Performance Analysis of OFDM Broadband Communications System Over Low Voltage Powerline with Impulsive Noise

Transcription

1 erforance Analysis of OFD Broadband Counications Syste Over Low Voltage owerline with Ipulsive oise. Airshahi (eber), S.. avidpour and. Kavehrad (FIEEE) The ennsylvania State University, Departent of Electrical Engineering, Center for Inforation & Counications Technology Research (CICTR) University ar, A 68 ABSTRACT - Broadband counications for indoor powerline networs with ipulsive noise using Orthogonal Frequency Division ultiplexing (OFD) is considered. Fro earlier investigations, it is nown that this channel suffers fro ultipath fading and frequency selectivity along with anade ipulsive bursty noise. evertheless, the calculated channel capacity liit proises very high data rates over this channel. In this paper the bit error rate (BER) perforance of the OFD syste under ipulsive noise and frequency fading is theoretically analyzed and closed for forulas for this perforance is derived. Furtherore, a theoretical upper bound on the perforance of coded OFD syste is obtained, given perfect interleaving and the effect of the interleaver length on coding perforance is also studied. Keywords - power-line counications, ipulsive noise, low voltage, OFD, error control coding, union upper bound. I. ITRODUCTIO The increasing interest in odern ultiedia applications, such as broadband Internet, HDTV, etc. requires new access techniques for connecting private preises to a counication bacbone. One proising technology, Broadband over ower-lines (BL), intends to use the existing power-line networ as a high-speed digital data channel to connect the private users to one another and to a very high data rate bacbone. The characteristics of low voltage (LV) power-lines are very well nown and there are a variety of research activities in this area to exploit different features of LV grid. One of the ost recent and coprehensive efforts of this ind is done by Galli and Banwell []. This research uses ulti Transission Line (TL) theory [], to characterize the indoor LV power-line networs. Since the power-line networ is not designed for counications purposes, the channel exhibits unfavorable frequency selective transfer function. Furtherore, this channel is distorted by ipulsive noise, and severe narrowband interference. Unlie any other counication channels, power-line channel does not represent an additive white Gaussian noise (AWG) environent. oise in LV power-line is characterized within two categories: bacground and ipulsive noise [3]. A large ipulse often causes an entire transitted sybol to be corrupted and it can be devastating to the overall syste perforance. The well-nown ulti-carrier technique, Orthogonal Frequency Division ultiplexing (OFD), is considered as the odulation schee for BL by ost researchers. By the application of OFD, the ost distinct property of powerline channel, its frequency selectivity, can be easily coped with. oreover, OFD can perfor better than single carrier odulation in the presence of ipulsive noise, because it spreads the effect of ipulsive noise over ultiple subcarriers. Lie other counications systes, coding can iprove the OFD syste perforance but because of the nature of this channel, the achieved iproveents are usually very restricted. Therefore, analysis of coded and uncoded OFD counications schee in this hostile environent sees to be a necessary procedure in order to provide an insight about the overall perforance and achievable iproveents for this syste. Earlier, the effect of ipulsive noise in narrowband powerline counications was studied in [4]. For BL, the effect of ipulsive noise on the perforance of the OFD syste is shown by siulations in [5]. Haring and Han Vinc in [6] developed the perforance bounds of QA odulation systes over ipulsive noise condition. a, So and Gunawan in [7] provided an inclusive analysis for uncoded OFD syste in an ipulsive noise and ultipath environent. In this paper, the effects of ipulsive noise and frequency selective channel on perforance of OFD BL syste are theoretically analyzed. The ipulsive noise odel used in our analysis is a ore realistic way of odeling than aforeentioned studies. We deploy two noise odels: the tie doain odel based on arov odeling and the statistical odel based on oisson distribution. Subsequently, we copare the results of both odels on our syste s perforance and we will verify that both odels provide the sae results for a long tie siulation period. Furtherore, we theoretically investigate upper bound of the perforance iproveent achieved by coding in such a syste and we will show by siulations the copensations needs to be considered in order to acquire this upper bound. The rest of the paper is as follows. In section II, a brief review of channel characteristics of our syste is presented /6/$. (c) 6 IEEE This full text paper was peer reviewed at the direction of IEEE Counications Society subject atter experts for publication in the IEEE ICC 6 proceedings.

