Performance Evaluation of Power-Line Communication Systems for LIN-Bus Based Data Transmission

electronics

Article Performance Evaluation of Power-Line Communication Systems for LIN-Bus Based Data Transmission

Martin Brandl * and Karlheinz Kellner

Department of Integrated Sensor Systems, Danube University, 3500 Krems, Austria; [email protected] * Correspondence: [email protected]; Tel.: +43-2732-893-2790

Abstract: Powerline communication (PLC) is a versatile method that uses existing infrastructure such as power cables for data transmission. This makes PLC an alternative and cost-effective technology for the transmission of sensor and actuator data by making dual use of the power line and avoiding the need for other communication solutions; such as wireless radio frequency communication. A PLC modem using DSSS (direct sequence spread spectrum) for reliable LIN-bus based data transmission has been developed for automotive applications. Due to the almost complete system implementation in a low power microcontroller; the component cost could be radically reduced which is a necessary requirement for automotive applications. For performance evaluation the DSSS modem was compared to two commercial PLC systems. The DSSS and one of the commercial PLC systems were designed as a direct conversion receiver; the other commercial module uses a superheterodyne architecture. The performance of the systems was tested under the inﬂuence of narrowband interference and additive Gaussian noise added to the transmission channel. It was found that the performance of the DSSS modem against singleton interference is better than that of commercial PLC transceivers by at least the processing gain. The performance of the DSSS modem was at least 6 dB better than the other modules tested under the inﬂuence of the additive white

Gaussian noise on the transmission channel at data rates of 19.2 kB/s.

Citation: Brandl, M.; Kellner, K. Keywords: power line communication; local interconnect network (LIN); direct sequence spread Performance Evaluation of spectrum; automotive sensor network Power-Line Communication Systems for LIN-Bus Based Data Transmission. Electronics 2021, 10, 85. https://doi. org/10.3390/electronics10010085 1. Introduction Power line communication (PLC) is a versatile method using existing infrastructure Received: 30 November 2020 like power cables for data transmission. This makes PLC an alternative and cost-efficient Accepted: 28 December 2020 technology by the dual use of the powerline to other communication solutions like wire- Published: 4 January 2021 less radio frequency communication. The PLC modems can be installed plug and play on the existing power infrastructure without the need for other costly installation proce- Publisher’s Note: MDPI stays neu- dures. Typically the rooms on each floor and beyond are linked by the same power line tral with regard to jurisdictional clai- infrastructure which can be used easily for PLC. However, the PLC transmission channel ms in published maps and institutional affiliations. is a very rough environment and need special attention to the design of the PLC [1–3]. PLC technology is a good alternative to wireless communication and is intended for use such as home automation, smart grid, city automation and cyber-physical systems as well as long-range communication. Another approaching field for PLC systems is given by Copyright: © 2021 by the authors. Li- the application in vehicular-, ship-, and aircraft- technology [4–14]. censee MDPI, Basel, Switzerland. Especially in vehicular technology CAN (Controller Area Network, ISO 11898) and LIN This article is an open access article (Local Interconnect Network, ISO 17987 [15,16]) buses are used for communication links distributed under the terms and con- between different components. The CAN bus offers data rates up to 1 Mbit/s (high speed ditions of the Creative Commons At- CAN) and the hard wiring between the CAN transceivers allows a lossless bitwise arbitra- tribution (CC BY) license (https:// tion method which makes CAN suitable as a real-time prioritized communication system. creativecommons.org/licenses/by/ This procedure also provides a hierarchy of messages among each other. The message with 4.0/).

Electronics 2021, 10, 85. https://doi.org/10.3390/electronics10010085 https://www.mdpi.com/journal/electronics Electronics 2021, 10, x FOR PEER REVIEW 2 of 18

arbitration method which makes CAN suitable as a real‐time prioritized communication system. This procedure also provides a hierarchy of messages among each other. The Electronics 2021, 10, 85 2 of 18 message with the lowest identifier may always be transmitted. For the transmission of time‐critical messages, a high‐priority identifier can be assigned in order to give the messagethe lowest priority identifier during may transmission. always be transmitted. In vehicular For technology the transmission LIN buses of time-critical are typical used mes- forsages, low a‐speed high-priority and low identifier priority can communication be assigned in between order to givesub‐systems. the message For priority cost‐sensitive during andtransmission. low speed In applications vehicular technology mainly the LIN LIN buses bus are is used typical in used automotive for low-speed applications. and low The pri- LINority bus communication serves as a sub between‐bus for sub-systems. cost‐effective For networking cost-sensitive of control and low devices speed in applications cars. LIN is usedmainly for the simple LIN sensor bus is usedand actuator in automotive applications applications. where the The CAN LIN busbus serves was not as an a sub-bus option forfor this cost-effective cost‐sensitive networking area, as ofthe control bandwidth devices and in versatility cars. LIN are is used not required for simple and sensor the costsand actuatorfor networking applications with wherethis bus the are CAN too bushigh. was Up not to an16 optionbus subscribers for this cost-sensitive can be net‐ workedarea, as in the a bandwidthLIN cluster, and with versatility a maximum are notdata required rate of 20 and kbit/s. the costs The forLIN networking bus is typically with usedthis busfor non are‐ toocritical high. safety Up to components 16 bus subscribers and sensors/actuators can be networked in cars in where a LIN cluster,the applica with‐ tiona maximum area includes data comfort rate of 20 functions, kbit/s. The such LIN as window bus is typically regulators, used central for non-critical locking, electric safety mirrorcomponents adjustment, and sensors/actuators electric seat adjustment, in cars whererain sensor, the application light sensor, area electric includes sunroof, comfort or airfunctions, conditioning such ascontrol window etc. regulators, central locking, electric mirror adjustment, electric seat adjustment, rain sensor, light sensor, electric sunroof, or air conditioning control etc. The LIN‐Bus The LIN-Bus With the demand for a cost‐effective communication system for use in the sen‐ sor/actuatorWith the area, demand LIN found for a cost-effectiveits way into communicationthe vehicle as a system so‐called for “sub use‐ inbus”. the LIN sen- communicationsor/actuator area, was LIN very found simple its and way does into not the require vehicle a as communication a so-called “sub-bus”. controller LIN or crystalcommunication oscillator wasfor synchronization. very simple and doesThe data not require transmission a communication takes place controller via a single or crys-line (singletal oscillator wire). for In synchronization.order to meet the The interference data transmission immunity takes requirements place via a typical single line for (singlemotor vehicles,wire). In the order transmission to meet the interferencelevels correspond immunity to the requirements battery voltage typical but for with motor slew vehicles, rates µ belowthe transmission 2 V/μs therefore levels correspond limiting the to thesymbol battery transmission voltage but withrate slewto 20 rates kbit/s. below The 2 V/mas‐s tertherefore‐slave architecture limiting the symbolmakes LIN transmission communication rate to 20 deterministic. kbit/s. The master-slave A master controls architecture the entiremakes communication LIN communication in a LIN deterministic. cluster on the A masterbasis of controls a well‐defined the entire time communication table (Figure 1). in Onea LIN LIN cluster frame on consists the basis of of the a well-defined two parts header time table and response. (Figure1). The One header LIN frame is always consists sent of the two parts header and response. The header is always sent by the LIN master, while by the LIN master, while the response is sent by either one dedicated LIN slave or the the response is sent by either one dedicated LIN slave or the LIN master itself. A LIN LIN master itself. A LIN slave addressed by the message responds with a frame which slave addressed by the message responds with a frame which can consist of up to eight can consist of up to eight data bytes. Due to the six‐bit wide identifier up to 64 LIN mes‐ data bytes. Due to the six-bit wide identifier up to 64 LIN messages can be specified. sages can be specified. In contrast to CAN, LIN is a centrally controlled message distri‐ In contrast to CAN, LIN is a centrally controlled message distribution system. A LIN bution system. A LIN message always begins with the so‐called “break‐field”. This helps message always begins with the so-called “break-field”. This helps all LIN slaves to syn- all LIN slaves to synchronize and is used to activate all attached LIN slaves to listen to the chronize and is used to activate all attached LIN slaves to listen to the following parts of following parts of the header. The “break‐field” command consists of one start bit and the header. The “break-field” command consists of one start bit and several dominant several dominant bits with a length of at least 11‐bit times. Data integrity is checked using bits with a length of at least 11-bit times. Data integrity is checked using parity bits in parity bits in the message header and a checksum transmitted in the message response. In the message header and a checksum transmitted in the message response. In this study thiswe focusedstudy we on focused the replacement on the replacement of the LIN busof the by LIN PLC bus systems by PLC for vehicularsystems for applications. vehicular applications.Especially for Especially low speed for and low low speed priority and buslow systemspriority likebus thesystems LIN bus,like the PLC LIN modems bus, PLC can modemsreplace the can wired replace interconnections the wired interconnections between the sub-systems.between the sub‐systems.

