THE ANALYSIS OF NEGATIVE INFLUENCES IN THE ENVIRONMENT OF HOMOGENEOUS SYMMETRIC LINES AT THE SIGNAL TRANSMISSION BY MEANS OF THE ADSL TECHNOLOGY

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1 Journal of ELECTRICAL ENGINEERING, VOL. 53, NO. 9-1, 22, THE ANALYSIS OF NEGATIVE INFLUENCES IN THE ENVIRONMENT OF HOMOGENEOUS SYMMETRIC LINES AT THE SIGNAL TRANSMISSION BY MEANS OF THE ADSL TECHNOLOGY Rastslav Róka Rastslav Csár For successful understandng of the sgnal transmsson on metallc homogeneous symmetrc lnes, t s necessary exactly to recognze essental negatve nfluences n the real envronment of local subscrber loops. Ths artcle dscusses n detal frequency characterstcs of lnear negatve nfluences on transmtted sgnal, near-end and far-end crosstalks and the mpulse nose. Also, the analyss of these negatve nfluences at the sgnal transmsson s presented. The results of ths analyss are based on the computer smulaton of the ADSL transmsson system. K e y w o r d s: propagaton loss, transmsson functon of the channel, transmsson functons of the NEXT and FEXT crosstalks, model of the ADSL transmsson system 1 INTRODUCTION In present days, an nterest n broadband servce provsonng such as multmeda servces, dstance learnng or teleworkng s ncreasng. However, hgh-speed connectons to the Internet are also desrable. Acceptaton and realzaton of these demands need to provde a data stream wth a suffcent transmsson capacty to end customers. For solvng a bottleneck problem n the access network, there are many new wred or wreless technologes. Utlzaton of already exstng metallc telephone lnes n cooperaton wth new hgh-capacty optcal cables s a compettve alternatve to other access technologes. A famly of xdsl ( x Dgtal Subscrber Lne) technologes allows a cost-effectve utlzaton of common metallc lnes at the hgh-speed data transport. Snce a majorty of nteractve servces are asymmetrcal accordng to the character of downstream and upstream sgnal rates, great attenton s dedcated to the ADSL (Asymmetrc DSL) technology. Ths s the reason why we focused on ths specfc type of xdsl technologes. Ths paper concerns the analyss of negatve nfluences at the sgnal transmsson n the envronment of metallc homogeneous lnes by means of ADSL technologes and s focused on concrete characterstcs of these negatve envronmental nfluences. Also a model s presented that allows to analyze performances of ADSL modems utlzng modfed modulaton and codng technques. Descrpton of the model constructon s made for the ADSL transmsson system wth regard to the man negatve nfluences of the transmsson envronment. Lately, telecommuncaton access networks were nearly exclusvely bult up by bundles of metallc homogeneous lnes. A majorty of local subscrber loops are used as underground cable bundles, but sometmes they occur as aeral cables. A preferred materal used n the core of wres s copper but also we can meet wres wth an alumnum core. Common local subscrber loops were used at the call sgnal transmsson n the frequency band from 3 Hz up to 34 Hz. The local subscrber loop starts on the man dstrbuton frame (MDF) n the local central offce (CO) marked as the lne termnaton unt (LTU). Then, t passes as a part of multpar cables to the cross-connect pont (CCP) where t s dvded nto smaller bundles of local subscrber loops or to the subscrber dstrbuton pont (SDP) where subscrber shunts are drectly created. The local subscrber loop s termnated at the subscrber locaton n the network termnaton unt (NTU). The structure of typcal subscrber lnes presented n Fg. 1 s ntroduced n [1]. The access cable bundle contans some jont sectons of local subscrber loops that may have unequal core dameters, numbers of neghbourng pars and types of nsulaton. The length of local subscrber shunts s n the range of hundreds meters up to a few klometres. It s very dffcult and pretentous to fnd characterstcs and features of all lne types used today n the access network. Therefore, t s necessary to determne the man envronmental characterstcs of lnes wth standard parameters that exactly represent ther features from the vewpont of sgnal transmsson LTU MDF CCP SDP NTU Fg. 1. A structure of typcal local subscrber loops 1 central offce cable, 2 man cable bundle, 3 dstrbuton cable, 4 nstallaton cable Department of Telecommuncatons, Faculty of Electrcal Engneerng and Informaton Technology, Slovak Unversty of Technology, Ilkovčova 3, Bratslava, Slovaka, e-mals: rroka@ktl.elf.stuba.sk, rastslav.csar@pobox.sk ISSN c 22 FEI STU

