PLC Physical Layer Link Identification with Imperfect Channel State Information
Abstract
:1. Introduction
 Full reciprocity of the measured signals can only be found in topologydependent CIR path delays.
 CIRbased solutions tend to assume perfect channel conditions and neglect the effect of impulsive noises.
 Key generation schemes are the only existing PLS mechanisms taking advantage of the path delays.
2. Related Work
 TimeDomain Solutions: In [27,28], a singlepoint reflectometry technique has been proposed for grid diagnosis in the automotive sector. The implementation uses a signal bandwidth from 300 MHz to 500 MHz, but it is intended only for short cables [29] and does not consider the impact of impulsive noise. Another technique has been proposed in [30] for low voltage (LV) topology estimations, using a signal ToA (Time of Arrival) twoway handshake. The solution requires a device at every endpoint [31], which presents a limitation of this work. In [32], a multipoint reflectometry with order statistics–constant false alarm rate (OSCFAR) detector [33] has been proposed for general topology estimation, assuming that the PLC noise follows a Gaussian distribution. In addition, it requires reflection measurements at multiple cable ends and should determine all possible graphs for each iteration, which significantly increases the algorithm complexity. The authors of [34] define a topology identification method for indoor PLC. The solution employs the ToA of signals but does not consider the effect of imperfect CSI and impulsive noise. The work in [6] introduces a onelevel CIR quantization solution for physical layer key generation, but it does not account for the negative impact of the channel estimation errors and, in some cases, might suffer from the obvious low entropy given by the infrequent changes in power line topology. In [35], a power line noisebased key generation has been proposed for pairing and authenticating IoT devices. The technique is based on contextual pairing and, therefore, has the drawback of not effectively rejecting malicious devices with access to the local power line. A singlepointreflectometrybased nonparametric method has been proposed in [36]. This technique uses the inverse Fourier transform of frequency domain (FDR) measurements for topology estimation in LV environments. As mentioned by the authors, singlepoint reflectometry systems are limited by the power line lengths, the number of branches, and the timefrequency uncertainty.
 FrequencyDomain Solutions: The authors of [6] propose a key generation technique based on the transmission matrix estimation requiring the exchange of the channel input impedance values between devices. In [37,38], the authors present different PLS key generation techniques using the channel frequency response (CFR). The assumptions of a perfect CSI and a high CFR symmetry present a limitation to these techniques. An EMIbased PLS key generation has been proposed in [39]. It is designed for systems where the devices are close enough to observe the same noise patterns. In [36,40], singlepoint reflectometry is used for LV topology estimation, and grid diagnostics. The required measurements are limited by distance, and by the number of branches due to the attenuation of signals [29]. In addition, computational complexity increases exponentially with the number of measured reflections [30,31].
 TimeFrequencyDomain Solutions: Topology estimation, PLC routing, and grid diagnosis applications are covered in [29,41] using a combination of signal arrival times but excluding the impact of impulsive noise. Singlepoint reflectometry is used in [31], where a nodebynode greedy algorithm is used for topology reconstruction and impulsive noises are used for dynamic reestimations of the topology. The authors of [42] present endtoend sensing and reflectometry algorithms to capture the topology of the power networks, as well as to monitor load changes, cable degradation, and faults. In addition to detecting and locating faults, the proposed solution classifies the anomalies between load impedance changes and local/distributed faults. A continuation of the previous work can be found in [25] with solutions employing singlepoint and multipoint reflectometry for grid diagnostics. The proposed techniques are not considering the impact of the channel estimation errors on the grid diagnostics accuracy.
3. PLC Channel Characteristics and Modeling
3.1. PLC Multipath Characteristics
3.1.1. Reciprocal Observations in PLC CIR
3.1.2. The Effect of Topology in Path Delays
 Distances between communicating nodes: An increase in the distance between the transmitter and receiver nodes is accompanied by an increment in all multipath components’ arrival time. Conversely, a decrease in the length will reduce the arrival time of the path delay impulses. Figure 3 depicts both behaviors.
