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Modeling of the Transfer Function of the Indoor Power Line Channel Stefano Galli Telcordia Technologies

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1 Modeling of the Transfer Function of the Indoor Power Line Channel Stefano Galli Telcordia Technologies sgalli@research.telcordia.com http://www.argreenhouse.com/bios/sgalli sgalli@research.telcordia.com http://www.argreenhouse.com/bios/sgalli Copyright © 2006 Telcordia Technologies. All Rights Reserved. Princeton University, ISS Seminars, April 20,2006

2 Telcordia Technologies Proprietary - Copyright 2006. 2 Outline of presentation 1)Applications of Power Line Communications (PLCs) 2)Modeling the (indoor) transfer function a)Time-domain and Frequency-domain models b)Multi-conductor transmission line theory c)The Symmetry Property d)Experimental Results 3)Conclusions

3 Telcordia Technologies Proprietary - Copyright 2006. 3 First applications date back to early 1920s, on HV lines. The first standard is the European CENELEC EN 50065, which mandates the use of the frequency range 3-148.5 kHz (1991). The first commercial attempt to use PLC for last mile access dates back to 1997, when Nortel announced the NorWeb partnership with United Utilities (a UK power utility company) Limited trials of broadband Internet access through power lines were conducted in Manchester and NorWeb prototypes were able to deliver data at rates around 1 Mbps. Cost and commercial viability became questionable and the pilot project was terminated few years later in 1999. In the past few years, interest in the technology has picked up again and possible applications have multiplied. Power Line Communications

4 Telcordia Technologies Proprietary - Copyright 2006. 4 Power Line Communications – outdoor (From ADVANCE, March 2005)

5 Telcordia Technologies Proprietary - Copyright 2006. 5 (From ADVANCE, March 2005) Power Line Communications – indoor

6 Telcordia Technologies Proprietary - Copyright 2006. 6 Power Line Communications – smart grid apps (From ADVANCE, March 2005)

7 Telcordia Technologies Proprietary - Copyright 2006. 7 Beyond Outdoor/Indoor… PLCs allows for easy in-vehicle networking: –In any vehicles (from automobiles to ships, from aircraft to space vehicles), separate cabling is used to establish the PHY of a local command and control network which is becoming broadband –The in-vehicle power distribution network may well perform double-duty, as an infrastructure supporting both power delivery and broadband digital connectivity. –Weight, space and cost savings (aircraft, auto) PLCs as the enabler for truly pervasive and ad-hoc networks: Just look around… power is everywhere –Traffic lights, lamp posts, etc. can easily become network nodes –Smart appliances for better power utilization

8 Telcordia Technologies Proprietary - Copyright 2006. 8 From Brett Kilbourne, UPLC Conference, Sep. 2005

9 Telcordia Technologies Proprietary - Copyright 2006. 9 Interference issues in the HF band Better understanding is needed, theoretical and experimental work Modulation and coding can help reducing interference There are very few channel models available: lack of general results in communications theory For the optimization of any communications system, it is imperative to understand the channel Modeling the transfer function of the power line channel is non-trivial problem Until recently, impossible to predict channel on the basis of the topology What is the “average” power line channel? Many differences between countries in the mains grid Plethora of grounding and wiring practices, wide variability of performance Channel standardization needed High data rates with QoS, robustness, coexistence, security More work in transceiver “robust” optimization needed MAC issues for outdoor/indoor coexistence Open Problems

10 Telcordia Technologies Proprietary - Copyright 2006. 10 Interference issues in the HF band Better understanding is needed, theoretical and experimental work Modulation and coding can help reducing interference There are very few channel models available: lack of general results in communications theory For the optimization of any communications system, it is imperative to understand the channel Modeling the transfer function of the power line channel is non-trivial problem Until recently, impossible to predict channel on the basis of the topology What is the “average” power line channel? Many differences between countries in the mains grid Plethora of grounding and wiring practices, wide variability of performance Channel standardization needed High data rates with QoS, robustness, coexistence, security More work in transceiver “robust” optimization needed MAC issues for outdoor/indoor coexistence Open Problems

11 Telcordia Technologies Proprietary - Copyright 2006. 11 International: – wiring system uses a star (e.g., a single cable feeds all of the wall outlets in one room only) or tree arrangement – ground bonding at the main panel Europe: – two wire (ungrounded) or three wire (grounded) outlets – If three phase supply is used, separate rooms in the same apartment may be on different phases UK exceptions: – special rings: a single cable runs all the way round part of a house interconnecting all of the wall outlets; a typical house will have three or four rings. – neutral not grounded in the home –Old wiring: two-wire 1 phase, neutral and ground share common wire Inside wiring environment

