Vol.20 No.2

JOURNAL OF ELECTRONICS

FINDING DATA FRAME

THE OPTIMAL LENGTH OF IN PLC COMPUTER NETWORK

Mar. 2003

1

Huang Ronghui Zhou Mingtian She Kun (College o[ Computer Science & Eng., UEST of China, Chengdu 610054) Abstract

The length of data frame is an important parameter in Medium Access Control

(MAC) layer protocol. A method of finding the optimal length of data frame when impulsive disturbance is involved in PowerLine Communications (PLC) is proposed. Having analyzed the characteristics of impulsive disturbance in powerline and the collision mechanism between the disturbance and data frame, this letter gives the function of the network channel utilization with the length of data frame in MAC layer and the impulsive disturbance. Our stochastic process simulation shows that it is feasible to get the optimal length of data frame. K e y words

Medium Access Control (MAC); PowerLine Communications(PLC); Computer

network

I. I n t r o d u c t i o n Nowadays, the researches of the PowerLine Communications (PLC) computer networks have become in vogue due to the increasing demand on the home automation and Internet access. As powerline is used mainly for energy transmission, the quality of PLC will be impacted heavily by amounts of noises from the online load. To build an optimal transmission system model and Medium Access Control (MAC) protocol model under the powerline circumstance is a key issue of PLC computer networks. The length of data frame is an important parameter in MAC layer protocol. After studying a lot of investigations relative with PLC, we find that various periodic impulsive noises have been efficiently solved by some current transmission models and transfer functions in physical layer. However, asynchronous non-periodic impulsive noise has not been solved by means of physical layer because of its randomness. It must be taken into account to deal With the asynchronous non-periodic impulsive noise in layers beyond physical layer. In LLC and MAC layers, no significant progress to eliminate the impulsive noises has been made. Although some solutions, such as the Carrier Sense Multi-Access and Collision Detection (CSMA/CD), adaptive equalization with short data frame, the reservation protocols and so on,[ 1-4] have been put out, most of them have not researched deeply the influence from the impulsive disturbance in PLC; only one or two of them such as Ref.[1] pay attention to the relation between the length of data frame and the impulsive disturbance; none of them has solved the problem of getting the optimal length of data frame. Our researches focus on finding the optimal length of data frame. The characteristics and formal expression of the impulsive disturbance are elucidated. The impact on the transmission channels from the impulsive disturbance is discussed while the Orthogonal Frequency Division Multiplexing (OFDM) modulation scheme is applied. The letter explains why the impulsive disturbance in PLC can not be eliminated by physical layer. For the 1Manuscript received date: July 1, 2002; revised date: August 9, 2002.

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function of the channel utilization proposed in this letter, we also did a simulation test with the help of stochastic process. The letter is organized as follows: in Section II, we discuss the characteristics and formal expression of the impulsive disturbance in PLC. We also analyze how the disturbance affects the OFDM transmission channel. Section III gives the mathematical reasoning and the simulation test. In Section IV, we discuss some related work. In section V, the research results and future work are concluded.

II. Analysis of Impulsive Disturbance There are five kinds of additive noise in the powerline environment, i.e., colored background noise, narrow-band noise, the periodic impulsive noise which is asynchronous to the mean frequency, periodic impulsive noise which is synchronous to the mean frequency, asynchronous non-periodic impulsive noise [1,5-r]. The first four kinds can be eliminated in physical layer. The fifth, named impulsive disturbance, is a key obstacle for powerline communicationsI~]. To discuss the characteristic of impulsive disturbance and its impact on transmission channel, we begin with following definition. Definition 1 The impulsive disturbance is a kind of asynchronous non-periodic impulsive noise in the low-voltage powerline, which is produced by the electric appliances of consumer and the switches of utilities in power system. In terms of amplitude, width and time interval, we analyze the disturbance.The amplitude of impulsive disturbance in PLC depends largely on the types of the load of the power system [r]. In general industry powerline, the amplitude above 10dB is about 1,,,5%. The amplitude above 15dB is about 0.01%. It increases obviously when some devices, such as copycat, are online. Powerline in house has the impulsive disturbance of 0.1--,1%, with amplitude over 20dB. Generally speaking, the impulsive disturbance with about 10dB amplitude will influence the powerline communications. The impulsive disturbance with amplitude over 20dB certainly influences the powerline communications. The width of the impulsive disturbance in the PLC follows the normal distribution Is]. The time arrival of impulsive disturbance in PLC follows the Poisson distribution [r]. The arriving probability of n impulsive disturbances within t seconds is shown as:

pn(t) = ()~t)ne-Xt n!