2 242 R. Róka R. Csár: THE ANALYSIS OF NEGATIVE INFLUENCES IN THE ENVIRONMENT OF HOMOGENEOUS... u s (t) par j FEXT NEXT par x NEXT (t) Fg. 2. Types of crosstalks 2 THEORETICAL PART x FEXT (t) from the expresson for the propagaton constant γ(ω) n (1). The loss of a sgnal power s also nfluenced by other mportant parameters the core dameter and the constructon materal of the core [2]. For lower frequency regons, for whch s vald ωl R and G can be neglected, the propagaton constant expressed n (1) can be smplfed to ωrc [ γ(ω) = α(ω) + jβ(ω) 1 ωl ] 2 2R ωrc [ + j 1 + ωl ] f < 2 khz (5) 2 2R 2.1 Prncpal negatve nfluences on transmtted sgnals Propagaton loss and dstortons of the module and phase characterstcs as well as the group delay characterstc n a frequency band of nterest are nearly proportonal to the physcal and constructon parameters such as the lne length, core dameter of the wre, msmatch of mpedances n cross-connectng ponts of sectons [2]. We frst dscuss the propagaton loss L db n a perfectly termnated lne. If R, L, G and C are the prmary constants of a lne and ω = 2πf, where f s the frequency, then and γ(ω) = α(ω) + jβ(ω) = (R + jωl)(g + jωc) Z(ω) = (R + jωl) (G + jωc) (1) (2) where γ(ω) denotes the propagaton constant of the lne, α(ω) s the specfc constant of the attenuaton, β(ω) s the specfc constant of the phase-shft and Z(ω) s the characterstc mpedance of a lne. For a perfectly termnated lne wth length l, the transfer functon H(l, f) of metallc homogeneous symmetrc lnes s gven by H(l, f) = e lγ(f) = e lα(f) e jlβ(f) (3) and the propagaton loss L db s gven at the dstance l and the frequency f as L db (l, f) = 2 log 1 H(l, f) = 2 ln 1 lα(f) 8.686lα(f) = a lne (l, f) [db]. (4) We must place emphass on the nterchangeable use of the words the attenuaton of the lne a lne (l, f) and the propagaton loss L db (l, f) to desgnate the quantty n (4) only for the case of a perfectly termnated lne. We can see the lnear dependence of the propagaton loss L db on the lne length l. The loss s also an ncreasng functon of the frequency f as should be apparent For frequences less than 2 khz, both the real and magnary parts α(ω) and β(ω) are approxmately proportonal to f. At hgher frequences, the frequency dependences of the prmary lne parameters R and L (except for C ) become notceable and the propagaton constant n (1) can be approxmated by γ(ω) = α(ω) + jβ(ω) R(ω) C 2 L(ω) + jω CL(ω), f > 15 khz (6) In ths case, the magnary part β s approxmately a lnear functon of frequency. Major varatons for the real part α are due to the frequency dependence of R, whch becomes proportonal to f because of the skn effect for large frequences. Therefore, t s necessary to take nto account the ncreased sgnal attenuaton n the area of hgh frequences. The phase τ φ and envelope τ e delays of a loop can be expressed as τ φ (ω) = β(ω) ω τ e (ω) = dβ(ω) dω (7) where β(ω) s the magnary part of the propagaton constant. The group envelope delay τ e and the phase delay τ φ are at hgher frequences approxmately constant, equal, frequency-ndependent and acqure a value of about τ e τ φ = 5.4 µs/km [2]. 2.2 Near-end and Far-end crosstalks The word crosstalk generally refers to the nterference that enters a communcaton channel through some couplng paths. Fgure 2 presents a knd of generaton and propagaton of two crosstalk types n a multpar cable. At the nput of par j, the nformaton sgnal u s (t) s generated. Ths sgnal, when propagatng through a lne, can generate two types of crosstalk sgnals arsng n par. The crosstalk sgnal x NEXT (t) s called a near-end crosstalk NEXT. The crosstalk sgnal x F EXT (t) s called a far-end crosstalk FEXT. From a data communcaton