2 Section III details the ipulsive noise characteristics and odel in our syste. In section IV, the analytical closed for perforance of OFD syste in a fading channel under ipulsive noise is presented. Siulation results and observations are deonstrated in section V. Concluding rears and references end the discussion. II. LV OWERLIE CHAEL ODEL AD ITS TRASISSIO CAACITY As it is entioned in [], the conventional two-conductor transission line (TL) is not able to explain the physical reasons of propagation behavior on LV power-line networs, copletely. Characteristics of LV power-line grids have to be utilized by eans of TL theory. This approach for odeling LV power-line networs is described in details and coprehensively in [,]. Using ethods and algoriths entioned in this research, we siulated the channel configuration shown in Fig. 7 of []. The ipulse response of this channel is illustrated in Fig.- (a). It is seen fro Fig.- (a) that the axiu delay spread is less than icroseconds and there are 4 significant paths fro the transitter to the receiver. The Shannon capacity liits of this channel are depicted in Fig.-(b). For evaluation of these liits we assue an additive unifor bacground noise, with db/hz as spectral density level [8]. According to [8], this level is a realistic aount of bacground noise in a typical apartent. The effect of ipulsive noise for these capacity liits is not considered. (a) (b) Fig.- (a) ipulse response of a LV power-line networ depicted in [] and (b) its associated capacity liits III. IULSIVE OISE ODEL AD ITS CHARACTERISTICS odeling of ipulsive noise over broadband power-line channels has been a challenge for researchers since early 98s. Several different odeling ethods are available. Zieran and Dostert in [3] proposed one of the first odeling ethods for this ind of noise at high frequencies. In this paper, as in [9], we use two siplified arov odels to represent the burst errors caused by ipulsive noise. This odel has two layers. The first layer (higher layer) describes the incidence of the burst groups and the second layer (lower layer) articulates a single ipulse within the burst group. For higher layer, the arov odel has two states of disturbed and undisturbed. In the disturbed state, a burst group of burst noises occurs, while in the undisturbed state there is no ipulsive noise. Within the disturbed state, we define two other arovian states with a lower tie resolution: noise and no noise. Fig.- illustrates these two arov odels along with their transition probabilities. (b) Fig.- arov odel for burst noise: (a) odeling burst groups (b) odeling single ipulses within a burst group (a) A easureent in [] shows that the average tie of the disturbed state in the higher level is 5-sec. and the average tie of undisturbed state is second. The expected tie of the syste in the disturbed state is given as: E,, { } t, = tr. = Undisturbed State o noise State,,,,, Disturbed State oise State.( p, ). p, = tr. p, within which t r is the tie resolution for the first layer. If one considers t r to be s,, will be equal.8, which aes, equivalent to.. Based on the average tie of disturbed and undisturbed states, the stationary state distribution of the first layer odel is expressed as: π =[π, π, ]=[.995.5] () Thus, the transition probability atrix for the first level is:.999. = (3)..8 The tie resolution for the second layer is selected as t r = icrosecond. The stationary state probabilities in the second layer are independent rando variables with equal probabilities. π =[π, π, ]=[.5.5] (4) We assue the average duration of the disturbed and undisturbed states are 5 icroseconds. This will yield the transition atrix for the lower layer as:, () This full text paper was peer reviewed at the direction of IEEE Counications Society subject atter experts for publication in the IEEE ICC 6 proceedings.

