Virtual PLC Lab Enabled Physical Layer Improvement Proposals for PRIME and G3-PLC Standards

Narrowband (NB) powerline communication (PLC) is extensively adopted by utilities for the communication in advanced metering infrastructure (AMI) systems. PLC technology needs to overcome channel disturbances present in certain grid segments. This study analyzes improvement proposals of the physical layer of the main narrowband PLC technologies approved by international communication organizations that are currently deployed in Europe: Powerline Intelligent Metering Evolution (PRIME) 1.3.6, PRIME 1.4, and G3-PLC, in order to improve PLC performance under channel disturbances. This thorough study is based on simulations carried out by an innovative ad hoc Virtual PLC Lab, developed by the authors, applied in replicable, fully-automated, and cost reduced test scenarios. The analysis is performed by applying standardized test methods and metrics, and by evaluating the influence of a set of representative channel disturbances defined by the European Telecommunications Standards Institute (ETSI) and selected noises generated by distributed energy resources (DER) in normal operation. PLC performance improvements in terms of equalizer curve fitting, error correction codes, and noisy subcarrier suppression mechanisms are presented. The performance gain due to each physical improvement proposal is accurately measured and compared under the same conditions in a replicable and automated test environment in order to evaluate the use of the proposals in the evolution of future PLC technologies.


Introduction
Advanced metering infrastructure (AMI) deployments have changed the perception of the low voltage (LV) distribution grid. Smart meters scattered over the network offer LV grid visibility and accessibility. Distribution companies are now able to go one step beyond towards an advanced real-time representation, visibility, control, operation, and management of the LV network. LV narrowband (NB) powerline communication (PLC) is the most extended solution for the communication in these AMI systems [1]. Focusing on NB PLC technologies deployed in Europe, Powerline Intelligent Metering Evolution (PRIME) and G3-PLC are the most common standards [1].
The downside of this solution is that the electricity network is a complex communication channel with interferences and disturbances introduced by other devices connected to the network. In the LV grid, there is a very large variety of types and levels of disturbances in the communication channel, mainly classified by propagation channel effects, interfering noise, and non-intentional emissions. This variety, together with the high number of configurations of the communication technologies, complicates the detailed study of the effects of each types of disturbance on the different configurations.

Objectives and Scope
Focused on the improvement lines identified in [10], this research work covers two main objectives. Firstly, the aim is to define improvement proposals for the physical layers of PRIME 1.3.6 [11], PRIME 1.4 [12], and G3-PLC [13,14] technologies, trying to improve their response against disturbances present in the LV grid. Secondly, the goal is to measure and evaluate the performance enhancement of each proposed physical layer modifications following standardized test method and metrics according to European Telecommunications Standards Institute (ETSI) Technical Specification (TS) 103 909 v1.1.1 [16] and using a set of representative channel disturbances.
The work will be organized as follows: Based on the PLC performance results obtained in [10], several physical layer improvement proposals for PRIME and G3-PLC are identified in Section 3. For each physical layer parameter under test, their original status, their room for improvement and the improvement proposal will be described. Once the improvements are defined, Section 4 introduces the methodology for the performance analysis of these physical layer modification proposals. Following this methodology, unitary results of each physical layer improvement are presented and discussed in Section 5. Section 6 extracts the main highlights of the PLC physical layer improvements under test. This study concludes in Section 7 exploring possibilities for future studies.

Physical Layer Improvement Proposals for PRIME and G3-PLC
Based on the future evolutions concluded in [10], three improvement proposals are selected for the physical layer of PRIME 1.3.6 [11], PRIME 1.4 [12], and G3-PLC [13,14] technologies, trying to improve their response against the disturbances present in LV grids. Two types of improvement are studied: implementation changes within the scope of the standard, and proposals for the modification of PLC specifications. 1. PRIME implementation option: Improvement of the equalizer curve fitting. 2. PRIME modification to the standard: Reed-Solomon outer encoder as an addition to the convolutional encoder. 3.
G3-PLC implementation option and modification to the standard: Implementation of tone mapping as defined in the standard, and proposal of technical improvements beyond the standard Tone Mapping.