3 Journal of ELECTRICAL ENGINEERING VOL. 53, NO. 9-1, pont of vew, the NEXT crosstalk s generally more damagng than the FEXT crosstalk because the NEXT does not necessarly propagate through a lne length and thus does not experence a propagaton loss of the sgnal. If ether sngle or multple nterferers generate a crosstalk sgnal, we can defne a gan of the NEXT crosstalk path accordng to [2], [3] usng the followng relaton H NEXT (l, f) 2 = π2 f 2 k NEXT α(f) [ 1 e 4α(f)l] K NEXT f 3/2 (8) where varables are gven as K NEXT = N.6 d, N d s the number of dsturbng pars dsturbers), f s the frequency n Hz. An approxmaton on the rght n (8) s vald when the lne length l s large and for frequency regons where the real part α(ω) of the propagaton constant s proportonal to f. We can also derve the gan of the FEXT crosstalk path accordng to [2], [3] n a smlar manner usng the followng relaton H F EXT (l, f) 2 = 4π 2 f 2 k F EXT le 2α(f)l K F EXT l 328. f 2. H( l, f) 2 (9) where varables are gven as K F EXT = , l s the lne length n km, f s the frequency n Hz and H(l, f) expresses the transfer functon of a metallc homogeneous symmetrc lne. 2.3 Impulse nose In unshelded twsted pars, varous equpment and envronmental dsturbances such as sgnallng crcuts, transmsson and swtchng gear, electrostatc dscharges, lghtnng surges and so forth can generate mpulse nose. The mpulse nose has some reasonably well-defned characterstcs. The features of the typcal mpulse nose can be summarzed usng [2] as follows: t occurs about 1 5 tmes per mnute (on an average 4 tmes per mnute), t has peak values n the range 2 33 mv, t has most of ts energy concentrated below 4 khz, t has tme duraton n the range 3 15µs. Of course, the mentoned features do not characterze all possble mpulse nose sgnals. 2.4 Other negatve nfluences In addton to the nfluences descrbed prevously, there are some other well known negatve nfluences on xdsl dgtal transmsson systems usng metallc homogeneous lnes such as changes of the core dameter, msmatched mpedances and other nose types (thermal nose, background nose, radofrequency nterference). These nfluences are small n comparson wth the mentoned man negatve nfluences and can be neglected n our analyss. 3 EXPERIMENTAL PART 3.1 The envronment of smulaton and the basc scheme of the model For consderng of the sgnal transmsson on metallc homogeneous lnes by means of xdsl technologes, t s necessary comprehensvely to know the characterstcs of negatve envronmental nfluences and features of appled modulaton and codng technques. It s dffcult to realze exact analytcal descrpton of complex systems such as xdsl technologe n the real envronment of local access networks. Also, due to dynamcal nature of some processes, t s not sutable. For analyzng the modulaton and codng technques used by xdsl technologes, a sutable and flexble enough tool are computer smulatons and modellng schemes of real envronmental condtons at sgnal transmsson. For our modellng of the transmsson path we used the software program Matlab v5.3 together wth the dynamc system smulaton envronment Smulnk 3.. Matlab s a powerful collecton of tools for algorthm development, computaton and vsualzaton. It provdes more control and flexblty compared wth a tradtonal hghlevel programmng language and s based on felds and matrxes equpped wth many functons for program-run controllng and data structures processng. From addtonal lbrares, Sgnal Processng Toolbox 4.2 and Communcaton Toolbox 1.4, functons for sgnal processng, were utlzed [4]. The proposed and realzed modellng scheme represents the transmsson of hgh-speed data sgnals n the downstream or upstream drecton by means of the ADSL technology utlzng metallc homogeneous lnes. Ths model can be dvded nto three man parts transmtter, envronment of the transmsson channel, and recever. The transmtter for dgtal communcaton systems may nclude blocks of source codng, data compresson, error-control codng, dgtal modulaton and multple accesses. The transmtter s prmarly responsble for transmtted data protecton and for the modulaton of the sgnal nto the form whch can be transported through the lne. I addton to the propagaton loss, the sgnal transmsson envronment n the local subscrber loop s characterzed also by negatve nfluence of crosstalk noses from neghbourng pars and by actvtes of the mpulse nose. Because these negatve nfluences expressvely nterfere nto the communcaton and represent ts man lmtng factors, they consttute a crtcal part of the model and, therefore, t s necessary exactly to recognze and express ther characterstcs by correct parameters. The recever s conceptually nverse n comparson wth the transmtter. Its man functons are demodulaton and correcton of corrupted nformaton bts. Before demodulaton, the receved sgnal s amplfed to compensate for the propagaton loss arsen n the transmsson lne. Basc functonal blocks realzed n our smulaton model are shown n Fg. 3.

