eo) and (P) factors. This feedback chart was effective to improve learners' acceptability of computerized test.

  • Endurance of Ceramic Hydrophone for the Measurement of Acoustic Pressures of ESWL

    Naoto INOSE  Masao IDE  

     
    LETTER

      Page(s):
    1755-1757

    This paper describes the endurance of a ceramic hydrophone to measure high acoustic pressures at the focal point of Extracorporeal Shockwave Lithotripter (ESWL).

  • Two-Dimensional Electromagnetic Wave Analysis of Single Laser Beam Trapping of Particles

    Yoshinari ISHIDO  Toshiyuki SAITO  Akio NISHIMOTO  Yoshimi KAKUI  

     
    LETTER

      Page(s):
    1758-1761

    With the use of a two-dimensional model, single laser beam trapping of particles is analyzed as the electromagnetic boundary-value problem. From the numerical results, it is found that the trapping mechanism for this system depends upon the surface field distribution of the object.

  • Scattering from Conductor or Complementary Aperture Array on a Semi-infinite Substrate

    Hideaki WAKABAYASHI  Masanobu KOMINAMI  Shinnosuke SAWA  Hiroshi NAKASHIMA  

     
    LETTER

      Page(s):
    1762-1764

    Frequency Selective Screens (FSS) with conductor or complementary aperture array are investigated. The electric current distribution on conductor or the magnetic current distribution on aperture is determined by the moment method in the spectral domain. In addition, the power reflection coefficients are calculated and the scattering properties are considered.

  • Polarization Characteristics of Plane Waves Scattered by a Strip Grating with an Anisotropic Substrate

    Masamitsu ASAI  Jiro YAMAKITA  Shinnosuke SAWA  

     
    LETTER

      Page(s):
    1765-1767

    In this paper, scattering waves by a strip grating with an anisotropic substrate for the incidence of inclined polarization are analyzed, and polarization characteristics of scatterd waves are calculated. For simplicity, the analysis is limitted to the case of normal incidence and a perfectly conducting strip grating is assumed.

  • Analysis of Head Movement in the Depth Direction and Vergence Eye Movement Coordination

    Mitsuho YAMADA  Kenya UOMORI  

     
    LETTER

      Page(s):
    1768-1773

    We analyzed vergence change by moving both the target and the subject toward depth direction simultaneously. It has been suggested that the command for vergence movement caused by depth-direction-head-movement and that caused by target movement are generated separately, then combined in the oculomotor system.

  • An MOS Operational Transconductance Amplifier and an MOS Four-Quadrant Analog Multiplier Using the Quadritail Cell

    Katsuji KIMURA  

     
    LETTER

      Page(s):
    1774-1776

    This letter describes an MOS operational transconductance amplifier and an MOS four-quadrant analog multiplier using the quadritail cell, which provides an output current proportional to the square of a differential input voltage. As a result, a linear transconductance amplifier and a quarter-squarer multiplier can be obtained in theoretical circuit analysis.

  • Regular Section
  • A Realization of Low Sensitivity RCCS-Controlled Monolithic Integrators and Their Application to RC Active Filters

    Yukio ISHIBASHI  Fujihiko MATSUMOTO  

     
    PAPER-Analog Circuits and Signal Processing

      Page(s):
    1777-1784

    Up to present, some automatically tunable active RC filters have been proposed for the monolithic integrated continuous-time filters. In this paper a synthesis method of monolithic active RC filters is presented, whose characteristic is hardly dependent on temperature, supply voltage and so on, theoretically. First, this paper describes a variable integrator controlled by bias current. Second, a resistor controlled current source circuit (RCCS) is also proposed, which contains the voltage controlled current source (VCCS) being identical with that used in the realization of the integrator and whose current is controlled by an external resistor. The use of this VCCS in the RCCS can completely compensate the variation of the integrator characteristics. Finally, these circuits are applied to realize a third-order elliptic low-pass filter, which is simulated on PSPICE. From the simulations, we obtain excellent results as follows: The deviation of gains in the passband due to the variation of temperature with a range of -10 to 60 is within 0.02 dB; A total harmonic distortion with a 1 Vp-p input voltage at 100 kHz is less than 0.4% when the cut-off frequency is 1 MHz and the supply voltage is 5 V.

