An HF Multipath-Propagation Analysing Method for Power Delay Profile estimations of Indoor Single-Phase Low Voltage PLC Channels

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1 An HF Multpath-Popagaton Analysng Method fo Powe Delay Pofle estmatons of Indoo Sngle-Phase Low Voltage PLC Channels Ioanns C.PAPALEONIDOPOULOS 1, Constantnos G.KARAGIANNOPOULOS 2, Ioanns E. ANAGNOSTOPOULOS 3, Nckolas J.THEODOROU 4 1 Natonal Techncal Unvesty of Athens, Faculty of Electcal and Compute Engneeng, Hgh Voltages and Electc Measuements Laboatoy, 9 Heoon Polytechnou St., GR Athens, Geece. Phone: , Fax: , E- mal: Jpap@cental.ntua.g. 3 Natonal Techncal Unvesty of Athens, Faculty of Electcal and Compute Engneeng, Multmeda Laboatoy, 9 Heoon Polytechnou St., GR Athens, Geece. Phone: , Fax: , E- mal: Janag@telecom.ece.ntua.g. 2 Natonal Techncal Unvesty of Athens, Faculty of Electcal and Compute Engneeng, Hgh Voltages and Electc Measuements Laboatoy, 9 Heoon Polytechnou St., GR Athens, Geece. Phone: , Fax: , E- mal: ckaag@cental.ntua.g. 4 Natonal Techncal Unvesty of Athens, Faculty of Electcal and Compute Engneeng, Hgh Voltages and Electc Measuements Laboatoy, 9 Heoon Polytechnou St., GR Athens, Geece. Phone: , Fax: , E- mal: ntheodo@cental.ntua.g. Abstact Focalsed on the statstcal chaactesaton of fadng ndoo PLC channels, a method povdng the Hgh Fequency tansfe popetes of such channels on account of multpath popagaton s ntoduced. Takng nto account a fnte set of paths, channel's tansfe functon s calculated n tems of cable's type and the vcnal netwok topology. Accuacy of the method has been justfed by tansfe-functon measuements of sample channels n the 2-3MHz band, wheeas applcablty stands wheeve cablng meets the two-conducto tansmsson-lne model. Pelmnay powe-delay-pofle smulatons ae also demonstated, ndcatng utlty of the method fo channel capacty estmatons. 1. Intoducton Electc gd tuns out patculaly hostle as tansfe medum n the aea of MHz. The pncpal constants ae mposed due to ntesymbol ntefeence geneated by multpath popagaton effects and the esultng delay spead. That s to say, not only the desed sgnal, but also one o moe delayed and attenuated copes of t beng heeafte efeed to as paths ave at ecepton as a esult of seveal eflectons caused at ponts whee mpedance msmatches occu. Multpath fadng channels ae gouped and desgnated n tems of the path ampltude and aval-tme pobablty dstbutons, as the powe delay pofle s equste fo lnk capacty estmatons. Seveal channel analysng technques stemmng fom multpath-popagaton pncples have up to now been suggested (e.g. [1]-[3], [6]). The wok pesented n [2] and [3] les n fact vey close to the appoach ntoduced heen; the same notaton s theefoe mantaned to cetan extent. In ths pape, a completely analytcal method s poposed, so that no expemental feedback s equed to defne the model paametes. Havng cables dstbuted constants and electc netwok s topology n the vcnty of the channel, tansfe functon s estmated as the supeposton of a fnte path multtude. Tacng along path popagaton outes s compsed, and lmtng the analyss wthn the set of paths that le no lowe than two odes of magntude below the lne-of-sght-equvalent path makes up the man appoxmatve step. In Secton 2, analytcal fomulaton of the method s deployed. Measuement esults and elevant evaluaton ae gven n Secton 3. Powe-delay-pofle smulatons that have been pefomed ae pesented n Secton 4. A concludng dscusson on the utlty of the wok pesented closes ths pape n Secton Multpath Popagaton Model Let a postvely tavellng snusodal voltage wave component be assumed, towads a pont of dscontnuty. Such could be ethe an open-ccuted end, o a pont of whch the aggegate chaactestc mpedance to the ght s dffeent fom the one to the left,.e. a load temnaton, a seal connecton of dffeent cables, o a cable juncton. Denotng tansmsson coeffcent by t and eflecton coeffcent by ρ, t s obtaned