FigureFigure 1. 1. LINLIN schedule. schedule.

A further advantage is that the wiring of additional components or device upgrades is much easier, since only the power line and no additional LIN bus cables are required for

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A further advantage is that the wiring of additional components or device upgrades is much easier, since only the power line and no additional LIN bus cables are required for data communication. After power connection of the new component, it logs on via the PLC at the master unit and immediately becomes part of the LIN network.

2. Performance of PLC Systems for LIN Data Transmission

Electronics 2021, 10, 85 The goal of our development was to design a robust communication system for au3‐ of 18 tomotive applications and to radically reduce component costs to less than 1 Euro. For applications in the automotive industry, the cost of the components is of high importance anddata can communication.be kept very low After by almost power connectioncomplete system of the newimplementation component, itin logs a low on‐ viacost the mi PLC‐ crocontroller.at the master Direct unit sequence and immediately spread spectrum becomes part(DSSS) of theis a LIN promising network. technology for in‐ terference‐resistant PLC data transmission, and because of its low computational power requirements,2. Performance it can of be PLC easily Systems implemented for LIN Data in a Transmissionlow‐performance microcontroller. For evaluationThe of goal our ofcost our optimized development DSSS wasPLC tosystem design (Figure a robust 2c), communicationit was compared system to two for commercialautomotive PLC applications modules #1 and and to #2 radically (Figure 2a,b) reduce which component are dedicated costs to for less automotive than 1 Euro. use.For The applications modules were in theanalyzed automotive regarding industry, their sensitivity the cost of to the single components‐tone interferers is of high and im- additiveportance white and Gaussian can be kept noise very (AWGN) low by almoston the completetransmission system channel, implementation as well as incom a low-‐ paredcost with microcontroller. theoretical results. Direct sequenceClassical spreadPLC modules spectrum which (DSSS) are is used a promising for low‐ technologyvoltage householdfor interference-resistant networks (e.g., Homeplug PLC data‐ transmission,Standard IEEE and‐1901) because were ofnot its used low computationalwithin this studypower because requirements, they are not it canqualified be easily for implementedautomotive applications. in a low-performance microcontroller. ForDSSS evaluation is a well of‐known our cost and optimized established DSSS data PLC systemtransmission (Figure method2c), it was for compared robust trans to two‐ missioncommercial over distorted PLC modules channels #1 and and is #2 often (Figure used2 a,b)because which of its are easy dedicated implementation for automotive [17–24]. use. In spreadThe modules spectrum were technology, analyzed regarding the signal their to be sensitivity transmitted to single-toneis spread over interferers a wide andfre‐ ad- quencyditive range, white with Gaussian spreading noise being (AWGN) achieved on the by transmissionmodulating the channel, carrier as frequency well as compared with a pseudostatisticalwith theoretical spreading results. Classical code. During PLC modules spreading, which the arebits used of the for user low-voltage data are householdspread withnetworks the spreading (e.g., Homeplug-Standard sequence. IEEE-1901) were not used within this study because they are not qualiﬁed for automotive applications.

(a) (b)

(c)

FigureFigure 2. (a 2.,b)( aEvaluation,b) Evaluation boards boards of the of commercial the commercial PLC PLCmodules modules #1 and #1 #2; and (c) #2; board (c) board of the of the self- self‐designeddesigned DSSS DSSS modem. modem.

DSSS is a well-known and established data transmission method for robust transmission over distorted channels and is often used because of its easy implementation [17–24]. In spread spectrum technology, the signal to be transmitted is spread over a wide frequency range, with spreading being achieved by modulating the carrier frequency with a pseu- dostatistical spreading code. During spreading, the bits of the user data are spread with the spreading sequence. This spreading results in a high-bit-rate code sequence, which is called a chip sequence to distinguish it from the bit sequence. The “chips” represent the smallest spread information units. The chip rate depends on the spreading factor which corresponds to the quotient of the chip rate to the bit rate. The wider the spread, the less susceptible the transmission is Electronics 2021, 10, x FOR PEER REVIEW 4 of 18

This spreading results in a high‐bit‐rate code sequence, which is called a chip se‐ quence to distinguish it from the bit sequence. The “chips” represent the smallest spread information units. The chip rate depends on the spreading factor which corresponds to Electronics 2021 10 , , 85 the quotient of the chip rate to the bit rate. The wider the spread, the less susceptible4 the of 18 transmission is to interference from other signals. At the same time, spreading provides a certain degree of protection against unauthorized eavesdropping. to interference from other signals. At the same time, spreading provides a certain degree of protectionAll modules against operate unauthorized with carrier eavesdropping. modulation, where the carrier frequency is ad‐ justableAll within modules a certain operate range. with carrierThe carrier modulation, frequency where of the the DSSS carrier modem frequency is free is adjustable adjusta‐ blewithin but typically a certain set range. to 8 TheMHz carrier and depend frequency on ofthe the clock DSSS‐oscillator modem crystal is free adjustablefrequency but(fcarrier typ- = fcrystal/4). Both commercial modules can operate on different carrier frequencies in the ically set to 8 MHz and depend on the clock-oscillator crystal frequency (fcarrier = fcrystal/4). rangeBoth from commercial 1.75 MHz modules to 13 MHz can operate in coarse on steps different (module carrier #1) frequencies and from 5 inMHz the to range 30 MHz from with1.75 MHza spacing to 13 of MHz 100 in kHz coarse for stepsmodule (module #2. All #1) modems and from are 5 MHz able toto 30transfer MHz with the LIN a spacing bus specificof 100 kHzdata for rate module of 19.2 #2. kbit/s. All modemsIn our DSSS are able system to transfer an N = the7 bit LIN Barker bus specificcode is dataused rate as spreadingof 19.2 kbit/s. function In our which DSSS is systemmodulo an 2 Nadded= 7 bit to Barkerthe binary code data is used sequence as spreading where N function is the lengthwhich of is modulothe sequence. 2 added Each to the data binary bit is data spread sequence by a full where 7 bitN Barkeris the length sequence of the and sequence. there‐ foreEach the data chip bit duration is spread T byc is aT fullb/N of 7 bit the Barker bit duration sequence Tb (Figure and therefore 3a). An the overview chip duration about Tthec is proposedTb/N of theDSSS bit modem duration andTb first(Figure results3a). Anwere overview also given about [25]. the The proposed used Barker DSSS code modem has anand optimal first results autocorrelation were also given function [25]. which The used means Barker that code the hasautocorrelation an optimal autocorrelation peak has an amplitudefunction which of N and means the that sidelobes the autocorrelation are no larger peak than has 1 (Figure an amplitude 3b) [26]. of NAnand important the side- performancelobes are no largerparameter than of 1 (Figure spread3 b)spectrum [ 26]. An systems important is the performance processing parameter gain PG which of spread is definedspectrum as systemsthe ratio is theof the processing signal bandwidth gain PG which Bs on is definedthe transmission as the ratio channel of the signalafter spreadingbandwidth inB srelationon the transmissionto the message channel signal after bandwidth spreading B inm defined relation toby the the message symbol signal rate Equationbandwidth (1).B m defined by the symbol rate Equation (1).

