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

^{*}

## Abstract

**:**

## 1. Introduction

#### The LIN-Bus

## 2. Performance of PLC Systems for LIN Data Transmission

_{carrier}= f

_{crystal}/4). Both commercial modules can operate on different carrier frequencies in the range from 1.75 MHz to 13 MHz in coarse steps (module #1) and from 5 MHz to 30 MHz with a spacing of 100 kHz for module #2. All modems are able to transfer the LIN bus specific data rate of 19.2 kbit/s. In our DSSS system an N = 7 bit Barker code is used as spreading function which is modulo 2 added to the binary data sequence where N is the length of the sequence. Each data bit is spread by a full 7 bit Barker sequence and therefore the chip duration T

_{c}is T

_{b}/N of the bit duration T

_{b}(Figure 3a). An overview about the proposed DSSS modem and first results were also given [25]. The used Barker code has an optimal autocorrelation function which means that the autocorrelation peak has an amplitude of N and the sidelobes are no larger than 1 (Figure 3b) [26]. An important performance parameter of spread spectrum systems is the processing gain PG which is defined as the ratio of the signal bandwidth B

_{s}on the transmission channel after spreading in relation to the message signal bandwidth B

_{m}defined by the symbol rate Equation (1).

_{b}= 19.2 kB/s is modulo 2 added to the N = 7 Barker code. This means that the clock rate of the Barker code generator is R

_{C}= N·R

_{b}. For transmission over the powerline the spread message signal is DE-BPSK (differential encoded binary phase-shift keying) [27] modulated on an 8 MHz carrier by a balanced modulator. Incoherent detection, the receiver obtains its demodulation frequency and phase references using a carrier synchronization loop.

_{s}of the spreading function. Therefore the power of the interfering signal P

_{J}is reduced by an amount called the bandwidth expansion factor B

_{s}/B

_{m}which is equal to the processing gain PG [28]. The total power J

_{0}of the interference at the output of the receiver is:

## 3. Test Setup and Results

_{b}= 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 the number of packets sent.

#### 3.1. Sensitivity to Single-Tone Interference

_{carrier}− f

_{interferer}and a SIR adjusted by different channel attenuations of the PLC signal. Theoretically, the robustness of a DSSS system against single-tone interference must be by the process-gain PG better than that of a conventional receiver.

_{average}± 80 kHz = −4 dB) within the signal bandwidth f

_{c}± B

_{s}/2 = f

_{c}± 70 kHz. The DSSS process gain is as shown in Figure 8 in dependency of the received signal amplitude because of the nonlinear characteristic of the pre-amplifier where for increasing signal amplitudes the gain decreases [25]. Therefore, the best performance was found for low signal amplitudes (DSSS 2 mVrms and DSSS 5 mVrms). PLC module #1 show within the receiver bandwidth f

_{c}± 80 kHz given by the frontend BP-filter an about constant mean sensitivity of SIR

_{average}± 80 kHz = +3 dB against single-tone interference. Module #2 is designed as a superhet receiver with fix intermediate frequency of 10.7 MHz and an IF-filter bandwidth of ±165 kHz.

#### 3.2. Sensitivity to AWGN on the Transmission Channel

_{c}) can be calculated from the effective values of the modulation signal u

_{signal_rms}and the noise signal u

_{n_rms}at the input of the receiver which were measured with a high-speed sampling oscilloscope:

_{0}is the single-sided spectral noise power density and B

_{n}is the noise bandwidth of the generator.

_{n}of the function generator used is 50 MHz according to the data sheet which was also validated by measurements. A simplified performance comparison of different transceiver modules under AWGN conditions can be made based on the SNR on the transmission channel (SNR

_{c}) and on the resulting data error rates P

_{e}which are depicted in Figure 10. However, this comparison does not take into account the different system designs with regard to the possible data transmission rates and the necessary filter/noise bandwidths.

_{b}/N

_{0}) at the receiver’s sampler can be approximated by:

_{m}is the symbol rate at the noise limiting filter. The filter used depends on the system design and can be for the baseband case a LP-filter or for the passband case a BP-filter. The message bandwidth B

_{m}is defined by the modulation format and the data rate. The noise bandwidth of the receiver filter used is B

_{n_filter}and a

_{f}is a factor that depends on the power loss of the message signal due to signal shaping by the receiver filter. The specific system parameters are given in Table 1. As shown in Figure 4, the noise bandwidth of the DSSS system is given by the integration filter which is realized by a 2nd-order active Sallen-Key low pass filter with a corner frequency of 8.8 kHz which is about R

_{b}/2. The noise bandwidth of the LP filter was found to be about 19.2 kHz. The low pass filter shapes the almost rectangular modulation signal into an approximately sinusoidal signal where the signal power changes by the factor a

_{f}.

_{c}= T

_{b}/3. Therefore, the symbol rate R

_{m}on the channel is 3R

_{b}resulting in a passband message bandwidth B

_{m}of 3R

_{b}. Since a high-quality ceramic BP-filter is used (#773-0065, Oscilent Corporation, Irvine, CA, USA) the filter noise bandwidth of module #1 can be approximated with the filter bandwidth B

_{n_filter}= B

_{BP}= 160 kHz. The signal shaping by the BP-filter can be neglected with respect to the message bandwidth due to the high excess bandwidth and, therefore, a

_{f}= 0 dB.

#### 3.3. Calculation of the Bit Error Rate (P_{e})

_{e}for coherent detection of differentially encoded binary PSK signals [29] is given by:

_{min}between 2 antipodal signal points is $2\sqrt{{E}_{b}}$ despite to SDPSK where the distance is ${d}_{min}=\sqrt{2{E}_{b}}$ because of the 4 decision areas necessary. Since coherent demodulation with differential decoding is used, Equation (6) is also valid for SDPSK under the assumption that ${d}_{min}=\sqrt{2{E}_{b}}$ and therefore the bit error rate is:

_{b}/N

_{0}) at the receiver’s decision unit is calculated for all modules with Equation (5) and using Table 1.