2 1 +ρ= t, (1) Z t ρ =, (2) Z t Z + Z whee Z t the esultant chaactestc mpedance ght afte the msmatch pont. If mpedance msmatch s caused by a load temnaton, Z t equals load s mpedance Z L, wheeas n the case of a juncton, aggegate chaactestc mpedance ght afte the cable ntesecton s the esultant of the seveal chaactestc mpedances n paallel A sgnal tansmtted ove a PLC channel suffes numeous eflectons at netwok s ponts of dscontnuty, gvng thus se to the multpath popagaton effect, whch esults n a multtude of dscete paths avng at ecepton. A path s n fact the esult of a dstnct component that aves at ecepton va a unque oute along the gd, afte beng eflected a specfc numbe of tmes at specfc dscontnuty ponts of ts oute. Assumng the exstence of N dffeent paths, channel s patal tansfe functon wth egad to a sngle path, wth d the coespondng aggegate oute popagaton dstance, s theeby H ad jβd ( f ) g e e =, (3) whee a s popagaton constant and β the phase constant, and the oveall tansfe functon s gven as N ( f ) = H ( f ) = H = = whee g g e N g e ad e jβd, (4) jφ = (5) s a weghtng facto cayng the effect of tansmsson and eflecton coeffcents along the oute, defned as M t, M, g = t, mt ρ, m, (6) mt = 1 m = 1 whee the path s supposed to have come M tmes acoss ponts of dscontnuty and been eflected. The ampltude of path s H ad ( f ) g e M, t, tmes = (7) Fo convenence, the tem path s also used heen to descbe evey patal tansfe functon that coesponds to a path. The dect component, of whch the oute nvolves no eflectons, s chaactesed by the value =. Stctly, the path numbe s nfnte, but n pactce only a fnte multtude of paths ae of non-neglgble value. The sequence of paths angng wthn two odes of magntude below the dect one s heeby suggested as adequately descbng channel s tansfe popetes. The analyss developed so fa stands wheeve snglephase LV cables confomng to the two-conducto unfom tansmsson lne model ae utlzed. Seveal ndoo snglephase cable types fall unde ths categoy [2], [6] [7]. 3. Applcablty and Expemental Evaluaton 3.1. Expemental Gds Topology of the netwok paadgms measued s that of a backbone bus wth tansvese banches connected n paallel, as llustated n Fg. 1, of whch the multtude s heeafte denoted by n. The banches ae numbeed consecutvely fom tansmsson to ecepton,.e. ndex ( 1) s assgned to tansmtte banch and ndex (n) to the eceve one. Thee sample gds have totally been nvestgated. Let x[ b ] be the dstance of the -banch juncton fom the bus ogn, y[ b ] the length of banch b and S bus s length. Assembly of the expemental powelne ccutes has been as follows: 1.9m 1.7m 1 st bus: 3.8m = 1.6m n = 4, S = 32.7m, X =, Y 28.8m 2.2m 3.7m 2m Respectve path aval tmes ae 26.9m 2m d τ =, (8) 29.1m 1.9m c 2 nd bus: n = 5, S = 36.4m, X = 3.7m, Y = 1.6m whee c the popagaton velocty ove the powe lnes 32.7m 1.6m consdeed, whch usually emans constant, despte the 34.4m 2m utlzaton of dffeent dmensonal cable types. Phase constant s elated to popagaton velocty as 2πf β =. (9) c b

3 3 d bus: 1.9m 2m 26.9m 2.2m 28.5m 1.7m n = 6, S = 59.2m, X =, Y =. 3.6m 1.6m 32.3m 2m 57.3m 1.9m T x R x espectve dagam. H(f) (db) f(mhz) Fg. 2. Ampltude esponse of the 1 st bus ( N = 2691) : Open Ccut, T x : Tansmtte, R x : Receve Fg. 1. Topology of the measued gd paadgms. As ndcated n fg. 1, tansmtte and eceve have been set matched, wheeas all othe banches as well as the bus ends have been kept open ccuted. A sgnal/functon geneato has been used to tansmt, and a dgtal eal-tme osclloscope to captue nput and output snusodal sgnals. Havng all ove the same cable type, eflecton coeffcents at temnatons and junctons get espectvely ρ = 1 and ρ = 1 3, and tansmsson coeffcent comes L J out as t = 2 3. The cable type NYM 3x2.5mm 2 pe VDE- 25 has