PRIME: Equalizer
In a real propagation environment, the in-phase and quadrature (IQ) symbols extracted from the PLC signal appear distorted, due to the frequency response of the channel. This channel response may be estimated so the receiver is able to unmake that distortion and recover the transmitted data. That is the role of the equalizer, which will estimate the channel response using the pilot subcarriers in the header of the received frames. PRIME uses intercarrier differential modulations, which make it possible to decode its frames without channel estimation. Nevertheless, the equalization is intended to help in aligning the IQ symbols before soft decoding, reducing the error probability. However, using the pilot subcarriers for estimating the channel response has two drawbacks: the pilot subcarriers are not present in all the frequencies, and these samples are also distorted by the noise in the network.
The equalizer will therefore need to extrapolate and estimate the complete channel response, based on the pilot subcarriers, which are discrete and impaired by disturbances. The channel estimation performs curve fitting, in order to estimate the parts of the channel where there is no pilot subcarrier information, and in order to smooth the effect of the noise impact in the pilot subcarriers information. The equalizer performance, its ability to represent accurately the channel response and its immunity level against noise will depend on the curve model selected for the fitting.
For the previous PRIME study published in [10], a complex polynomial curve of degree 3 was selected to model the channel frequency response. The degree 3 was selected as a compromise between curve adaptability and stability. The coefficients are extracted through Least Square curve fitting, using the response of the pilot carriers as input. Polynomial curves, especially at higher degrees, might have negative properties. Figure 1 depicts the Runge effect, where small variations in the sampling of pilot subcarriers may cause large oscillations in the curves, increasing the resultant fluctuation with the degree of the polynomial.
An alternative spline curve model will be studied for the channel estimation of the equalizer. This first identified improvement is an implementation option of the receiver, and as such, it does not modify the transmitted signal and is transparent to the PRIME standard.
Studies available regarding interpolation based on spline curves are oriented to generic orthogonal frequency division multiplexing (OFDM) systems with diverse applications [16], but no studies particularizing the usage of spline curves on narrowband PLC systems have been found.
A spline is a function defined in segments formed by pieces of polynomials. Figure 2 shows a flat channel frequency response impaired by tonal noise, so that the 25th pilot subcarrier contains distorted information. The figure shows how spline estimation keeps a transfer function more stable for frequencies farther from the tonal noise. By contrast, with a polynomial curve, the noise affects a wider set of frequencies that are located farther from the tonal noise. Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 23 An alternative spline curve model will be studied for the channel estimation of the equalizer. This first identified improvement is an implementation option of the receiver, and as such, it does not modify the transmitted signal and is transparent to the PRIME standard.
Studies available regarding interpolation based on spline curves are oriented to generic orthogonal frequency division multiplexing (OFDM) systems with diverse applications [16], but no studies particularizing the usage of spline curves on narrowband PLC systems have been found.
A spline is a function defined in segments formed by pieces of polynomials. Figure 2 shows a flat channel frequency response impaired by tonal noise, so that the 25th pilot subcarrier contains distorted information. The figure shows how spline estimation keeps a transfer function more stable for frequencies farther from the tonal noise. By contrast, with a polynomial curve, the noise affects a wider set of frequencies that are located farther from the tonal noise.  An alternative spline curve model will be studied for the channel estimation of the equalizer. This first identified improvement is an implementation option of the receiver, and as such, it does not modify the transmitted signal and is transparent to the PRIME standard.
Studies available regarding interpolation based on spline curves are oriented to generic orthogonal frequency division multiplexing (OFDM) systems with diverse applications [16], but no studies particularizing the usage of spline curves on narrowband PLC systems have been found.
A spline is a function defined in segments formed by pieces of polynomials. Figure 2 shows a flat channel frequency response impaired by tonal noise, so that the 25th pilot subcarrier contains distorted information. The figure shows how spline estimation keeps a transfer function more stable for frequencies farther from the tonal noise. By contrast, with a polynomial curve, the noise affects a wider set of frequencies that are located farther from the tonal noise.  Comparison of spline (purple) and polynomial curve fitting (yellow) channel estimation, over a flat channel frequency response (blue) whose pilot tones (red) are impaired by tonal noise. The values in the Y-axis are given in linear units and normalized to the average frequency response.

PRIME: Reed-Solomon Encoding
PRIME specification defines an optional convolutional encoder for certain modulation schemes. A previous study from the authors concluded that modulation schemes without convolutional encoder are not efficient for real field scenarios [10], an observation that is consistent with other studies [17,18].
Based on the results of [10], the use of G3-PLC Reed-Solomon outer encoder as an addition to PRIME convolutional encoder was identified as an interesting option. The Reed-Solomon error correction mechanism, as described in G3-PLC specification [13,14], will be analyzed, as a particularization of its generic definition [19]. Its normal mode of eight correctable symbols is selected, which is obtained with the introduction of 16 parity bytes.
Most PRIME hardware platforms also support G3-PLC with a firmware change. This means that the Reed-Solomon algorithm is already available without hardware modification.
Published studies oriented to G3-PLC and PRIME performance improvements mention the advantages of Reed-Solomon in G3-PLC compared to PRIME standard [8]. Nevertheless, they do not explore the possibility of adding Reed-Solomon to PRIME technology.
For this proposal, PRIME based transmitter and receiver are modified so that a Reed-Solomon encoder and decoder are introduced, as shown in Figures 3 and 4. This modification is introduced over the best PRIME implementation of the ones previously assessed, this is, including the spline curve model for the channel estimation of the equalizer described in the previous section. The convolutional decoder being used in the modems of this study and [10] are based on soft input Viterbi algorithm with Euclidean metric.