3 .98. = (5)..98 ow that we have transition probabilities, it is interesting to investigate the behavior of burst and ipulse rates. By the paraeters in the burst rate is equal to burst per second. π, p, n = = per second (6) E{ t, } t r The ipulse rate during a burst noise is also calculated by equation (7) as well as the paraeters in. n π, π, = + E{ t,} E{ t, } ( π. p + π. ) = = p t r,,,, The total average ipulse rate is per second n B = π,. n= per second (8) The statistical odeling of ipulsive noise has been of interest to researchers for a long tie. iddleton in [] categorizes ipulsive noise in two classes of A and B. The noise in BL can be considered as class A iddleton noise. Based on this odel, the noise, ipulsive plus bacground noise, is a sequence of i.i.d rando coplex variables with the probability distribution function (DF) of: α z p Z ( z) = exp( ) (9) = πσ σ with A A α = e ()! The variance σ is defined as: ( ) + Γ σ = ( + ) A σ g σ i () + Γ σ g Γ = () σ i where σ g and σ i are the power of bacground noise and ipulsive noise, respectively. The paraeter A is called the ipulsive index, which is the product of average rate of ipulsive noise and ean duration of a typical ipulse. With our notation, the ipulsive index, A is equal to n B t r. For a sall A, we get highly structured ipulsive noise whereas for large values of A, the noise DF becoes Gaussian []. The paraeter Γ is called bacground-toipulsive noise ratio. Equation (9) shows that the DF of noise is a weighted su of Gaussian DFs with zero ean, therefore the ean and variance of noise can be acquired by the following equations: (7) z µ z = E{ z} = z. Z ( z). dz = α..exp( ) = z (3) πσ σ A = = e σ g A σ z = E{ z } = ( +Γ) (4) Γ! A IV. OFD SYSTE AALYSIS ulti-carrier odulation has long been nown as an efficient odulation schee for bandliited channels []. OFD is considered as one of the ost proising odulation ethods for powerline counications [3]. Besides its high spectral efficiency, OFD has soe favorable properties, which can be utilized properly in order to itigate harsh characteristics of powerline channels. The basic idea of OFD is to split a high rate data strea into a nuber of lower rate streas and transit these streas siultaneously, and in parallel over a nuber of orthogonal subcarriers. The orthogonality of subcarriers guarantees that the streas do not interfere with one another. It is possible that subcarriers lose their orthogonality due to ultipath or the channel non-stationary behavior. In this case, sub-carriers interfere with one another and cause inter-carrier interference (ICI). Each data strea is sent in one subchannel, so that each has its own coherence bandwidth. If the bandwidth of transitted signal is less than coherence bandwidth of the channel, inter-sybol interference (ISI) is eliinated. Therefore, if we choose enough subcarriers, we will be able to have very low-rate parallel data streas in each such that each subchannel will be ISI free. The division of data strea to several sub-carriers can be ipleented easily using Inverse Fast Fourier Transfor (IFFT). The atch filtering of each sub-channel also is done by Fast Fourier transfor (FFT). Further justification of OFD syste considerations can be found in []. oreover, the deep fades in the frequency response of the channel cause soe groups of subcarriers to be less reliable than other groups and hence cause bit errors to occur in bursts rather than, independently. Burst errors can degrade the perforance of coding, extensively. To solve this proble, several ways are considered in the literature. The easiest ethod is to use stronger codes for those faulty subchannels, if they are nown. In the case that the subchannel situations are not nown, an interleaving technique along with coding can guarantee the independence aong errors by affecting randoly scattered errors. For analysis of the OFD syste, first we exaine the uncoded situation and then we will analyze the effect of coding under coded OFD condition. A. Uncoded OFD syste: When the transitted signal is an OFD sybol, the received sybol after front-end filtering and sapling, assuing perfect ISI and ICI copensation, is given by: This full text paper was peer reviewed at the direction of IEEE Counications Society subject atter experts for publication in the IEEE ICC 6 proceedings.