all ove been employed, fabcated by coppe and PVC. Conductvty and elatve delectc constant have 7 been theefoe assumed σ = S and ε, m = 3.6 and cable s dstbuted paametes and tansmsson constants have been estmated accodng to [7] Results and Dscusson Fo evaluaton puposes, a pogam n Pascal has been compled that calculates tansfe functon executng the supeposng pocess descbed n Secton 2 above. Input nfomaton ncludes the bus topology,.e. paametes n and S as well as X and Y vectos, cable s mateal constants ( ε, µ and σ ), and dmensonal paametes. Compason between theoetcal and expemental esults s set out n fg At the computatonal pocess, all paths havng multtude g.1 N have been counted n, of whch the fo evey sample gd tested s ndcated on H(f) (db) f(mhz) Fg. 3. Ampltude esponse of the 2 nd bus ( N = 6431) H(f) (db) f(mhz) Fg. 4. Ampltude esponse of the 4 th bus ( N =13447) Inspecton of the gaphs set above appeas ndeed confmatve of the model poposed. Theoetcal cuves eman n all thee cases close to the measued ones. No devaton above 1dB s obseved. Vaaton of 1dB coesponds of couse to an absolute-value ato aound (3.2), but when consdeng quanttes that fluctuate acoss two o moe odes of magntude, lke the ampltude of HF

4 sgnals popagatng ove powe-lne netwoks, such dffeences ae acceptable and consdeed of mno ange. Most of the dvegence accued should come fom mpefectons of the expemental set-up, and especally due to mpedance msmatches between connectos, cables and the equpment. Although temnaton at ecepton has been well matched, eflecton up to 3% has been noted at tansmsson, but not taken nto account dung calculatons. Fom a scentfc pont of vew, the dscepances could n the fst place be attbuted to vaaton of the elatve delectc constant along the band tested, whch has been taken constant all ove the computatonal pocedue. In addton, a slght matte concenng sound applcaton of the path-selecton cteon ases at hee. Decdng ncopoaton of a component o not to the multpath analyss by vtue of the weghtng facto modulus g n elaton to a peset theshold does not peseve absolutely equal teatment of all paths. Impact of longe echoes s moe ntensely taken nto account, as two paths wth the same weghtng facto may n fact have consdeably unequal magntudes due to long dffeence between espectve oute uns. Amendng the above two flaws of the method s easly attaned and ncopoated to the computatonal pocedue. In any case, the model seems wde sutable fo appoxmatve PLC channel smulatons, not demandng any expemental feedback. 4. Powe-Delay-Pofle Aspects 4.1. Smulaton Indoo cablng s n geneal nstalled at tee topology, fomed of eplcated sta and bus stuctues. The sta cente s nomally a dstbuton panel, fom whch load-feedng lnes ognate confgued lke a bus, fomng the banches of the tee, of whch panels ae the nodes. Load-feedng banches also seve sometmes as seconday buses. Such tee topologes usually compse two banch layes, as the panels ae commonly nstalled at two-level nteconnecton achtectue along the gd. The man electc panel to whch powe supply fom dstbuton LV netwok s coupled feeds dstbuton sub-panels whee the load lnes ognate fom, although moe sub-panel levels may be found n huge buldngs. Hence, bus stuctue consttutes the pmay element of ndoo gds topology. In fact, powe-lne netwoks ae assembled of adjonng bus topologes, so that statstcal chaactestcs of a banched backbone lne should nheently be assgned to ndoo PLC channels. Havng open-ccuted temnatons, the wostcase scenao s taken nto account, as by the esultant untay eflecton coeffcent at the banch ends multpath delay spead effect gets maxmzed. On the bass of the study ntoduced above, pelmnay powe-delay-pofle estmatons have been attempted. To ths effect, an addtonal pogam n Pascal has been compled that calculates and ecods n appopate data fles the path