KALP: A Kalman Filter-Based Adaptive Clock Method with Low-Pass ...

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KALP: A Kalman Filter-Based Adaptive Clock Method with Low-Pass Prefiltering for Packet Networks Use Kyeong Soo Kim, Member, IEEE and Byeong Gi Lee, Fellow, IEEE

Abstract—In this paper we consider the issue of source clock frequency recovery in packet networks and propose a new adaptive clock method based on the Kalman filter (KF) with low-pass prefiltering—KALP (Kalman filter-based Adaptive clock method with Low-pass Prefiltering) in short. Noting that because of the difficulty in modeling as well as the nonwhite Gaussian nature of the packet jitter most existing adaptive clock methods could not successfully adopt the Kalman filter, we take a new approach to packet jitter modeling for the KALP. We model the packet jitter not directly but after shaping its characteristics by low-pass prefiltering. This low-pass prefiltering is an important arrangement as it helps to convert the packet jitter into a low-pass signal regardless of its original characteristics, thus enabling to model the prefiltered packet jitter using a simple first-order autoregressive [AR(1)] process. The low-pass prefilter should be carefully selected not to lose the timing information while prefiltering, and the moving averager employed in this paper satisfies this requirement. The AR(1)-modeled jitter component is amenable to the KF-based processing, which in this case becomes an optimal estimator. The design parameters including the initial conditions of the KF and AR(1) parameters can be determined based on the service clock specification and packet interarrival times during the delay smoothing process. We carry out various simulations to compare the performance of the KALP with the existing buffer-based adaptive clock method and demonstrate that the KALP can significantly reduce the fluctuation in the level of receiving buffer as well as the time to recover the source clock frequency. Index Terms—Adaptive clock method, Kalman filter, KALP, packet jitter, prefiltering, source clock frequency recovery.

I. INTRODUCTION

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ECENT advances in integrated broad-band packet networks where both real-time and nonreal-time services are multiplexed and transmitted together in the form of packet streams have stimulated research in the area of source clock frequency recovery (SCFR) in packet networks. The SCFR is intended to reproduce the source clock of the sender (i.e., the source node) at the receiver (i.e., the destination node) Paper approved by R. Rao, the Editor for Packet Multiple Access of the IEEE Communications Society. Manuscript received August 22, 1997; revised December 17, 1998 and October 7, 1999. This work was supported in part by the Korea Telecom under Contract 23 and by a Special Researcher Fellowship from the Institute of New Media and Communications (INMC), Seoul National University, Seoul, Korea. K. S. Kim was with the INMC, Seoul National University, Seoul, Korea. He is now with PON Systems Research and Development, Lucent Technologies, Murray Hill, NJ 07974 USA (e-mail: [email protected]). B. G. Lee is with the School of Electrical Engineering, Seoul National University, Seoul 151-742, Korea (e-mail: [email protected]). Publisher Item Identifier S 0090-6778(00)06163-8.

as closely as possible [2]. If the reading clock at the receiver is slower or faster than the average rate at which the sender transmits packets, buffer overflow or underflow may occur, thus resulting in packet losses or long pulse gaps in the recovered data stream. So SCFR is an essential function in transmitting real-time services in packet networks. The fundamental problem of SCFR in the packet network is in estimating the source clock frequency out of the jittered packet stream. The packet jitter, that is, the fluctuation in packet interarrival times, occurs because each packet experiences random delay during transit. The large magnitude of packet jitter, together with its strong correlation, makes it very difficult to estimate the source clock frequency from the jittered packet stream. Therefore algorithms for SCFR in packet networks should be able to address this issue properly. Several SCFR schemes [1], [3]–[6] have been proposed. They may be categorized into synchronous and asynchronous SCFR schemes. In the case of the synchronous SCFR schemes, which is depicted in Fig. 1, the sender delivers via the outgoing packet stream information on the frequency difference between the source clock and the reference clock, which is generated out of the common network clock available to both the sender and the receiver. The receiver can recover the original source clock frequency using this frequency difference information and the same reference clock. The asynchronous SCFR schemes differ from the synchronous ones in that they extract the source clock information out of the packet stream itself arriving at the receiver because no common network clock is available. Fig. 2 depicts a typical asynchronous SCFR scheme. Noting that the packet interarrival time or the buffer fill state at the receiver contains the source clock frequency information, the receiver extracts the source clock frequency out of this information by applying an appropriate digital filter. The estimated frequency then drives the phase-locked loop (PLL) to regenerate the source clock frequency. As such, the asynchronous schemes do not resort to the common network clock, and most of them do not need additional frame structure, at higher layer, for delivery of the information on the clock frequency difference.1 Therefore, asynchronous SCFR schemes are applicable to a broader range of networks where the common network clock is not available and adoption of additional frame structure at higher layer is not feasible. Such an asynchronous SCFR scheme is also called adaptive clock method and is recommended as one of standard 1As an exception, the asynchronous scheme proposed in [6] resorts to the frame structure for negative stuffing.