PRIME: Reed-Solomon Encoding
PRIME specification defines an optional convolutional encoder for certain modulation schemes. A previous study from the authors concluded that modulation schemes without convolutional encoder are not efficient for real field scenarios [10], an observation that is consistent with other studies [17][18].
Based on the results of [10], the use of G3-PLC Reed-Solomon outer encoder as an addition to PRIME convolutional encoder was identified as an interesting option. The Reed-Solomon error correction mechanism, as described in G3-PLC specification [13][14], will be analyzed, as a particularization of its generic definition [19]. Its normal mode of eight correctable symbols is selected, which is obtained with the introduction of 16 parity bytes.
Most PRIME hardware platforms also support G3-PLC with a firmware change. This means that the Reed-Solomon algorithm is already available without hardware modification.
Published studies oriented to G3-PLC and PRIME performance improvements mention the advantages of Reed-Solomon in G3-PLC compared to PRIME standard [8]. Nevertheless, they do not explore the possibility of adding Reed-Solomon to PRIME technology.
For this proposal, PRIME based transmitter and receiver are modified so that a Reed-Solomon encoder and decoder are introduced, as shown in Figures 3 and 4. This modification is introduced over the best PRIME implementation of the ones previously assessed, this is, including the spline curve model for the channel estimation of the equalizer described in the previous section. The convolutional decoder being used in the modems of this study and [10] are based on soft input Viterbi algorithm with Euclidean metric.

G3-PLC: Tone Map
G3-PLC technology includes in its specification [13,14] an adaptive mechanism named tone map. Based on channel estimation, the Tone Map identifies a list of subcarriers that can be affected by channel disturbances and, therefore, they will not be used to exchange data in the communication between two PLC modems.
The previous work published by the authors [10] did not implement the tone map option but highlighted the interest of analyzing its technical possibilities. This third improvement combines the study of this technique as defined in G3-PLC, with an evolution proposal that consists of redistributing the power of the unused subcarriers.
The study included in [20] evaluates the implementation limit of static subcarrier suppression or notching for G3-PLC manufacturers. However, the state of art of subcarriers suppression mechanisms does not analyze the unitary impact of the dynamic suppression tone map in G3-PLC technology.

PRIME: Reed-Solomon Encoding
PRIME specification defines an optional convolutional encoder for certain modulation schemes. A previous study from the authors concluded that modulation schemes without convolutional encoder are not efficient for real field scenarios [10], an observation that is consistent with other studies [17][18].
Based on the results of [10], the use of G3-PLC Reed-Solomon outer encoder as an addition to PRIME convolutional encoder was identified as an interesting option. The Reed-Solomon error correction mechanism, as described in G3-PLC specification [13][14], will be analyzed, as a particularization of its generic definition [19]. Its normal mode of eight correctable symbols is selected, which is obtained with the introduction of 16 parity bytes.
Most PRIME hardware platforms also support G3-PLC with a firmware change. This means that the Reed-Solomon algorithm is already available without hardware modification.
Published studies oriented to G3-PLC and PRIME performance improvements mention the advantages of Reed-Solomon in G3-PLC compared to PRIME standard [8]. Nevertheless, they do not explore the possibility of adding Reed-Solomon to PRIME technology.
For this proposal, PRIME based transmitter and receiver are modified so that a Reed-Solomon encoder and decoder are introduced, as shown in Figures 3 and 4. This modification is introduced over the best PRIME implementation of the ones previously assessed, this is, including the spline curve model for the channel estimation of the equalizer described in the previous section. The convolutional decoder being used in the modems of this study and [10] are based on soft input Viterbi algorithm with Euclidean metric.

G3-PLC: Tone Map
G3-PLC technology includes in its specification [13,14] an adaptive mechanism named tone map. Based on channel estimation, the Tone Map identifies a list of subcarriers that can be affected by channel disturbances and, therefore, they will not be used to exchange data in the communication between two PLC modems.
The previous work published by the authors [10] did not implement the tone map option but highlighted the interest of analyzing its technical possibilities. This third improvement combines the study of this technique as defined in G3-PLC, with an evolution proposal that consists of redistributing the power of the unused subcarriers.
The study included in [20] evaluates the implementation limit of static subcarrier suppression or notching for G3-PLC manufacturers. However, the state of art of subcarriers suppression mechanisms does not analyze the unitary impact of the dynamic suppression tone map in G3-PLC technology.

G3-PLC: Tone Map
G3-PLC technology includes in its specification [13,14] an adaptive mechanism named tone map. Based on channel estimation, the Tone Map identifies a list of subcarriers that can be affected by channel disturbances and, therefore, they will not be used to exchange data in the communication between two PLC modems.
The previous work published by the authors [10] did not implement the tone map option but highlighted the interest of analyzing its technical possibilities. This third improvement combines the study of this technique as defined in G3-PLC, with an evolution proposal that consists of redistributing the power of the unused subcarriers.
The study included in [20] evaluates the implementation limit of static subcarrier suppression or notching for G3-PLC manufacturers. However, the state of art of subcarriers suppression mechanisms does not analyze the unitary impact of the dynamic suppression tone map in G3-PLC technology.