4 244 R. Róka R. Csár: THE ANALYSIS OF NEGATIVE INFLUENCES IN THE ENVIRONMENT OF HOMOGENEOUS... transmttng part Source Nose generator Error-control codng PSD flter of transmtter Modulaton NEXT couplng + transmsson channel - metallc homogeneous lne Comparson Recpent Nose generator Bt error rate Error-control decodng PSD flter of transmtter Demodulaton FEXT couplng Correcton amplfer D s t u r b n g p a r D s t u r b e d p a r + Whte nose AWGN Impulse nose recevng part Fg. 3. The block scheme of the smulaton model 3.2 The transmttng part of the model The transmtted message carred to the recevng part s generated as a random bnary chan wth a gven length. Ths message s also saved for the comparson wth the receved message because of the calculaton of the bt error rate. Because of usng forward error correcton technques, the generated message s encoded and s extended wth control characters. Optonal parameters for the FEC block are the knd of used codes (Reed-Solomon, Bose- Chaudhur-Hocquenghem... ), ts redundancy and the codeword length for block codes. For preventng cell losses at the transmsson of undrectonal vdeo data sgnals through an ATM network and for provdng a hgh qualty of servce, t s asked for the protecton wth an nterleavng technque. The nterleavng scheme uses a twodmensonal memory array. The ncomng cell-data are wrtten columnwse nto the memory. The outcomng data are read n blocks row by row. The optonal parameter for nterleavng s ts depth. Determnaton of approprate methods for the data protecton and ts parameters s one of applcaton opportuntes of our model [5], [6]. The encoded message s converted from the bt sequence enterng the modulaton block nto k -bt symbols (k = log 2 M ) due to M -ary dgtal modulatons. Optonal parameters for ths block are the type of modulaton, the number of modulaton states, the symbol rate, the nput sgnal power, the carrer frequency and the samplng frequency. Due to good senstvty to the mpulse nose and crosstalks [6], [7], the 16-QAM (Quadrature Ampltude Modulaton) modulaton s the basc modulaton n our proposed model. 3.3 The recevng part of the model The nput nto the recever s the sgnal dscarded and attenuated by the transmsson. For correct demodulaton, the receved sgnal must be recovered as soon as possble nto the orgnal form of the transmtted sgnal. In the correcton amplfer, the compensaton for the propagaton loss s executed. As the transmsson characterstcs of each metallc homogeneous lne n the local subscrber loop are dfferent, t s necessary to know the frequency characterstcs of the partcular transmsson channel. The recever can get ths nformaton by measurng the receved sgnal levels durng the startup ntalzaton sequence n the precse frequency spacng. The amplfed and corrected sgnal acqured n ths way s sutable for processng of the demodulaton. The acqured symbols are transformed nto the form of bnary messages. In the error-control decodng block, possble errors are detected and corrected. The corrected message s shfted to the nformaton snk. In the fnal part of the modellng, we compared the orgnal message from the source and the resultng message n the recpent. The output of ths comparson s the number of erroneous transmtted bts expressed n the form of the bt error rate and can be used n our next analyss. 3.4 The transmsson lne From relatons (5) and (6) t results that the propagaton loss s drectly proportonal to f for both low and hgh frequences. In the transton regon, the loss functon ncreases wth frequency somewhat slower and

