DESIGN OF CHANNEL CODING MEHODS IN HV PLC COMMUNICAIONS Aljo Mujčić, Nermin Suljanović, Matej Zajc, Jurij F. asič University of Ljubljana, Faculty of Electrical Engineering, Digital Signal Processing Laboratory ržaša 5, Ljubljana, epublic of Slovenia aljo.mujcic@ldos.fe.uni-lj.si Abstract he paper describes the design approach of channel coding methods in high voltage power-line communications system. he model of noise is obtained from measurement results and theoretical research is adapted for investigation of channel coding methods. he theoretically derived bit error rate of MQAM and MPSK modulations via this channel is given. he obtained characteristics represent the starting point for coding gain estimation. he bandwidth efficient coding schemes based on rellis Coded Modulation (CM) and Bit Interleaved urbo Coded Modulation (BICM) is used. he basic limitation factor is periodical impulse noise caused by discharges along the power line. he interleavers are used for spreading the impulse noise inside the transmitted data blocs. BICM system at low SN yields a better coding gain over powerline channel than the CM system, which also includes the symbol interleaver.. Introduction he reliability of digital modems for high-voltage (HV) power-line carrier (PLC) communications presents the limiting factor for the substitution of analog modems with digital modems. he power-line noise is the prime-limiting factor causing the synchronization problems and burst errors in data transmission. Using channel coding methods we increase the overall signal to noise ratio (SN) of a communication system and reduce the noise effects. he parameters of channel coding methods have to be matched to the characteristics of the power-line noise. It is crucial issue for data transmission at a foul weather condition when the noise exceeds the average root mean square (MS) level [, ]. he investigation of channel coding techniques uses the discrete channel model describing the power-line noise at normal operation of power line and different weather conditions []. he bacground noise and noise caused by corona discharges along the line and station apparatus is synthesized by filtering white noise source multiplied by relative corona noise function [, ]. his function describes dependence on the power frequency []. he estimation of coding gain requires the nowledge of performance bounds of the uncoded system. We derived the upper bounds for the MQAM and MPSK modulations [3]. he estimation of the upper bound of symbol error probability is derived for the model given in []. he impulse noise in uncoded PSK and QAM system over PLC channel cause approximately 6 db performance degradation compared to the AWGN channel and the same average noise level. We have investigated the both CM and BICM bandwidth efficient coding schemes. CM is widely used in the existing dplc systems while BICM [5, 6] with the turbo code [4] represents a new possible solution for channel coding methods in HV power-line communications systems. BICM coding is based on the serial concatenation of the turbo encoder, bit interleaver and mapper. he disadvantage of CM is its sensitivity to burst noise. We used the channel symbol interleaver in order to improve the performance of CM over HV PLC channel. he parameters and the type of the interleaver have significant influence on the system performance. Modulation coded schemes containing turbo codes [4] are used because of good performance of turbo codes at low SN and well spreading of impulse noise. We are motivated to achieve large coding gains where the interleaver length has to be limited to eep overall acceptable delay as upper bound and well spreading inside data frame as lower bound. In order to obtain optimal solution, the performance of BICM system over PLC channel with various parameters including the code rate, length of data frame are examined. his paper is organized as follows. First, the classification of power-line noise and its modeling is presented in Section. he bit error rate of MQAM and MPSK modulations for this channel is derived in Section 3. he system description of CM and BICM channel coding methods are discussed in Section 4. he simulation results of these two systems in PLC channel are presented in Section 5. Finally, the conclusions are drawn in Section 6.. he Model of Noise in PLC Channel he power-line noise can be divided into the noise arising from the existing high voltage on overhead power lines, interference with external sources (lightening, narrow band interferences-other power line carriers and different radio systems), and bacground noise. Power-line noise caused by the high voltage on the conductors and station apparatus can be divided into two categories: noise in normal operation: corona noise; partial discharges on insulators and station apparatus;