12 Telcordia Technologies Proprietary - Copyright 2006. 12 NM-B BX Inside wiring environment

13 Telcordia Technologies Proprietary - Copyright 2006. 13 Wiring and grounding come in many flavors, and this makes channel modeling (modem design) much more challenging. However, international harmonization is happening: –Typical outlets have three wires: hot, neutral and ground –Classes of appliances (light, heavy duty appliances, outlets, etc.) fed by separate circuits –Neutral and ground separate wires within the home, except for the main panel where they are bonded Although complex topologies may exist, today’s regulations can simplify analysis of signal transmission Inside wiring environment

14 Telcordia Technologies Proprietary - Copyright 2006. 14 SERVICE PANEL FEED LIGHTING CIRCUITS Non-symmetric geometry for B&W RECEPTACLE CIRCUITS 15-20 amps, branching, and symmetric geometry for B&W GROUND BONDING EMBEDDED APPLIANCES 50 amps, non-branching, and symmetric geometry for B&W Wiring and Grounding Practices

15 Telcordia Technologies Proprietary - Copyright 2006. 15 Wiring and Grounding Practices Typical service panel, showing bonding between the neutral and the ground cable through R SB. Grounding and bonding has been completely ignored in indoor PLC modeling

16 Telcordia Technologies Proprietary - Copyright 2006. 16 B 0.3 FREQUENCY ( MHz) 30.0 LOSS 3dB/DIV Ground bonding introduces non negligible resonant modes due to pair-mode excitation. Effects of Grounding on Signal Propagation Same topology with bonding Topology without bonding

17 Telcordia Technologies Proprietary - Copyright 2006. 17 Two-Conductor Transmission Line Model Hooijen - ISPLC’98 Straightforward approach, follows TPC/coax modeling Frequency domain model Transfer function can be computed a priori Limitations: Knowledge of whole topology is needed Accuracy of results depend on accuracy of cable models Incomplete model, presence of third wire not included so that wiring and grounding practices not explicitly accounted for Some aspects of signal propagations cannot be explained with this model Channel Modeling Approaches

18 Telcordia Technologies Proprietary - Copyright 2006. 18 B LOSS 4dB/DIV 0.3 FREQUENCY ( MHz) 30.0 Current Models (no bonding) Measurements (when bonding present) Effects of Grounding on Signal Propagation

19 Telcordia Technologies Proprietary - Copyright 2006. 19 Multipath Model Phillips, and Dostert & Zimmermann - ISPLC’99, T-COM’02 The multipath nature arises from the presence of several branches and impedance mismatches that cause reflections. Channel Modeling Approaches Direct path X  A  Y (i=0): Secondary paths X  A  B  A  (B  A) i-1  Y(i>0):

20 Telcordia Technologies Proprietary - Copyright 2006. 20 The multipath model is a good model, but has some limitations: modeling is based on parameters that can be estimated only after the actual channel transfer function has been measured wiring and grounding practices not explicitly accounted for, but “phenomenologically” included computational cost in estimating the delay, amplitude and phase associated with each path (time-domain model)  drawback for some indoor/in-vehicle channels. Channel Modeling Approaches g i : is a complex number that depends on the topology of the link;  (f) is the attenuation coefficient (skin effect and dielectric loss);  i is the delay associated with the ith path; d i is the path length; N is the number of non-negligible paths.

21 Telcordia Technologies Proprietary - Copyright 2006. 21 Channel Modeling Approaches Direct path (i=0): Secondary paths of Type 1 (i>0): Secondary paths of Type 2 (j>0): Secondary paths of Type 3 (i, j>0): Adding discontinuities, the computational cost of the multipath model grows very fast

22 Telcordia Technologies Proprietary - Copyright 2006. 22 Multi-Conductor Transmission Line Model Galli & Banwell - ISPLC’01, T-PD’05 Part I and II Based on Multi-conductor Transmission Line Theory and Modal Decomposition: takes into account multi-conductor nature of PL cables, as well as wiring and grounding practices. Transfer function can be computed a priori Frequency domain model (limited computational complexity) unveilAllows to unveil interesting and useful properties of the PLC, e.g. superposition of resonant modes, isotropy of channel. Limitations: Knowledge of whole topology is needed Accuracy of results depend on accuracy of cable models Recent Results on Channel Modeling: MTL