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Fig. 1.

IEEE TRANSACTIONS ON COMMUNICATION, VOL. 48, NO. 7, JULY 2000

Basic concept of the synchronous SCFR method.

Fig. 2. Basic concept of the asynchronous SCFR method.

SCFR methods for the ATM adaptation layer (AAL) type 1 together with synchronous residual time stamp (SRTS) that is a synchronous SCFR scheme [3]. In this paper, we focus our discussions on this adaptive clock method. One well-known adaptive clock method is a buffer-based method [1]. The buffer-based method takes the time-average of the observed receiver buffer state for use in reducing the packet jitter and estimating the frequency difference between the source and the receiver clocks, which is then used for controlling the receiver clock frequency. While the buffer-based method is easy to implement due to its simplicity and independence of packet jitter characteristics, its convergence speed is relatively low. This is because the buffer-based adaptive clock method does not employ the optimal Kalman estimation algorithm but employs a suboptimal estimation algorithm that relies on the long-term averaging effect of packet jitter. The reason why the buffer-based method employed the suboptimal estimation algorithm, as described in [1], is that the optimal Kalman estimation algorithm based on the additive white Gaussian noise (AWGN) assumption exhibited lack of convergence in simulating the first-come first-served (FCFS) multiplexer. In addition, this method did not provide any systematic procedure for determining its several design parameters including the that initial measurement time interval and the parameter controls the time sequence to estimate the frequency difference. In the case of the adaptive terminal synchronization method [4], packet interarrival time is measured instead of the receiver buffer level, which is then time-averaged for the source clock period estimation. This method employs a set of design equations for determining the order of the time-averaging filter which is based on the assumption that the probability distribution of each packet delay in the packet network is identical and independent of each other. In reality, however, this assumption is not valid in

general, so the equations cannot be applied in determining the design parameter. Regarding the packet jitter characteristics, we have carried out an extensive simulation study for multi-node packet network environments to get answers to the following two questions [7]: 1) Is the AWGN assumption is valid? 2) Is it possible in general to capture the important characteristics of packet jitters in various network environments using a simple, well-known random process model for use in SCFR? According to the simulation results the answers to both questions were negative: Even though the packet jitter characteristics approach those of AWGN as the number of intermediate nodes increases, the packet jitter cannot be modeled as an AWGN in most cases. In addition, as the packet jitter characteristics are decided by a number of factors such as the source packet period, the background traffic characteristics, the node service discipline, and the number of intermediate nodes, it is practically impossible to model the packet jitter characteristics using a simple random process. Therefore, it is useful to devise a totally different approach to packet jitter modeling. Based on the observations that the existing SCFR methods in packet networks are not rooted in optimal estimators and that direct modeling of packet jitter is nearly impossible, we propose a new adaptive clock method named KALP—Kalman filter-based Adaptive clock method with Low-pass Prefiltering. The KALP is distinctive in that it models the packet jitter after shaping its characteristics by low-pass prefiltering. The low-pass prefiltering contributes to the following two important points: First, it shapes the packet jitter into a low-pass signal irrespective of its original characteristics, thereby making it possible to effectively model the prefiltered packet jitter using a simple first-order autoregressive [AR(1)] process. Secondly, once the jitter component is AR(1)-modeled, it is possible to employ the KF as an optimal estimator. The organization of this paper is as follows. We first describe the KALP algorithm in detail in Section II, including the procedures to determine the initial conditions of the KF and the AR(1) parameters. Then, in Section III, we carry out a comparative study, through various simulation experiments, on the SCFR performances of the KALP and the existing buffer-based adaptive clock method in terms of the frequency estimation error and the receiver buffer state. Then, we conclude the discussions in Section IV.