4 jπn = r h ane + z, =,,... (5) n= where h is the ipulse response of the channel, a n is the sent data sybol, is the nuber of carriers used in the odulation schee and z is the noise in th subcarrier and its DF is expressed by (9).The transitted sybols are recovered fro the received sequence by perforing an point discrete Fourier transfor, as follows: = j πn R rn e = Ha + G, =,,... (6) n= where H is the channel transfer function of th subchannel, G is the Fourier transfor of z and is expressed as: n n jπn = G z e, =,,... (7) = As it is entioned earlier, z n s are i.i.d rando variables with a distribution function as in (9). According to Central Liit Theore, if a saple ean x is obtained fro saples that are taen fro a large population, and the saples are of sufficiently large enseble size, the distribution of x is well approxiated by a Gaussian distribution. This Gaussian distribution is characterized by a ean µ x = µ and a standard deviation σ x = σ /, where µ and σ are the ean and standard deviation of the population and K is the saple size. By considering (7), we can rephrase G as: G (8) = z n n= in which jπn ne zn = z (9) Therefore, based on Central Liit Theore, G is Gaussian with ean µ = and standard deviation g = µ z σ g =.( σ z / ) = σ z, in which σ z is expressed by (4). DFT procedure spreads the effect of ipulsive noise over ultiple subcarriers in a way that noise on each subband exhibits a Gaussian behavior. This is one of the ajor benefits of OFD syste in an ipulsive noise environent. By assuing long enough guard interval to avoid ICI, each subband can be considered as a regular ISIfree additive Gaussian noise (AG) channel and the analysis becoes a straight forward procedure. We now fro [4] that the Bit Error Rate (BER) of a QA schee under AG regie follows () and (). BER = ( ) () 3 Eav = ( ) Q( ) () ( ) where is the odulation level and = when is even. E av is the average sybol power and is the noise power. Thus, if QA odulation is used for each subcarrier, we can express the average BER of an OFD syste with subcarriers (assuing no ISI and ICI) as: BER avg, ( ), = = () 3 H Eav = ( ) Q( ) (3) ( ) B. Coded OFD syste The air-wise Error robability (E) represents the probability of choosing the coded sequence X ˆ = xˆ, xˆ,..., ˆ when indeed another code ( x L ) sequence = ( x x,..., ) X, x L was transitted, where L is the frae length. Under the assuption of perfect channel state inforation (CSI), the conditional E with respect to the = H, H,..., is given as: channel coefficients ( ) H ( ) ( ε X,Xˆ X,Xˆ H = Q ) where ( X, X ˆ ) H (4) ε is the energy difference between two codewords. With the assuption of BSK we have, ( ) Es X, Xˆ H = Q Ω (5) where E is the total transitted energy and Ω is the set s of bit intervals locations where X and Xˆ differ in the th subchannel and where Ω is the cardinality of Ω, which also corresponds to the length of the error event. Defining the signal-to-noise ratio as τ = E s and using the upper bound on Gaussian-Q function, i.e. Q( z ).5exp( z / ), under the assuption of sybol-by-sybol interleaving which guarantees independency aong bits in the th subchannel, we obtain ( X,Xˆ ) exp( τ Ω ) H (6) E is the basic tool for the derivation of union bounds on the error rate perforance of a coded counication syste. A union bound on the average BER on the th subchannel can be found as in [4] X q X,Xˆ X,Xˆ (7) ( ) ( ) ( ) b H X X Xˆ where ( X) is the probability that the sequence X is q X, X ˆ is the nuber of inforation bit errors transitted, ( ) in choosing another coded sequence Xˆ instead of X. For unifor error probability codes, a syetry property exists, eliinating the need for averaging over all possible transitted sequences, which leads to This full text paper was peer reviewed at the direction of IEEE Counications Society subject atter experts for publication in the IEEE ICC 6 proceedings.