 Length of branches: An increase in the length of a branch between two communicating nodes will not affect the first detectable signal’s arrival ${\tau}_{0}$. The remaining multipath components will experience a delay (extension) or an advance (shortening). The above, represented in Figure 4, will hold for the general cases, where the distance between the branch is lower than the distance between the segment.
 Number of branches: Adding or removing branches to the same node or along the power line will represent an increase or decrease, respectively, in the number of path delays as shown in Figure 5.
3.1.3. Path Delay Detection Resolution
3.2. PLC Multipath Channel Model
4. Physical Layer Identification Scheme Description
 Step 1: Consisting of a channel probing, using initial signaling and synchronization between the corresponding nodes of the considered link. In particular, by using ${N}_{{}_{Obs}}$ received signals, the relevant CIRs $\widehat{h}\left(n\right)$, $n\in \{1,..{N}_{{}_{Obs}}\}$ should be estimated. While node access control is outside the scope of this contribution, we assume that all legitimate nodes are registered and synchronized in the considered local network to accurately estimate the corresponding CIRs.
 Step 2: In this Step, the channel estimation error can be reduced by averaging the ${N}_{{}_{Obs}}$ estimated CIRs. This error minimization is crucial to offer accurate PL ID as well as to increase the received SNR, and hence to improve the data transmission quality in general.
 Step 3: A standard quantization can be used in this final Step to generate the PL ID.
Algorithm 1 PL Identification Scheme. 

5. Simulation Results and Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Processing Domain  Ref.  Technique  Applications  Environment  CSI  IN  Limitations 

Time  [27,28]  SinglePoint Reflectometry  Grid Diagnosis  Automotive  NC  NC   A highfrequency sampling is needed.  Short PL application only. 
[30]  ToAbased TwoWay Handshake  Topology Estimation  LV  NC  NC   A device at every node is required.  
[32]  MultiPoint Reflectometry and OSCFAR Detector [33]  Topology Estimation.  General  NC  NC (G)   Reflection measurements at multiple cable ends.  A high implementation complexity.  
[34]  ToA  Topology Estimation  Indoor  NC  NC   Multiple measurements are needed at each end point of the topology.  
[6]  CIRbased PLS Key Generation  PLC Security  General  Imperfect Known  C   The channel estimation error is ignored.  
[35]  PL Noisebased Key Generation  IoT Devices Pairing and Authentication.  Indoor  NC  C   The malicious devices cannot be avoided.  
[36]  SinglePoint Reflectometry  Topology Estimation  LV  Perfect Known  NC   Attenuated received signals due to long PL lengths and branching.  
Frequency  [6]  Tx Matrix Estimationbased PLS Key Generation.  PLC Security  General  Imperfect Known  C   A device at each point is needed to estimate Tx Matrix. 
[37]   CFRbased PLS Key Generation  FEXT Functionbased PLS Key Generation  PLC Security  General  Perfect Known  C   A High CFR symmetry assumption.  
[38]  CFRbased Random PLS Key Generation  PLC Security  General  Perfect Known  C   A High CFR symmetry assumption.  
[39]  EMIbased PLS Key Generation  PLC Security  Indoor  NC  C   The devices must be close to each other to observe the same noise patterns.  
[36,40]  SinglePoint Reflectometry  Topology Estimation and Grid Diagnostics  LV  Perfect Known  NC   Significant effects of the signal attenuation.  A high implementation complexity.  
TimeFreq.  [29,41]  ToA  Topology Estimation, PLC routing and Grid Diagnosis  LV  Perfect Known  NC   The impact of impulsive noise is not considered. 
[31]   SinglePoint Reflectometry  Nodebynode greedy algorithm  Topology Estimation  Indoor  perfect Known  C   The proposed technique assumes a perfect known of CSI.  