noise due to switching operation (isolator switch, circuit breaer) and faults. he noise caused by switching operation, faults and lightening has high amplitude of noise voltage and mostly cause short breas in digital signal transmission. his noise has relatively small probability of occurrence. It can be modeled using the hidden Marov models with the states that correspond to the occurrence of some events lie switching, faults or lightening discharge. he interferences with external sources and other powerline carriers can be avoided by appropriate frequency planning for new dplc systems. he influence of these interferences isn t included in our model. he discharges along the power line nown as corona and partial discharges on insulators and station apparatus in substations are always present on the line. his paper presents the modeling of noise in normal operation of power line. he most significant influence on the noise level in normal operation of power line is devoted to the atmospheric conditions. Other factors such as power-line design, rated voltage also influence the level of power spectrum density of noise but they are nearly constant at all weather conditions and normal operation of power line. heir influence is included in the model through the average level of noise. his level can be determined for particular power line []. he noise level at a foul weather is approximately 5 db above the fair weather noise []. he power spectrum density (PSD) of the corona noise and other partial discharges decreases with increasing frequency. Discharges on the three different phase conductors occur at different instants of time. Each time when the voltage on a particular phase is high enough a corona burst occurs and noise is generated. hese changes are described by relative corona noise function [,] while the average noise level is defined in spectral domain by PSD and average MS noise voltage U MS in time domain. he ratio of the MS voltage at any moment in period of power frequency U ) to the average MS voltage NMS ( t U NMS of corona noise is described by relative noise function [,] U NMS ( t ) u ( t ) = t =,..., () U NMS where is power frequency period. his function can be approximated by three cosine signals π with a period = seconds and cos = t amplitude U NMSi max [, ] (3 * 5) u( t) = U NMS U U U NMSmax NMSmax NMS3max < t + < t + 3 < t + + ( + ) Voltage U NMSi max and UNMS represents maximum MS values of noise generated on particular phase of a power line and average MS voltage of noise, respectively. he bacground and corona noise can be synthesized by filtering white noise source multiplied by function u ( t ) that describes dependence on the power frequency. his model is presented in Fig. []. he influence of weather conditions and used coupling is incorporated in the simulation through average noise level and different maximums of relative corona noise function. White noise source Average MS and ratio of three peas ransmitted signal Noise shaping filter A i e j φ i n i u i Dependence on power frequency () eceived signal corrupted by noise Fig. HV PLC channel with dominant noise in normal operations 3. he Error Probability of Uncoded Signals Let s consider the baseband equivalent signals received over the power-line channel in the i-th signaling interval r i = jφi Ai e + niu ~ i where A - is the amplitude of the transmitted signal, i φ - is the phase angle of the transmitted signal, i n i - is zero mean complex Gaussian random variable, u~ i - is the average relative corona noise function in the i-th signaling interval. he second term in (3) can be written inside a power frequency period as (3)
niu ~ i ( t) = ni ( i+ ) i s s u ( t) dt (4) For rectangular MQAM in which M =, where is even, the signal constellation is equivalent to two pulse amplitude modulation (PAM) signals on quadrature / carriers, each having M = signal points. he symbol error rate for MQAM in the AWGN channel is upperbounded as [7] ( M ) 3 log Eavb P M 4Q. (5) M N where the Q(z) is Gaussian probability integral, and E avb is the average energy per bit. he upper bound of symbol error probability for MQAM over the power-line channel is obtained by scaling in (5) with u (t) and averaging over power frequency period P M + = Q 4 Q u BE N avb ( t) u BE N avb ( t) dt ( M ) dt + Q u BE N avb ( t) dt 3log where B =. M Fig. shows the symbol error rate for 6 QAM in AWGN and PLC channel numerically computed from (5) and (6) versus the average SN per bit. Using the same approach, we can obtain also the probability of error for other modulation schemes in PLC channel. Fig. 3 shows the numerically computed symbol error rate for 8 PSK in AWGN and PLC channel versus the average SN per bit. he burst impulse noise, caused by unequal SN inside the power frequency period, reduces the system performance of uncoded system. he average SN inside the power frequency period is equal to the equivalent AWGN channel used for the comparison. From Fig and 3, we see that the system performance is degraded about 6 db compared to the AWGN channel. N (6) Fig. he theoretical symbol error rates for 6 QAM over PLC channel (o), and AWGN ( ) channel Fig. 3 he theoretical symbol error rates for 8 PSK over PLC channel (o), and AWGN ( ) channel With the Gray bit mapping, the equivalent BE for MPSK and MQAM is well approximated with [7, 8] Pb P M (7) he obtained results for probability of error represent a starting point for coding gain estimation of coded systems via PLC channel.