5 Journal of ELECTRICAL ENGINEERING VOL. 53, NO. 9-1, u (V) 2. PSD dbm/hz) t ( s) Fg. 4a. The tme representaton of the modulated sgnal Fg. 4b.The frequency characterstc of the modulated sgnal s approxmately proportonal to f 1/4. The transton regon s a functon of the core dameter [2]. For modellng, the frequency dependence of the propagaton loss s suffcently perceved by the representaton of the transmsson functon that we derved usng relatons (5) and (6) H(l, f) = e lξf, (1) where l s the lne length and f s the frequency. We specfed the constant ξ ncdent to a homogeneous lne so that the transmsson functon representaton by (1) smulated the transmsson functon representaton calculated by prmary constants of the model lne. For typcal metallc lnes wth core dameter.4 mm (26 AWG) and Cu core materal, we calculated the value ξ = Near-end and Far-end crosstalks Because crosstalk sgnals from the POTS servce n dsturbng pars do not have sgnfcant nfluences on the ADSL sgnal n the dsturbed par, we supposed both dsturbng and dsturbed sgnals to have the same power spectral denstes P SD 1 (f) = P SD 2 (f). Ths stuaton occurs when n the neghbourng pars are also ADSL sgnals we can talk about the self-next crosstalk and the self-fext crosstalk. For local subscrber loops we assgned the power spectral densty of NEXT and FEXT crosstalks usng relatons (8) and (9) as follows P SD NEXT (f) = P SD(f) H NEXT (l, f) 2, (11) H NEXT (l, f) 2 K NEXT f 3/2, (12) P SD F EXT (f) = P SD(f) H F EXT (l, f) 2, (13) H F EXT (l, f) 2 K F EXT l 328f 2 H(l, f) 2, (14) where varables K NEXT and K F EXT are functons of dsturbed pars. Equatons (1) (13) allow very good approxmaton of practcally observed knd of multple nterferer crosstalks. Before startng the smulaton, we determned the values of varables K NEXT and K F EXT n our smulaton model as a functon of the number of dsturbng pars N d for typcal 5-pars cable as: Nd.6 K NEXT = K NEXT 49 1, (15) Nd.6 K F EXT = K F EXT (16) The value of the K NEXT 49 constant s gven as , the value of the K F EXT 49 constant s emprcally estmated as /328 [1], [3] Impulse nose Due to the mportant effect of ths negatve nfluence, we took nto account also ths type of nose. The most common and the most damagng type of mpulse nose seems to occur when a dsturbed par shares a common cable sheath wth the swtched dsturbng pars that s usual n the local access network. Sharp voltage changes can occur on analogue pars because of the openng and closng of relays. These voltage changes, when coupled nto neghbourng pars through the NEXT and FEXT couplng path, create spurous, mpulsve-lke voltages wth ampltudes that can be qute sgnfcant [2]. 4 RESULTS OF THE ANALYSIS Before transmttng of the sgnal nto the transmsson lne, we arranged the ampltude of the modulated sgnal to requred transmtted sgnal powers. Values of the sgnal power level range between 9 and 19 dbm. In the realzed model, we set a default basc value of the nput sgnal level to 14 dbm correspondng to the transmtted sgnal power 25 mw. In Fgs. 4a, 4b there are shown a tme representaton and frequency characterstc of the power spectral densty for the modulated sgnal wth basc parameters

6 246 R. Róka R. Csár: THE ANALYSIS OF NEGATIVE INFLUENCES IN THE ENVIRONMENT OF HOMOGENEOUS... H (db) l = 3. km l = 3.5 km l = 4. km l = 4.5 km l = 5. km PSD (dbm/hz) Fg. 5a. Frequency characterstcs of the transmsson functon module for varous lne lengths Fg. 5b. The frequency characterstc of the transmtted sgnal through the transmsson lne G (db) PSD (dbm/hz) Fg. 6a. The frequency characterstc of the gan functon module at the recever Fg. 6b. The frequency characterstc of the PSD of the regenerated sgnal the bt rate Mbt/s, the modulaton 16-QAM, the baud rate 4 kbd/s, the nput sgnal power 14 dbm. Before startng of the smulaton, we calculated the transmsson functon of the lne for gven parameters (l, ξ). The values of ths functon are sampled n equal proportoned frequency ntervals n the range from Hz up to the half of the samplng frequency (f samp /2). The number of samples s optonal. For sgnal processng, t s desrable to choose the number of samples equal to 2 N, where N s an nteger number. Usng sampled values, the mpulse characterstc of the transmsson lne h(t) s calculated usng the nverse Fourer transform wth the same number of samples (from practcal vewpont, the number of 512 samples s adequate). Ths sampled mpulse characterstc s used as coeffcents for the dgtal flter. Smulaton of the sgnal transmsson through the lne tself s executed