ampltudes and aval tmes. Fo the measued gd paadgms No 1 to No 3 defned above, path nventoy of all components havng the weghtng facto wthn two odes of magntude below the weghtng g facto g of dect path has been pefomed. Smulaton at 15MHz has been conducted fo each of the thee buses, and the esults ae depcted n fg Symbol µ denotes the mean paamete and σ the standad devaton. The theoetcal Nomal and Lognomal dashed cuves ae n each dagam dawn wth the mean and standad-devaton paametes of coespondng path set. 4.2 Dscusson Resultng channel powe-delay pofles ognate fom a sngle-fequency smulaton pocess, but ae stll ndcatve of the multpath-popagaton effect n the HF band, and lead to concepts of consdeable pactcal and theoetcal value. To begn wth, only bus No 2 has gven a sngle path set n the sense of unnteupted path-aval sequence. Cumulatve aval-tme and ampltude dstbutons ae theefoe plotted n fg. 6, whee espectve complance wth the Nomal and Lognomal dstbutons s appaent. Smulaton ove the othe two sample gds eveals that the aggegate multtude of paths aves at ecepton at welldefned goups n the tme doman; the pobablty densty functon (pdf) cuves dsplayed n fg. 5 and 7 efe thus to the ndvdual domnant path subsets that have n each case been obseved. Good confomance to the Nomal and Lognomal dstbutons espectvely fo the aval-tme and ampltude sequences s also obvous wthn a path goup. Clea ndcaton on the effect of netwok s spatal confguaton upon the geneaton of domnant path goups and ncdent statstcal behavous s n addton obtaned. Along the gd No 2, wheeat path multtude aves as a sngle goup, the tansvese banches ae coupled at smla dstances n between, along a secton 7.5m long some 27m fom tansmsson and 2m fom ecepton. Consdeng bus No 1, two dstant banched sectons exst, and two path sets have ndeed asen. Thee dstant banched sectons ae confgued along bus No 3, and thee path goups ae obseved. It s theefoe deduced that any gd secton assembled at equable allocaton of scatteng ponts (junctons and temnatons) gves se to an ndvdual path goup dsplayng the Nomal aval-tme dstbuton and the Lognomal ampltude one. The latte s also vaguely ntepeted n theoy, as multpath popagaton, chaactesed as a multplcatve pocess due to multple eflectons, could be expected to yeld Lognomal

5 dstbuton n the same way that an addtve pocess esults n Nomal dstbuton as descbed by the Cental Lmt Theoem. Fom the easonng deployed heetofoe t comes up that fadng behavou of ndoo sngle-phase PLC channels should be chaactesed by a path set of a Nomal avaltme sequence and a Lognomal ampltude fluctuaton, as unfom spatal dstbuton of junctons and temnatons theen moe o less pevals. Howeve, seveal domnant path goups as defned above would pobably exst at PLC lnks along the access LV netwok, as each consume (house, pemses etc.) could be consdeed a dstant, solated banched secton. The atonale developed so fa s of couse not genealzed, but ndcant and based on the pelmnay study descbed above. A vald aspect concenng statstcal fadng popetes of PLC channels s though pofoundly suggested. Futhe nvestgaton s heeby encouaged, concentatng on the goupng and chaactesaton of ndoo PLC nstallatons on multpathfadng pncples. The analyss and statstcal smulaton that have been pesented concen popagaton of dstnct snusodal sgnals, beng thus dectly applcable to the naowband o mult-cae (e.g. OFDM) case, whee the bandwdth occuped s small compaed to cae fequency. Equvalent wdeband analyss of the powe delay pofle would though be feasble though a vey smla pocedue to the one caed out above. In that case, channel s tansfe popetes would be teated n the tme doman by use of the mpulse esponse nstead of tansfe functon. Estmatng tansfe functon by the multpath analysng method ntoduced, an nvese Foue tansfomaton would gve the mpulse esponse, so that all sutable fomulsm and computatonal pocedues should be theeon developed. 