[42]   MultiPoint Reflectometry  ToA  Topology Estimation Grid Diagnostics  General  Perfect Known  NC   The impact of impulsive noise is not considered.  A significant signal attenuation impact on the result accuracy.  
[25]   SinglePoint Reflectometry  MultiPoint Reflectometry  ToA.  Grid Diagnostics  General  Imperfect Known  C   The channel estimation error is ignored. 
#  Path Type  Path Index  ${\mathit{l}}_{\mathit{i}}$  ${\mathit{g}}_{\mathit{i}}$ 

1  ABi(BAB)  $i\in [0,10]$  ${L}_{{}_{AB}}(1+2i)$  ${(1\alpha {L}_{{}_{AB}})}^{{}^{2i+1}}{(1{\rho}_{{}_{A}})}^{{}^{i}}{(1{\rho}_{{}_{B}})}^{{}^{i}}$ 
2  ACB  $i=0$  ${L}_{{}_{AB}}$  $(1\alpha {L}_{{}_{AC}})\phantom{\rule{4pt}{0ex}}(1\alpha {L}_{{}_{CB}})\phantom{\rule{4pt}{0ex}}(1{\delta}_{{}_{C}})$ 
ACACB  $i=1$  $3{L}_{{}_{AC}}+{L}_{{}_{CB}}$  ${(1\alpha {L}_{{}_{AC}})}^{{}^{3}}(1\alpha {L}_{{}_{CB}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{A}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{C}})\phantom{\rule{4pt}{0ex}}(1{\delta}_{{}_{C}})$  
ACDCB  $i=2$  ${L}_{{}_{AC}}+2{L}_{{}_{CD}}+{L}_{{}_{CB}}$  $(1\alpha {L}_{{}_{AC}})\phantom{\rule{4pt}{0ex}}{(1\alpha {L}_{{}_{CD}})}^{{}^{2}}(1\alpha {L}_{{}_{CB}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{D}})\phantom{\rule{4pt}{0ex}}{(1{\delta}_{{}_{C}})}^{{}^{2}}$  
ACACACB  $i=3$  $5{L}_{{}_{AC}}+{L}_{{}_{CB}}$  ${(1\alpha {L}_{{}_{AC}})}^{{}^{5}}\phantom{\rule{4pt}{0ex}}(1\alpha {L}_{{}_{CB}}){(1{\rho}_{{}_{A}})}^{{}^{2}}{(1{\rho}_{{}_{C}})}^{{}^{2}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}(1{\delta}_{{}_{C}})$  
ACDCACB  $i=4$  $3{L}_{{}_{AC}}+2{L}_{{}_{CD}}+{L}_{{}_{CB}}$  ${(1\alpha {L}_{{}_{AC}})}^{{}^{3}}\phantom{\rule{4pt}{0ex}}{(1\alpha {L}_{{}_{CD}})}^{{}^{2}}(1\alpha {L}_{{}_{CB}})(1{\rho}_{{}_{A}})(1{\rho}_{{}_{D}})\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}{(1{\delta}_{{}_{C}})}^{{}^{3}}$  
ACACDCB  $i=5$  $3{L}_{{}_{AC}}+2{L}_{{}_{CD}}+{L}_{{}_{CB}}$  ${(1\alpha {L}_{{}_{AC}})}^{{}^{3}}\phantom{\rule{4pt}{0ex}}{(1\alpha {L}_{{}_{CD}})}^{{}^{2}}(1\alpha {L}_{{}_{CB}})(1{\rho}_{{}_{A}})(1{\rho}_{{}_{C}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{D}})\phantom{\rule{4pt}{0ex}}{(1{\delta}_{{}_{C}})}^{{}^{2}}$  