by dgtal flterng of the sampled modulated sgnal usng the proposed flter. In Fgs. 5a, 5b there are shown frequency characterstcs of the transmsson functon module for the transmsson lne (φ =.4 mm, Cu) for varous lne lengths and a frequency characterstc of the power spectral densty for the transmtted sgnal through the lne. The nfluence of the transmsson channel that we can derve from ts transmsson functon s expressed above all n the attenuaton of the transmtted sgnal. Sgnal attenuaton s more damaged for areas of hgher frequency components of power spectral densty characterstcs. Ths nfluence s more expensve for longer lne lengths. However, we fnd out that the nfluence s decreased wth ncreasng the core dameter of wres. Ths results from the change of values for the prmary constant of the lne, concretely R and L. As mentoned above n paragraph 2.1, at hgher frequences (above 15kHz) the magnary part of propagaton constant s approxmately lnear functon and ths characterstc s suffcent for the smulatons purposes. We focus on specfc features of the phase frequency characterstc n our next research. In our model, we supposed the knowledge of frequency characterstcs of the transmsson functon for used lo-

7 Journal of ELECTRICAL ENGINEERING VOL. 53, NO. 9-1, H NEXT (db) PSD NEXT (dbm/hz) -8-1 N d = 49 N d = 25 N d = N d = a) Fg. 7a. Frequency characterstcs of the NEXT crosstalk transmsson functon module for varous numbers of dsturbers Fg. 7b. The frequency characterstc of the NEXT nose sgnal for 25 dsturbers H NEXT (db) -6-8 PSD FEXT (dbm/hz) N d = 49 N d = 25 N d = N d = Fg. 8a. Frequency characterstcs of the FEXT crosstalk transmsson functon module for varous numbers of dsturbers Fg. 8b. The frequency characterstc of the FEXT nose sgnal for 25 dsturbers cal subscrber loop (wth the precson 1 db). The number of frequences and therefore also the frequency spacng are optonal parameters. Usng the approxmaton of values acqured n ths way, the recever can approxmate transmsson characterstcs of metallc homogeneous lnes. These characterstcs can be used as the opposte value for amplfyng of the receved sgnal. Moreover, the maxmum of the gan characterstc of the correcton amplfer s lmted by the background nose level to predcton of wasted amplfyng of hgh frequency components of the sgnal. For exact compensatng of the propagaton loss, these frequences should use substantal gans. In Fgs. 6a, 6b there are presented the frequency characterstc of the gan functon module and the frequency characterstc of the power spectral densty of regenerated sgnal. We created the NEXT crosstalk nose sgnal by formng of the whte nose spectrum (constant P SD(f) = db/hz) that s generated by a random number generator. Frst, we calculated a frequency characterstc of the H NEXT (l, f) crosstalk transmsson functon module usng (11). Its parameters are the number of dsturbng pars and the approprate value of the varable K NEXT. In Fg. 7a, the NEXT crosstalk transmsson functon module for varous numbers of dsturbers s presented. Next, ths functon of the NEXT crosstalk path multples the power spectral densty of the transmtted sgnal. Ths PSD functon s acqured by calculaton from a sgnal consstng of a suffcently hgh count of random symbols produced by a chosen type of modulaton. In ths manner, we obtaned a spectral characterstc of the NEXT crosstalk sgnal P SD NEXT (f) (Fg. 7b) n accordance wth (1). Ths characterstc s used for calculatng the mpulse characterstc and ts samples created coeffcents of dgtal flters. For modellng of the NEXT negatve nfluence, the NEXT crosstalk nose sgnal acqured by flterng s added to the transmtted sgnal enterng the transmsson lne. The nfluence of the NEXT crosstalk transmsson functon s determned by the power spectral densty of the NEXT crosstalk sgnal and by the NEXT crosstalk path. Ths nfluence s accentuated at hgher frequency