(1)

where, A is the arriving ratio of the impulsive disturbance in one unit time. In a word, the impulsive disturbance has features of probability, vanishing, distribution and timeliness. As the PLC networks have the similar channel model to wireless networks [9], the OFDM modulation is used [31. The transmission system with OFDM modulation schemes has a number of sub-carriers divided in a frequency spectrum. Every sub-carrier can transmit data solely and serially. The k sub-carriers transmit data in parallel. Many sub-carriers can be combined into a large channel to transmit data in parallel when the load of network is not heavy. Namely, k codes serially transmitted in a sub-carrier can be simultaneously transmitted within 0nly one code period. The time-domain function of the k-th OFDM sub-carrier is: oo

xk(t) :

E l=--oo

C~¢k(t - IT)

(2)-

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where k is the number of sub-carriers, l is the sequence number of code and T is the width of modulated signal which is not less than the time width of code, Cl,k is the modulation signal of/-th frame for k-th sub-carrier. Ck is the channel carrier function of the k-th sub-carrier. To reveal the impact of amplitude of disturbance on sub-carriers of OFDM, we focus the amplitude with fixed width and time interval first. So the gate time-domain function can be shown as: co

pu(t) =

~

APD(t- nta)

(3)

n~--OO

where, A is the amplitude of the gate time-domain function, D the width and ta the time arrival of the function, PD(t) is the unit pause function which width is equal to D. In the case that A, D, ta are stochastic variables, the gate time-domain function can not be settled mathematically. To analyze the impact of amplitude of disturbance on the sub-carriers signal, we assume D and ta are constant in Eq.(3). The power spectrum function of the impulsive disturbance is shown as follows:

Spu(w) = 12 DS2A(Dw)

(4)

From Eq.(2) and Eq.(4), we know that the amplitudes of harmonic weight change with the amplitude of impulsive disturbance. They influence many sub-carriers of OFDM which have the same spectrum as the harmonic weight. It has been proven that the error will occur in the transmission channel if the duration of impulsive disturbance is wider than that of OFDM modulation signal. Definition 2 Parallel errors across multiple sub-carriers are the errors occurring in multiple sub-carriers within one code period owing to impulsive disturbance. Definition 3 Serial errors of single sub-carrier are the errors occurring in multiple codes in one sub-carrier within a string of code time. Therefore, the impact of impulsive disturbance on the transmission channel can be concluded as: the "sharp spike" disturbance with more high-frequency weight and shorter duration will lead to the parallel errors defined in Definition 2. Oppositely, the "flat" disturbance with less high-frequency weight and longer duration will lead to the serial errors defined in Definition 3. Since A, D, ta are stochastic variables, Eq.(3) can not be solved mathematically. The transfer function in physical layer can not handle this type of impulsive disturbance, which contains multiple stochastic variables. For that reason, the impact on the data frame will be shown in the LLC layer and MAC sublayer.

III. T h e C o m p u t a t i o n and S i m u l a t i o n The influence from disturbance on data frame is shown as Fig.1. It is not difficult to learn the impact of the amplitude, the width and the time intervals of the impulsive disturbance on data frame transmission. The impulse whose amplitude is above signal will destroy data frame if it occurs during transmission. The wider the impulsive disturbance is, the more severely the data frames are damaged. The more the arriving impulses, the more severely the data frames are damaged. As the impulsive disturbance can not be treated by the transfer function in physical layer, there is transmission failure in the MAC layer of network because of collision between

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Noise f D

Fig.1 T h e influence of d i s t u r b a n c e on d a t a f r a m e

data frame and disturbance. For that reason, the Forward Error Correction (FEC) and Automatic Response Query (ARQ) are employed to handle such errors. For convenience of analysis, we condition that the impulsive disturbance within one period of data frame has enough amplitude and width to destroy the frame transmission. Given the length of data frame F(bit), and the speed of OFDM channel S(bps), the duration of data frame is shown as: F TF = -(5) S The arriving probability of n impulsive disturbances within TF is shown as:

p , ( T F ) --

(ATF)ne -xTr n!

