Techniques For Power Line Communication Engineering Essay

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Abstract

The subject of this project is to analyze the Orthogonal Frequency Division Multiplexing (OFDM) Techniques for Power Line Communication (PLC). Communication over power-lines existing in homes is considered to be an interesting transmission-technique but at the same time several technical challenges arise like varying impedance, noise and attenuation from these power-lines. Therefore these factors make data transmission over power-lines unfavorable. In this project, an attempt is being made to show that OFDM could be used to transmit the signal at a high data rate over a power-line channel. The proposed OFDM technique in this project works on a comprehensive summary of transmission properties and the noise scenario on public mains supply used for data transmission taken from Theoretical Postulation of PLC Channel Model by Open PLC European Research Alliance document (opera). [9, 15, 6]

For the sake of analysis, Model one of five taps from opera have been considered in this project. Matlab software is used to simulate the OFDM over five-taps power-line channel. In the first part of the project, the reasons behind using OFDM for PLC have been analyzed. In the second part, detail study of OFDM blocks and power-line channel has been presented. In the third part, simulation results are shown in order to judge the performance of OFDM over five-taps power-line channel. [6]

1. Introduction

As power-lines are easily seen in every home, researchers from all over world are busy spending their time in laboratory working for a multipurpose power-line medium technology delivering energy, voice and various data services over the existing power-lines."In particular, Internet access is currently in the focus of the efforts of various research activities" [8, 18]. However, implementing the power-lines for Home-networking could be cumbersome and the noisy channel that fluctuates with high attenuation and varying impedance and this restricts the transmission of a signal with a high data rate. Therefore there was a need to look for a suitable efficient digital transmission technique which can overcome above mentioned problems and deliver with a high data rate. [10]

In this project, Orthogonal Frequency Division Multiplexing (OFDM) is the proposed technique being used over power-line channels. The reason is that OFDM is able to provide a reliable and bandwidth-efficient communication even in the presence of problems mentioned above and also it converts Frequency selective channel (power-line) to flat fading subchannels thereby reducing the variations of channel frequency response on individual subchannels in OFDM. OFDM can be implemented efficiently by implementing Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT) to calculate Discrete Fourier Transform (DFT) and Inverse Discrete Fourier Transform of symbols belonging to individual subcarriers. [15]

This project was investigated in the following order: The project was initiated with the study and detail analysis of OFDM blocks/functions. In the second phase, general procedure was studied for creating an in-house channel model for five-taps as per given by opera [6] and then simulations were carried out on OFDM over five-taps power-line channel. In the third phase of pilot project study, simulated outputs were analyzed and the analyzed results declared that performance was not impressive so there was a need to introduce coding and interleaving in OFDM to improve the performance which will be carried out in summer.

2. Project Overview

2.1 OFDM Introduction and System Model

Figure1: Representation of OFDM over Power-Line channel left side represents Transmitter (Tx) and right side represents Receiver (Rx). [15]

"OFDM is a parallel transmission technique, where a high-rate serial data stream is split up into a set of low-rate substreams, each of which is modulated on a separate SC (FDM). Therefore, the bandwidth of the SCs become small compared with the coherence bandwidth of the channel: that is, individual subcarriers experience flat-fading, which allows for simple equalization. This implies that the symbol period of the substreams is made long compared to the delay spread of the time-dispersive radio channel". [2] OFDM is implemented with a use of IFFT on block of incoming complex symbols. To mitigate the effects of Inter Symbol Interference (ISI) caused by the channel, the co-efficients of IFFT is prefixed with a Cyclic Prefix (CP) or guard interval, such that CP is almost equal to or greater than channel length. Therefore this leads to transformation of linear convolution of transmitted sequence and channel to circular convolution. As a result, ISI is completely eliminated. This procedure makes OFDM to implement DFT at the receiver side [10]. In this way, complexity of implementation is reduced and thus OFDM can be easily implemented with IFFT/FFT.

Figure2: Subcarriers representation in OFDM spectrum.

( ref: http://ofdm.tu-harburg.de/tutorial.htm).