8 248 R. Róka R. Csár: THE ANALYSIS OF NEGATIVE INFLUENCES IN THE ENVIRONMENT OF HOMOGENEOUS... components of the transmtted sgnal. It s necessary to take nto account the NEXT crosstalk at sgnals of symmetrc servces and applcatons, and at very hgh bt rates of nformaton sgnals because they occupy hgher frequency bandwdths of metallc homogeneous lnes. As we can see n Fg. 7a, the crosstalk couplng for the lne wth the core dameter.4 mm for 49 dsturbng pars s approxmately about 1 db larger than the crosstalk couplng for only sngle dsturbng par. The FEXT crosstalk sgnal s created n a smlar manner as the NEXT crosstalk sgnal (ts spectrum s presented n Fg. 8b). Because ths type of a crosstalk must be propagated through a dsturbng lne, we ncluded nto calculatng the FEXT crosstalk transmsson functon module (Fg. 8a) also the transmsson functon of the lne H(l, f) usng (9) wth gven parameters (the lne length 4.6 km). The FEXT crosstalk sgnal s added to the transmtted nformaton sgnal attenuated at a transmsson through the metallc homogeneous lne. The nfluence of the FEXT crosstalk transmsson functon s characterzed by the power spectral densty of the FEXT crosstalk sgnal and by the FEXT crosstalk path. Ths FEXT crosstalk path s depend on the lne length, on the frequency of sgnal and on the transmsson functon of the transmsson lne because of propagatng of crosstalk sgnals through the dsturbng par. For longer lne lengths, the nfluence of the FEXT crosstalk can be neglected. On the other sde, ths nfluence s accentuated at hgher frequency components of the transmtted sgnal. Therefore, t s necessary to take nto account the FEXT crosstalk for the new VDSL technology transmttng sgnals of asymmetrc servces and applcatons at very hgh bt rates of nformaton sgnals and on very short dstances because they occupy hgher frequency bandwdths of metallc homogeneous lnes. the most lkely case. The densty of mpulse occurrences s optonal (common 4 tmes per mnute). From the vewpont of the smulaton tme, there are relatve long tme perods between mpulse occurrences, therefore we chose more frequent occurrences and arranged the consequence of ther effects. In Fg. 9 s shown the tme representaton of one of the generated mpulse patterns used n the smulaton model created on the bass of the work [7]. In the smulaton model, we represented a background nose and thermal nose usng the addtve whte Gaussan nose (AWGN). Its parameter s a level of the power spectral densty. The level of the PSD for the AWGN nose s determned emprcally and s moved n the range from 15 dbm/hz n the favourable nose envronment to 11 dbm/hz n the ncreased expressve nose envronment. Due to the addtve character of the AWGN nose, we realzed ts effects by addng to the transmtted sgnal. The receved sgnal constellaton of modulaton states (the modulaton 16-QAM, the baud rate 4 kbd/s, the nput sgnal power 14 dbm) after transmttng on the lne wth gven parameters (φ =.4 mm, l = 4.6 km, N d = 1 dsturbers) n the envronment of the AWGN nose wth the level 125 dbm/hz s demonstrated n Fg. 1. u (mv) Fg. 1. The state constellaton of the modulated sgnal wth the AWGN nose t (ms) Fg. 9. The tme representaton of typcal model mpulse nose A tme representaton of mpulses can be acqured by measurement n the access network [7] and typcal representatons consdered for testng are ntroduced n an approprate standard [8]. At every mpulse, the value s chosen randomly from the range between 2 33 mv that s 5 CONCLUSIONS Ths paper analyzes basc features of the real transmsson envronment of metallc homogeneous lnes and presents possbltes for modellng and smulatng the nformaton sgnal transport n ths envronment by means of ADSL technology. The basc block scheme of the proposed model for the ADSL transmsson path s composed of 3 parts that are closely specfed. We focused on the determnaton and