Standard Tone Map
A tone map is defined as a six-bit field where each bit represents the content of a group of six subcarriers. If a bit is set to '1 , its associated group of subcarriers are active for the payload and include data. If it is set to '0 , they are inactive and a pseudo-random sequence is introduced instead Whereas the standard definition limits tone map usage to non-robust modes, this study applies this technique to all modulation schemes.
Using a tone map means that fewer payload subcarriers are used for data exchange in the payload, requiring more OFDM symbols, resulting in lower system throughput for a certain modulation scheme.
The tone map used for this research work is obtained with the automatic tone map selection algorithm integrated in the G3-PLC modems. For this tone map autodetection algorithm security thresholds are defined for the average SNR of each modulation scheme, and represented in Table 1. For each modulation scheme, this minimum SNR is checked for each of the subcarrier groups. If the average SNR of the group is higher than the defined threshold, the bit that represents that group of subcarriers will be selected as '1 , otherwise it will be '0 . This process for calculating the tone map is repeated for each available modulation scheme. The combination of the tone map and modulation scheme that has better throughput is selected. In a complete G3-PLC communication, this process would be invoked during the neighbor discovery process of the medium access control (MAC) layer.
The threshold values presented in Table 1 are between 4 and 6 dB higher than the minimum SNR required for the receiver to decode the frames in presence of AWGN noise [10]. This security margin is included in order to handle possible worse channel conditions not directly measurable by SNR, and to handle variations of the channel in time after its negotiation.

Reallocation of the Power Assigned to Inactive Tones
The specification of G3-PLC tone map defines that all the subcarriers transmit either data or a pseudo-random sequence. In this work, an alternative approach will be analyzed. P1901.2 [21] supports, for FCC and ARIB bands, the option of not introducing energy in inactive subcarriers. This nulling technique will be applied to G3-PLC CENELEC A band and will be extended reallocating that power within the rest of subcarriers. The total transmission power will be maintained constant, but the transmission power spectral density of the active carriers changes with the number of inactive subcarriers. The expected increase of the power spectral density for these subcarriers can be represented in dB as: The impact of this power reallocation is depicted in Figure 5. It represents the spectral evolution of the payload for different tone map combinations, while the total power is kept constant to 120 dBµV.

Methodology for the Performance Analysis of the Physical Layer Proposals
The methodology of this study is based on standardized procedure, test setup, and metrics. Moreover, the evaluated channel disturbances are divided into noises defined by ETSI and a selection of noises caused by distributed energy resources (DER) obtained from field trials. Additional details about the methodology can be found in a previous work from the authors [10].

Test Method and Setup Based on ETSI TS 103 909 v1.1.1 Integrated into a Virtual PLC Lab
ETSI TS 103 909 v1.1.1 [15] defines a standard and reproducible environment to determine the performance of narrowband PLC technologies under realistic channel conditions. It defines a test setup where a transmitter and receiver are connected independently, through a channel characterized by a nearly flat in-band frequency response, with controlled attenuation and additive noise sources and waveforms. This setup, described in detail in [15], is defined for a controlled alternating current (AC) mains environment, where the transmitter and receiver are connected through two isolated mains branches.
These standardized setup and environment are integrated into the Virtual PLC Lab [22], which is a fully automated, cost effective, and repeatable test environment. This is a system that replicates all the analogue elements of a PLC laboratory in digital technology. This tool runs multiple virtual PLC modems connected through a virtual digital medium with configurable characteristics, such as attenuation, noise patterns, and transfer function models. Each modem and the medium are software processes running in a computer. These processes interchange the digital representation of the PLC signals through UNIX sockets.

Standard and Controlled Channel Disturbances
The overall analysis comprises 38 disturbance input sources selected in [10] as a set of representative channel disturbances to be found in the LV distribution grid. First, the ETSI TS 103 909 v1.1.1 [15] standard defines a real-world noise collection composed of 31 waveforms, which are well defined, repeatable, and supported by the scientific community. This collection aims to represent the most challenging situations for PLC communications. Second, this set of noises is completed with a

Methodology for the Performance Analysis of the Physical Layer Proposals
The methodology of this study is based on standardized procedure, test setup, and metrics. Moreover, the evaluated channel disturbances are divided into noises defined by ETSI and a selection of noises caused by distributed energy resources (DER) obtained from field trials. Additional details about the methodology can be found in a previous work from the authors [ [15] defines a standard and reproducible environment to determine the performance of narrowband PLC technologies under realistic channel conditions. It defines a test setup where a transmitter and receiver are connected independently, through a channel characterized by a nearly flat in-band frequency response, with controlled attenuation and additive noise sources and waveforms. This setup, described in detail in [15], is defined for a controlled alternating current (AC) mains environment, where the transmitter and receiver are connected through two isolated mains branches.
These standardized setup and environment are integrated into the Virtual PLC Lab [22], which is a fully automated, cost effective, and repeatable test environment. This is a system that replicates all the analogue elements of a PLC laboratory in digital technology. This tool runs multiple virtual PLC modems connected through a virtual digital medium with configurable characteristics, such as attenuation, noise patterns, and transfer function models. Each modem and the medium are software processes running in a computer. These processes interchange the digital representation of the PLC signals through UNIX sockets.