As shown in figure2, this tells us that K= W/∆f subchannels where W is the available bandwidth. Here different information symbols can be tranmsitted through Frequency Division Multiplexing (FDM) in the K-subchannels simultaneously.We associate each subchannel with a carrier

Xk (t) = sin 2πfkt, k = 0, 1, 2,……………………………K-1

Where fk is the mid-frequency of the Kth subchannel."By selecting the symbol rate 1/T on each of the subchannel to be equal to the separation ∆f of adjacent subcarriers, the subcarriers are Orthogonal over the symbol interval T, independent of the relative phase relationship between subcarriers; i.e.,

Where fk-fj = n/T, n =1,2,………,independent of the values of the phases Φk and Φj. In this case, we have Orthogonal Frequency Division Multiplexing" [7]. Here channel experienced by each subcarrier is flat fading as long as cyclic prefic (CP) is longer than the delay-spread of the channel thus leading to zero ISI in the system.

As shown in figure1 the binary input data enters into the system it is coded and interleaved so that data becomes immune to multipath propagation effects and the noise,then symbol mapping is performed. Now at the input of IFFT,data constellation points are present and then these constellations are taken according to the given Phase Shift Keying (PSK) or QAM signalling set (symbol mapping/modulation). The output samples of IFFT which is in TD forms the baseband signal carrying the data symbols on a set of K Orthogonal SCs . In order to decompose ISI in the channel, CP of length l should be added to the output of IFFT samples. Then total length K+l symbols are sent serially onto the power-line channel.At the reciever side, CP is removed and the FFT is used to demodulate all the subcarriers. Each subcarrier obtained can then be divided by the complex channel gain for that subcarrier to perform symbol demapping (equalisation) [4]. Differential detection can be implemented, where the constellations of OFDM symbols on adajacent subcarriers are compared to recover the data.Decoding and deinterleaving is performed after the data is recovered. This type of technique is called Coded OFDM (COFDM) system. In Conventional multicarrier systems, N independent RF chains are required and high quality Low Pass Filter (LPF) is required to maintain orthogonality among subcarriers at the reciever side. Thus OFDM overcomes above mentioned conditions and therefore transforms frequency-selctive channel into a bank of flat-fading. [2, 4]

2.2 Topology of the mains network from opera

In Europe the network configuration is classified based on the voltage levels: The High voltage, Medium voltage and the Low voltage. For a communication process, the low voltage is of great interest as the "last-mile" to the customer. The low voltage "the local loop access network" existing between the customer houses and the substation are often operated in a star shaped structure.For a power-line communication, PLC signal should be applied to the bus bar.From the substation to the main backbone network,

Figure3: Spectrum efficiency achieved by OFDM, the total bandwidth W=∆fK where K is ten in above figure. [5]

physical connection could be carried out by means of fiber optics, radio relay cables or broadband cables.On an average, four to ten - cables branch off the bus bar, which leads to the customer houses.These cables are placed underground or sometimes overhead lines could be seen in some places.These cable supplies power to tens and hundreds of domestic appliances.Every house has a connection boxes where these cables coming from access networks ends thus turning into an inhouse network as shown in figure4. Here cable splits up if required using separate electricity meter. [6]

Figure4: Structure of a inhouse network. [6]

PLC modem should be placed in parallel to the connection box separating access network and inhouse netrwork. By this method, different frequency usage can be considered for both networks. "The advantage is that in access networks with its distant low pass characteristic, lower frequencies may be used, and in inhouse networks not having those characteristic higher frequencies may be used. [6]

3. The study of OFDM

In order to avoid having N RF radios in both transmitter and reciever, OFDM implements an efficient computation known as Discrete Fourier Transform (DFT), which leans itself towards a high efficient technique known as Fast Fourier Transform (FFT). The FFT and its inverse i.e., IFFT, works together on a orthogonal subcarriers using a single radio. [4]

3.1 Block Transmission with Guard Interval

Here the N data symbols are grouped into a block to form an OFDM symbol. An OFDM symbol has a duration of T seconds, where T=NTs. To avoid interference between OFDM symbols and keep them independent of others after passing through a channel, it is necessary to introduce a guard interval between OFDM symbols which is larger than the delay spread of the channel. [4, 5]

Figure5: OFDM symbol transmitted with Guard interval to avoid interfence and received OFDM symbol interfering only with itself. (ref: [5])

