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We propose an efficient bottom-up power-line communication (PLC) channel simulator that exploits transmission-line theory concepts and that is able to generate statistically representative in-home channels. We first derive from norms and practices a statistical model of European in-home topologies. The model describes how outlets are arranged in a topology and are interconnected via intermediate nodes referred to as derivation boxes. Then, we present an efficient method to compute the channel transfer function between any pair of outlets belonging to a topology realization. The method is based on a systematic remapping technique that leads to the subdivision of the network in elementary units, and on an efficient way to compute the unit transfer function referred to as the voltage ratio approach. The difference from the more conventional and complex ABCD matrix approach is also discussed. We finally show that the simulator can be configured with a small set of parameters and that it offers a theoretical framework to study the statistical PLC channel properties as a function of the topology characteristics, which is discussed in Part II of this work.