Standard and Controlled Channel Disturbances
The overall analysis comprises 38 disturbance input sources selected in [10] as a set of representative channel disturbances to be found in the LV distribution grid. First, the ETSI TS 103 909 v1.1.1 [15] standard defines a real-world noise collection composed of 31 waveforms, which are well defined, repeatable, and supported by the scientific community. This collection aims to represent the most challenging situations for PLC communications. Second, this set of noises is completed with a selection of disturbances generated by DER, which have demonstrated to be critical noise sources for PLC [23,24]. Therefore, the complete selection of disturbances is composed of:  [26]. A compilation of these noise recordings is available in [23,27]. The six noises are identified as der04, der06, der34, der36, der50, and der51.
Furthermore, the performance under additive white Gaussian noise is evaluated to serve as a reference whose results can be compared to other kinds of noise.

PLC Performance Metrics Based on ETSI TS 103 909 v1.1.1
The test metrics used for this PLC performance study are defined by ETSI TS 103 909 V1.1.1 [15]. The usage of these metrics is thoroughly described in [10]. These metrics are given in terms of the link budget and effective data rate.
Effective packet layer data rate (DR PKT ) [15] is the number of bits delivered to the data-link layer divided by a full formatted packet cycle time. It provides a measurement of the cost of the physical mechanisms in the data rate available to upper layers.
The link budget is a measure of how much signal attenuation can be present between transmitter and receiver such that a specified level of successful message delivery is achieved. That level of successful message delivery is established as a frame error rate (FER) of 5% [15]. As described in [10], given a physical configuration of the transmitter and a specific noise pattern, the Virtual PLC Lab calculates through iterations the minimum reception power that matches the target FER, which compared with the nominal transmission power provides the link budget.
ETSI TS 103 909 V1.1.1 [15] specifies link budget metrics for each of the disturbance types defined in the document and some composite ones: • Tonal noise link budget: First, the 25 individual measured link budgets are calculated and identified as LB tonal,i for i from 1 to 25, corresponding to switching frequencies of 21 + 5·i kHz. These individually calculated link budgets are averaged. To provide added statistical weight to the most challenged result, while also considering the average, the overall tonal noise link budget is specified to be the lowest of the 25 individually measured link budgets, averaged with the previously calculated average, giving equal weight to those two figures. The unimpaired link budget averaged for the composite link budget is capped to 80 dB.
These metrics have been extended following the same approach to the non-intentional emissions selected from DER: • dernn link budget (where nn is 04, 06 34 36, 50 and 51): Each of these link budgets is defined as the link budget measured in presence of one of the der noises that gives its name. • der average link budget: Defined to be the average of the six individual link budget values of DER.
The information given by these metrics is complemented with new metrics defined as part of the research process described in [10]: • Signal to Noise Ratio (SNR) required for AWGN: The minimum SNR required in order to decode physical packets with FER lower than 5% in the presence of AWGN. Reference the metric for the analysis of the results.

Summary of Performed Simulations for G3-PLC and PRIME Technologies
PLC performance is measured with a complete implementation of physical layer modems in the Virtual PLC Lab, whose technology is certified by G3-PLC and PRIME Alliances. As such, the implementation includes realistic synchronization, frequency offset correction, and automatic gain control mechanisms. The comparison of the proposed improvements is carried out for all CENELEC-A modes available for G3-PLC and PRIME technologies and evaluated under the same circumstances. Tests are performed with 22 physical layer options configured in the Virtual PLC Lab:

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Eight options of the physical layer for G3-PLC: Four non-coherent and four coherent modes.

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Fourteen options of the physical layer for PRIME: Six modulation schemes for type A frames, which are common to PRIME 1.3.6 and 1.4 versions, and eight for type B, which is available only in PRIME 1.4 and introduces increased physical robustness.
Each of these configurations is evaluated under the 38 disturbances selected in [10], considered as a set of representative channel disturbances to be found in the LV distribution grid. For the above-mentioned configurations and for each channel disturbance, FER is evaluated per each SNR and the corresponding link budget is calculated.
For PRIME, the process is repeated twice: for the equalization improvement and Reed-Solomon improvement. Table 2 represents the different parameters used in [10] and the two additional simulation steps of this study. For G3-PLC, the process is executed three times: for tone map calculation, standard tone map testing and tone map with power reallocation evaluation. The tone map is calculated following the algorithm described in Section 3.3.1. The communication parameters are configured according to the communication limit defined by ETSI [15] (attenuation corresponding to FER 5% with tone map '111111'). The algorithm will then obtain the tone map value that improves the FER under these conditions. The different parameters used in [10] and the additional simulation steps of this study are summarized in Table 3. In summary, this study involves 52 physical configuration options in channel conditions impaired by 38 disturbances. In total, the Virtual PLC Lab has generated 1782 FER-SNR curves whose calculations involved the exchange of 848 million frames.