ACBCB  $i=6$  ${L}_{{}_{AC}}+3{L}_{{}_{CB}}$  $(1\alpha {L}_{{}_{AC}})\phantom{\rule{4pt}{0ex}}{(1\alpha {L}_{{}_{CB}})}^{{}^{3}}(1{\rho}_{{}_{B}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{C}})\phantom{\rule{4pt}{0ex}}(1{\delta}_{{}_{C}})$  
ACDCDCB  $i=7$  ${L}_{{}_{AC}}+4{L}_{{}_{CD}}+{L}_{{}_{CB}}$  $(1\alpha {L}_{{}_{AC}})\phantom{\rule{4pt}{0ex}}{(1\alpha {L}_{{}_{CD}})}^{{}^{4}}(1\alpha {L}_{{}_{CB}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{C}})\phantom{\rule{4pt}{0ex}}{(1{\rho}_{{}_{D}})}^{{}^{2}}\phantom{\rule{4pt}{0ex}}{(1{\delta}_{{}_{C}})}^{{}^{2}}$  
ACACBCB  $i=8$  $3{L}_{{}_{AC}}+3{L}_{{}_{CB}}$  ${(1\alpha {L}_{{}_{AC}})}^{{}^{3}}\phantom{\rule{4pt}{0ex}}{(1\alpha {L}_{{}_{CB}})}^{{}^{3}}(1{\rho}_{{}_{A}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{B}})\phantom{\rule{4pt}{0ex}}{(1{\rho}_{{}_{C}})}^{{}^{2}}\phantom{\rule{4pt}{0ex}}(1{\delta}_{{}_{C}})$  
ACBCACB  $i=9$  $3{L}_{{}_{AC}}+3{L}_{{}_{CB}}$  ${(1\alpha {L}_{{}_{AC}})}^{{}^{3}}\phantom{\rule{4pt}{0ex}}{(1\alpha {L}_{{}_{CB}})}^{{}^{3}}(1{\rho}_{{}_{A}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{B}})\phantom{\rule{4pt}{0ex}}{(1{\delta}_{{}_{C}})}^{{}^{3}}$  
3  ACB  $i=0$  ${L}_{{}_{AB}}$  $(1\alpha {L}_{{}_{AC}})\phantom{\rule{4pt}{0ex}}(1\alpha {L}_{{}_{CB}})\phantom{\rule{4pt}{0ex}}(1{\delta}_{{}_{C}})$ 
ACACB  $i=1$  $3{L}_{{}_{AC}}+{L}_{{}_{CB}}$  ${(1\alpha {L}_{{}_{AC}})}^{{}^{3}}(1\alpha {L}_{{}_{CB}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{A}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{C}})\phantom{\rule{4pt}{0ex}}(1{\delta}_{{}_{C}})$  
ACDCB  $i=2$  ${L}_{{}_{AC}}+2{L}_{{}_{CD}}+{L}_{{}_{CB}}$  $(1\alpha {L}_{{}_{AC}})\phantom{\rule{4pt}{0ex}}{(1\alpha {L}_{{}_{CD}})}^{{}^{2}}(1\alpha {L}_{{}_{CB}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{D}})\phantom{\rule{4pt}{0ex}}{(1{\delta}_{{}_{C}})}^{{}^{2}}$  
ACACACB  $i=3$  $5{L}_{{}_{AC}}+{L}_{{}_{CB}}$  ${(1\alpha {L}_{{}_{AC}})}^{{}^{5}}\phantom{\rule{4pt}{0ex}}(1\alpha {L}_{{}_{CB}}){(1{\rho}_{{}_{A}})}^{{}^{2}}{(1{\rho}_{{}_{C}})}^{{}^{2}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}(1{\delta}_{{}_{C}})$  