23 Telcordia Technologies Proprietary - Copyright 2006. 23 Recent Results on Channel Modeling: MTL Three-conductor Analysis A three-conductor cable supports six propagating modes (TEM approximation): three spatial modes (differential, common and pair) each for two directions of propagation: The differential mode current, generally the desired signal. The common mode current I cm represents overall cable current imbalance, which creates a current loop with earth ground. Lossy mode, can be neglected. The pair-mode current (flowing between ground and the white/black wires “tied together”). This mode is excited due to certain wiring and grounding practices. Pair-mode has been completely neglected in previous models

24 Telcordia Technologies Proprietary - Copyright 2006. 24 PROPAGATING MODES WHERE MTL Modal Decomposition Parameters  describes shielding by the ground conductor Parameter  describes asymmetry between the hot and return wires, with respect to the ground conductor

25 Telcordia Technologies Proprietary - Copyright 2006. 25 SERVICE PANEL MAINS BLK WHT GND RTN HOT RSRS SERVICE PANEL BONDING MTL Modeling: bonding

26 Telcordia Technologies Proprietary - Copyright 2006. 26 RSRS MAINS GND DISTRIBUTION RTN HOT MTL Modeling: Measurements

27 Telcordia Technologies Proprietary - Copyright 2006. 27 MTL Modeling: bonding BLK WHT V DIFF PULSE GEN R 1 GND V R 1 R 2 R SB 7.6m R 3 TEST CABLE TEST CABLE

28 Telcordia Technologies Proprietary - Copyright 2006. 28 MTL Modeling: bonding The reciprocal of the scalar reflection coefficient exhibits a simple linear dependence on R SB.

29 Telcordia Technologies Proprietary - Copyright 2006. 29 BONDING FAULT -1/  dif Resistance R SB ohms MTL Modeling: measurements

30 Telcordia Technologies Proprietary - Copyright 2006. 30 BLK GND WHT BLK GND WHT 1+  1-  1-   Z dif Z pr Z cm I dif I pr I cm 1+  1-  1-   I BLK I WHT I GND (I dif + V dif /Z dif )e -  dif (I pr + V pr /Z pr )e -  pr (I cm + V cm /Z cm )e -  cm Parameters  describes shielding by the ground conductor Parameter  describes asymmetry between the hot and return wires, with respect to the ground conductor MTL Modeling: Modal Decomposition Validation

31 Telcordia Technologies Proprietary - Copyright 2006. 31 MTL Modeling: SPICE simulation

32 Telcordia Technologies Proprietary - Copyright 2006. 32 MTL Modeling: Measurements

33 Telcordia Technologies Proprietary - Copyright 2006. 33 MTL Modeling: Modal Transformer Differential and pair modes can be modeled as two independent networks of simple two-conductor TLs strongly coupled at one location through a modal transformer

34 Telcordia Technologies Proprietary - Copyright 2006. 34 From MTL Modeling to 2PNs MTL was the starting point for the modeling, but it is not a convenient tool for communications engineers. The full model requires knowledge of both  and . We can assume  =0 since this parameter primarily affects EMC. An “average”  must be estimated form measurements. If we assume symmetry between hot and return with respect to the ground cable along the whole PL link, then we can neglect  and no preliminary measurements are then necessary. We have shown that this approximation: still allows for accurate channel modeling allows for a convenient representation in terms of 2PNs and transmission matrix formalism S. Galli, T. Banwell, “A Deterministic Frequency-Domain Model for the Indoor Power Line Transfer Function,” IEEE JSAC Special Issue on PLCs, July 2006

35 Telcordia Technologies Proprietary - Copyright 2006. 35 Recent Results on Channel Modeling: MTL The proposed channel model requires crossing several layers of abstraction: Derive the differential mode and pair mode circuit models of power line link Tie the two modes through a transformer Describe each circuit models as cascaded two-port networks Obtain transfer function using transmission matrices Treat with same formalism both grounded and ungrounded links

36 Telcordia Technologies Proprietary - Copyright 2006. 36 Modeling the PL channel: ABCD matrix modeling Two-port network (2PN) and ABCD matrix notation:

37 Telcordia Technologies Proprietary - Copyright 2006. 37 Modeling a transmission line as a 2PN: 1) A=D for any frequency; 2) B  C for any frequency; 3) Unitary determinant: det(T)=AD-BC=1 (reciprocal 2PN); 4) Recalling the convention on positive currents, T=T –1. Modeling the PL channel: ABCD matrix modeling

38 Telcordia Technologies Proprietary - Copyright 2006. 38 Modeling shunt impedances along the line: Modeling the PL channel: ABCD matrix modeling

39 Telcordia Technologies Proprietary - Copyright 2006. 39 Modeling series impedances along the line: Modeling the PL channel: ABCD matrix modeling

40 Telcordia Technologies Proprietary - Copyright 2006. 40 The chain rule: If a link is constituted of several sections, each of which can be modeled as a 2PN, the the overall ABCD matrix of the end-to- end circuit is obtained by multiplying the ABCD matrices of the single portions of the network. Modeling the PL channel: ABCD matrix modeling

41 Telcordia Technologies Proprietary - Copyright 2006. 41 MTL Channel Modeling

42 Telcordia Technologies Proprietary - Copyright 2006. 42 MTL modeling: ungrounded links

43 Telcordia Technologies Proprietary - Copyright 2006. 43 MTL modeling: grounded links

44 Telcordia Technologies Proprietary - Copyright 2006. 44 MTL modeling: grounded links

45 Telcordia Technologies Proprietary - Copyright 2006. 45 MTL modeling: grounded links

46 Telcordia Technologies Proprietary - Copyright 2006. 46 25ft 14/2 15ft 14/2 60ft 6/2 SERVICE PANEL ( X )( Y ) MAINS TXRCVR Example

47 Telcordia Technologies Proprietary - Copyright 2006. 47 Example No ground bonding

48 Telcordia Technologies Proprietary - Copyright 2005. Example With ground bonding

49 Telcordia Technologies Proprietary - Copyright 2006. 49 Example

50 Telcordia Technologies Proprietary - Copyright 2006. 50 Example

51 Telcordia Technologies Proprietary - Copyright 2006. 51 Applying the chain rule, we finally obtain a single 2PN: Example

52 Telcordia Technologies Proprietary - Copyright 2006. 52 MTL Approach: Better Accuracy Current models (no bonding) MTL model LOSS 4dB/DIV 0.3 FREQUENCY ( MHz) 30.0 B

53 Telcordia Technologies Proprietary - Copyright 2006. 53 Channel property: Symmetry Let us define the forward and backward ABCD matrices:

54 Telcordia Technologies Proprietary - Copyright 2006. 54 Channel property: Symmetry overall The overall forward and backward ABCD matrices are: However, T f = T b iff they share all common eigenvectors If T f =T b, then forward and backward transfer functions are the same: H f (f)=H b (f)

55 Telcordia Technologies Proprietary - Copyright 2006. 55 Channel property: Symmetry Eigenvectors of ABCD matrices depend on Zo: Although counterintuitive, cascading two sections of different cables yields to different overall forward and backward matrices !! Nevertheless, it can be shown that the forward and backward transfer functions of the power line channel are the same regardless of topology if and only if Z S =Z L. (IEEE Trans. on Power Delivery, Part II, July 2005)

56 Telcordia Technologies Proprietary - Copyright 2006. 56 Channel property: Symmetry

57 Telcordia Technologies Proprietary - Copyright 2006. 57 Plethora of grounding and wiring practices, but harmonization of regulations can simplify analysis of signal transmission Wiring and grounding practices must be taken into account ! We have now a better understanding of the physics of channel propagation and predict the channel on the basis of its topology How do we characterize the “average” link? Average Channel Statistical or deterministic approach?

58 Telcordia Technologies Proprietary - Copyright 2006. 58 Several groups are pursuing methods to deduce relevant statistical behavior from ensembles of physical models (Dostert, Zimmerman,etc.). Other groups are instead following a deterministic approach based on precise channel models (Sartenaer, Issa, Esmailian, Galli, Banwell, etc.). Statistical models do not require knowledge of the link topology nor of the cable models, but require extensive measurement campaign. Deterministic models require detailed knowledge of the link topology and of the cable models, but do not require extensive measurements. A statistical approach should preserve inherent determinism as much as possible, including correlations between differential and companion (pair mode) models. It is likely that several topology elements will be associated with regular features of the transfer function: the ability to correlate these elements with their effect on the transfer function will be helpful in generating good statistical models. This important property can be obtained by combining both statistical and deterministic models Deterministic versus Statistical Models