From Figure5 it is very clear that after receiving a series of OFDM symbols, as long as guard interval Tg is larger than the delay spread of the channel, each OFDM symbol will interfere only with itself. Therefore OFDM transmissions allows ISI within the symbol, but by introducing a sufficiently large guard interval it is possible to avoid interference between subsquent OFDM symbols. [4]

3.2 Circular Convolution and the DFT

From above analysis it is clear that we should remove Inter-Symbol Interference (ISI) within each OFDM symbol. The Channel considered here is an linear time-invariant Finite Impulse Response (FIR), h[n]. Thus the output should be linear convolution of transmitted sequence x[n], and the channel impulse response h[n]:

y [n] = x[n]*h[n]

Let's compute y[n] in terms of circular convolution: y[n] = x[n]©h[n] = h[n]©x[n],

Therefore, y[n] = N ,

Then we have the circular function x[n]N = x[n mod N] is an periodic version of x[n] with period N. From this, each value of y[n] =x[n]©h[n] is the sum of the product of all N terms.Through this operation it is possible to use DFT to recover exactly x[n].

DFT(y[n]) = DFT[(x[n]©h[n])],

Which yields in the frequency version, Y[m] = H[m] X[m],

The above frequency version equation is free from ISI, where each input symbol X[m] has been scaled by complex channel value H[m]. So, by having known H[m] channel frequency response at the reciever, it is possible to get the transmitted symbol by computing, X'[m] = Y[m]/H[m],

Where estimate X'[m] is imperfect due to the exposure to channel impulsive noise and other noises. But through this analysis the most serious form of interference existing between OFDM symbols has been mitigated. [4]

x[n-l]N = x[n - l] for n = 0,1,2…………………,N-1

i.e x[-l] = x[n -l] for l = 1,2,3……………,L»»»Guard Interval=CyclicPrefix (ref: [p])

Figure6: OFDM symbol + Guard Interval [5].

3.3 The Cyclic Prefix

The reason behind OFDM to realize practically, is due to the use of FFT algorithm in the system which has low complexity involved in it. For IFFT/FFT to decompose ISI effect in the channel, the channel must be able to provide a circular convolution, as analyzed above. Adding a cyclic prefix to the output of IFFT signal, creates a signal that looks like x[n]N , and so y[n] = x[n]©h[n]. [4]

Figure7 : OFDM Cyclic Prefix representation. [4]

The channel output is given by ycp = h * xcp, where h is channel impulse response of length v+1 .Therefore the output ycp has (N +v) + (v +1)-1 = (N + 2v) samples. There is an interference existing from the preceding OFDM symbols contributed by the first v samples, so they are discarded.The last v samples are dispersed into the subsquent OFDM symbol and hence they are also discarded.Now remaining are only N samples which we are interested to recover the N data symbols present in x. Now we can claim that the N samples are equivalent to the output y = h © x .[4]

Figure8: Discrete-time baseband signal model, here Ncp=v= L .[5]

From the figure8, the value of y[k:0],y[k:1]………………y[k:N-1] results from y=x©h.

Circulant matrices are analyzed with the DFT matrix and it is shown by,

Ĥ(hammation) = HF,

[ F]m,n = 1/sqrt(N)(), n =0,….N-1;m =0,……..,N-1

H =diag{H0,……….HN-1}; Hm = ,

Therefore the kth received OFDM symbol:

y[k] = Ĥ x[k] + v[k] = HFx[k] + v[k]

v[k] is the noise content in the channel.

Therefore x[k] is obtained after IDFT done on s[k] symbols and after this each element will experience a flat fading channel. Later s[k] can be obtained by DFT and one-tap equalizer . [5]

The cyclic prefix which looks more simple and easy technique to remove ISI, at the same time it introduces bandwidth and power penalty. Since by adding v redundant symbols to the transmitted signal the bandwidth requirement for OFDM increases from B to (N+v/N)B. Similarly, cyclic prefix also introduces power peanlty of 10log10(N + v/N)dB.The inefficiency arising due to the Cyclic prefix can be made smaller by increasing the number of subcarriers (L). But this can also lead to other sort of problems which would be discussed in later part of this report. [4]