KIM AND LEE: KALP FOR PACKET NETWORKS USE

II. THE KALP ALGORITHM In this section, we describe the proposed KALP algorithm in detail. We first define the related clock frequencies and time periods based on the operational assumptions on the system. Then we construct a state space model for the packet interarrival time at the receiver and derive the source clock frequency estimation algorithm based on this model. Next, we discuss the procedures to determine the initial conditions for the KF and AR(1) parameters, finally considering possible extensions of the KALP algorithm to address the issues of packet losses and time-varying nature of the system. A. Definition of Clock Frequencies and Time Periods The system we consider in this paper consists of a sender, a packet network, and a receiver. The sender converts the incoming data flow into a fixed-sized packet stream and transmits it to the receiver via the packet network where each packet experiences random delay, i.e., packet jitter, whose statistical characteristics are assumed to be time-invariant. The service type of the incoming data flow (e.g., DS1 signal) is known to both the sender and the receiver, and for its transmission, the sender and the receiver clocks should meet certain requirements specific to the service type, which are described by a nominal value and a tolerance to the service clock frequency. Regarding the service clock generation at the sender and the receiver, we assume that there are stable local clock sources that generate service clocks satisfying these requirements. This assumption implies that all the operations of the KALP algorithm at the receiver, including packet receiving, packet interarrival time measuring, and filtering, are done based on this local clock source. This is because we consider a packet network where no reference clock is available at both the sender and the receiver. So the local clock source is the only reference that all operations rely on. Based on this system model and the operational assumptions, we define clock frequencies and time periods with respect to the local clock source at the receiver. Note that in most existing studies the algorithms are described in terms of absolute clock frequencies only, which are measured with respect to the reference clock. These absolute clock frequencies may be used in derivation of an algorithm, but the final SCFR procedure actually implemented at the receiver should be described in terms of clock frequencies defined with respect to the local clock because by assumption, such a reference clock is not available at the receiver. In the following, we define some useful clock frequencies and time periods based on both the conceptual reference clock and the local clock at the receiver. Packet size (bits). Source clock frequency measured with respect to the reference clock (hertz). Source clock frequency measured with respect to the receiver clock (hertz). Packet interdeparture time measured with respect to (secthe reference clock, which is defined as onds). Packet interdeparture time measured with respect to (seconds). the receiver clock, which is defined as