5 q( X,Xˆ ) ( X,Xˆ ) (8) b H X Xˆ In the case that E is given in a product for, the transfer function technique [4] provides an efficient ethod for the coputation of (8), i.e.,, (9) b T ( D s) s where ( D s) s= T, is the transfer function associated with the error state diagra of the code under consideration, s is an indicator variable taing into account the nuber of bits in error and D is given as the base of the th subchannel E expression derived for the channel odel under consideration. coding, analytically and by coputer siulations, under the channel conditions shown earlier in Fig.-, for two different levels of. For siulation results, two noise odels were considered: the tie-arov odel of Fig.- and the statistical odel of equation (9). Both odels are utilized by the paraeters found in section III. It is shown that results by both these odels are in agreeent and also with analytical results. One should notice that arov based odel is a tie representation of the noise, whereas iddleton odel is a statistical illustration, therefore the statistical characteristics of the tie doain odel over a very long tie will be the sae as iddleton s expression. Our siulations using arov odel are run for an extensively long period of tie. Consequently, as it is confired in Fig.-4, both odels results are quite siilar. Fig. -3. Rate=/ convolutional encoder with constraint length 3. As an exaple, we consider a convolutionally coded syste to deonstrate BER results. The convolutional code under investigation is illustrated in Fig. -3. It has a code rate of / and a constraint length of 3. The transfer function of this code is found to be T ( D, s) 5 D s = (3) ( sd) Since the code satisfies the unifor error property, we can use (3) for BER perforance evaluation and after averaging over subchannels, the BER perforance is obtained as b ( D ) = D 5. (3) V. SIULATIO AD AALYTICAL RESULTS For our analysis and siulation purposes, we design an OFD syste for the channel introduced in Fig.-. The occupied bandwidth of the syste is chosen to be 6 Hz. The capacity liit of this channel at 6 Hz with -db launched power fro Fig.- is around 6 bits/sec. The delay spread of the channel is icroseconds. To avoid ISI and ICI, while losing less than a db due to guard interval insertion, we chose an OFD sybol interval equal to ties the delay spread, which is equal to icroseconds. The subcarrier spacing is now the inverse of -=8 icroseconds, providing 55 KHz. By considering 6 Hz bandwidth, at ost we can use subcarriers. We designed a syste with 4 subcarriers and one nown pilot channel for estiation. On each subchannel QA odulation with appropriate odulation level is chosen. Fig.-4 shows the perforance of such a syste without Fig.-4 The perforance of uncoded OFD syste in a fading channel with ipulsive noise analytically and by siulation Burst errors deteriorate the perforance of the coding schee used in any counications syste. These bursts can happen either by ipulsive noise or by deep frequency fades. owerline channels suffer fro both of these deficiencies; therefore a echanis is needed to disperse the error bursts both in tie and frequency. For this purpose, interleavers have been utilized since early days of digital counications. OFD syste has an inherent property that it disperses ipulsive noise bursts by sybols ( is the nuber of carriers). However, by using a tie interleaver this property is destroyed. Thereby, in OFD systes shuffling bits in tie and frequency is desired. In doing so, we adopt the ethod introduced by Raseier in [5] for our designed syste. The interleaver size has two constraints on length and depth. The length paraeter accounts for reordering the bits in one OFD sybol and it is responsible to disperse the affected bits by channel fadings. The depth factor justifies shuffling the bits over several OFD sybols in tie and it taes care of separating the distorted sybols by ipulsive noise. For our siulations, we considered four different interleavers: one interleaver with size 4, which reorders bits of one OFD sybol with 4 subcarriers, another interleaver with size 4 6, which shuffles bits of sixteen OFD sybols and two other interleavers with sizes of 4 8 This full text paper was peer reviewed at the direction of IEEE Counications Society subject atter experts for publication in the IEEE ICC 6 proceedings.