59 Telcordia Technologies Proprietary - Copyright 2006. 59 On the basis of engineering rules, regulatory constraints, it is possible to generate (randomly) a “realistic” topology. This sample topology would represent “a house”. For a given topology, we can again randomly generate possible terminating impedances. These variations of the basic topology representing a house represent the variations that can be found within a home. We now compute, using a deterministic model, the transfer functions of the sample topology with the sample terminating impedances for every pair of plugs. We compute the “capacity” of all the computed transfer functions between pair of power plugs (nodes) We can now build a CDF with the rates per home, as a function of the percentage of plugs within the home. We can then average again over the homes, and extract meaningful statistics, e.g. delay spread, attenuation, etc. Hybrid procedure

60 Telcordia Technologies Proprietary - Copyright 2006. 60 Concluding Remarks We have today a better understanding of the PL channel PL channel more deterministic than originally thought – Determinism should be exploited for transceiver optimization Plethora of grounding and wiring practices, but harmonization of regulations can simplify analysis of signal transmission – Wiring and grounding practices must be taken into account Lack of traditional research funding has kept PLC research out of academia, so that most work has been done within an industrial environment and has been directed towards winning skepticism – Lack of a solid theoretical approach System modeling and optimization is challenging – Wide variability of environment – PLCs is one of the most inter-disciplinary fields we have

61 Telcordia Technologies Proprietary - Copyright 2006. 61 8-3 SUB-PANEL FEED 1:3 SPLIT 1WAY 2×3WAY 4-WAY RELAY SOME CIRCUITS WILL ALWAYS BE DIFFICULT!! 14-214-2-2 12-3 14-3 14-2 12-2 12-2 (FEED) 14-2 Epilogue…

62 Telcordia Technologies Proprietary - Copyright 2006. 62 Back-Up Slides…

63 Telcordia Technologies Proprietary - Copyright 2006. 63 World Trends in PLCs (From ADVANCE, March 2005)

64 Telcordia Technologies Proprietary - Copyright 2006. 64 Coexistence Issues There is no demarcation between access and in-home power line cables  it is a bus running from sub-station transformer to every plug in the home Access signals and in-home signals must co-exist From Mike Stelts (CEPCA), UPLC Conference, Sep. 2005

65 Telcordia Technologies Proprietary - Copyright 2006. 65 Power line cables are a shared medium, like coax cable and unlike DSL Signals in your home become interference for your neighbor, and viceversa Not only complicated MAC problem, but also security issues Coexistence Issues From Mike Stelts (CEPCA), UPLC Conference, Sep. 2005

66 Telcordia Technologies Proprietary - Copyright 2006. 66 high voltage level: 110..380 kV medium voltage level 10...30kV low voltage distribution grid 3 Phases: 230V, 400V LV transformer stations supply cells  up to 350 households  cable length 100...400m transformer station European Power Supply Network Structure From Klaus Dostert, Keynote Talk, ISPLC 2005

67 Telcordia Technologies Proprietary - Copyright 2006. 67 Single phase Single phase: hot/neutral connectors (sometimes separate “earth” wire) –typical for residences 240V (UK) or 220V (rest of EU), but harmonization process towards 230 V (±10%) Three phase: Three phase: three hot wires and one return –230V/400V (typical for homes in Germany, Sweden and Finland), but sometimes 127/220V (Finland and Belgium), and 230V and no neutral in the supply - outlets are wired between two phases (Scandinavia) European power distribution details Typical access network in Europe is composed of LV lines (underground cables)

68 Telcordia Technologies Proprietary - Copyright 2006. 68 high voltage level: 110..380 kV 1 st medium voltage level 10…30 kV low voltage distribution grid single or split phase supply 125V, 250V many LV transformers transformer station 2 nd medium voltage distribution level 6 kV  small supply cells  few households per transformer  cable length  100m  grounding of 3 rd wire American Power Supply Network Structure From Klaus Dostert, Keynote Talk, ISPLC 2005

69 Telcordia Technologies Proprietary - Copyright 2006. 69 Single phase Single phase: hot and neutral connectors –120V AC, sometimes separate ground wire Two phase Two phase: two hot conductors (opposite polarity) with one neutral. – Typical 120V AC (120/240V AC split phase), but sometimes two legs of 120/208 wye (apartment complexes) Three phase: Three phase: three hot wires and one return –120/208 V, but rare for homes American power distribution details Typical access network in the US is composed of both MV and LV lines (overhead cables)