3.4 OFDM Modulation

Now let us consider the kth OFDM symbol being transmitted without cylic prefix,

i.e

x[k: n] = 1/sqrt(N)

kth transmitted OFDM symbol with cyclic prefix,

xcp[k: n] = 1/sqrt(N) , n = -Ncp,……..,N-1; for k

Output of parallel to serial,

u [i] = u[kNg + n] = xcp [k;n], n = -Ncp,………..,N-1. [5]

Figure9:Block diagram of OFDM, Ncp ≥ L no ISI . [5]

3.5 OFDM Demodulation

Figure10 : Block diagram of OFDM . [5]

The recived analogue signal would be sampled at rate of 1/Ts = W, we get

y [k; n] = 1/sqrt(N) , n= 0,…………,N-1; for k

After passing through FFT, the frequnecy domain signal would be,

Ym[k] = Hm Sm [k] + Vm[k], m= 0,……………,N-1.

Maximum Liklihood detection would be and is equivalent to zero-forcing detection,

[k] = arg min ⃒ Ym [k] - Hm α⃒ , m = 0,……….,N-1 for k (α: alphabet). [5]

3.6 Performance of OFDM systems

OFDM modulation transforms a Frequency-selective channel to a set of Flat-fading channels.

Signal to Noise ratio (SNRs) experienced by subcarriers would be different and is given by

γ m = ; = E { ⃒ } .

BER for each subcarrier depends on

Pe ( Hm) = Q(sqrt(2)) for BPSK ;

The average BER over the subcarriers, conditioned on h, is given by

Pe(h) = 1/N , therefore it is clear that high BER is found in lower SNR subcarrier.

Hence subcarriers associated with high SNR due to lower attenuation can be taken for modulation with more bits/symbol to carry than the subchannels associated with low SNR due to high attenuation and also the BER would be high in these subchannels.

For fading channels, frequency-selectivity would be desirable as it provides diversity. Uncoded OFDM fails to capture multipath diversity since the channel experienced by individual subcarrier is flat and its magnitude is rayleigh distributed.

Hm = = CN (0, ), taps are assumed to be uncorrelated.

Consider a case where symbol has been transmitted over that subcarrier that has experienced a deep fade, then the symbol at the reciever would be wrongly detected.

For a BPSK and assuming uncorrelated taps, the average BER is given by

Pe = ½ (1- ) 1/4SNR

where BER is inversly proportional to SNR and fails to provide diversity factor.

From above analysis it is clear that Uncoded OFDM has poor performnace and so there is a need for channel coding across subcarriers to capture multipath diversity through Coded OFDM (COFDM). [5, 7, 17]

3.8 Drawbacks

3.8.1 The Peak-to-Average Ratio

Peak-to-Average ratio (PAR) is generally known as Peak-To-Power-Ratio (PAPR) which is considerably high in OFDM then in single-carrier signals. When the signal is in time-domain, at that time sum of many narrowband signals create a multicarrier signal. This sum may be large at some instances and small at other times, which means that peak value of the signal is larger than the average value. This PAR is one of the critical challenge that OFDM face, because it reduces the performance and hence increase the cost of RF power amplifier. [4]

Figure11: Power amplifier characteristic. [5]

When a non-constant amplitude signal is passed through non-linear High Power Amplifier (HPA), there is generation of spectral regrowth and in-band distortion like constellation tilting and scattering. These features could badly affect the performance of the system. Therefore, a backoff from the compression region as shown in figure11 is necessary.

PAPR for a transmitted signal can be defined as,

PAPR =

Where x(t) = 1/ , 0.

From equation it is clear that PAPR increases with number of subcarriers, N.When N is large, then by applying central limit theorem, the PDF of the instantaneous signal power i.e., p = ⃒ can be approximated by exp(-p).

" The distribution of OFDM PAPR has been studied by many researchers. Among these, van Nee and de Wild introduced a simple and accurate approximation of the CCDF for large L (64):

CCDF(L,εmax) = 1 - (1-,

Where εmax is the peak power level and β is the pseudoapproximation of the oversampling factor,which is given emprically by β=2.8 ". [4, 5]

Figure12: Spectral re-growth vs Amplifier backoff using QPSK. 10dB and 5dB backoff from 1dB compression point of the amplifier. [5]

3.8.2 PAPR reduction techniques

Clipping or windowing could be implemented to reduce PAPR but introduces distortion.