4. System Description of CM and BICM he efficient exploitation of available spectrum reserved for PLC communications can be achieved by multilevel coded modulation systems. he CM and the bit interleaved coded modulation (BICM) systems represent the most important multilevel coded modulation systems. We have investigated the bandwidth efficient coding schemes employing CM as widely used in the existing dplc systems and BICM with the turbo codes implemented in the constituent encoder [5, 6]. 4.. CM he bloc diagram of CM is illustrated in Fig. 4. CM encoder consists of /3 rate convolutional encoder followed by the 8 PSK signal mapper based on the set partitioning mapping. We have used natural mapping that is also shown in the Fig. 4. Input Output D D D ate /3 Convolutional encoder CM Encoder CM decoder 8 PSK signal mapper 3 4 5 6 7 Symbol Deinterleaver Fig. 4 Bloc diagram of CM in PLC system Symbol Interleaver Power line channel he symbol interleaver after 8 PSK signal mapper permutes the symbols in order to avoid the burst impulse noise in power-line channel. he soft demodulated symbols at the receiver are firstly deinterleaved before feeding into the CM decoder. he CM decoder is based on the maximum lielihood sequence decoding principle using the Viterbi algorithm [7]. he decoded are compared with the original in order to obtain probability of error for given SN in PLC channel. In the selection of data frame length, the periodicity character of impulse noise must be considered. 4.. BICM BICM system based on the serial concatenation of the turbo encoder, bit interleaver and mapper is shown in Fig 5. he information are first forwarded to the turbo encoder bloc [5, 6]. wo parallel constituent convolutional encoders connected by interleaver form the typical turbo encoder [4]. In simulations presented in the paper, we have used recursive systematic convolutional encoder with generator polynomials (7, 5) 8, and (3, 35) 8. he output sequence consists of the information and parity of both encoders. Puncturing is used to increase the code rate of the overall code. he channel bit interleaver is used to scatter the systematic and parity into different symbols. After the interleaver operation, the are mapped into a symbol selected from the finite discrete alphabet using Gray-mapping rule for QAM constellations. We use MQAM as an example throughout this paper, although the method can be easily extended to other modulation formats. he output of the channel is unquantized symbols corrupted by noise using principle presented in Section (Fig. ). he received symbols from the power-line channel are firstly forwarded to the LL module, which estimates the log lielihood ratio (LL) of each transmitted bit [5]. Input Output urbo Encoder urbo Decoder Channel bit Interleaver Channel bit Deinterleaver Symbol Mapper LL Module Fig. 5 Bloc diagram of CM in PLC system PLC Channel After the LL estimation, these LL values are passed into deinterleaver. he turbo decoder [6, 3] estimates the in the deinterleaved data bloc consisting of soft LL values. he decoder is based on log-map algorithm [4]. he resulting from the decoder are compared with the original. he number of wrong transmitted bit errors is accumulated for calculation of probability of error for given SN. 5. Simulation esults In this section, we present the BE performance of CM (Fig. 4) and BICM (Fig. 5) system in the PLC channel.
hese coding systems were built in Matlab and tested using equivalent baseband Monte Carlo simulation method. We can see in Section that the PLC noise is concentrated causing the burst errors in data transmission. he channel coding algorithms are sensitive to this type of errors. In order to achieve a better performance, we have to spread the noise inside the data frame. he spreading is realized by including symbol interleaver in the CM system and the bit interleaver in the BICM system. hese interleavers provide a uniform distribution of noise inside the transmitted data blocs. he data blocs in the channel must include regions with dominant impulse noise and regions with a low value of noise voltage MS. In such case, the interleaving operation can distribute the burst errors uniformly in the whole bloc. he average noise voltage MS in the bloc must be approximately equal to the overall average MS. he shorter data blocs can not provide the above defined condition. he number of errors per frame depends on the position of data frame inside the power frequency period. he data frames located in the burst region are corrupted by noise with a large average MS in the frame and obtained errors cannot be corrected at receiving side. In such cases, the average MS of noise in the data frame significantly differs from the average MS of noise in the power frequency period. Fig. 6 presents the bit error rate of the 8PSK scheme via HV PLC channel for different data frame durations and the other parameters defined in the previous section. We observe from the figure that the data frame duration