ACDCACB  $i=4$  $3{L}_{{}_{AC}}+2{L}_{{}_{CD}}+{L}_{{}_{CB}}$  ${(1\alpha {L}_{{}_{AC}})}^{{}^{3}}\phantom{\rule{4pt}{0ex}}{(1\alpha {L}_{{}_{CD}})}^{{}^{2}}(1\alpha {L}_{{}_{CB}})(1{\rho}_{{}_{A}})(1{\rho}_{{}_{D}})\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}{(1{\delta}_{{}_{C}})}^{{}^{3}}$  
ACACDCB  $i=5$  $3{L}_{{}_{AC}}+2{L}_{{}_{CD}}+{L}_{{}_{CB}}$  ${(1\alpha {L}_{{}_{AC}})}^{{}^{3}}\phantom{\rule{4pt}{0ex}}{(1\alpha {L}_{{}_{CD}})}^{{}^{2}}(1\alpha {L}_{{}_{CB}})(1{\rho}_{{}_{A}})(1{\rho}_{{}_{C}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{D}})\phantom{\rule{4pt}{0ex}}{(1{\delta}_{{}_{C}})}^{{}^{2}}$  
ACBCB  $i=6$  ${L}_{{}_{AC}}+3{L}_{{}_{CB}}$  $(1\alpha {L}_{{}_{AC}})\phantom{\rule{4pt}{0ex}}{(1\alpha {L}_{{}_{CB}})}^{{}^{3}}(1{\rho}_{{}_{B}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{C}})\phantom{\rule{4pt}{0ex}}(1{\delta}_{{}_{C}})$  
ACDCDCB  $i=7$  ${L}_{{}_{AC}}+4{L}_{{}_{CD}}+{L}_{{}_{CB}}$  $(1\alpha {L}_{{}_{AC}})\phantom{\rule{4pt}{0ex}}{(1\alpha {L}_{{}_{CD}})}^{{}^{4}}(1\alpha {L}_{{}_{CB}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{C}})\phantom{\rule{4pt}{0ex}}{(1{\rho}_{{}_{D}})}^{{}^{2}}\phantom{\rule{4pt}{0ex}}{(1{\delta}_{{}_{C}})}^{{}^{2}}$  
ACACECB  $i=8$  $3{L}_{{}_{AC}}+2{L}_{{}_{CE}}+{L}_{{}_{CB}}$  ${(1\alpha {L}_{{}_{AC}})}^{{}^{3}}\phantom{\rule{4pt}{0ex}}{(1\alpha {L}_{{}_{CE}})}^{{}^{2}}(1\alpha {L}_{{}_{CB}})(1{\rho}_{{}_{A}})(1{\rho}_{{}_{C}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{E}})\phantom{\rule{4pt}{0ex}}{(1{\delta}_{{}_{C}})}^{{}^{2}}$  
ACECECB  $i=9$  ${L}_{{}_{AC}}+4{L}_{{}_{CE}}+{L}_{{}_{CB}}$  $(1\alpha {L}_{{}_{AC}})\phantom{\rule{4pt}{0ex}}{(1\alpha {L}_{{}_{CE}})}^{{}^{4}}(1\alpha {L}_{{}_{CB}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{C}})\phantom{\rule{4pt}{0ex}}{(1{\rho}_{{}_{E}})}^{{}^{2}}\phantom{\rule{4pt}{0ex}}{(1{\delta}_{{}_{C}})}^{{}^{2}}$  
4  AB  $i=0$  ${L}_{{}_{AB}}$  $(1\alpha {L}_{{}_{AB}})$ 
ABFB  $i=1$  ${L}_{{}_{AB}}+2{L}_{{}_{BF}}$  $(1\alpha {L}_{{}_{AB}})\phantom{\rule{4pt}{0ex}}{(1\alpha {L}_{{}_{BF}})}^{{}^{2}}(1{\rho}_{{}_{F}})\phantom{\rule{4pt}{0ex}}(1{\delta}_{{}_{B}})$  
ABFBFB  $i=2$  ${L}_{{}_{AB}}+4{L}_{{}_{BF}}$  $(1\alpha {L}_{{}_{AB}})\phantom{\rule{4pt}{0ex}}{(1\alpha {L}_{{}_{BF}})}^{{}^{4}}(1{\rho}_{{}_{B}})\phantom{\rule{4pt}{0ex}}{(1{\rho}_{{}_{F}})}^{{}^{2}}(1{\delta}_{{}_{B}})$  