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Receiver clock frequency measured with respect to the reference clock (hertz). Receiver clock frequency measured with respect to the receiver clock (hertz). Nominal value for a service clock frequency specific to a service type (hertz). Tolerance to the nominal clock frequency (ppm). Nominal value for packet interdeparture time defined (seconds). as We distinguish the clock frequencies/periods measured with respect to the reference clock from those measured with respect to the receiver clock by putting tildes on the former. Note that and , where and are unknown at the receiver. So the problem of SCFR is now reduced to the estimation of , or equivalently , at the receiver. B. Modeling of Packet Interarrival Times As we consider a packet network with fixed packet size, the interdeparture time between two consecutive packets at the sender is determined by the source clock frequency, and is constant in the case of a constant bit rate (CBR) service. But the interarrival time of the packets at the receiver deviates from the interdeparture time due to the packet jitter in the network. th So the interdeparture time between the th and the , and the corresponding interarrival packets at the sender, may be expressed by time at the receiver (1) that is defined as the difference between for the packet jitter delays of two consecutive packets in the packet network. If the is AWGN, then the optimal estimation of packet jitter can be easily achieved using the Kalman filter. In general, however, the packet jitter has complicated statistical characteristics that cannot be modeled as AWGN [1], [7]. As discussed in Section I, it is practically impossible to exactly model the packet as is. In [4], a maximum likelihood estimator (MLE) jitter approach was employed instead, which could be a good choice of estimator for the jitter of unknown statistical characteristics [8], but cannot be an optimal estimator. In addition, it does not take advantage of the a priori information on the source clock and . frequency C. Estimation of Source Clock Frequency The prefilter in the KALP is intended to transform the packet into a low-pass signal, which then can be modeled by jitter the AR(1) process, one of the simplest models with low-pass characteristic. The low-pass prefilter should be carefully selected not to lose timing information while prefiltering. As the moving averager satisfies this requirement and is simple to implement, we take it as the low-pass prefilter for the KALP in this paper. The packet interarrival time filtered by a moving averager of is given by order

(2)

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If we denote by

and hence we get

the moving-averaged jitter, i.e., (3)

then by (1) and (2), we get

(9a) (4)

Now that the noise component has become a low-pass signal , we may take the AR(1) process for its modeling, i.e., (5) denotes the AWGN whose average and variance are where 0 and 1, respectively, and and are weighting parameters. If we apply the KF equations for the colored noise [9], then we obtain the following results. • Initialization (6) • For

(7)

, is the estimated value of , the where , and the Kalman gain. variance of the difference D. Determination of Initial Conditions and AR(1) Parameters and , that The initial conditions of KF, we need in implementing the KALP algorithm can be derived from the nominal value and the tolerance of the service clock is a frequency, which are a priori information. Note that random variable denoting the value of . Since the source clock and the receiver clock should meet these requirements for the service clock frequency, we get

In order to model the uncertainty in the source and receiver and clock frequencies, we define two random variables to denote the source and the receiver clock frequencies respectively measured with respect to the reference clock. The proband are usually determined by ability distributions for the manufacturing process as well as the type of clock source (e.g., quartz) [10]. In this paper, we assume, as an example, that and have a uniform probability distribution in . Note, however, that the following derivation is not bound by this uniform distribution assumption. , , and , Since we have (8)

(9b) Considering that

, we may rewrite (9) as (10a) (10b)

The AR(1) parameters and , which are used in modeling prefiltered packet jitter, can be obtained before applying the KALP algorithm by the following procedure. The incoming packets are stored in the receiving buffer for a certain duration of time (which is called smoothing delay) until about half the buffer is filled up, before being read out of the buffer. This prebuffering helps to reduce the effect of packet jitter on the operation of packet read-out and to prevent underflow. During this prebuffering, we can gather data on the packet interarrival times for use in deriving AR(1) parameters. In implementing the KALP algorithm, we initialize the internal registers of such that even the first the moving averager to data can be used in estimating the AR(1) parameters. In this estimation we may employ a common off-line algorithm such as the covariance method [11]. E. Considerations for Practical Application of KALP Algorithm For practical application of the KALP algorithm, it is necessary to be able to handle the packet loss problem. Packet loss could be a critical source of clock recovery error by generating a gap in the received packet stream as the KALP algorithm relies on the interarrival times in retrieving the source clock frequency. Fortunately, we can detect the existence of packet loss by checking the continuity of the packet sequence number. Therefore we can resolve the packet loss problem by inserting a dummy packet into the receiving buffer whenever a packet loss is detected. At the same time, we insert a dummy datum whose into a data buffer, value is set to the current estimation of from which the stored packet interarrival times are read. The time-invariant state space model in (4) may not properly describe the time-varying nature of the real system. The time-varying nature stems from the deviation of the source clock and the packet jitter. The assumption underlying (4) that the source clock is stable and its frequency or period is constant over time is in fact reasonable as the clock sources used nowadays are highly stable. As for the packet jitter, the AR(1) parameters used in modeling the prefiltered packet jitter are estimated using the information gathered during the prebuffering stage and are maintained over the whole connection period. This should work well in normal operation but may cause some residual error or