´1´ ´0´ ´1´

Tb Tc

(a) (b)

FigureFigure 3. 3. (a(a) )Generation Generation of of a a DS DS spread spread spectrum spectrum signal signal (dashed (dashed line: line: data data bits, bits, full full line: line: spreading spreading function function modulo modulo 2 2 addedadded to to the the data data sequence); sequence); (b (b) )autocorrelation autocorrelation function function of of an an NN == 7 7 bit bit Barker Barker code. code.

IfIf BPSK BPSK modulation modulation is is used, used, the the processing processing gain gain for for the the proposed proposed barker barker code code with with lengthlength NN == 7 7is is PGPG = =7 7or or 8.5 8.5 dB: dB:

Bs 𝐵 Tb𝑇 R𝑅c PG =𝑃𝐺 = = =N7→8.5N = 7 → 8.5 dB dB (1) (1) Bm 𝐵 Tc 𝑇 R𝑅b AA simplified simpliﬁed block block structure structure of of the the DSSS DSSS transceiver transceiver is is given given in in Figure Figure 4a.4a. The The LIN busbus data data stream stream with with a data a data rate rate of R ofb =R 19.2b = 19.2kB/s kB/sis modulo is modulo 2 added 2 addedto the N to = the 7 BarkerN = 7 code.Barker This code. means This that means the clock that therate clock of the rate Barker of the code Barker generator code generatoris RC = N∙R isb. RForC = trans N·R‐b. missionFor transmission over the powerline over the powerline the spread the message spread signal message is DE signal‐BPSK is DE-BPSK(differential (differential encoded binaryencoded phase binary‐shift phase-shift keying) [27] keying) modulated [27] modulatedon an 8 MHz on carrier an 8 MHz by a balanced carrier by modulator. a balanced Incoherentmodulator. detection, Incoherent the detection, receiver the obtains receiver its obtains demodulation its demodulation frequency frequency and phase and refer phase‐ encesreferences using usinga carrier a carrier synchronization synchronization loop. loop.

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(a)

(b)

Figure 4. (a) Block diagram of the proposed DSSS transceiver; (b) detailed structure of the DE-BPSK Figure 4. (a) Block diagram of the proposed DSSS transceiver; (b) detailed structure of the DE‐receiver.BPSK receiver. Such synchronization circuits can lead to a phase ambiguity in the detected phase, Such synchronization circuits can lead to a phase ambiguity in the detected phase, which can lead to wrong decisions in the demodulated bits. For example, the Costas loop which can lead to wrong decisions in the demodulated bits. For example, the Costas loop has a phase ambiguity of integer multiples of pi-radians at the locking points. As a result, has a phase ambiguity of integer multiples of pi‐radians at the locking points. As a result, carrier recovery may lock into pi-radians out of phase, resulting in a situation where all carrier recovery may lock into pi‐radians out of phase, resulting in a situation where all detected bits are completely inverted compared to the bits at perfect carrier synchronization. detected bits are completely inverted compared to the bits at perfect carrier synchroni‐ Phase ambiguity can be efﬁciently addressed by applying differential coding at the input of zation. Phase ambiguity can be efficiently addressed by applying differential coding at the BPSK modulator and by performing differential decoding at the output of the coherent thedemodulator input of the atBPSK the receivermodulator side and (Figure by performing4b). Via capacitive differential coupling decoding the modulated at the output signal of theis fed coherent onto the demodulator power line. at In the the receiver receiver, side the despreading(Figure 4b). Via is performed capacitive by coupling synchronous the modulatedmultiplication signal of is the fed received onto the signal power with line. a replica In the of receiver, the Barker the code despreading sequence asis usedper‐ in formedthe transmitter. by synchronous After multiplication despreading the of the bandpass received signal signal is with transferred a replica into of thethe basebandBarker codeby sequence synchronous as used demodulation. in the transmitter. The carrier After frequency despreading synchronization the bandpass and the signal time is syn- transferredchronization into of the the baseband despreading by codesynchronous generator demodulation. are done by carrier/code The carrier tracking frequency loops. synchronizationAs noted previously, and the one time of the synchronization advantages of spreadof the spectrumdespreading is the code ability generator to reject are inter- doneferences by carrier/code which is very tracking useful loops. especially As innoted a heavy previously, electromagnetic one of pollutedthe advantages environment of spreadlike automotivespectrum is applications.the ability to reject If the interferences interference iswhich within is very the passband useful especially of the receiver in a heavyinput electromagnetic ﬁlter, the jammer polluted will be environment spread by the like Barker automotive code sequence applications. to the If bandwidth the inter‐ Bs ferenceof the is spreading within the function. passband Therefore of the receiver the power input of filter, the interfering the jammer signal will PbeJ is spread reduced by by

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Electronics 2021, 10, 85 the Barker code sequence to the bandwidth Bs of the spreading function. Therefore6 the of 18 power of the interfering signal PJ is reduced by an amount called the bandwidth expan‐ sion factor Bs/Bm which is equal to the processing gain PG [28]. The total power J0 of the interferencean amount calledat the output the bandwidth of the receiver expansion is: factor Bs/Bm which is equal to the processing gain PG [28]. The total power J0 of the interference at the output of the receiver is: 𝐵 𝑃 𝐽 𝑃 (2) B𝐵s 𝑃𝐺PJ J0 = PJ = (2) Bm PG The reduction of interference power by the processing gain PG is one of the main advantagesThe reduction using spread of interference spectrum powertransmission by the systems processing in interference gain PG is one polluted of the envi main‐ ronmentsadvantages like using automotive spread spectrumapplications. transmission systems in interference polluted environments like automotive applications. 3. Test Setup and Results 3. Test Setup and Results TheThe test test setup setup for for characterizing characterizing the the robustness robustness of of the the different different transceivers transceivers against against singlesingle-tone‐tone interference interference and and AWGN AWGN on on the the transmission transmission channel channel is is shown shown in in Figure Figure 55..

FigureFigure 5. 5. TestTest setup setup for for all all transceivers. transceivers.

TheThe transmission transmission channelchannel was was realized realized by by a switchable a switchable resistive resistive damping damping circuit circuit where different attenuation factors can be adjusted for varying the signal to interference ratio where different attenuation factors can be adjusted for varying the signal to interference (SIR) and the signal to noise ratio (SNR) on the receiver input. For electrical decoupling ratio (SIR) and the signal to noise ratio (SNR) on the receiver input. For electrical decou‐ and avoidance of crosstalk between the transmitter and the receiver separated power pling and avoidance of crosstalk between the transmitter and the receiver separated supplies and optocouplers are used. Predeﬁned LIN-packets are delivered from a LIN- power supplies and optocouplers are used. Predefined LIN‐packets are delivered from a packet generator. LIN‐packet generator. The transmitted LIN-packets are designed to enable an asynchronous data trans- The transmitted LIN‐packets are designed to enable an asynchronous data trans‐ mission and packet error detection by transmitting an incrementing counter value in mission and packet error detection by transmitting an incrementing counter value in the the payload and a checksum byte (Figure6) A LIN-packet error was detected if a counter payload and a checksum byte (Figure 6) A LIN‐packet error was detected if a counter error between two subsequent received packets or a CRC error occurs. LIN-packets were error between two subsequent received packets or a CRC error occurs. LIN‐packets were transmitted every 10 ms with data rate of Rb = 19.2 kB/s. The LIN-packet error rate (PER) transmitted every 10 ms with data rate of Rb = 19.2 kB/s. The LIN‐packet error rate (PER) was calculated from the number of faulty or missing packets output by the receiver to wasthe calculated number of from packets the sent. number of faulty or missing packets output by the receiver to the number of packets sent

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BR: Break signal (minimum 13‐bit low)

Byte 0: Sync message 0x55 h

Byte 1: LIN Protected Identifier 0x08 h

Byte 2..5: Data Byte 0..3 = 32‐bit; packet counter

Byte 6..9: Data Byte 4..7 = 32‐bit; copy of the packet counter

C: LIN checksum byte. For each transmitted byte (B0C) one start of the byte and two end of the byte bits are used (LIN compliance)

FigureFigure 6. 6.ConfigurationConﬁguration and and waveform waveform of ofthe the transmitted transmitted LIN LIN-packets.‐packets.

