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Channel modeling for high-speed indoor powerline communication systems: the lattice approach

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Abstract

The transmission of high-frequency signals over powerlines, known as powerline communications (PLC), plays an important role in contributing toward global goals for broadband services inside the home and office. In this paper, we aim to contribute to this ideal by presenting a powerline channel modeling approach which describes a powerline network as a lattice structure. In a lattice structure, a signal propagates from one end into a network of boundaries (branches) through numerous paths characterized by different reflection/transmission properties. Due to theoretically infinite number of reflections likely to be experienced by a propagating wave, we determine the optimum number of paths required for meaningful contribution toward the overall signal level at the receiver. The propagation parameters are obtained through measurements and other model parameters are derived from deterministic powerline networks. It is observed that the notch positions in the transfer characteristics are associated with the branch lengths in the network. Short branches will result in fewer notches in a fixed bandwidth as compared to longer branches. Generally, the channel attenuation increase with network size in terms of number of branches. The proposed model compares well with experimental data.

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Authors and Affiliations

  1. School of Electrical, Electronic & Computer Engineering, University of KwaZulu-Natal, Durban, 4041, South Africa

    Modisa Mosalaosi & Thomas Afullo

Authors
  1. Modisa Mosalaosi
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  2. Thomas Afullo
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Corresponding author

Correspondence to Modisa Mosalaosi.

Appendix

Appendix

Derivation of total reflection/transmission combinations along numerous paths as viewed at branching points. Reflections from a fifth branch are considered in the equations. This is simply to affirm solution consistency at the fourth branch.

Type (1) Paths [direct paths]

$$\begin{array}{@{}rcl@{}} {\Psi}_{br,1}^{(1)}&=&T_{1} \end{array} $$
(A.1a)
$$\begin{array}{@{}rcl@{}} {\Psi}_{br,2}^{(1)}&=&T_{1}T_{2} \end{array} $$
(A.1b)
$$\begin{array}{@{}rcl@{}} {\Psi}_{br,3}^{(1)}&=&T_{1}T_{2}T_{3} \end{array} $$
(A.1c)
$$\begin{array}{@{}rcl@{}} {\Psi}_{br,4}^{(1)}&=&T_{1}T_{2}T_{3}T_{4} \end{array} $$
(A.1d)

Type (2) Paths [single reflection]

$$\begin{array}{@{}rcl@{}} {\Psi}_{br,1}^{(2)}&=&r_{2}{T_{1}^{2}}+r_{3}{T_{1}^{2}}{T_{2}^{2}}+r_{4}{T_{1}^{2}}{T_{2}^{2}}{T_{3}^{2}}\\ &&+r_{5}{T_{1}^{2}}{T_{2}^{2}}{T_{3}^{2}}{T_{4}^{2}} \end{array} $$
(A.2a)
$$\begin{array}{@{}rcl@{}} {\Psi}_{br,2}^{(2)}&=&r_{3}T_{1}{T_{2}^{2}}+r_{4}T_{1}{T_{2}^{2}}{T_{3}^{2}}+r_{5}T_{1}{T_{2}^{2}}{T_{3}^{2}}{T_{4}^{2}} \end{array} $$
(A.2b)
$$\begin{array}{@{}rcl@{}} {\Psi}_{br,3}^{(2)}&=&r_{4}T_{1}T_{2}{T_{3}^{2}}+r_{5}T_{1}T_{2}{T_{3}^{2}}{T_{4}^{2}} \end{array} $$
(A.2c)
$$\begin{array}{@{}rcl@{}} {\Psi}_{br,4}^{(2)}&=&r_{5}T_{1}T_{2}T_{3}{T_{4}^{2}} \end{array} $$
(A.2d)

Type (3) Paths [double reflection]