9 Journal of ELECTRICAL ENGINEERING VOL. 53, NO. 9-1, analyss of concrete characterstc features for substantal negatve nfluences of nternal and external envronments and on the representaton of frequency dependences of transmtted nformaton sgnals. For realzng of ndvdual model blocks, we concentrated on the choce of approprate parameters so that these blocks could be adjusted and modfed for future demands. The attenuaton determned by the channel transmsson functon s more damaged for areas of hgher frequency components of power spectral densty characterstcs for transmtted sgnals. Ths attenuaton s more expensve for longer lne lengths. However, we can partly lmt ths negatve nfluence wth ncreasng the core dameter of wres. The nfluence of the NEXT crosstalk sgnal s accentuated at hgher frequency components of the transmtted sgnal. The nfluence of the FEXT crosstalk sgnal depends on the lne length, on the frequency of sgnal and on the transmsson functon of the transmsson lne because of propagatng of crosstalk sgnals through the dsturbng par. For long enough lne lengths, the nfluence of the FEXT crosstalk can be neglected. On the other sde, ths nfluence s agan accentuated at hgher frequency components of the transmtted sgnal. Therefore, for the new VDSL technology that transmt nformaton sgnals of asymmetrc and symmetrc servces at very hgh bt rates of nformaton sgnals and on very short dstances, t s necessary to take nto account of the NEXT and FEXT crosstalks at sgnals occupyng hgher frequency bandwdths of metallc homogeneous lnes. Due to the damagng effect of the mpulse nose, we must take nto account also ths type of negatve envronmental nfluence. The most common type of the mpulse nose seems to occur n the local access network, when a dsturbed par shares a common cable sheath wth swtched dsturbng pars. Appendx abbrevatons ADSL Asymmetrc DSL NEXT Near End Crosstalk AWGN Addtve Whte Gaussan Nose NTU CCP Network Termnaton Unt Cross-Connect Pont POTS Plan Old Telephone Servce CO PSD FEC QAM Central Offce Power Spectral Densty Forward Error Correcton Quadrature Ampltude Modulaton FEXT Far End Crosstalk SDP LTU Subscrber Dstrbuton Pont Lne Termnaton Unt VDSL Very hgh bt rate DSL MDF xdsl Man Dstrbuton Frame x Dgtal Subscrber Lne References [1] ČUCHRAN, J. RÓKA, R. : The Analyss of the Possbltes for the Utlzaton of xdsl Technologes n Access Networks of Slovak Telecom, Fnal report of the techncal project ZoD 1163, Bratslava, February 1999 (n Slovak). [2] WERNER, J. J. : The HDSL Envronment, IEEE Journal On Selected Areas In Communcatons, vol. SAC-9, no. 6, August 1991, pp [3] ASLANIS, J. T. CIOFFI, J. M. : Achevable Informaton Rates on Dgtal Subscrber Loops: Lmtng Informaton Rates wth Crosstalk Nose, IEEE Transactons on Communcatons, vol. 4, no. 2, February 1992, pp [4] WANG, W. : Smulnk Communcatons Toolbox User s Gude, The MathWorks Inc., [5] CISÁR, R. : The Model of the xdsl Transmsson System n the Real Envronment and the Influence of Encodng Technques at the Transport, ŠVOČ project, Aprl 2, (n Slovak). [6] KERPEZ, K. J. SISTANIZADEH, K. : Hgh Bt Rate Asymmetrc Dgtal Communcatons over Telephone Loops, IEEE Transactons On Communcatons, vol. COM-43, no. 6, June 1995, pp [7] KERPEZ, K. J. GOTTLIEB, A. M. : The Error Performance of Dgtal Subscrber Lnes n Presence of Impulse Nose, IEEE Transactons On Communcatons, vol. COM-43, no. 5, May 1995, pp [8] ANSI-Standard T1.413: Network and Customer Installaton Interfaces ADSL, August Receved 26 March 22 Rastslav Róka (Ing, PhD) was born n Šal a, Slovaka on January 27, He receved hs MSc and Ph degrees n Telecommuncaton from the Slovak Unversty of Technology, Bratslava, n 1995 and 22. Snce 1997, he has worked as a senor lecturer at the Department of Telecommuncatons, FEI STU, Bratslava. At present, hs research actvty s focused on the hgh-speed sgnal transport through metallc access networks by means of xdsl technologes usng varous modulatons and codng technques. Rastslav Csár (Ing) was born n Bratslava, Slovaka on Aprl 19, He receved hs BSc. degree n Informatcs (Telecommuncaton specalzaton) from the Slovak Unversty of Technology, Bratslava, n 2 and MSc degree n the same specalzaton n 22. Hs research actvty has been focused on the analyss of the features of varous codng technques n the real envronment at the utlzaton of the xdsl transmsson systems.