3.1. Sensitivity to Single‐Tone Interference 3.1. Sensitivity to Single-Tone Interference The PLC data communication in industrial or automotive environments is fre‐ quentlyThe corrupted PLC data by communication interferences based in industrial on harmonics or automotive from, e.g., environments switched power is frequently sup‐ pliescorrupted and other by interferenceselectronic components based on coupling harmonics high from,‐frequency e.g., switched radiation power into suppliespower lines.and To other investigate electronic the components influence of coupling narrowband high-frequency interference radiation on the into quality power of lines.LIN data To investigate the influence of narrowband interference on the quality of LIN data transmission, transmission, a sinusoidal interference signal was superimposed on the PLC signal on the a sinusoidal interference signal was superimposed on the PLC signal on the transmis- transmission channel. A sine wave generated by a function generator (33250A, Keysight, sion channel. A sine wave generated by a function generator (33250A, Keysight, Santa Santa Rosa, CA, USA) was coupled to the transmission line and swept over a frequency Rosa, CA, USA) was coupled to the transmission line and swept over a frequency band band Δf = ±200 kHz around the PLC carrier center frequency. The SIR was calculated ∆f = ±200 kHz around the PLC carrier center frequency. The SIR was calculated from from the RMS amplitude of the PLC signal and the RMS amplitude of the interferer on the RMS amplitude of the PLC signal and the RMS amplitude of the interferer on the trans- the transmission channel. Depending on the design of the PLC transceivers, the sensitiv‐ mission channel. Depending on the design of the PLC transceivers, the sensitivity to ity to interference depends on the absolute amplitude of the received PLC signal which interference depends on the absolute amplitude of the received PLC signal which can be can be caused by amplifier saturation, amplifier slew rate, etc. caused by amplifier saturation, amplifier slew rate, etc. The SIR was also measured in dependency of the PLC signal attenuation over the The SIR was also measured in dependency of the PLC signal attenuation over the trans- transmissionmission channel. channel. All All PLC PLC modules modules show show a threshold a threshold sensitivity sensitivity in PER in PERto the to amplitude the am‐ plitudeof the of single-tone the single‐ interferertone interferer where where the PER therises PER inrises a very in a closevery close interval interval from from low values low valuesto 1 (Figure to 1 (Figure7). The 7). differences The differences of the of evaluated the evaluated PLC modulesPLC modules in interference in interference sensitivity sen‐ sitivityare mainly are mainly based based on the on used the filtersused filters for interference for interference rejection rejection and the and spreading the spreading gain for gainDSSS for systems. DSSS systems. In the DSSSIn the module DSSS module a 2nd-order a 2nd LC‐order bandpass LC bandpass (BP) filter (BP) at the filter PLC at center the PLCfrequency center frequency is used in front is used of the in receiverfront of and the areceiver 10 kHz 2nd-orderand a 10 activekHz 2nd lowpass‐order (LP) active filter lowpassbuilds (LP) a signal filter matched builds a filtersignal in matched front of filter the ADC in front [25 ].of Module the ADC #1 [25]. and Module module #1 #2 and PLC moduletransceivers #2 PLC are transceivers using commercial are using high-Q commercial ceramic BP-filters high‐Q where ceramic module BP‐filters #1 is operating where

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Electronics 2021, 10, 85 8 of 18 module #1 is operating with a 6.5 MHz ± 80 kHz frontend BP‐filter (#773–0065, Oscilent Corporation, Irvine, CA, USA) and module #2 with a 10.7 MHZ ± 165 kHz IF‐filter with a 6.5 MHz ± 80 kHz frontend BP-filter (#773–0065, Oscilent Corporation, Irvine, (#762‐0107‐A20, Oscilent Corporation, Irvine, CA, USA) in the standard configuration, CA, USA) and module #2 with a 10.7 MHZ ± 165 kHz IF-filter (#762-0107-A20, Oscilent respectively. Module #2 is an evolution of module #1 and uses instead of a direct con‐ Corporation, Irvine, CA, USA) in the standard configuration, respectively. Module #2 is version receiver which needs for each adjusted PLC center frequency a different ceramic an evolution of module #1 and uses instead of a direct conversion receiver which needs for frontend filter, a superhet receiver with a fixed intermediate frequency (IF) at 10.7 MHz each adjusted PLC center frequency a different ceramic frontend filter, a superhet receiver with the advantage that the PLC carrier frequency can be adjusted independently of the with a fixed intermediate frequency (IF) at 10.7 MHz with the advantage that the PLC filter center frequency. carrier frequency can be adjusted independently of the filter center frequency.

Figure 7. Sensitivity of thethe packetpacket errorerror rate rate ( (PERPER)) to to the the SIR, SIR, which which shows shows a a distinct distinct threshold threshold effect ef‐ fect for all different transceivers. for all different transceivers.

In Figure 88,, thethe SIR threshold level, level, where where no no further further data data transmission transmission was was possible possible(PER (PER = 1),= of 1), the of different the different PLC PLC modules modules against against single single-tone‐tone interference interference is depicted. is depicted. The Thesingle single-tone‐tone interferer interferer was was a sine a sine wave wave generated generated by by a afunction function generator generator at differentdifferent carrier interferer frequency offsets to thethe transmissiontransmission center frequency Δ∆f == ffcarrier − −f finterferer andand a SIR a SIRad‐ adjustedjusted by by different different channel channel attenuations attenuations of of the the PLC PLC signal. signal. Theoretically, Theoretically, the robustness of a DSSSDSSS systemsystem againstagainst single-tonesingle‐tone interference must be byby thethe process-gainprocess‐gain PGPG betterbetter than thatthat of a conventional receiver.receiver.

Figure 8.8. Sensitivity toto single single tone tone interference interference with with a frequencya frequency offset offset∆f Δtof theto the PLC PLC carrier carrier frequency. fre‐ quency. As expected, the DSSS module had an on average 7 dB better SIR performance (SIRaverage ± 80 kHz = −4 dB) within the signal bandwidth fc ± Bs/2 = fc ± 70 kHz.