(6)

The arriving probability of zero impulsive disturbances within TF is shown as:

p o ( T f ) = e -xTF

(7)

An inverse proportion function 7" is defined as: h 7" = -F

(8)

where, h is the head of data frame, (F - h) is the actual data bits of the frame. Definition 4 Network channel utilization ~f without disturbance is defined as: ,

=

1-

(9)

In computer networks with special transmission medium, the length of data frame is usually up to kilobytes. In powerline computer networks, however, many investigations indicate that the length of data frame must be shorter than common occasions because of the complex interference[2'1°J1], especially the impulsive disturbance mentioned in this letter. On the contrary, Eq.(9) indicates that the channel utilization decreases rapidly if the data frame is too short. To obtain a suitable length of frame, we define the channel utilization with disturbance as follows. Definition 5 The network channel utilization ~? is defined as the number of data frame transmitted successfully within TF period, while the impulsive disturbance is involved. Therefore, we can obtain the following equation from Eqs.(7), (9):

rl = ~?'p o ( T f )

(10)

Given a coordinate plane where the horizontal axis is ~/and the vertical axis is F(see Fig.2), 7/t is the result that the inverse proportion function ~/" moves 1 up along the vertical axis. It has the point of intersection with horizontal axis when F = h.

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So we are informed from Eq.(10) that, when (F -+ h), (1 - h )

-+0

and

F.--}hlim ~=0

(11)

lim

77 = 0

(12)

F' e (h, oo)

(13)

when (F -+ oo),

(i-~-)-+I

and

F-+oo

So we can always find an F ~ which satisfies: y(F') > = ~ ( F ) ,

-4 F D,

Fig.2 The relation among the ~f, 77" and P0

We verify Eq.(10) with simulation test. The simulation with discrete event can be modeled by a Markovian chain with two-states. Both the data frame and the impulsive disturbance have the random time intervals. The simulation clock is advanced by event. Preconditions and assumptions are made as follows: (1) multiple users of MAC layer compete for one OFDM sub-carrier in the manner of slot ALOHA; (2) the transmission speed of channel is 2Mbps; (3) h--32bit; (4) the whole average of frames for all users to send in an OFDM sub-carrier is 1 in every frame period; (5) the mean arrival of the impulsive disturbance for every millisecond A=0.1, 1, 10, just similar as Refs.[5-7, 9]; (6) the a of normal distribution of impulsive disturbance is 200#s; (7) the a of normal distribution of impulsive disturbance is 0.5. The curves of theoretic computation and simulation are figured as Fig.3 and Fig.4, where the x-axis is F (bit) and the y-axis is ~. Based on the computation in Fig.3, it can be found that: (1) when ),=0.1, and while the length of data frame is about 800bit, the network channel utilization 77 reaches its maximum value about 0.92; (2) when A=I, and while the length of data frame is about 300bit, the network channel utilization 7/reaches its maximum value about 0.76. In this case, the duration of a frame is about 150 ms. Namely, an impulsive disturbance will arrive in every 6.7 data frames.

No.2

FINDING THE OPTIMAL LENGTH OF DATA FRAME

o.8 t~

/

ol,I

;~=o.i

0.6 0.2 0.4

0

\ '

50

159

100

'

200

400 F

800

1600 3200

Fig.3 Computation results

50

100

200

400 F

800

1600 3200

Fig.4 Simulation results

(3) when A=10, and while the length of data frame is about 120bit, the network channel utilization 77 reaches its maximum value about 0.41; (4) when A becomes smaller, the curve related will move up. We can find easily that the length of the data frame has less impact on the channel utilization when A <0.1. (5) when A becomes bigger, the curve related will move down. We do not think that powerline is suitable for communications when A _>10. The curves in Fig.4 have the similar trends to those in Fig.3. In a word, when 0.1 < A < 1, we can easily figure out the optimal length of data frame with the help of the equation proposed in the letter.

