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.

The communication technology that exploits the power delivery network to convey data is commonly referred to as power line communication (PLC). PLC is broadly deployed and, recently, it has been recognized as a key technology to enable the communication within the smart grid. The last node of the smart grid is the home, where PLC is suitable for both home entertainment, with datarates of about 200 Mbps, and home-automation, with lower data-rates but higher robustness and reliability.

The design of the PLC transceiver is a challenging task due to the severe attenuation, fading effects, and noise impairments that characterize the communication media. In other application scenarios, as wireless, the transceivers are designed to fulfill the maximum power transfer condition. Basically, the maximum power transfer is achieved under complex matching conditions, that is, when the internal impedance of the transmitter and the input impedance of the receiver are the complex conjugate of the characteristic impedance of the transmission medium. In wireless, this corresponds to the input impedance of the antenna. Indeed, the absence of reflections and stationary waves is obtained under simple (not complex) matching conditions, that is, when the impedance of the transmitter and the receiver are equal to the characteristic impedance of the transmission medium. Reflections and stationary waves are not desired. The reflected waves yield to multiple delayed echoes in the channel impulse response and they can be either due to the multipath nature of the channel or due to the unmatched termination nodes. Matching ensures the absence of the latter type of reflections. The stationary waves yield to voltage values along the line that are higher than necessary and that may damage the transmission medium, especially in wireline communications as, for instance, over coaxial cables.

When the characteristic impedance of the medium is real, the maximum power transfer and the absence of reflections are ensured by the same matching conditions. In the following, we simply indicate with impedance matching the receiver design that enables the maximum power transfer. In wireless, impedance matching can be easily satisfied by letting the characteristic impedance of the antenna and the cables, the internal impedance of the transmitter and the input impedance of the receiver be equal to the reference value of

In PLC, impedance matching is typically achieved through the use of impedance matching networks, so that the received signal power is maximized. Basically, the matching network is a loss-less network of lumped elements whose input impedance is matched to that of the power delivery network. The latter is frequency dependent and it varies significantly from outlet to outlet. Furthermore, it may exhibit a time-varying behavior [

The effective formulation of the SNR is in signal amplitude rather than in power terms. The reason is that the analog front-end of the PLC receiver is designed to convert the analog amplitude of the received signal into a digital sample stream. In this respect, the amplitude of the received signal is more important than its power, though the two quantities are related once the receiver impedance is given.

In PLC, the maximum power transfer condition does not imply the maximization of the SNR in amplitude terms because power matching may turn into a higher noise contribution. Concerning an in-home network, the noise injected by the household devices is attenuated by the insertion loss of the path followed to reach the receiver outlet. In general, the latter is different from that followed by the communication signal. The receiver impedance affects the insertion loss, and common impedance matching techniques do not take into account the impact of the receiver impedance on the insertion loss experienced by the noise. It follows that impedance matching may reduce the attenuation of the noise path, thus increasing the noise amplitude at the receiver port. Furthermore, the receiver impedance itself contributes to the increase of the amplitude of the noise.

In this work, we discuss the optimal design of the receiver impedance that enables achieving the maximum SNR in broadband PLC. We formulate the SNR in terms of amplitude and we focus on in-home networks.

Firstly, we propose an analytic description of the noise as the sum of multiple contributions. We consider the resistive noise of the network by itself, the noise injected by the household devices, and the noise introduced by the receiver impedance. From the experimental evidence, we show that the noise injected by the household devices, namely, the active noise, dominates among all noise contributions.

Then, we formulate the SNR as a function of the receiver impedance. To this aim, we assume the transmitter impedance to be constant and known. We study the convexity of the optimization problem and we derive the optimal receiver impedance that maximizes the SNR at each single frequency.

Finally, we validate the results for real-life in-home networks. We exploit the results of an experimental measurement campaign that we carried out in Italy, where we collected more than 1200 channel responses in different premises. For each site, we performed measurements between all couples of available outlets in the 1.5–100 MHz frequency range. The measured database is useful to provide a realistic description of the frequency response and the line impedance that characterizes the signal paths.