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Fig. 3. Configuration of the one-stage multiplexing system.

convergence delay in case there happens a big change in network traffic, as it will cause discrepancy between the modeled packet jitter characteristics and the true ones. This problem may be eased if we reset the KALP algorithm whenever the buffer level reaches the predetermined upper or lower threshold. It is also possible, alternatively, to model the AR(1) parameters and as random work processes. III. COMPARATIVE STUDY OF SCFR PERFORMANCES: KALP SCHEME VERSUS BUFFER-BASED ADAPTIVE CLOCK METHOD In this section, we carry out several simulation experiments under various network environments for a comparative study of the SCFR performances of the KALP and the existing buffer-based adaptive clock method [1]. First, we consider a simple one-stage FCFS multiplexing system where the background traffic is all periodic. Secondly, in order to model a bursty characteristic of background traffic in real packet networks, we consider a three-stage FCFS multiplexing system where Markov-modulated Poisson process (MMPP) is used as the background traffic model. A. One-Stage Multiplexing System with Periodic Background Traffic In Fig. 3, we show the multiplexing system for simulation that is similar to the one used in [1]. We assume that packet size is 1000 bits, but do not consider header or overhead separately. We take the output line rate of 150 Mb/s and connect ten CBR traffic streams to the system as listed in Fig. 3, which corresponds to a traffic load of 0.999. We synchronize clocks of the 10 input traffic streams at the frequencies , , and , which are the nominal frequencies of DS1, DS2, and DS3 signals, respectively, and set the initial frequencies of the corresponding receiver clocks at 1.5438, 6.311 79, and 44.735 109 MHz with the frequency differences of 129.5, 33.26, and 19.91 ppm, respectively. We design the simulation such that packets are read in and read out discretely and 0.1 s (100 ms) of smoothing delay is allowed before the start of the SCFR algorithms. As for the KALP algorithm, we assume the tolerance of 200 ppm for each clock frequency and employ the order of 50 for the moving averager. For the estimation of AR(1) parameters, we employ the modified covariance method [12].

As for the buffer-based method, we set the initial measurement time intervals of 1.0, 0.5, and 0.1 s for , , and , respectively, and stop adjusting the measurement time intervals when the frequency estimation error falls under 10 ppm. In both the SCFR schemes, we measure the frequency estimation error and the buffer level whenever a change occurs in their values during simulation. Note that the buffer level is measured as the relative position with reference to the buffer position at the beginning of the SCFR procedure. We limit the total simulation run time to 4.5 10 packet times, which corresponds to 5 min of real time. Fig. 4 plots the frequency estimation errors, and Tables I and II list the resulting frequency differences and buffer levels, respectively. Note that the maximum values in the tables denote the maximum in absolute values and the same is true for the minimum values. The initial and the minimum buffer levels, which are always zero by definition, are not listed in the Table II. In the figures, we observe that the convergence speeds of both the SCFR methods depend on the packet rates of the sources, but the dependency is weaker for the KALP scheme than for the buffer-based method. This happens because the frequency estimation occurs at each packet service time in the KALP scheme, while it occurs once per several packet service times in the buffer-based method. We also observe from the tables as well as the figure that the KALP exhibits much faster convergence with smaller residual error in all cases. In addition, we observe that the KALP scheme has less fluctuation in the buffer level compared to the buffer-based method for all CBR sources. B. Three-Stage Multiplexing System with Bursty Background Traffic The first experiment was a fundamental one in which only one-stage multiplexing system was considered and the background traffic sources were all CBR. As is well known, the extent of packet jitter of such a system is less than that of a system that has correlated background traffic [1]. In addition, as the packet flow that has experienced packet jitter has finite period, it is likely that the low-pass filtering has better effect on the CBR traffic system than on others. Therefore, in the second experiment, we consider a three-stage multiplexing system which better simulates the real environment. In support of this, we use the MMPP as the background traffic model, as it can better

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Fig. 4.