Results and Discussion
This section summarizes the main results obtained for each of the improvement proposals under analysis. Additionally, these results are interpreted and discussed.
Two tables per improvement are presented, showing first the absolute obtained results and then offering the incremental results that quantify the performance improvement with respect to the initial configuration of the PLC technology under study. [15]. The rows of the tables include the test metrics listed in Section 4.3. This covers disturbance sources of ETSI and DER, metrics defined by ETSI, and additional metrics defined in [10].
The columns of the tables represent the modulation schemes of the physical layer defined for each PLC technology.
In most of the analysis, if not stated otherwise, the mean results are calculated by averaging the results of the composite in-band link budget and the DER average link budget. Table 4 collects the results with the alternative spline curve model for the channel estimation of the equalizer. Table 5 represents the incremental results compared to the initial configuration with a polynomial curve published in [10].   As this proposal for PRIME equalization is an implementation option of the receiver, it does not affect the data rate of the transmitted signal. By contrast, the link budget experiences a 1.2 dB improvement.

PRIME: Equalizer
As shown in Table 5, schemes without a convolutional encoder do not improve with the proposed new equalizer. The reason is that, despite the improvement of the equalizer, any disturbance affecting the pilot subcarriers introduces errors in the payload, and with no error correction, the reception of the frames fails.
With respect to the different types of disturbance, for the noise sources with the highest tonal component (ETSI tonal noises and der04, der06), modulations with a convolutional encoder show 6.6 dB improvement in their in-band metrics. This confirms the expectations about the Spline stability described in Section 3.1. By contrast, the average increase in their in-band metrics for these modulations is 0.1 dB in the case of non-tonal noises. Therefore, the subsequent analysis of the equalizer improvement is focused on modulation schemes with convolutional encoder and for the noises with high tonal components, where the performance enhancement is noticeable.
DBPSK and DQPSK PRIME 1.4 robust modes increment 7.3 dB their link budget for high tonal noises. Similarly, the equivalent non-robust modes with convolutional encoder show a 7.2 dB increase with respect to the implementation of a polynomial equalizer. Therefore, the equalizer performance is independent from the by-4 repetition mechanism. This is because the by-4 repetition is limited to the payload, so that pilot subcarriers used as data input for the equalizer remain untouched between robust and non-robust modes.
With the spline model, the link budgets of header type B modulations improve 6.9 dB for high tonal noises with convolutional encoder, while header type A modulations improve 6.1 dB. Header type A occupies two OFDM symbols, so it has 26 IQ points for the equalization, while header type B occupies four OFDM symbols, meaning 52 IQ points for the equalizer. The higher the number of the pilot subcarriers, the better the improvement of the spline-based equalizer, although it is non-proportional to the number of pilot subcarriers available.
Some situations, like the most robust modulations with ETSI periodic impulse, have a link budget decrease of 0.4 dB. This worsening is due to the higher degree of freedom of the spline. This also happens when AWGN is used as a reference, where the required SNR also increases slightly. This is the only drawback identified for this improvement proposal. Table 6 summarizes the results introducing Reed-Solomon as an outer encoder, additional to the convolutional encoding mechanism. Table 7 represents the incremental results compared to Table 4, which gathers the performance results for PRIME including the improved spline curve model for the equalizer. This way, the absolute and incremental results offer a more accurate idea of the physical improvement under study.  The PRIME link budget values including a Reed-Solomon outer encoder are 3.5 dB higher on average than the results without Reed-Solomon. It is an improvement for all the scenarios, with the drawback of decreasing the data transfer rate and increasing complexity in the transmitter and receiver.