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Electronics 2021, 10, 85 As expected, the DSSS module had an on average 7 dB better SIR performance9 of(SI 18‐ Raverage ± 80 kHz = −4 dB) within the signal bandwidth fc ± Bs/2 = fc ± 70 kHz. The DSSS process gain is as shown in Figure 8 in dependency of the received signal amplitude be‐ The DSSS process gain is as shown in Figure8 in dependency of the received signal cause of the nonlinear characteristic of the pre‐amplifier where for increasing signal am‐ amplitude because of the nonlinear characteristic of the pre-amplifier where for increasing plitudes the gain decreases [25]. Therefore, the best performance was found for low sig‐ signal amplitudes the gain decreases [25]. Therefore, the best performance was found for nal amplitudes (DSSS 2 mVrms and DSSS 5 mVrms). PLC module #1 show within the low signal amplitudes (DSSS 2 mVrms and DSSS 5 mVrms). PLC module #1 show within receiver bandwidth fc ± 80 kHz given by the frontend BP‐filter an about constant mean the receiver bandwidth fc ± 80 kHz given by the frontend BP-filter an about constant mean sensitivity of SIRaverage ± 80 kHz = +3 dB against single‐tone interference. Module #2 is de‐ sensitivity of SIRaverage ± 80 kHz = +3 dB against single-tone interference. Module #2 is signed as a superhet receiver with fix intermediate frequency of 10.7 MHz and an IF‐filter designed as a superhet receiver with fix intermediate frequency of 10.7 MHz and an IF-filter bandwidth of ± 165165 kHz. kHz. Module #2 shows aa strongstrong sensitivity sensitivity against against single-tone single‐tone interferer interferer located located in in a range a range of ofabout about±30 ± 30 kHz kHz around around the the carrier carrier frequency frequency and and is independent is independent on the on IF-filter the IF‐filter properties. prop‐ erties.We assume We assume that the that carrier the trackingcarrier tracking of the internal of the carrierinternal recovery carrier recovery loop is probably loop is shiftedproba‐ blyto the shifted single-tone to the single interferer‐tone andinterferer not to and the not carrier; to the therefore carrier; additionaltherefore additional bit errors bit occur er‐ rorsand theoccur properties and the properties of the loop of filter the areloop mirrored filter are in mirrored Figure8. in In Figure general, 8. theIn general, sensitivity the sensitivityto single-tone to single interference‐tone interference follows the follows characteristics the characteristics of the BP-filter of the used BP‐filter and isused highest and isin highest the passband in the (Figurepassband9). (Figure Transmission 9). Transmission methods having methods a process having gain a process like DSSS gain canlike DSSSsignificant can significant reduce the reduce sensitivity the sensitivity to interferences. to interferences. The low order The low and order quality and of quality the input of thefilters input of thefilters DSSS of the system DSSS compared system compared to module to #1 module and module #1 and #2,module which #2, uses which ceramic uses ceramicfilters of filters high quality, of high shows quality, clear shows disadvantages clear disadvantages against interference against interference reduction forreduction signals forthat signals are several that are hundred several kHz hundred away kHz from away the carrier. from the This carrier. fact shouldThis fact be should improved be im in‐ provedthe next in evolution the next ofevolution the DSSS of system. the DSSS system.

Figure 9. Wideband measurement of the SIR sensitivity. 3.2. Sensitivity to AWGN on the Transmission Channel 3.2. Sensitivity to AWGN on the Transmission Channel The effect on bit, byte and packet errors under inﬂuence of additive white Gaussian The effect on bit, byte and packet errors under influence of additive white Gaussian noise (AWGN) on the transmission channel was investigated for all transceiver modules. noise (AWGN) on the transmission channel was investigated for all transceiver modules. The noise source for all measurements was a function generator (33250A, Keysight, Santa The noise source for all measurements was a function generator (33250A, Keysight, Santa Rosa, CA, USA) with a noise bandwidth of 50 MHz. The transmission channel was Rosa, CA, USA) with a noise bandwidth of 50 MHz. The transmission channel was modeled by a resistive damping network and the noise was supplied to the test setup modeled by a resistive damping network and the noise was supplied to the test setup as as shown in Figure5. The numbers of corrupted bits, bytes, and LIN data packets were showncounted in during Figure transmission 5. The numbers and the of corresponding corrupted bits, error bytes, rates and were LIN calculated. data packets In general were counted during transmission and the corresponding error rates were calculated. In gen‐ the SNR on the transmission channel (SNRc) can be calculated from the effective values eral the SNR on the transmission channel (SNRc) can be calculated from the effective of the modulation signal usignal_rms and the noise signal un_rms at the input of the receiver valueswhich wereof the measured modulation with signal a high-speed usignal_rms and sampling the noise oscilloscope: signal un_rms at the input of the re‐ ceiver which were measured with a high‐speed sampling oscilloscope: 2 P u P = s = signal_rms = s SNRc 2 (3) Pn u N0Bn n_rms Electronics 2021, 10, x FOR PEER REVIEW 10 of 18

𝑢 Electronics 2021, 10, 85 𝑃 _ 𝑃 10 of 18 𝑆𝑁𝑅 (3) 𝑃 𝑢_ 𝑁𝐵

TheThe noise noise power power was was calculated calculated by: by: 𝑃 𝑢2 _ 𝑁𝐵 (4) Pn = un_rms = N0Bn (4) where N0 is the single‐sided spectral noise power density and Bn is the noise bandwidth ofwhere the generator.N0 is the single-sided spectral noise power density and Bn is the noise bandwidth of the generator.The noise bandwidth Bn of the function generator used is 50 MHz according to the data sheetThe noise which bandwidth was alsoB validatedn of the function by measurements. generator used A is simplified 50 MHz according performance to the com data‐ parisonsheet which of different was also transceiver validated modules by measurements. under AWGN A simpliﬁed conditions performance can be made comparison based on of different transceiver modules under AWGN conditions can be made based on the SNR the SNR on the transmission channel (SNRc) and on the resulting data error rates Pe which areon thedepicted transmission in Figure channel 10. However, (SNRc) this and comparison on the resulting does datanot take error into rates accountPe which the dif are‐ ferentdepicted system in Figure designs 10. with However, regard this to comparisonthe possible doesdata nottransmission take into accountrates and the the different neces‐ sarysystem filter/noise designs bandwidths. with regard to the possible data transmission rates and the necessary ﬁlter/noise bandwidths.

FigureFigure 10. PerformancePerformance of of different different transceiver systems under AWGN conditions. On On the DSSS systemsystem the the bit bit and and byte byte error error rate rate was measured, on module #1 and #2 the bit and byte byte-frame‐frame (preamble+byte) error rate. (preamble+byte) error rate.

TheThe DSSS DSSS transceiver transceiver is is designed designed for for a amaximum maximum data data rate rate of of19.2 19.2 kbit/s kbit/s where where the commercialthe commercial modules modules are designed are designed for maximum for maximum data rates data up rates to up115 to kbit/s 115 kbit/sand, there and,‐ fore,therefore, their receiving their receiving filter filterbandwidths. bandwidths. For data For rates data ratesbelow below the maximum the maximum possible possible data rate,data the rate, filter the filterbandwidths bandwidths of the of receivers the receivers are not are matched not matched to the to transmitted the transmitted data rate. data Comparedrate. Compared to an toideally an ideally matched matched filter, filter,there thereis an isexcess an excess bandwidth bandwidth which which leads leads to a deteriorationto a deterioration of the of SNR the atSNR the atreceiver’s the receiver’s decision decision unit. The unit. SNR The perSNR bit (Eperb/N bit0) at ( Etheb/ Nre0‐) ceiver’sat the receiver’s sampler samplercan be approximated can be approximated by: by:

𝐸 𝐵 𝐵 Eb 𝑆𝑁𝑅 ∙Bn ∙ Bm ∙𝑎 𝑁 = SNRc· 𝑅 · 𝐵 ·a f (5)(5) N0 RmBn_f ilter_

where Rm is the symbol rate at the noise limiting filter. The filter used depends on the where Rm is the symbol rate at the noise limiting filter. The filter used depends on the sys- systemtem design design and and can can be be for for the the baseband baseband case case a LP-filter a LP‐filter or foror for the the passband passband case case a BP- a filter. The message bandwidth Bm is defined by the modulation format and the data rate. The noise bandwidth of the receiver filter used is Bn_filter and af is a factor that depends on the power loss of the message signal due to signal shaping by the receiver filter. The specific Electronics 2021, 10, x FOR PEER REVIEW 11 of 18