70 Telcordia Technologies Proprietary - Copyright 2006. 70 Inside wiring environment

71 Telcordia Technologies Proprietary - Copyright 2006. 71 The Noise Environment narrowband- interference background noise + periodic impulsive noise asynchronous with the mains periodic impulsive noise synchronous with the mains aperiodic asynchronous impulsive noise Colored background noise, significantly higher at low frequencies Narrow-band interference consisting of modulated sinusoids, e.g. broadcast radio stations Periodic synchronous Impulse Noise (IN), by rectifiers within DC power supplies and appliances. Periodic asynchronous IN, by switching of power supplies of appliances Aperiodic asynchronous IN caused by switching transients, which occur all over a power supply network at irregular intervals

72 Telcordia Technologies Proprietary - Copyright 2006. 72 The Noise Environment Colored background noise Characterized by a fairly low power spectral density, which, however, significantly increases toward lower frequencies. It is caused, for example, by common household appliances like computers, dimmers, or hair dryers, which can cause disturbances in the frequency range of up to 30 MHz. Narrowband interference Normally consists of modulated sinusoids, the origin of which are broadcast radio stations in the frequency range of 1–22 MHz (typical). Figure 2 includes an example of a measurement showing colored background noise together with typical narrowband interference.

73 Telcordia Technologies Proprietary - Copyright 2006. 73 The Noise Environment From M. Götz et al., IEEE Comm. Mag., April 2004

74 Telcordia Technologies Proprietary - Copyright 2006. 74 The Noise Environment Periodic Impulsive Noise Periodic impulsive noise is further divided into interference synchronous or asynchronous to the mains frequency. The synchronous portions are mainly caused by rectifiers within DC power supplies and appliances such as thyristor- or triac- based light dimmers. Generally, repetition rates of multiples of the mains frequency are observed. The asynchronous portion exhibits considerably higher repetition rates of 50–200 kHz. Such interference is mainly caused by extended use of switching power supplies found in various household appliances today.

75 Telcordia Technologies Proprietary - Copyright 2006. 75 The Noise Environment Aperiodic Asynchronous Impulsive Noise Mainly caused by switching transients, which occur all over a power supply network at irregular intervals. This type of noise contains a broadband portion significantly exceeding the background noise, and a narrowband portion appearing only in certain frequency ranges. Impulses containing frequencies up to 20 MHz are not unusual. The broadband portion results from sharp rising edges, whereas the narrowband portions arise from oscillations. For the majority of impulses, it was found that amplitudes were around 1 V, impulse widths were in the range of 100 us, and interarrival times were of the order of 100 ms.

76 Telcordia Technologies Proprietary - Copyright 2006. 76 The Noise Environment From M. Götz et al., IEEE Comm. Mag., April 2004

77 Telcordia Technologies Proprietary - Copyright 2006. 77 B open B B B (X)(Y) Isolation of Resonant Modes

78 Telcordia Technologies Proprietary - Copyright 2006. 78 Isolation of resonant modes Ground bonding shunt creates dips at 3.3, 9.9, 16.7, 23.3 MHz; First bridged tap (R2 =  ) creates a dip at 11.4 MHz Second bridged tap creates dips at 7.0 and 21 MHz The mains feed (shorted bridged tap, R4=0) creates dips at 4.8, 9.8, 14.9, 19.8 and 24.8 MHz. When the PL channel transfer function changes because of a change in the boundary conditions, some features do not change  correlation

79 Telcordia Technologies Proprietary - Copyright 2006. 79 Isolation of resonant modes Although some appliances in the home may be switched on or off several times during the day, some appliances are usually always on and their input impedance varies slowly during the day. Some other features of the network can be considered constant during the day: the presence of the mains feed, the bonding, some unused plugs in certain rooms, etc. Therefore, it is not unreasonable to assume that the transfer function between two PL modems located at two home network nodes may always exhibit notches at certain frequencies. This suggests the possibility that PL modems could effectively try to map particular features of the entire PL home network. This mapping could be accomplished adaptively by continuously transmitting training sequences or by embedding into the modems some a priori information on the topology. Over time, it is likely that all the states of the channel are encountered so that the PL modem can infer and, therefore, exploit, the actual state of the network on the basis of the estimated channel transfer function, e.g. with a look-up table.


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