have great influence on probability of error. At BE of -6 the system with ms data frame duration have about. db greater coding gain in comparison with the 6.5 ms data frame duration. he data frame duration of ms has good trade off between the performance and the total signal delay. he proper selection of interleaver additionally improve the performance of CM system via PLC channel. For reasons of comparison, we have also shown in this figure the theoretical bound for the BE of 4 PSK uncoded system over PLC channel. he bit error rate performance of the described BICM system over AWGN and PLC channel is presented in Fig. 7. he turbo encoder uses recursive systematic convolutional encoders and coding rate /. he other parameters of the system are given in the title of Fig. 7. From Fig. 7, we note that the larger constraint length of (3, 35) 8 generator polynomials provide significant coding gain compared with the (7, 5) 8 generator polynomial. he difference between these two systems is approximately db. he increasing of the generator polynomial constraint length and the frame size results in the increasing computational complexity and longer processing delay in the turbo decoder. hese parameters represent a limitation factor in system design. Fig. 6 BE of the trellis-coded 8 PSK transmission systems for different data frame duration and constant bit rate 64 bit/s (Оuncoded system, *- data frame duration 6.5 ms, >- data frame duration ms,) Fig. 7 BE of the 6 QAM BICM with data frame duration ms and bit rate 8 bit/s, O- uncoded 4 QAM via PLC channel, -uncoded 4 QAM via AWGN channel, - coded BICM system via AWGN channel, BICM system via PLC channel: *- generator polynomials (7, 5), <- generator polynomials (3, 35)) Further, we will compare the performance of the BICM system with different data frame durations or interleaver lengths. In these simulations, we have employed the data frame duration and 6.5 ms while the other parameters are the same as in the previous example. he probability of error of the BICM system with these interleaver lengths is
shown in Fig. 8. he improved performance of the system with the data frame duration ms compared with the system with 6.5 ms is 4 db. Simulation results from Fig. 7 indicate that the data frame duration ms has a good trade-off between the performance and accomplished delay in data transmission. Fig. 8 Influence of data frame duration using equal bit rate 8 bit/s and generator polynomials (3, 35) 8, channel bit interleaver length: *- 6.5 ms, <- ms 6. Conclusion he performance of CM and BICM channel coding methods in HV PLC communications is presented in this paper. he noise characteristics in PLC channel are provided for the normal operation of power line and foul weather condition. he model of HV power-line channel involving impulse noise is adapted for investigation of channel coding methods. he error probabilities of MQAM and MPSK system have greater values in the PLC channel then in the AWGN channel. he derivation of error bounds assumes the same average noise level in these two channels. We have shown that SN in uncoded system over the PLC channel have to be 6 db greater than in the AWGN channel. he influence of burst errors in PLC channel is decreased by including a symbol and bit interleaver in CM and BICM system. CM with the symbol interleaver is more sensitive to burst errors than BICM system. Both systems suffer data frame duration. Using BICM system, the obtained difference between the AWGN and PLC channel is. db with the data frame duration of ms and (3, 35) 8 generator polynomial. herefore, the new generation of the digital high-speed PLC modems should incorporate carefully selected and adjusted channel coders as the major mean of overcoming the problems of impulsive noise character in the PLC channel. eferences [] CIGE SUDY COMMIEE 35 Woring Group 9, eport on Digital Power Line Carrier, April [] Mujčić A., Suljanović N., Zajc M., asič J., Corona noise on the 4 V overhead power line - measurements and computer modeling, Electrical Engineering, Springer-Verlag, January 4. [3] Mujčić A., Suljanović N., Zajc M., asič J. Error probability of MQAM signals in PLC channel, Proceedings of the eleventh International Electrotechnical and Computer Science Conference EK 3, Portorož, Slovenia, 3. [4] C. Berrou, A. Glavieux, and P. hitimajshima, "NearShannon Limit Error-Correcting Coding and Decoding:urbo Codes", pp. 64-7, Proc. of IEEE ICC, 993. [5] S. Le Goff, A. Glavieux, and C. Berrou, "urbo- Codes and High Spectral Efficiency Modulation", Proc. of IEEE ICC, pp. 645-649, 994. [6] S. Le Goff, "Performance of bit-interleaved turbocoded modulations on ayleigh fading channels", Electronics Letters, Vol. 36, No. 8, pp. 73-733, April. [7] John G. Proais, Digital Communications, McGraw- Hill, 995. [8] Lu J.,.. jhung, and C.C. Chai, Error rates and tight bounds for L diversity reception of MQAM and MPSK signals in ayleigh fading International Conference on elecommunication, Melbourne, April 97, pp.5-.