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Frequency estimation errors for (a) DS1 signal (f~ = 1:544 MHz), (b) DS2 signal (f~ = 6:312 MHz), and (c) DS3 signal (f~ = 44:736 MHz). TABLE I FREQUENCY DIFFERENCE (IN PPM) OF ONE-STAGE MULTIPLEXING SYSTEM

reflect the bursty and correlated nature of real background traffic than the Poisson process does [13], [14]. The MMPP we use in the simulation has two states, 0 and 1, whose sojourn times and , respectively. When the MMPP is in state are , the packet arrival process is Poisson with the packet arrival rate . Fig. 5 shows the configuration of the three-stage multiplexing system we take for the experiment. The MMPP parameters for the background traffic (BT) are as summarized in Table III. The service clock frequencies of the CBR sources 1 and 2 are 1.5

TABLE II BUFFER LEVEL (IN PACKETS) OF ONE-STAGE MULTIPLEXING SYSTEM

and 50 MHz, respectively, and the corresponding initial receiver clock frequencies are set to 1.4997 and 49.99 MHz, respectively, which amount to the frequency deviation of 200 ppm. We take the values of packet size, line bit rate, and smoothing delay to be the same as those in the first experiment. In this case, the total traffic load becomes 0.6. As for the KALP related parameters, we assume the tolerance of 200 ppm for each clock frequency and take the same AR(1) parameter estimation algorithm as before. We set the initial measurement time intervals of the buffer-based adaptive clock method to 1.0 and 0.5 s, respectively, for CBR sources 1 and 2. In this experiment we reduce the simulation time to 10 packet, which corresponds to 66 s of real time, as it is satisfactory in comparing the performances of two adaptive clock schemes.

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Fig. 5. Configuration of the three-stage multiplexing system. TABLE III MMPP PARAMETERS FOR BACKGROUND TRAFFIC TYPES 1 AND 2

quency differences and buffer levels. From these results, we observe that the convergence speed depends on the source packet rates, with the dependency becoming dominant for the bufferbased SCFR scheme than for the KALP scheme. For both CBR sources, the KALP exhibits much faster convergence speed with smaller residual error. Further, the KALP exhibits better performance in the buffer level as it has much less fluctuation than the buffer-based case. The differences in the performances of both the SCFR schemes in the first and second simulation experiments may be attributed to the background traffic that was periodic in the first experiment, while bursty and highly correlated in the second experiment. The effect of this background traffic characteristics can be well demonstrated if we compare the power spectrums of packet jitters of the first and second simulation experiments. Fig. 7 shows such spectrums for the first and the second experiments. Comparing plots in the figure, we observe that the packet jitter of the periodic background traffic case has several peaks in the power spectrum, which reflects strong periodic components, while the packet jitter of the bursty and correlated background traffic case has a rather smooth power spectrum but with significant amount of lower frequency component values, especially for higher rate sources, which make it difficult to estimate the source clock frequency. This indicates that the bursty and correlated characteristics of the background traffic, in general, deteriorate the performance of the SCFR schemes. Even with such bursty background traffic, the KALP scheme still manifests a better SCFR performance than the buffer-based adaptive clock method does. IV. CONCLUDING REMARKS

Fig. 6. Frequency estimation errors for (a) CBR source 1 and (b) CBR source 2.

Fig. 6 plots the frequency estimation errors obtained from the experiment, and Tables IV and V summarize the resulting fre-

In this paper, we have introduced the new adaptive clock method KALP that properly employs the optimal Kalman estimator for an efficient SCFR in packet networks. It overcomes the difficulty of direct packet jitter modeling by transforming the measured packet interarrival times into a low-pass signal through prefiltering and by applying the KF for the estimation of source clock frequency, with the prefiltered packet jitter modeled by AR(1) process. AR(1) process is one of the simplest models with a low-pass characteristic and the construction of Kalman filter is rather straightforward for the AR(1)-modeled noise. The low-pass prefilter should guarantee no timing infor-