6 and 4 4. The coding schee we chose for our syste is the convolutional code of Fig.-3 and BSK is selected as the odulation schee of choice. Fig.-5 shows the perforance results of the coded OFD syste with ipulsive noise in the channel ediu of Fig.- for different interleaver sizes. These results are also copared to the upper bound of equation (3) in Fig.-5. The siulation results clearly show that increasing the size of the interleaver iproves the perforance. Specifically, increasing the interleaver depth fro to 6 yields ore than.5db gain in SR at a BER of -5. However, further increasing the interleaver depth fro 8 to 4 gives less than.5db gain. Fig.-5 also shows the calculated upper bound in (3). As it can be seen, the upper bound is very close to the curve of interleaver size of 4 4. Furtherore, it shows that the upper bound curve is in fact lower since it is calculated under the assuption of ideal (infinite) interleaver size. Fig.-5 The effect of interleaver length on the coded OFD perforance and analytical upper bound on the coding schee perforance VI. COCLUSIOS In this paper, we investigated counications syste perforance for an indoor power-line channel with bursty ipulsive noise. The channel characteristics and capacity liit were obtained in earlier research and siulation results have shown that the OFD transission lin, equipped with extra bits allocation for pilot, is required to cope with the channel fading. The ipulsive noise characteristics and odel also have been discussed briefly and an appropriate realistic odel is chosen, as well. We derived the perforance expression for an uncoded OFD syste under ipulsive noise and highly frequency selective powerline channel ediu. Our siulations show that the closed for expression and siulation results are in agreeent. Furtherore, we deployed two noise odels for ipulsive noise environent, statistical and tie doain odels, and coputer siulations confired the fact that both odels represent the sae environent with the sae results. Additionally, the upper bound for a coded OFD syste was calculated, given independency of consecutive sybols provided by perfect interleaving. Our siulations revealed that the derived upper bound is quite tight for the case of eploying a longer interleaver. It was also shown that interleaver depth is of iportance due to ipulsive noise and increasing this paraeter iproves the overall perforance to soe extent. VII. REFERECES [] T. Banwell, S. Galli, A ovel Approach to the odeling of the Indoor ower Line Channel -- art I: Circuit Analysis and Copanion odel, IEEE Transactions on ower Delivery, Volue, Issue, pp , April 5. [] Clayton R. aul, Analysis of ulti-conductor Transission Lines, ew Yor: Wiley, 994. [3]. Zieran, K. Dostert, Analysis and odeling of ipulsive noise in broad-band power-line counications, IEEE transactions on Electroagnetic copatibility, Volue, pp.7, 8 Oct.- ov.. [4]. H. L. Chan, D. Friedan, and R. W. Donaldson, erforance enhanceent using forward error correction on power line counication channels, IEEE Trans. ower Delivery, vol. 9, no., pp , Apr.994. [5] G. Bianchi and G. Conigliaro, An hybrid reservation-pollingac protocol for powerline counications, in roc. ISLC Conference,. [6] R. Harring, A.J. Han Vinc, erforance bounds for optiu and suboptiu reception under Class-A ipulsive noise, IEEE Trans. On Counications, Vol. 5, o. 7, pp. 3-36, July. [7] Y. H. a,. L. So, E. Gunawan, erforance analysis of OFD systes for broadband power line counications under ipulsive noise and ultipath effects, IEEE transaction on power delivery, Vol., no., pp , April 5. [8] J. Lee, S. Choi, H. Oh, W. Lee, K. Ki, D. Lee, easureents of the Counications Environent in ediu Voltage ower Distribution Lines for Wide-band ower Line Counications, roc. of ISLC4, pp , 4. [9]. Babic,. Hagenau, K. Dostert, J. Bausch, Theoretical postulation of LC, Deliverable D4 for OERA. IST integrated project o Funded by European Coision. [] eng, H. Guan, Y.L. Chen, S., odeling and analysis of noise effects on broadband power-line counications, IEEE Transactions on ower delivery, Volue, Issue, pp , April 5. [] D. iddleton, Statistical-physical odel of electroagnetic interference, IEEE Trans. Electroagn. Copat., vol. 9, no. 3, pp. 6-6, Aug [] Richard Van ee, Rajee rasad, OFD for wireless ultiedia counications, Boston, Artech House,. [3] Halid Hrasnica, Abdelfatteh Haidine, Ralf Lehnert, Broadband owerline Counivations, London, Willey, 4. [4] John G. roais, Digital Counications, ew Yor, cgraw- Hill,. [5] S. Raseier, Shuffling bits in tie and frequency: an optiu interleaver for OFD, IEEE Conference on Counications ICC 3, Vol. 5, pp , -5 ay 3. This full text paper was peer reviewed at the direction of IEEE Counications Society subject atter experts for publication in the IEEE ICC 6 proceedings.