IV. R e l a t e d W o r k Some efforts have been made about the MAC layer of PLC computer networks: In Refs. [1,3], a relation between the length of data frame and network channel utilization is given, i.e., smaller data frames(300byte) are less affected by the impulsive disturbance than larger data frames(1500byte) and it makes little difference between network channel utilization, whether with or without disturbance. In Ref.[2], a hybridized token passing architecture and short powerline data frame in the MAC layer of PLC computer networks is proposed. The MAC layer provides a flexible and uniform interface to other applications or data link control sub-layer. This approach was utilized in the products that supply transmission speed up to 100kbps. In Ref.[4], the MAC sub-layer of CEBus standard provides only acknowledged connectionless service. The MAC is responsible for assembly and disassembly of message frames. The theory and simulation results in this letter show that our methodology is benefit to find the optimal length of data frame with the impulsive disturbances. On the other hand, we pay more attention to some of the characteristics of the power distributing system in China. First, unlike in Europe, the end transformer in China is connected to subscribers more than two hundred. Thus the load of the power system is heavy. Secondly, as the nocoaxial aluminium conductor is used, the capacity of PLC channel is quite limited. Thirdly, both the electric appliances of consumer and the switches in the power system of China lead to much impulsive disturbance. In our simulation model, the characteristics of the power distributing system of China are taken into account.

V . C o n c l u s i o n and F u t u r e W o r k s This letter has discussed the impact from impulsive disturbance on powerline transmis-

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sion channels with OFDM modulation schemes. We elucidate why the disturbance pulse can not be eliminated in the physical layer. Stochastic variables are used to express the amplitude, the duration, and the time intervals of impulsive disturbance. The function of the network channel utilization with the length of data frame in MAC layer and the impulsive disturbance is deduced. The simulation with discrete event shows that the results of simulation test of stochastic process is in conformity with theory function computation basically. In other words, the optimal length of the data frame, when the disturbance pulse is involved, can be captured in the way of theory and simulation. Along this way, there follow some researches to be done. First, we will investigate the function between the length of data frame and the mean access time, the relation between the length of data frame and the networks throughput. Secondly, because the parameters of PLC are variable in terms of different time or different place, and the efforts made in Ref.[8] are limited, we will investigate the further statistic data of powerline in China. References Ill H. Hrasnica, A. Haidine: Modeling MAC layer for powerline communications networks, SHE's (The International Society for Optical Ehgineering) Symposium on Information Technologies; Conference Internet, Performance and Control of Network Systems; November 5-8, 2000, Boston, MA, USA. [2] Chris Lads.s, Michael Propp, Reliable, 100kbps low voltage AC power line communications, Proceeding of the SPIE--The International Society for Optical Engineering, Vol.2601, 41-47. [3] M. Stantcheva, K. Begain, H. Hrasnica, R. Lehnert, Suitable MAC protocols for an OFDM based PLC network, Proceedings of ISPLC2000-4th International Symposium on Power-Line Communications and Its Applications, April, 5-7, 2000, Limerick, Ireland. [4] EIA-600.10 Introduction to the CEBus Standard from Revision: 2-5-95 DRAFT COPY, http://www. cebus.org/. [5] O. G. Hooijen, On the channel capacity of the residential power circuit used as a digital communications medium, IEEE Communications Letters, 2(1998)10, 267-268. [6] G. Marubayashi, S. Tachikawa, Spread spectrum transmission on residential power line, Proc. of IEEE ISSSTA'96, Mainz, Germany, Sept. 1996, 1082-1086. [7] Roger M. V, Noise on residential power distribution circuits, IEEE Trans. on Electromagnetic Compatibility, EMC-28(1984)4, 161-168. [8] Wang Guangxing, The design & implement of computer networks on the residential power circuit, MINI-MICRO S Y S Y T E M S , 17(1996)12, 33-37, (in Chinese). [9] I. F. Akyildiz, J. McNair, L. C. Martorell, R. Puigjaner, Y. Yesha, Medium access control protocols for multimedia traffic in wireless networks, IEEE Network-July/August, 1999, 39-47. [10] C. N. Krishnan, Powerline as Access Medium--A Survey, Dept. of Electronics Engg. M.I.T Campus of Anna University, Chennai, 2001. [11] The Powerline as a Reliable Multimedia-Cpatible Home-Network 1999, www.adaptivenetworks.com.