Coding technique combined with error correction code to reduce PAPR but reduces data rate.

Implementing Symbol scrambling which decreases the probability of having a high PAPR.

Set of tones are reserved known as Tone reservation to reduce PAPR but it also reduces data rate. [5]

3.8.3 Carrier Frequency Offset (CFO)

OFDM is highly sensitive to carrier frequency offset (CFO) and which disturbs the orthogonality condition between subcarriers.

Figure12: Carrier frequncy offset seen in an OFDM system. [5]

"The degradation of SNR in decibel due to CFO is quadratic in the number of subcarriers and so, accurate CFO estimation algorithms are required in OFDM systems". [5]

3.9 Advantages

Spectrum efficiency could be achieved through OFDM.

Simple implementation of IFFT/FFT in the system and less computational complexity involved in it.

By the use of Guard interval with Cyclic prefix insertion in the system to combat multipath propagation effects.

Adaptive modulation and coding works good for OFDM, when channel information is known at the transmitter.

OFDM supports coding and interleaving across the subcarriers in the frequency domain.

Equalization is easy as one-tap equalizer is required.

Multiple access technique could to applied to OFDM in order to make OFDMA, where subcarriers can be distributed among different number of users for commercial purpose. [5]

"Frequency ranges excluded from use for PLC due to regulation or bad quality can be faded out by zeroing the corresponding subcarriers". [14]

4.0 General Procedure for creating inhouse channel model

Table1 : Default values for in-house reference channels [6]

Here the table1 describes the model based on the selection of number of paths.For every model channel, the number of paths have been considered along with impulse response, delay, maximum and minimum amplitude.With these values given, it is possible to determine the transfer function and the attenuation characteristics through Fourier transform." The statistical procedure may be applied as in-house networks are highly branched randomly assumed distributions of length of branched cables. Additionally, channel properties are - in contrast to the access network - continually changing when electrical devices are turned on and off ".[6]

Procedure used for generating a reference channel impulse response as follows,

Impulse response starts with a positive impulse response of maximum amplitude and then decays exponentially until the last response reaches the minimum amplitude.

Polarities of single impulses are choosen randomly starting from second impulse.

Now the time positions of the single impulses starting from second to last are choosen randomly based on their variance of bandwidth of distance variation.

This procedure therefore generates the reference channels at low expenditure with arbitrarily default values.[6]

For our project analysis, we have considered five-taps channel where single impulses are equable distributed over duration of impulse response Th and this is seen in the form of,

ti = *i , i=0,………….Np -1 as time positions of single paths.[6]

f(t) is an exponential decaying envelope being experienced by amplitudes and are defined by f(0) = b0 f(Th) = b1.

Thus, we have

f (t) =b0 * ( .

Later, we can randomly change the sign of single Dirac-impulses. Further, time positions of paths can be varied randomly and also generated impulse response could be shifted to the right by the desired time delay. [6]

5. Simulation results

The procedure used to simulate OFDM over a PLC of 5 taps as follows,

Generation of random binary sequence of 1's and 0's with equal probability of 0.5.

For BPSK modulation, 0 is represented as '-1' and 1 represented as '+1'.

Subcarriers should be selected (like 64, 128, 256, 512) and also used subcarriers, cyclic prefix (Tcp), data symbol duration (Td) and total symbol duartion (Ts = Tcp + Td) should be intialised in the code.

The relation between bit energy (Eb_No) and symbol energy (Es_No) should be intialised such that,

Symbol energy (Tcp + Td) = Bit energy (Td),

Es_No/Eb_No = Td/(Tcp + Td ).

Therefore, Es_No_dB = log10 (data subcarriers/ Total subcarriers) + Eb_No_dB + log10 (Td/Td+Tcp) should be intialised in the code.

Assign data symbols to the used subcarriers and then perform IFFT on them.

Add cyclic prefix to the to the signal in time domain for better results Tcp should be larger than channel duration.

Convolue the data which is the combination of cyclic prefix and data symbols with channel response.Here each symbol experiences flat fading so we should compute the frequency resposne of each and wil be used at later stage.

Concatinate the symbols to form a long transmit symbol chain.

Introduce impulsive and additive noise to the received signal.