Electronics 2021, 10, 85 BP‐filter. The message bandwidth Bm is defined by the modulation format and the11 data of 18 rate. The noise bandwidth of the receiver filter used is Bn_filter and af is a factor that de‐ pends on the power loss of the message signal due to signal shaping by the receiver filter. Thesystem specific parameters system are parameters given in Tableare given1. As in shown Table in 1. Figure As shown4, the in noise Figure bandwidth 4, the noise of bandwidththe DSSS system of the is DSSS given system by the is integration given by filterthe integration which is realized filter which by a 2nd-order is realized active by a 2ndSallen-Key‐order active low pass Sallen filter‐Key with low a corner pass frequencyfilter with of a 8.8corner kHz frequency which is about of 8.8R bkHz/2. The which noise is bandwidth of the LP filter was found to be about 19.2 kHz. The low pass filter shapes about Rb/2. The noise bandwidth of the LP filter was found to be about 19.2 kHz. The low the almost rectangular modulation signal into an approximately sinusoidal signal where pass filter shapes the almost rectangular modulation signal into an approximately sinus‐ the signal power changes by the factor af. oidal signal where the signal power changes by the factor af.

Table 1. System parameters.Table 1. System parameters.

System Parameters (Rb=19.2System kB/s) Parameters (Rb=19.2 kB/s)DSSS DSSSM#1 M#1M#2 M#2

Rm = Rb Rm =19.2 Rb k 19.2 k Message rate Message rate m c b R = R = 3R Rm = Rc = 3Rb 57.6 k 57.6 k57.6 57.6 k k Bm = Rb/2 9.6 kHz Message bandwidth Bm = Rb/2 9.6 kHz MessageBm = bandwidth Rc = 3Rb 57.6 k 57.6 k Bm = Rc = 3Rb 57.6 k 57.6 k Noise bandwidth Bn_filter 19.2 kHz 160 kHz 330 kHz Noise bandwidth Bn_filter 19.2 kHz 160 kHz 330 kHz Filter shape factor af −1.7 dB 0 dB 0 dB Filter shape factor af −1.7 dB 0 dB 0 dB The noise power limitation of transceiver module #1 is done by a 160 kHz BP‐filter at the receiver’sThe noise frontend. power limitation A possible of transceiver receiver structure module for #1 isthe done used by SDPSK a 160 kHz modulation BP-filter formatat the receiver’s is given in frontend. Figure 11. A As possible described receiver in chapter structure II module for the used#1 and SDPSK #2 transmit modulation a data bitformat by 3 is chips given with in Figure a chip 11 time. As T describedc = Tb/3. Therefore, in chapter the II modulesymbol #1rate and Rm #2 on transmit the channel a data is 3bitRb byresulting 3 chips in with a passband a chip time messageTc = Tb bandwidth/3. Therefore, Bm theof 3R symbolb. Since rate a highRm on‐quality the channel ceramic is BP3Rb‐filterresulting is used in a (#773 passband‐0065, message Oscilent bandwidth Corporation,Bm Irvine,of 3Rb. CA, Since USA) a high-quality the filter noise ceramic band BP-‐ widthfilter is of used module (#773-0065, #1 can be Oscilent approximated Corporation, with Irvine, the filter CA, bandwidth USA) the filterBn_filter noise = BBP bandwidth= 160 kHz. Theof module signal shaping #1 can be by approximated the BP‐filter can with be the neglected filter bandwidth with respectBn_filter to the= BmessageBP = 160 band kHz.‐ Thewidth signal due shapingto the high by theexcess BP-filter bandwidth can be and, neglected therefore, with respectaf = 0 dB. to the message bandwidth due to the high excess bandwidth and, therefore, af = 0 dB.

Figure 11. Possible receiver structure of module #1 (direct conversion receiver) and module #2 (superhet receiver) with Figure 11. Possible receiver structure of module #1 (direct conversion receiver) and module #2 (superhet receiver) with SDPSK demodulation. SDPSK demodulation.

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3.3. Calculation of the Bit Error Rate (Pe) In all modules investigated, synchronous detection of the differential encoded 3.3. Calculation of the Bit Error Rate (Pe) symbols is done by a suppressed carrier tracking loop which is restoring the phase am‐ biguityIn (Figures all modules 4 and investigated, 11). For coherent synchronous detection detection of differentially of the differential encoded encoded signals, symbols the is done by a suppressed carrier tracking loop which is restoring the phase ambiguity assumption is that the channel phase characteristic is constant during the N‐1th and the (Figures4 and 11). For coherent detection of differentially encoded signals, the assumption nth transmission intervals which is equivalent to requiring that the loop does not lose is that the channel phase characteristic is constant during the N-1th and the nth transmission synchronism for at least two symbol periods. A general solution of the error probability intervals which is equivalent to requiring that the loop does not lose synchronism for at least Pe for coherent detection of differentially encoded binary PSK signals [29] is given by: two symbol periods. A general solution of the error probability Pe for coherent detection of differentially encoded binary PSK signals [29] is given by: 𝑑 1 𝑑 𝑃 𝑒𝑟𝑓𝑐s  1 𝑒𝑟𝑓𝑐s . (6) 24𝑁 2 2 4𝑁 dmin 1 dmin Pe = er f c 1 − er f c . (6) 4N0 2 4N0 In the DSSS module, coherent demodulation of the differentially encoded phase‐modulated signal (DE‐BPSK) is used. Under AWGN conditions the probability of In the DSSS module, coherent demodulation of the differentially encoded phase- a bit error for DE‐BPSK is given by modulated signal (DE-BPSK) is used. Under AWGN conditions the probability of a bit error for DE-BPSK is given by 𝐸 1 𝐸 𝑃 𝑒𝑟𝑓𝑐 1 𝑒𝑟𝑓𝑐 (7) s 𝑁!" 2 s !#𝑁 Eb 1 Eb Pe DE−BPSK = er f c 1 − er f c (7) N0 2 N0 where the Euclidian distance for antipodal signal constellations like in DE‐BPSK (Figure 12) 𝑑 2 𝐸 where the Euclidian was√ substituted distance forin Equation antipodal (6). signal The constellationsmodulation format like in used DE-BPSK in module (Figure #1 and12) #2dmin is SDPSK.= 2 EInb SDPSKwas substituted the present in symbol Equation is either (6). The +π/2 modulation or –π/2 in phase format from used the in previousmodule #1 symbol, and #2 depending is SDPSK. In on SDPSK whether the presentan input symbol data is is either‘l’ or ‘0’. +π /2For or symbol−π/2 in recon phase‐ structionfrom the 4 previous decision symbol, areas are depending necessary on (Figure whether 12). an In input DE‐BPSK data the is ‘l’ Euclidian or ‘0’. For distance symbol dreconstructionmin between 2 4antipodal decision areas signal are points necessary is 2 (Figure√𝐸 despite 12). In to DE-BPSK SDPSK the where Euclidian the distance distance d between 2 antipodal signal points is 2 E despite to SDPSK where the distance is is min𝑑 √2𝐸 because of the 4 decision areas bnecessary. Since coherent demodulation withdmin differential= 2Eb because decoding of the is 4used, decision Equation areas necessary. (6) is also Since valid coherent for SDPSK demodulation under the with as‐ differential decoding is used, Equation (6) is also valid for SDPSK under the assumption sumption that√ 𝑑 2𝐸 and therefore the bit error rate is: that dmin = 2Eb and therefore the bit error rate is:

s 𝐸 !" 1 s 𝐸!# 𝑃 𝑒𝑟𝑓𝑐 Eb 11 𝑒𝑟𝑓𝑐 Eb (8) Pe SDPSK = er f c 2𝑁 1 − 2er f c 2𝑁 (8) 2N0 2 2N0

ϕ=3π/4 ϕ=π/4 𝑑 _ 2𝐸 Decision area I

II 𝐸 I

III IV

ϕ=5π/4 ϕ=7π/4

Figure 12. Symbol constellation diagram of SDPSK with 4 decision areas for symbol reconstruction. Figure 12. Symbol constellation diagram of SDPSK with 4 decision areas for symbol reconstruction.