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TABLE IV FREQUENCY DIFFERENCE (IN PPM) OF THREE-STAGE MULTIPLEXING SYSTEM

TABLE V BUFFER LEVEL (IN PACKETS) OF THREE-STAGE MULTIPLEXING SYSTEM

mation loss during the filtering process and indeed the moving averager used in this paper satisfies this requirement. Furthermore, our extensive simulation study (only part of which is included in this paper) showed that this approach results in good overall performances. The proposed KALP algorithm makes it possible to effectively employ the optimal Kalman estimator for the SCFR in packet networks. It is interesting to note that the use of the optimal Kalman estimator is possible in the KALP owing to a simple but fundamental change in packet jitter modeling—from direct modeling to pre-shaped modeling. Another feature of the KALP algorithm is that it employs a systematic approach in determining the design parameter values. This is in contrast to existing adaptive clock methods, where no such systematic procedure was available, or design equations provided but were rooted in unrealistic assumptions on packet jitter. The KALP algorithm determines the design parameter values systematically based on the available information. It determines the initial conditions of KF based on a priori information on the service clock including the nominal value and the tolerance for the clock frequency that are specific to a given service type. Also the AR(1) parameters for the prefiltered packet jitter modeling can be obtained using the packet interarrival times measured during the prebuffering (smoothing delay) process. In the comparative study of the SCFR performances of the KALP scheme and the buffer-based adaptive clock method [1], we have carried out several simulation experiments under two different network environments. First, we have considered a simple one-stage FCFS multiplexing system where background traffic is all CBR, and secondly, a three-stage FCFS multiplexing system where MMPP’s are used as bursty background traffic models. From the simulation results, we have observed that the convergence speed depends on the packet rates of sources, but the dependency is weaker for the KALP scheme than for the buffer-based SCFR scheme. We have also observed that the KALP scheme significantly reduces the fluctuation in the level of a receiving buffer as well as the time to recover the

Fig. 7. Power spectral densities of packet jitters for (a) low-rate sources (DS1—, CBR source 1- -) and (b) higher-rate sources (DS3—, CBR source 2- -).

source clock frequency in all cases considered. Further, we have confirmed that the bursty and correlated characteristics of the background traffic, in general, deteriorate the performances of both SCFR schemes, and that, even with the bursty background traffic, the proposed KALP scheme demonstrates better SCFR performance than the existing buffer-based one. ACKNOWLEDGMENT The authors would like to thank the reviewers, especially Editor Dr. R. Rao, for their constructive comments and suggestions for this paper. REFERENCES [1] R. P. Singh, S.-H. Lee, and C.-K. Kim, “Jitter and clock recovery for periodic traffic in broadband packet networks,” IEEE Trans. Commun., vol. 42, pp. 2189–2196, May 1994. [2] B. G. Lee, M. Kang, and J. Lee, Broadband Telecommunications Technology. Norwood, MA: Artech House, 1993. [3] ITU-T, “B-ISDN ATM adaptation layer (AAL) specification: Type 1 AAL,”, Recommendation I.363.1, Aug. 1996.