  • On a Realization of "Flow-Saturation" by Adding Edges in an Undirected Vertex-Capacitated Network

    Yoshihiro KANEKO  Shoji SHINODA  Kazuo HORIUCHI  

     
    PAPER-Graphs, Networks and Matroids

      Page(s):
    1785-1792

    A vertex-capacitated network is a graph whose edges and vertices have infinite positive capacities and finite positive capacities, respectively. Such a network is a model of a communication system in which capacities of links are much larger than those of stations. This paper considers a problem of realizing a flow-saturation in an undirected vertex-capacitated network by adding the least number of edges. By defining a set of influenced vertex pairs by adding edges, we show the follwing results.(1) It suffices to add the least number of edges to unsaturated vertex pairs for realizing flow-saturation.(2) An associated graph of a flow-unsaturated network defined in this paper gives us a sufficient condition that flow-saturation is realized by adding a single edge.

  • Generalized Optimum Interpolatory Estimation of Multi-Dimensional Orthogonal Expansions with Stochastic Coefficients

    Takuro KIDA  Somsak SA-NGUANKOTCHAKORN  

     
    PAPER-Information Theory and Coding Theory

      Page(s):
    1793-1804

    Extended interpolatory approximations are discussed for some classes of n-dimensional stochastic signals expressed as the orthogonal expansions with respect to a given set of orthonormal functions. We assume that the norm of the weighted mutual correlation function of the signal is smaller than a given positive number. The presented approximation has the minimum measure of approximation error among all the linear and nonlinear statistical approximations using the similar measure of error and the same generalized moments of these signals.

  • The Higher-Order Moment Function of Superposed Markov Jumping Processes with Its Application to the Analysis of Membrane Current Fluctuations

    Kazuo YANA  Hiroyuki MINO  Nobuyuki MORIMOTO  

     
    PAPER-Nonlinear Phenomena and Analysis

      Page(s):
    1805-1813

    This paper describes the higher-order moment analysis of superposed Markov jumping processes. A superposed Markov jumping process is defined as a linear superposition of a finite number of piecewise constant real valued stochastic process whose value changes are associated with state transitions in an underlying descrete state continuous time Markov process. Some phenomena are modeled well by the process such as membrane current fluctuations observed at bio-membranes or load fluctuations in electrical power systems. Theoretical formula of the moment function of any order k is derived and the parameter estimation problem utilizing higher-order moment functions is discussed. A new method of estimating the kinetic parameters of membrane current fluctuations is proposed as a possible application.

  • Basic Characteristics of a Fractance Device

    Masahiro NAKAGAWA  Kazuyuki SORIMACHI  

     
    PAPER-Nonlinear Phenomena and Analysis

      Page(s):
    1814-1819

    In this work we propose a recursive electric circuit which has a fractal structure composed of resistances and capacitors. It is first confirmed in practice that such a device, which is referred as fractance, possesses a novel characteristics between the constituent elements, or the resistance and the capacitance. That is, the absolute value of the impedance shows such a characteristics as |Z|ω-1/2, whereas the phase angle does such a constant phase property as θ=-π/4 independent of the frequency. As an application of the presently proposed fractance device, we constructed a fractional integral circuit as well as a fractional differential circuit, and confirmed that the observed output wave forms agree well with those derived from a computer simulation.

  • Detecting Separability of Nonlinear Mappings Using Computational Graphs

    Kiyotaka YAMAMURA  Masahiro KIYOI  

     
    LETTER-Analog Circuits and Signal Processing

      Page(s):
    1820-1825

    Separability is a valuable property of nonlinear mappings. By exploiting this property, computational complexity of many numerical algorithms can be substantially reduced. In this letter, a new algorithm is presented that detects the separability of nonlinear mappings using the concept of "computational graph". A hybrid algorithm using both the top-down search and the bottom-up search is proposed. It is shown that this hybrid algorithm is advantageous in detecting the separability of nonlinear simultaneous functions.

  • An Adaptive Fuzzy Network

    Zheng TANG  Okihiko ISHIZUKA  Hiroki MATSUMOTO  

     
    LETTER-Fuzzy Theory

      Page(s):
    1826-1828

    An adaptive fuzzy network (AFN) is described that can be used to implement most of fuzzy logic functions. We introduce a learning algorithm largely borrowed from backpropagation algorithm and train the AFN system for several typical fuzzy problems. Simulations show that an adaptive fuzzy network can be implemented with the proposed network and algorithm, which would be impractical for a conventional fuzzy system.