5. Concluson In ths pape, a method povdng HF tansfe popetes of ndoo PLC channels has been poposed based on multpath-popagaton pncples, applcable wheeve cables fall nto the two-conducto unfom tansmssonlne model. Employng the genealzed multpath popagaton model, estmaton of the channel esponse by ncluson of the path set wthn two odes of magntude below the dect path has been suggested. A completely analytcal/computatonal pocess has been poposed, so that no expemental feedback o paamete calbaton s ncopoated. The cable dstbuted paametes and the gd netwok n the vcnty of the lnk need only be povded. Collaton wth measued ampltude-esponse cuves has vefed the method to be well adequate fo the appoxmate channel evaluatons equed n pactce. Pelmnay powe-delay-pofle estmatons that have been pefomed ndcate n elaton to ndoo PLC channels the Nomal dstbuton fo path aval tmes and the Lognomal fo path ampltudes. Futhe exploaton s heeby stongly encouaged, n ode fo netwok topology and ange to be quanttatvely nteelated wth the channel powe-delay-pofle. (a) Aval-Tme Dstbuton of the seveal path-sets. Pobablty Densty Functon Seveal Aval-Tme Dstbutons (sold) and esultng Nomal Dstbutons (dashed) ,2,4,6,8 Aval Tme (µs) 1 st subset: 114 paths, µ =. 32µs, σ =. 3µ s 2 d subset: 1587 paths, µ =. 63µs, σ =.31µ s (b) Ampltude Dstbuton of the seveal path-sets. Pobablty Densty Functon Seveal Ampltude Dstbutons (maked) and esultng Lognomal Dstbutons (dashed) 1,E+4 1,E+3 1,E+2 1,E+1 1,E+ 1,E-1 1,E-2 1,E-5 1,E-4 1,E-3 1,E-2 1,E-1 Nomalzed Ampltude H(f) µ, σ = st subset: 114 paths, [ ln ( f ) ] = H µ, σ = d subset: 1587 paths, [ ln ( f ) ] = 8. Fg. 5. Powe-Delay-Pofle of the 1 st bus ( N = 2691) H

6 (a) Cumulatve Aval-Tme Dstbuton Aval-Tme Dstbuton (sold) and esultng Nomal Dstbuton (dashed) (a) Aval-Tme Dstbuton of the seveal path-sets Seveal Aval-Tme Dstbutons (sold) and esultng Nomal Dstbutons (dashed) Pobablty Densty Functon ,2,3,4,5,6 Aval Tme (µs) µ =. 4µs, σ =.36µs Pobablty Densty Functon ,3,8 1,3 Aval Tme (µs) 1 st subset: 7152 paths, µ =. 53µs, σ =.35µ s 2 d subset: 562 paths, µ =. 83µs, σ =.36µ s 3 d subset: 693 paths, µ = 1. 13µs, σ =.41µ s Pobablty Densty Functon (b) Cumulatve Ampltude Dstbuton Ampltude Dstbuton (sold) and esultng Lognomal Dstbuton (dashed),1,1,1 Nomalzed Ampltude H (f) [ ln ( f ) ] = µ, σ =.667 H Fg. 6. Powe-Delay-Pofle of the 2 nd bus ( N = 6431) Refeences [1] H. Phlps, Modellng of Powelne Communcaton Channels n Poc. ISPLC 99, 1999, pp [2] M. Zmmemann and K. Dostet, A Mult-Path Popagaton Model fo the Powe-Lne Channel n the Hgh Fequency Range, n Poc. ISPLC 99, 1999, pp [3] M. Zmmemann and K. Dostet, A Multpath Model fo the Powelne Channel, IEEE Tansactons on Communcatons, vol. 5, No. 4, Apl 22, pp [4] T. Esmalan, F.R. Kschschang, and P.G. Gulak, An Inbuldng Powe Lne Channel Smulato, n Poc. ISPLC22, 22, pp [5] D. Anastasadou and T. Antonakopoulos, An expemental set-up fo chaactezng the esdental powe gd vaable behavo, n Poc. ISPLC22, 22, pp (b) Ampltude Dstbuton of the seveal path-sets Pobablty Densty Functon Seveal Ampltude Dstbutons (maked) and esultng Lognomal Dstbutons (dashed) 1,E+5 1,E+4 1,E+3 1,E+2 1,E+1 1,E+ 1,E-1 1,E-2 1,E-3 1,E- 5 1,E- 4 1,E- 3 1,E- 2 Nomalzed Ampltude H(f) 1 st subset: 7152 paths, [ ln ( f ) ] = H 1,E- 1 µ, σ = d subset: 562 paths, [ ln ( f ) ] = µ, σ =.531 H µ, σ =.3 3 d subset: 693 paths, [ ln ( f ) ] = 1. 7 Fg. 7. Powe-Delay-Pofle of the 4 th bus ( N =13447) [6] A. Matov, A Plannng Tool fo Hgh Bt Rate Tansmsson ove Powe Lne Communcaton Channels, n Poc. ISPLC21, 21, pp [7] I.C. Papaleondopoulos, C.G. Kaagannopoulos, N.J. Theodoou, C.E. Anagnostopoulos and I.E. Anagnostopoulos, Modellng of Indoo Low-Voltage Cables n the Hgh Fequency ange, n Poc. ISPLC22, 22, pp H