The SNR per bit (Eb/N0) at the receiver’s decision unit is calculated for all modules withThe Equation SNR per (5) andbit (E usingb/N0) Tableat the1 .receiver’s decision unit is calculated for all modules with Equation (5) and using Table 1.

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3.4. Calculation of the Byte Error Rate (Pe_byte) 3.4. Calculation of the Byte Error Rate (P ) If the bit transmission errors occure_byte randomly and independently with probability Pe the binomialIf the bit frequency transmission functions errors give occur the randomly probability and of independently errors in an n‐ withbit word: probability Pe the binomial frequency functions give the probability𝑛 of errors in an n-bit word: 𝑃𝑖, 𝑛 𝑃1𝑃. (9) 𝑖 n − P(i, n) = Pi(1 − P )n i. (9) The probability of at least one error ini an ne ‐bit worde without using forward error correction (FEC) is, therefore: TThe probability of at least one error in an n-bit word without using forward error hcorrection (FEC) is, therefore:𝑃_ 1𝑃0, 𝑛 11𝑃 . (10) e n Pe_word = 1 − P(0, n) = 1 − (1 − Pe) . (10) DSSS modem transmits in the UART‐mode single data bytes where each data byte isThe led DSSS by a modem start‐bit transmits and followed in the UART-mode by two stop single bits. dataA transmitted bytes where data each byte, data therefore,byte is led byconsists a start-bit of a and total followed of 11 bybits, two whereby stop bits. each A transmitted bit failure data leads byte, to therefore, a byte consists of a total of 11 bits, whereby each bit failure leads to a byte error. The probability error. The probability of a byte error by given bit error probability Pe_DBPSK is: of a byte error by given bit error probability Pe_DE-BPSK is: 𝑃__ 11𝑃 (11) 11 Pe_byte_DSSS = 1 − (1 − Pe_DE-BPSK) (11) and is shown in the following figures. and is shown in the following ﬁgures. A different situation is given at module #1 and #2. The data transmission principle is A different situation is given at module #1 and #2. The data transmission principle based on symmetric differential phase‐shift keying (SDPSK) [30]. Symmetric DPSK is a is based on symmetric differential phase-shift keying (SDPSK) [30]. Symmetric DPSK is quadrature version of differential phase‐shift keying (DPSK) where the relative phase a quadrature version of differential phase-shift keying (DPSK) where the relative phase shift between successive symbols is either +90 or −90 degrees depending on whether a shift between successive symbols is either +90 or −90 degrees depending on whether logic ‘1’ or ‘0’ is to be sent. Each data byte transmitted by modules #1 and #2 is started a logic ‘1’ or ‘0’ is to be sent. Each data byte transmitted by modules #1 and #2 is started with a preamble consisting of 5 chips with a chip time duration Tc = Tb/3. A data bit is with a preamble consisting of 5 chips with a chip time duration Tc = T /3. A data bit is transmitted by three consecutive phase shifts of +90° for a ‘1′ data bit andb three consecu‐ transmitted by three consecutive phase shifts of +90◦ for a ‘10 data bit and three consecutive tive phase shifts of◦ −90° for a ‘0’ data bit. Each phase shift has a time duration of Tb/3 phase shifts of −90 for a ‘0’ data bit. Each phase shift has a time duration of Tb/3 (Figure (Figure13). The 13). preamble The preamble which is which sent in is front sent of in each front data of each byte data consists byte of consists ﬁve chips of withfive chips phase with phase changes [+,−,+,◦ −,−]∙90° and total time duration 5∙Tc. changes [+,−,+,−,−]·90 and total time duration 5·Tc.

FigureFigure 13. 13. ExampleExample of of a byte a byte transmission transmission of ofmodule module #1 #1and and #2 consisting #2 consisting of SDPSK of SDPSK modulated modulated preamblepreamble and and data data bits. bits.

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EachEach transmitted transmitted data data byte byte is is preceded preceded by by a a preamble of of five ﬁve chips with chip time durationduration Tcc == TTbb/3./3. For For this this word word (preamble) (preamble) consisting consisting of of five ﬁve chips chips the the error error probability probability cancan be be calculated calculated by: by: 5 P = 1 − 1 − P (12) 𝑃e_pre__M_ 11𝑃e_SDPSK__chip_ (12)

wherewhere Pe_SDPSK_chipe_SDPSK_chip is calculatedis calculated from from Equation Equation (8) (8) substituting substituting the the Eb/NEb0/ byN0 theby theSNR SNR per per E N E N chipchip Ecc//N0 =0 =Eb/3bN/30. 0. SubsequentSubsequent to to the the preamble, preamble, a a data data byte byte with with 11 11 bits bits where where each bit consists of three chips with chip time duration T /3 (Figure 13) is transmitted. For a data bit consisting chips with chip time duration Tb/3b (Figure 13) is transmitted. For a data bit consisting of threeof three chips, chips, a triple a triple repetition repetition code code was wasused used where where a ‘1’ bit a ‘1’ is bitrepresented is represented by 111 by chips 111 andchips a ‘0’ and bit a ‘0’is represented bit is represented by 000 by chips. 000 chips.With this With encoding this encoding method method a lower a lowererror prob error‐ abilityprobability is expected. is expected. Based Based on the on majority the majority-rule‐rule decoding decoding of the of the triple triple repetition repetition code, code, a singlea single chip chip error error can can be becorrected. corrected. That That means means and and at least at least two two of the of thethree three chips chips per perbit bit must be correctly transmitted. Only double and triple errors result in a decoding error must be correctly transmitted. Only double and triple errors result in a decoding error which can be formulated by: which can be formulated by: P = P(2, 3) + P(3, 3) = 3P2 − 2P3 (13) 𝑃e_bit__M_ 𝑃2,3 𝑃3,3 3𝑃e__SDPSK__chip 2𝑃e_SDPSK__chip_ (13) TheThe probability probability of of a a data data byte byte error error where where the byte consist equal to the DSSS modem ofof a a leading leading start start-bit,‐bit, eight eight data data bits, and two stop bit is then:

11 Pe𝑃_byte__M_=11𝑃1 − (1 − Pe_bit_M)_ (14)(14)

AsAs previously previously described described a a transmitted transmitted frame frame for for a a data byte by module #1 and #2 consistsconsists in in total total of of a a five ﬁve-chip‐chip preamble and eight data bits with an additional one start andand two stopstop bits.bits. Thus, Thus, the the total total error error probability probability of theof the transmitted transmitted frame frame is a combination is a combi‐ nationof the preambleof the preamble error probability error probabilityPe_pre_M Pande_pre_M the and data the bit data error bit probability error probabilityPe_byte_M P.e_byte_M Since. Sincea triple a triple repetition repetition code is code used is for used the datafor the bits, data the bits, probability the probability of an error of inan the error preamble in the preambleis much greater is much than greater that ofthan a data that bitof a error. data However,bit error. However, a single chip a single error chip in the error preamble in the preambleleads to a leads preamble to a errorpreamble and thuserror to and a loss thus of theto a full loss data of the byte. full Both data error byte. probabilities Both error probabilitiesare depicted inare Figure depicted 14 for in comparison.Figure 14 for From comparison. theoretical From calculations, theoretical it wascalculations, found that it wasthe errorfound probability that the error of a probability data frame of consisting a data frame of a ﬁve-chip consisting preamble of a five and‐chip a preamble data byte anddepends a data mainly byte depends on the error mainly probability on the error of the probability preamble. of the preamble.