$$\begin{array}{@{}rcl@{}} {\Psi}_{br1}^{(3)}&=&0 \end{array} $$
(A.3a)
$$\begin{array}{@{}rcl@{}} {\Psi}_{br,2}^{(3)}&=&r_{1}r_{2}T_{1}T_{2}+r_{1}r_{3}T_{1}{T_{2}^{3}}\\ &&+r_{1}r_{4}T_{1}T_{2}T^{3}{T_{3}^{2}}+r_{1}r_{5}T_{1}{T_{2}^{3}}{T_{3}^{2}}{T_{4}^{2}} \end{array} $$
(A.3b)
$$\begin{array}{@{}rcl@{}} {\Psi}_{br,3}^{(3)}&=&r_{1}r_{2}T_{1}T_{2}T_{3}+r_{2}r_{3}T_{1}T_{2}T_{3}+r_{1}r_{3}T_{1}{T_{2}^{3}}T_{3}\\ &&+r_{2}r_{4}T_{1}T_{2}{T_{3}^{3}}+r_{1}r_{4}T_{1}T_{2}T^{3}{T_{3}^{3}}\\ &&+r_{2}r_{5}T_{1}T_{2}{T_{3}^{3}}{T_{4}^{2}}+r_{1}r_{5}T_{1}{T_{2}^{3}}{T_{3}^{3}}{T_{4}^{2}} \end{array} $$
(A.3c)
$$\begin{array}{@{}rcl@{}} {\Psi}_{br,4}^{(3)}&=&r_{1}r_{2}T_{1}T_{2}T_{3}T_{4}+r_{2}r_{3}T_{1}T_{2}T_{3}T_{4}+r_{3}r_{4}T_{1}T_{2}T_{3}T_{4}\\ &&+r_{1}r_{3}T_{1}{T_{2}^{3}}T_{3}T_{4}+r_{2}r_{4}T_{1}T_{2}{T_{3}^{3}}T_{4}+r_{1}r_{4}T_{1}{T_{2}^{3}}{T_{3}^{3}}T_{4}\\ &&+r_{3}r_{5}T_{1}T_{2}T_{3}{T_{4}^{3}}+r_{2}r_{5}T_{1}T_{2}{T_{3}^{3}}{T_{4}^{3}}+r_{1}r_{5}T_{1}{T_{2}^{3}}{T_{3}^{3}}{T_{4}^{3}}\\ \end{array} $$
(A.3d)

Type (4) Paths [source reflections]

$$\begin{array}{@{}rcl@{}} {\Psi}_{br,1}^{(4)}&=&r_{1}r_{s}T_{1}+r_{2}r_{s}{T_{1}^{3}}+r_{3}r_{s}{T_{1}^{3}}{T_{2}^{2}}\\ &&+r_{4}r_{s}{T_{1}^{3}}{T_{2}^{2}}{T_{3}^{2}}+r_{5}r_{s}{T_{1}^{3}}{T_{2}^{2}}{T_{3}^{2}}{T_{4}^{2}} \end{array} $$
(A.4a)
$$\begin{array}{@{}rcl@{}} {\Psi}_{br,2}^{(4)}&=&r_{1}r_{s}T_{1}T_{2}+r_{2}r_{s}{T_{1}^{3}}T_{2}+r_{3}r_{s}{T_{1}^{3}}{T_{2}^{3}}\\ &&+r_{4}r_{s}{T_{1}^{3}}{T_{2}^{3}}{T_{3}^{2}}+r_{5}r_{s}{T_{1}^{3}}{T_{2}^{3}}{T_{3}^{2}}{T_{4}^{2}} \end{array} $$
(A.4b)
$$\begin{array}{@{}rcl@{}} {\Psi}_{br,3}^{(4)}&=&r_{1}r_{s}T_{1}T_{2}T_{3}+r_{2}r_{s}{T_{1}^{3}}T_{2}T_{3}+r_{3}r_{s}{T_{1}^{3}}{T_{2}^{3}}T_{3}\\ &&+r_{4}r_{s}{T_{1}^{3}}{T_{2}^{3}}{T_{3}^{3}}+r_{5}r_{s}{T_{1}^{3}}{T_{2}^{3}}{T_{3}^{3}}{T_{4}^{2}} \end{array} $$
(A.4c)
$$\begin{array}{@{}rcl@{}} {\Psi}_{br,4}^{(4)}&=&r_{1}r_{s}T_{1}T_{2}T_{3}T_{4}+r_{2}r_{s}{T_{1}^{3}}T_{2}T_{3}T_{4}\\ &&+r_{3}r_{s}{T_{1}^{3}}{T_{2}^{3}}T_{3}T_{4}+r_{4}r_{s}{T_{1}^{3}}{T_{2}^{3}}{T_{3}^{3}}T_{4}\\ &&+r_{5}r_{s}{T_{1}^{3}}{T_{2}^{3}}{T_{3}^{3}}{T_{4}^{3}} \end{array} $$
(A.4d)

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Mosalaosi, M., Afullo, T. Channel modeling for high-speed indoor powerline communication systems: the lattice approach. Ann. Telecommun. 72, 499–511 (2017). https://doi.org/10.1007/s12243-016-0554-3

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