PRIME: Reed-Solomon Encoding
Reed-Solomon implies a 6.1 dB average increase for modulation schemes without a convolutional encoder. In this scenario, introducing any coding mechanism has its maximum improvement. This is the key reason why this evolution to the PRIME standard would be interesting.
Opposed to the peak improvement of modulation schemes without a convolutional encoder, repetition by-4 robust modes have the lowest increase (0.8 dB). Having two encoding mechanisms already, convolutional encoding with repetition code has the consequence that adding Reed-Solomon as a third robustness mechanism has little margin for improvement.
Reed-Solomon impact is independent from the header type, both type A and type B headers have an average improvement of 3.9 dB. As Reed-Solomon coding is applied to the payload only, given that the header is robust enough to be decoded, the improvement introduced by Reed-Solomon is the same for both types of header.
If analyzed from the point of view of the different disturbance types, Reed-Solomon increases the link budget against every type of noise. Noise sources with the highest tonal component accumulate 5.3 dB improvement. Noises with high tonal component, combined with modulation schemes without convolutional encoder, accumulate 9.8 dB average improvement. Narrowband noises distort fewer subcarriers, but to a higher degree, which is directly related to the Reed-Solomon error recovery mechanism. Focusing on non-tonal noises, the link budget increase goes from 1 to 3.2 dB.
The convolutional encoder and Reed-Solomon can be compared as alternative coding and error correction mechanisms. Reed-Solomon has less overhead, so it offers higher values of packet layer data rate, whereas its link budget values are worse than the values using the convolutional encoder. In order to show this, modulations with similar data rates are compared. DQPSK_CC without Reed Solomon (Table 4) has 4.2 dB higher link budget than DBPSK with Reed Solomon (Table 6). In a similar way, D8PSK_CC without Reed-Solomon (Table 4) has 2 dB higher link budget than DQPSK with Reed-Solomon ( Table 6). The most interesting scheme for this proposal is D8PSK with header Type A, with 5.7 dB link budget decrease in exchange for 43.4% increase in terms of data rate if compared to D8PSK_CC with header type A and without Reed-Solomon (see Table 4).

G3-PLC: Tone Map
The implementation of the standard tone map in G3-PLC introduces 3.4 dB of average improvement.
Link budget in presence of ETSI in-band noises increases 3.7 dB with the tone map whereas, under DER noises, it improves 3 dB. It is especially useful under narrowband tonal noises, as the tone map will not transmit data in those subcarriers affected by the noise. This way, for ETSI in-band tonal noises, it accumulates a 7 dB average increase of the link budget.
On the contrary, the most complex situations for the tone map are disturbances with a nearly flat spectrum pattern. A 0.5 dB decrease of the link budget is observed for ETSI periodic impulse noise, whose tone map is '000111 . This is because frames need to be longer to accommodate the payload and the probabilities of time impulse noises affecting the frame slightly increase.
Repetition by-4 robust modes with the tone map increase their link budget 0.6 dB, whereas non-robust modes improve 4.3 dB. It should be reminded that, by specification, the tone map is applied to non-robust modes only, i.e., the application to robust modes is for research purposes in this study. Robust modes present low improvement because the combination of the repetition mechanism with the interleaver provides high frequency diversity. Additionally, most of their errors are related to header decoding or payload alignment, where the tone map, which is applied to payload only, is not helpful.
The tone map improvement increases with the density of the modulation scheme. 8PSK differential and coherent modes have a 5.2 dB link budget increase, while BPSK modes improve 3.5 dB. The 8PSK modes have a higher SNR requirement because the distance between their constellation points is lower and, thus, lower amplitude noises have larger impact in these modulations. Consequently, the tone map technique becomes more efficient in these scenarios. Table 11 represents the absolute results applying the tone map combinations (Table 8) to G3-PLC with the proposed power reallocation. Table 12 summarizes the incremental results compared to Table 9, i.e., G3-PLC performance results with a standard tone map implementation. On average, the proposed power usage reallocation for the G3-PLC tone map introduces 1.1 dB of improvement.

Reallocation of the Power Assigned to Inactive Tones
Comparing the column about the link budget of the header and the rest of Table 11, it can be noticed that, in many of the combinations of noise types and transmission configurations, the link budget of the header is no higher than the ones including the payload. This implies that, in those situations, the limiting factor is the decoding of the header, and no improvement on the payload, like the ones proposed about the tone map, will increase the final link budget. This is the case of the robust modes. Tone map power usage reallocation for repetition by-4 robust modes increases 0.2 dB their link budget. Comparing header and ROBO modes columns in Table 11 with the absolute results of this improvement, it is observed that header decoding limits are reached. Differential modes have 1.5 dB link budget increase while coherent modes improve 0.7 dB. These values are influenced by the tone map number of '0 selections per mode and the header decoding limits. It was expected a theoretical link budget increase according to Equation (1), with an increase of the power spectral density based on the number of '0 . Nevertheless, robust modulation schemes were close to the header decoding limits, so this power usage technique does not offer the expected improvement.
The performance of this tone map implementation shows a high dependency on the different noise types. The gain of redistributing the power of inactive tones will directly depend on the number of '0 s of the tone map. ETSI periodic impulse noise and certain DER noises whose selected tone map is '000011' and '000001', where header decoding limits are not reached, have the highest link budget increase of 1.8 dB and 2.1 dB.
Another aspect to be considered is that regulated conducted emissions for electromagnetic compatibility tests to be performed to the transmitter device [28] will be more complex due to this tone map power usage reallocation. Results presented in this research process assume that all the power not used in subcarriers marked with '0 in the tone map can be reallocated in subcarriers marked with '1'. There are three emission limits to be considered:

•
Regulation limits: CENELEC regulation sets power transmission requirements for devices operating in the frequency range 3 kHz to 148.5 kHz [28]. • Technology limits: PLC amplifier and power supply design will have a limit for power transmission not to distort the signal or have thermal issues.
Focusing on CENELEC [28], it regulates in-band and out-of-band emission limits, which are tested in a laboratory setup with the help of a 50 Ω line impedance stabilization network (LISN). Figure 6 represents a hypothetical situation of a transmitter implementation whose signal spectrum for a tone map '111111' meets out-band quasi-peak emission limits [28], whereas tone map '011100' exceeds the regulation limit, and even more for tone map '010000'. This effect must be considered while designing and testing a hardware implementing this proposal, in order to be able to reallocate all the power and comply with out-of-band quasi-peak emission limits [28].

Conclusions
The simulation-based proposals analyzed in this paper for the physical layer of PRIME 1.3.6, PRIME 1.4, and G3-PLC technologies are proven to improve their response against disturbances present in the LV grid. PLC performance is enhanced with a combination of implementation improvements and modifications to the standards that could be included in future versions of PLC protocols.
Advanced metering infrastructure (AMI) deployments evolve to applications of higher complexity and innovation. PLC technologies that will enable these applications require robust testing and thorough performance analysis and evolution. The Virtual PLC Lab used in the present study has proven to be much more efficient than the conventional laboratory analog approach, saving a considerable amount of time and resources. PRIME PLC technology performance and robustness increase when the improvements under analysis are introduced. A PRIME equalizer based on the spline curve model is more stable than the original polynomial curve model when adapting to channel responses impaired by tonal noises. Reed-Solomon makes PRIME modulation schemes without a convolutional encoder usable for real field scenarios. Reed-Solomon encoding is especially interesting for D8PSK without convolutional encoding.
The G3-PLC standard tone map increases the link budget for in-band tonal noises and its benefit is higher for high-density modulation schemes. The impact of the modification to the standard tone map using power reallocation in the link budget is related to the number of '0′s in the tone map. The header robustness limit can be reached as the tone map is applied to the payload only, and CENELEC out-of-band emission levels [28] affected by the tone map with power reallocation must be considered for the hardware design of this option.

Future Work
As pointed out in [29], the smart grid is evolving in order to address the energy challenges of the society. The communication technologies will need to evolve in order to fulfill the requirements for this evolution. Therefore, more studies will be required to improve PLC technologies.
Further physical-level improvements can be studied oriented to communications robustness: using more complex coding schemes like low density parity check (LDPC) codes and turbo codes, or exploring adjustment options of OFDM parameters.

Conclusions
The simulation-based proposals analyzed in this paper for the physical layer of PRIME 1.3.6, PRIME 1.4, and G3-PLC technologies are proven to improve their response against disturbances present in the LV grid. PLC performance is enhanced with a combination of implementation improvements and modifications to the standards that could be included in future versions of PLC protocols.
Advanced metering infrastructure (AMI) deployments evolve to applications of higher complexity and innovation. PLC technologies that will enable these applications require robust testing and thorough performance analysis and evolution. The Virtual PLC Lab used in the present study has proven to be much more efficient than the conventional laboratory analog approach, saving a considerable amount of time and resources. PRIME PLC technology performance and robustness increase when the improvements under analysis are introduced. A PRIME equalizer based on the spline curve model is more stable than the original polynomial curve model when adapting to channel responses impaired by tonal noises. Reed-Solomon makes PRIME modulation schemes without a convolutional encoder usable for real field scenarios. Reed-Solomon encoding is especially interesting for D8PSK without convolutional encoding.
The G3-PLC standard tone map increases the link budget for in-band tonal noises and its benefit is higher for high-density modulation schemes. The impact of the modification to the standard tone map using power reallocation in the link budget is related to the number of '0 s in the tone map. The header robustness limit can be reached as the tone map is applied to the payload only, and CENELEC out-of-band emission levels [28] affected by the tone map with power reallocation must be considered for the hardware design of this option.

Future Work
As pointed out in [29], the smart grid is evolving in order to address the energy challenges of the society. The communication technologies will need to evolve in order to fulfill the requirements for this evolution. Therefore, more studies will be required to improve PLC technologies.
Further physical-level improvements can be studied oriented to communications robustness: using more complex coding schemes like low density parity check (LDPC) codes and turbo codes, or exploring adjustment options of OFDM parameters. Improvements at higher levels can be studied. MAC layer mechanisms could be evolved improving the medium access algorithms or dynamic routing. Additionally, application layer bandwidth usage could be reduced, making the communication more robust.
Broadband powerline (BPL) communications technologies were originally designed for in-home communications. Adapting them in order to fulfill the smart grid requirements could provide increased throughput and reduced latency, in comparison with NB-PLC technologies. This could open the possibility for new applications beyond metering.