Figure 14. Theoretical error probability of module M#1 and M#2 for the transmission of a preamble Figure 14. Theoretical error probability of module M#1 and M#2 for the transmission of a preamble (Pe_pre_M) or a data byte (P ). (Pe_pre_M) or a data byte (Pe_byte_Me_byte_M).

For a rough but reasonable performance estimate, the probability of a byte frame decoding error is given by the approximation:

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For a rough but reasonable performance estimate, the probability of a byte frame decoding error is given by the approximation:

Npre Nbyte Pe_byte_ f rame = Pe_pre_M + Pe_byte_M (15) Nf rame Nf rame

In Equation (15), the number of decisions required to decode a preamble is given by Npre (Npre = 5), the number of decisions required to decode a data byte is Nbyte (Nbyte = 11) and Nframe is the total number of decisions required to decode a data byte frame, which is the sum of Npre and Nbyte.

3.5. LIN-Packet Error Rate (PER) The format of a transmitted LIN-packet is given in Figure6. A LIN-packet error (PER) was counted if the LIN preamble or one or more bytes of the transmitted LIN- packet payload were corrupted. The theoretical LIN-packet error rate was calculated under the assumption that in a corrupted LIN-packet at least one preamble chip or data bit is incorrect. The preamble of a LIN-packet consists of the ‘break-ﬁeld’ (13 bit low) and the bytes B0 and B1 of 11 bit each. The ‘break-ﬁeld’ is not part of the error analysis. The LIN preamble is followed by 8 payload data bytes and a terminating CRC byte where each byte contains an additional 1 start and 2 stop bits. Therefore, the total number of bits of a transmitted LIN-packet is n = 121 bits (Figure6). The probability of at least one error in a transmitted LIN-packet of n = 11 bytes·11 bits = 121 bits transmitted with the DSSS system and, thus, a LIN-packet error can be calculated by:

121 PERDSSS = 1 − (1 − Pe DE−BPSK) (16)

The commercial modules #1 and #2 transmit each of the 11 LIN-packet bytes with an additional preamble of 5 chips as discussed in chapter III.B.2. Due to the error correction capability by the triple repetition coding of the data bits, a LIN-packet error is therefore mainly caused by chip errors in the 11 data byte preambles with each consisting of ﬁve chips. The PER based on chip errors in the preambles of one LIN-packet is given by:

5∗11 PERpreamble = 1 − 1 − Pe_SDPSK_chip (17)

and the PER based on bit errors is given by:

11∗11 PERbit = 1 − (1 − Pe_bit_M) . (18)

For module #1 and #2 the overall probability of a LIN-packet error caused by an error in the preamble or a data bit error is:

NLIN_pre NLIN_bit PERM = PERpreamble + PERbit (19) NLIN NLIN

where NLIN_pre = 11 × 5 = 55 indicates the number of decisions necessary to decode all preambles, NLIN_bit = 11 × 11 = 121 indicates the number of decisions necessary to decode all bits and NLIN is the total number of decision necessary to decode a LIN-packet (NLIN = NLIN_pre + NLIN_bit = 176). In Figure 15a–c a comparison of the theoretical and the measured bit error rates (BER), byte error rates (Byte_err) and packet error rates (PER) for all transceiver modules are given. All measurements were repeated three times and the mean values are depicted. The AWGN performance of the DSSS transceiver Figure 15a ﬁts excellent with theories given in Equations (8), (11), and (16) using the system parameters given in Table1. Only for low error rates do the measurements show a degradation in performance with respect to the theory. This might be caused by jitter in the carrier recovery loop. Electronics 2021, 10, x FOR PEER REVIEW 16 of 18

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(a) (b)

(c)

Figure 15. MeanMean values values of of the the measured measured bit bit-,‐, byte byte-‐ and and packet packet error error rates rates under under AWGN AWGN conditions conditions in comparison in comparison to the to theoreticalthe theoretical values values of the of the(a) DSSS (a) DSSS system, system, (b) module (b) module #1, and #1, and (c) module (c) module #2. #2.

TheThe AWGN performance of the commercial modules #1 andand #2#2 isis givengiven inin FigureFigure 15b,c.15b,c. A direct conversion receiverreceiver is is used used in in module module #1 #1 and and a a superhet superhet receiver receiver in in module mod‐ ule#2. The#2. The performance performance of the of bit-errorthe bit‐error rate andrate theand byte-frame the byte‐frame error error rate of rate module of module #1 show #1 showa good a good fit to thefit to theoretical the theoretical calculations calculations which which are given are given in Equations in Equations (13), (13), (15), (15), and and (19) (19)using using the systemthe system parameters parameters of Table of Table1. From 1. From the measurements, the measurements, we found we found that the that noise the noisefilter bandwidthfilter bandwidth of module of module #1 was #1 determined was determined by the bandwidth by the bandwidth of the ceramic of the frontendceramic frontendfilter (Table filter1) and(Table fit excellently1) and fit excellently to the theoretical to the predictions.theoretical predictions. However, in However, module #2 in modulethe obtained #2 the measurement obtained measurement results do results not match do not to match the noise to the bandwidth noise bandwidth of the IF of filter the IF(Table filter1, (Table dotted 1, lines dotted in Figure lines in15 Figurec). Based 15c). on Based the measurement on the measurement results, we results, assume we that as‐ sumemodule that #2 module contains #2 an contains internal digitalan internal filter withdigital a filterfilter noise with bandwidtha filter noise of aboutbandwidth 100 kHz of

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in addition to the IF filter. This assumption also supports the minimum channel spacing of 100 kHz mentioned in the datasheet. Based on the assumption of an approximate filter noise bandwidth of Bn_filter = 100 kHz, the measurements obtained fit exactly to the theoretical prediction shown in Figure 15c. This confirms that the system design of the commercial modules has been largely optimized. The significant deviation of the LIN-packet error rate from the theoretical prediction for both modules could not be clearly explained. Especially for module #1 it could be found that, at a low SNR, a valid preamble was erroneously detected in transmission breaks and, thus, the following noise was erroneously decoded as a data byte leading to an increased error rate. If these de-coding errors occur during LIN-packet transmission, LIN-packets are erroneously decoded and the packet error rate can increase considerably.

4. Conclusions The performance of a self-designed direct sequence spread spectrum modem for PLC in automotive applications was investigated. The DSSS modem was compared with two commercial PLC modems which are qualiﬁed for automotive applications based on a direct conversion receiver (module #1) and a superhet receiver (module #2). It was shown that the performance of the DSSS modem against single-tone interference was as expected about the processing gain PG of 8 dB better than the commercial modules. At data rates of 19.2 kB/s used for LIN packet transmission, the performance of the DSSS module was better than the other modules by about 6 dB in bit error rate under AWGN conditions. It was clearly shown that the better performance of the DSSS system is due to the different designs of the transceiver modules regarding their maximum transferable data rate and was proven by theoretical analysis. If this aspect is taken into account, the performance is comparable in terms of bit error and byte error rate. Only in the transmission of LIN packets does the performance of the commercial modules appear to be lower than that of the DSSS system. The main advantage of the DSSS system is the signiﬁcantly better interference suppression and the very low-cost design of the entire module with component costs of about 1 Euro.

Author Contributions: Conceptualization, M.B. and K.K.; software, K.K.; validation, M.B. and K.K. formal analysis, M.B.; writing—original draft preparation, M.B.; project administration, M.B.; funding acquisition, M.B. All authors have read and agreed to the published version of the manuscript. Funding: Open Access Funding by the University for Continuing Education Krems. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: No available data. Acknowledgments: This work is co-funded by the government of Lower Austria and the European Regional Development Fund (ERDF). Project ID: WST3-F-5030664/004-2017. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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