We consider the design of the front-end receiver for broadband power line communications. We focus on the design of the input impedance that maximizes the signal-to-noise ratio (SNR) at the receiver. We show that the amplitude, rather than the power, of the received signal is important for communication purposes. Furthermore, we show that the receiver impedance impacts the amplitude of the noise term. We focus on the background noise, and we propose a novel description of the noise experienced at the receiver port of a PLC network. We model the noise as the sum of four uncorrelated contributions, that is, the active, resistive, receiver, and coupled noise components. We study the optimal impedance design problem for real in-home grids that we assessed with experimental measurements. We describe the results of the measurement campaign, and we report the statistics of the optimal impedance. Hence, we study the best attainable performance when the optimal receiver impedance is deployed. We focus on the SNR and the maximum achievable rate, and we show that power matching is suboptimal with respect to the proposed impedance design approach.