KIM AND LEE: KALP FOR PACKET NETWORKS USE

[4] H. M. Ahmed, “Adaptive terminal synchronization in packet data networks,” in Proc. GLOBECOM’89, 1989, pp. 728–732. [5] K. S. Kim and B. G. Lee, “Three-level traffic shaper and its application to source clock frequency recovery for VBR video services in ATM networks,” IEEE/ACM Trans. Networking, vol. 3, pp. 450–458, Aug. 1995. [6] M.-K. Liu, “Using negative stuffing retiming for circuit emulation in a packet switching network,” IEEE Trans. Commun., vol. 40, pp. 1522–1531, Sept. 1992. [7] K. S. Kim, K. S. Seo, and B. G. Lee, “On jitter characteristics in multi-node packet network environment: The white Gaussian noise assumption is valid?,” in Proc. ICT’99, vol. 2, June 1999, pp. 521–526. [8] F. Lewis, Optimal Estimation With an Introduction to Stochastic Control Theory. New York: Wiley, 1986. [9] C. K. Chui and G. Chen, Kalman Filtering With Real-Time Applications, 2nd ed. New York: Springer-Verlag, 1990. [10] D. R. Smith, Digital Transmission Systems, 2nd ed. New York: Chapman & Hall, 1993. [11] L. Ljung, System Identification: Theory For the User. Englewood Cliffs, NJ: Prentice-Hall, 1987. [12] , System Identification Toolbox For Use With MATLAB: The Math Works, Inc., 1993. [13] H. Heffes and D. M. Lucantoni, “A Markov modulated characterization of packetized voice and data traffic and related statistical multiplexer performance,” IEEE J. Select. Areas Commun., vol. SAC-4, pp. 856–868, Sept. 1986. [14] J. W. Lee and B. G. Lee, “Performance analysis of ATM cell multiplex with MMPP input,” IEICE Trans. Commun., vol. E75-B, pp. 709–714, Aug. 1992.

Kyeong Soo Kim (S’89–M’97) was born in Taejeon, Korea, on September 7, 1966. He received the B.S., M.E., and Ph.D. degrees, all in electronics engineering, from Seoul National University, Seoul, Korea, in 1989, 1991, and 1995, respectively. From 1996 to1997, he was engaged in development of multichannel ATM switching systems as a Postdoctoral Researcher at Washington University, St. Louis, MO, where he also taught courses as an Instructor of Washington University and Adjunct Professor of University of Missouri, St. Louis. Since 1997, he has been working with the PON Systems Research and Development organization of Lucent Technologies, and he is responsible for the development of ATM-PON systems, which won the 1999 Bell Laboratories President’s Silver Award. His current research interests include theoretical study and architectures and systems development in high-speed integrated networks including ATM-PON and ATM switching systems, ATM/B-ISDN traffic control, synchronization in packet networks, and applications of DSP in telecommunications.

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Byeong Gi Lee (S’80–M’82–SM’89–F’97) received the B.S. and M.E. degrees from Seoul National University, Seoul, Korea, in 1974, and Kyungpook National University, Taegu, Korea, and 1978, respectively, both in electronics engineering. He received the Ph.D. degree in electrical engineering from the University of California, Los Angeles, in 1982. He was with the Electronics Engineering Department of ROK Naval Academy as an Instructor and Naval Officer in active service from 1974 to 1979. He was with Granger Associates, Santa Clara, CA, from 1982 to 1984 as a Senior Engineer responsible for applications of digital signal processing to digital transmission, and with AT&T Bell Laboratories, North Andover, MA, from 1984 to 1986 as a Member of Technical Staff responsible for optical transmission system development along with related standard works. In 1986, he joined the faculty of School of Electrical Engineering, Seoul National University, where he is a Professor. He is a co-auhor of Broadband Telecommunication Technology, 2nd ed., (Norwood, MA: Artech House, 1996) and Scrambling Techniques for Digital Transmission (New York: Springer Verlag, 1994). He holds six U.S. patents with two more patents pending. His current fields of interest include signal processing, communication systems, and integrated telecommunication networks. Dr. Lee is a Member of the National Academy of Engineering of Korea, a Member of the Board of Governors of IEEE ComSoc, and a member of Sigma Xi. He is the Associate Editor-in-Chief of the Journal of Communications and Networks, the past Editor of the IEEE Global Communications Newsletter, and a past Associate Editor of the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY. He is the Director for Membership Programs Development, the past Director of Asia Pacific Region, and a Member-at-Large of IEEE Communications Society (ComSoc). He is the Chair of the APCC (Asia Pacific Conference on Communications) Steering Committee, and was the Chair of the ABEEK (Accreditation Board for Engineering Education of Korea) Founding Committee. He received the 1984 Myril B. Reed Best Paper Award from the Midwest Symposium on Circuits and Systems and Exceptional Contribution Awards from AT&T Bell Laboratories.