In this work, we focus on the time invariant description of the network because, from the experimental evidence, we observed that very little (or inexistent) time variation was present in the sites that we considered, namely, in the order of few dBs. More in general, the PLC channel can be periodically time variant. In such a case, an extension of our analysis can be obtained under the assumption that both the channel and the noise exhibit a slow periodic variation that is synchronous with the mains. Thus, the mains period can be divided into short time intervals (slots) during which we can reasonably assume both the channel and the noise to be time invariant. Hence, we can apply the analysis that we propose in this work to each single slot.

We study the attainable SNR improvement when the optimal receiver impedance is used. We compare the results to the case of impedance matching, when the receiver impedance is constant and equal to the reference value of 50 Ω, and when it is constant and equal to 1 kΩ. The latter case is representative of a receiver with high input impedance.

The remainder of the work is as follows. In Section

PLC experiences high attenuation and deep fading effects that are a function of the loads and the layout of the network. We focus on in-home networks. In [

From a data transmission perspective, we can abstract the power delivery network to obtain an equivalent representation that is suitable for the SNR analysis of the following sections. In Figure

Equivalent model of the power delivery network.

The signal path between two ports of the network is characterized by the channel frequency response (CFR). We refer to the CFR as the ratio, in the frequency domain, between the voltage at the output and input ports.

We introduce the following notation. We denote the complex amplitude of the source signal, the internal impedance of the transmitter, the complex amplitude of the voltage at the transmitter port, the complex amplitude of the voltage at the receiver port, and the input impedance of the receiver with

We consider the analog front-end (AFE) of the transceiver. At the transmitter side, the AFE amplifies the signal. The final amplification stage is the line driver. In this work, we do not consider the impairments related to the design of the line driver and we model it as a real voltage generator with an internal impedance

At the receiver side, the AFE processes the received signal to make it suitable for the analog-to-digital (AD) conversion. The final goal is to convert the (analog) amplitude of the received signal into a digital sample stream. Thus, the focus is on the amplitude of the received signal, rather than its power, and this motivates the formulation of the SNR in amplitude terms. Furthermore, to preserve the signal amplitude, the input impedance of the analog-to-digital converter (ADC) circuit is typically high [

At the receiver, the AFE consists of several blocks. In Figure

Block diagram of the PLC receiver AFE [

Practical receiver schemes adopt matching techniques to interface the blocks of the AFE. In wireless, where the communications are in the range of GHz, the reference impedance value is 50

In PLC, the transmission interests the frequency range below 100 MHz, where the presence of reflected waves can be tolerated to preserve the amplitude of the received signal. Therefore, the interface between the blocks can be designed in high-impedance mode.

The use of an impedance matching network (IMN) before the AFE provides some benefits. Strictly, the matching network allows the receiver to be matched to the complex and frequency-dependent impedance of the power delivery network, regardless of the input impedance of the first stage of the AFE. In the literature, the design of the matching network was aimed at obtaining the maximum transfer of power from the network [

We follow the notation of Figure

To obtain (

Now, we study the terms in (

Hence, let us focus on the noise term. In this work, we limit the study to the stationary noise components, and we explicit the PSD of the noise at the receiver port, namely,

In the next sections, we describe the noise terms in (

The active noise is generated by the power-supply circuitry of the household appliances that are connected to the power delivery network. We model the household appliances as real and independent voltage generators. We show the equivalent model in Figure

Equivalent models for the active, resistive, and receiver noise terms.

Now, we introduce the following approximations. We assume that

In Section

To be consistent with the measurement setup in [

Resistive elements introduce thermal noise [

We isolate the thermal noise due to the receiver from the contribution due to the rest of the network and we refer to it as receiver noise, namely,

We do not account for the noise contribution due to the VGA because the input impedance of the VGA is modeled as noiseless. In fact, all noise contributions due to the amplification stage are described by the noise figure of the AFE [

In Figure

From (

We now explicit the dependencies of the SNR from the impedance of the receiver. To this aim, we proceed as follows. Firstly, we formulate the CFR and the output impedance of the power delivery network as a function of the chain-matrix parameters, that is, [

where

We formulate the SNR optimization problem as follows:

Now, we focus on the denominator in (

We substitute (

Consequently, we performed the exhaustive search to identify the optimal pair

We have studied the optimal receiver impedance in real networks. To this aim, we carried out a measurement campaign in Italy and we collected more than 1200 channel responses. We considered three sites, with 11, 23, and 26 outlets, respectively. We followed an exhaustive approach. For each site, we performed measurements between all pairs of available outlets, where no loads were connected.