Removal of Cyclic prefix for retaining the original data.

Perform FFT operation on the time domain signal to get frequency domain signal.

Simple equalisation is performed, dividing the frequency domain signal by channel frequency response.

Demodulation is performed.

Difference between the reccieved symbols and transmitted symbols are computed.

BER is calculated, dividing the difference by total number of symbols transmitted .

BER vs Eb_No_dB has been plotted to analyse the overall OFDM system.

5.1 Simulation of Model 1 considereing five-Paths

Graph1: Design of in-house reference channel by considereing five-paths and single impulses are equable distributed over the Th impulse response duration.

5. 2 OFDM over Rayleigh channel

clear all

SC = 64;

Dsc =52;

Eb_No_dB = [0:30]

Es_No_dB = Eb_No_dB + 10*log10(Dsc/SC) + 10*log10(64/80);

Ns = 52;

sym=10000;

for ii = 1:length(Eb_No_dB)

G = rand(1,Ns*sym)>0.5;

Gmod = 2*G - 1;

Gmod = reshape(Gmod,52,sym).';

Index = [zeros(sym,6) Gmod(:,[1:26]) zeros(sym,1) Gmod(:,[27:52]) zeros(sym,5)];

TD = ifft(fftshift(Index.')).';

TX = (64/sqrt(52))*TD;

Cp = [TX(:,[49:64]) TX];

Taps =12;

ht = 1/sqrt(2)*1/sqrt(Taps)*(randn(sym,Taps)+ j*randn(sym,Taps));

Hf = fftshift(fft(ht,64,2));

for jj= 1:sym

cn(jj,:)= conv(ht(jj,:),Cp(jj,:));

end

Cp = cn;

Cp = reshape(Cp.',1,sym*(80+Taps-1));

noise =1/sqrt(2)*[randn(1,sym*(80+Taps-1))+1i*randn(1,sym*(80+Taps-1))];

Rx = [(sqrt(10^(-Es_No_dB(ii)/10))*noise) + (sqrt(80/64)*Cp)];

Rx = reshape(Rx.',79+Taps,sym).';

Rx = Rx(:,[17:80]);

ff =fftshift(fft(Rx.')).';

Rf = (sqrt(52/64))*ff;

Eq = Rf./Hf;

Extraction = Eq(:,[6+[1:26] 7+[27:52] ]);

Demodulation=2*floor(real(Extraction/2))+ 1;

Demodulation(find(Demodulation>1)) = +1;

Demodulation(find(Demodulation<-1)) = -1;

Bits = (Demodulation+1)/2;

Bits = reshape(Bits.',sym*52,1).';

Err(ii) = size(find(Bits-G),2);

end

BER = Err/(sym*52);

Eb_No_Lin = 10.^(Eb_No_dB/10);

Theortical = 1/2.*(1-sqrt(Eb_No_Lin./(Eb_No_Lin + 1)));

semilogy(Eb_No_dB, Theortical)

hold on

semilogy(Eb_No_dB,BER)

axis([0 30 10^-5 1])

6. Conclusion

OFDM overcomes intersymbol interference through the simple implementation of IFFT and a cyclic prefix. The two things should be kept in mind while designing OFDM system i.e., synchronization and management of peak-to-average-power-ratio. However, with these system design problems, sometimes efficiency needs to be traded against cost and required tolerances. [4]

Firstly, the project investigated the OFDM and its blocks through mathematical approach. Some serious problems were encountered while making analysis like PARP and CFO. Some techniques were discussed in the report in short to reduce these problems. Later power-line channel was introduced in the OFDM through simulation and performance was analyzed. The most important reason of considering OFDM over PLC is its capability to combat frequency-selectivity which is the characteristic property of PLC.

From the pilot study work analysis, it is clear that performance of Uncoded-OFDM over PLC is not impressive so there is a need to do coding and interleaving before signal is injected into the system. From the simulations, it is also clear that some subcarriers of OFDM system affected by deep fades are dominated by high BER and therefore symbol detection is very tough in these cases, which ultimately leads to wrong detection i.e., error. Therefore, the next stage of this project is to use forward error correction techniques (introduction of some error correcting codes into the data transmissions) to compensate these losses at the receiver end. [3, 1]

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