ABFBFBFB  $i=3$  ${L}_{{}_{AB}}+6.\ast {L}_{{}_{AB}}$  $(1\alpha {L}_{{}_{AB}})\phantom{\rule{4pt}{0ex}}{(1\alpha {L}_{{}_{BF}})}^{{}^{6}}{(1{\rho}_{{}_{B}})}^{{}^{2}}\phantom{\rule{4pt}{0ex}}{(1{\rho}_{{}_{F}})}^{{}^{3}}(1{\delta}_{{}_{B}})$  
ABAB  $i=4$  $3{L}_{{}_{AB}}$  ${(1\alpha {L}_{{}_{AB}})}^{{}^{3}}(1{\rho}_{{}_{A}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{B}})$  
ABABFB  $i=5$  $3{L}_{{}_{AB}}+2{L}_{{}_{BF}}$  ${(1\alpha {L}_{{}_{AB}})}^{{}^{3}}{(1\alpha {L}_{{}_{BF}})}^{{}^{2}}(1{\rho}_{{}_{A}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{B}})\phantom{\rule{4pt}{0ex}}(1{\rho}_{{}_{F}})\phantom{\rule{4pt}{0ex}}(1{\delta}_{{}_{B}})$  
ABFBAB  $i=6$  $3{L}_{{}_{AB}}+2{L}_{{}_{BF}}$  ${(1\alpha {L}_{{}_{AB}})}^{{}^{3}}{(1\alpha {L}_{{}_{BF}})}^{{}^{2}}(1{\rho}_{{}_{A}}){(1{\rho}_{{}_{F}})}^{{}^{2}}{(1{\delta}_{{}_{B}})}^{{}^{2}}$  
ABFBABFB  $i=7$  $3{L}_{{}_{AB}}+4{L}_{{}_{BF}}$  ${(1\alpha {L}_{{}_{AB}})}^{{}^{3}}{(1\alpha {L}_{{}_{BF}})}^{{}^{4}}(1{\rho}_{{}_{A}})\phantom{\rule{4pt}{0ex}}{(1{\rho}_{{}_{F}})}^{{}^{2}}\phantom{\rule{4pt}{0ex}}{(1{\delta}_{{}_{B}})}^{{}^{3}}$  
ABABFBFB  $i=8$  $3{L}_{{}_{AB}}+4{L}_{{}_{BF}}$  ${(1\alpha {L}_{{}_{AB}})}^{{}^{3}}{(1\alpha {L}_{{}_{BF}})}^{{}^{4}}(1{\rho}_{{}_{A}})\phantom{\rule{4pt}{0ex}}{(1{\rho}_{{}_{B}})}^{{}^{2}}\phantom{\rule{4pt}{0ex}}{(1{\rho}_{{}_{F}})}^{{}^{2}}\phantom{\rule{4pt}{0ex}}(1{\delta}_{{}_{B}})$  
ABABAB  $i=9$  $5{L}_{{}_{AB}}$  ${(1\alpha {L}_{{}_{AB}})}^{{}^{5}}{(1{\rho}_{{}_{A}})}^{{}^{2}}{(1{\rho}_{{}_{B}})}^{{}^{2}}$ 
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Hernandez Fernandez, J.; Omri, A.; Di Pietro, R. PLC Physical Layer Link Identification with Imperfect Channel State Information. Energies 2022, 15, 6055. https://doi.org/10.3390/en15166055
Hernandez Fernandez J, Omri A, Di Pietro R. PLC Physical Layer Link Identification with Imperfect Channel State Information. Energies. 2022; 15(16):6055. https://doi.org/10.3390/en15166055
Chicago/Turabian StyleHernandez Fernandez, Javier, Aymen Omri, and Roberto Di Pietro. 2022. "PLC Physical Layer Link Identification with Imperfect Channel State Information" Energies 15, no. 16: 6055. https://doi.org/10.3390/en15166055