We performed measurements in the frequency domain. We deployed a vector network analyzer (VNA) in combination with broadband couplers and extension cables. We removed the effect of the couplers and the cables from the measures to obtain the actual scattering parameters of the PLC channel. We connected the VNA to the network through coaxial cables and broadband couplers. Couplers protect the equipment from the mains and they show an attenuation of 50 dB at the mains frequency, and lower than 5 dB up to 100 MHz.

We calibrated the VNA when only the cables were connected and we removed the effect of the couplers by exploiting the chain rule of the ABCD matrices. To this aim, we characterized the couplers in terms of ABCD matrices. The procedure proved to be the most reliable.

From the measured scattering parameters, we computed the CFR. In Figure

Measured channel frequency responses. From top to bottom, sites 1, 2, and 3. In all cases, the mean profile is also shown (dashed line).

Frequency (MHz)

Frequency (MHz)

Frequency (MHz)

From the measured scattering parameters, we also computed the output impedance. We define it as in (

Quantiles of the resistive (a) and reactive (b) component of the output impedance. Three probability values are considered, that is, 10, 50 and 90%.

Frequency (MHz)

Frequency (MHz)

The measured values of

For the analysis of the effect of the optimal impedance, we focus on the 1.5–100 MHz frequency range and the resolution of the measurements is

We carried out an exhaustive search of the optimal receiver impedance for the measured channels. We limited the search domain to

Quantiles of the resistive component of the optimal and power matched receiver impedance. Three probability values are considered, that is, 20, 50, and 80%.

Quantiles of the reactive component of the optimal and power matched receiver impedance. Three probability values are considered, that is, 20, 50, and 80%.

In Figures

Now, we study the SNR, namely,

We compute the SNR when the receiver impedance is optimal, matched in power, or constant in frequency and equal to

Best cubit fit of the SNR quantile profiles associated to the probability values

Now, we study the performance in terms of achievable rate. We assume the transmitted signal and the noise to be Gaussian, and we define the achievable rate as follows:

(a) C-CDF of the achievable rate when the receiver impedance is optimal, matched in power or constant and equal to 50

Achievable Rate (Mbps)

Improvement (%)

Now we quantify the improvement with respect to

In the previous section, we have shown the performance when the receiver impedance is optimal, matched in power or constant and equal to 50

As a final remark, we note that the optimal impedance provides the best gain in terms of achievable rate. However, it is rather complex to be implemented in practice. Therefore, more simpler though suboptimal solutions, as

We have investigated the optimal design of the receiver input impedance for the maximization of the SNR in broadband PLC. We have firstly presented a comprehensive description of the power delivery network. We have modelled the contribution of the household appliances on the noise at the receiver port. Then, we have discussed the front-end design for broadband PLC transceivers. We have pointed out that the amplitude (and not the power) of the received signal is important for data communication purposes.

Therefore, we have formulated the SNR in amplitude terms, and we have modelled the noise as the sum of four contributions, namely, the active, resistive, receiver, and coupled noise. Basically, the active noise is the noise that is injected by the household appliances, the resistive noise accounts for the thermal noise due to the resistive components of the network, the receiver noise is the thermal noise due to the receiver impedance, and the coupled noise is the noise that couples into the wirings, for example, due to broadcast radios.

We have studied the dependency of the SNR from the receiver impedance and we have highlighted the latter impacts not only on the amplitude of the useful signal, but also on the amplitude of the noise at the receiver port. Hence, we have found the optimal receiver impedance that maximizes the SNR. To this aim, we have exploited the results of an experimental measurement campaign where we have collected the scattering parameters of PLC channels in real home grids. From the measurement results, we have found that the optimal impedance is purely reactive and not equal to that obtained according to the power matching approach, namely, the matched impedance. We have compared the performance of the optimal impedance to that of the matched impedance in terms of SNR and achievable rate for real-life scenarios. We have assumed the performance of a 50-

We aim to simplify the SNR formulation in (

Now, we focus on the output impedance

We exploit (