#### 3.4. Calculation of the Byte Error Rate (P_{e_byte})

_{e}the binomial frequency functions give the probability of errors in an n-bit word:

_{e_DE-BPSK}is:

_{c}= T

_{b}/3. A data bit is transmitted by three consecutive phase shifts of +90° for a ‘1′ data bit and three consecutive phase shifts of −90° for a ‘0’ data bit. Each phase shift has a time duration of T

_{b}/3 (Figure 13). The preamble which is sent in front of each data byte consists of five chips with phase changes [+,−,+,−,−]·90° and total time duration 5·T

_{c}.

_{c}= T

_{b}/3. For this word (preamble) consisting of five chips the error probability can be calculated by:

_{e_SDPSK_chip}is calculated from Equation (8) substituting the E

_{b}/N

_{0}by the SNR per chip E

_{c}/N

_{0}= E

_{b}/3N

_{0}.

_{b}/3 (Figure 13) is transmitted. For a data bit consisting of three chips, a triple repetition code was used where a ‘1’ bit is represented by 111 chips and a ‘0’ bit is represented by 000 chips. With this encoding method a lower error probability is expected. Based on the majority-rule decoding of the triple repetition code, a single chip error can be corrected. That means and at least two of the three chips per bit must be correctly transmitted. Only double and triple errors result in a decoding error which can be formulated by:

_{e_pre_M}and the data bit error probability P

_{e_byte_M}. Since a triple repetition code is used for the data bits, the probability of an error in the preamble is much greater than that of a data bit error. However, a single chip error in the preamble leads to a preamble error and thus to a loss of the full data byte. Both error probabilities are depicted in Figure 14 for comparison. From theoretical calculations, it was found that the error probability of a data frame consisting of a five-chip preamble and a data byte depends mainly on the error probability of the preamble.

_{pre}(N

_{pre}= 5), the number of decisions required to decode a data byte is N

_{byte}(N

_{byte}= 11) and N

_{frame}is the total number of decisions required to decode a data byte frame, which is the sum of N

_{pre}and N

_{byte}.

#### 3.5. LIN-Packet Error Rate (PER)

_{LIN_pre}= 11 × 5 = 55 indicates the number of decisions necessary to decode all preambles, N

_{LIN_bit}= 11 × 11 = 121 indicates the number of decisions necessary to decode all bits and N

_{LIN}is the total number of decision necessary to decode a LIN-packet (N

_{LIN}= N

_{LIN_pre}+ N

_{LIN_bit}= 176).

_{n_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

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**(

**a**,

**b**) Evaluation boards of the commercial PLC modules #1 and #2; (

**c**) board of the self-designed DSSS modem.

**Figure 3.**(

**a**) Generation of a DS spread spectrum signal (dashed line: data bits, full line: spreading function modulo 2 added to the data sequence); (

**b**) autocorrelation function of an N = 7 bit Barker code.

**Figure 4.**(

**a**) Block diagram of the proposed DSSS transceiver; (

**b**) detailed structure of the DE-BPSK receiver.

**Figure 7.**Sensitivity of the packet error rate (PER) to the SIR, which shows a distinct threshold effect for all different transceivers.

**Figure 8.**Sensitivity to single tone interference with a frequency offset Δf to the PLC carrier frequency.

**Figure 10.**Performance of different transceiver systems under AWGN conditions. On the DSSS system the bit and byte error rate was measured, on module #1 and #2 the bit and byte-frame (preamble+byte) error rate.

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

**Figure 13.**Example of a byte transmission of module #1 and #2 consisting of SDPSK modulated preamble and data bits.

**Figure 14.**Theoretical error probability of module M#1 and M#2 for the transmission of a preamble (P

_{e_pre_M}) or a data byte (P

_{e_byte_M}).

**Figure 15.**Mean values of the measured bit-, byte- and packet error rates under AWGN conditions in comparison to the theoretical values of the (

**a**) DSSS system, (

**b**) module #1, and (

**c**) module #2.

System Parameters (R_{b}=19.2 kB/s) | DSSS | M#1 | M#2 | |
---|---|---|---|---|

Message rate | R_{m} = R_{b} | 19.2 k | ||

R_{m} = R_{c} = 3R_{b} | 57.6 k | 57.6 k | ||

Message bandwidth | B_{m} = R_{b}/2 | 9.6 kHz | ||

B_{m} = R_{c} = 3R_{b} | 57.6 k | 57.6 k | ||

Noise bandwidth | B_{n_filter} | 19.2 kHz | 160 kHz | 330 kHz |

Filter shape factor | a_{f} | −1.7 dB | 0 dB | 0 dB |

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Brandl, M.; Kellner, K. Performance Evaluation of Power-Line Communication Systems for LIN-Bus Based Data Transmission. *Electronics* **2021**, *10*, 85.
https://doi.org/10.3390/electronics10010085

**AMA Style**

Brandl M, Kellner K. Performance Evaluation of Power-Line Communication Systems for LIN-Bus Based Data Transmission. *Electronics*. 2021; 10(1):85.
https://doi.org/10.3390/electronics10010085

**Chicago/Turabian Style**

Brandl, Martin, and Karlheinz Kellner. 2021. "Performance Evaluation of Power-Line Communication Systems for LIN-Bus Based Data Transmission" *Electronics* 10, no. 1: 85.
https://doi.org/10.3390/electronics10010085