Analysis of a Power Line Communication System over a Non-white Additive Gaussian Noise Channel and Performance Improvement Using Diversity Reception

Performance improvement of a power line communication system is presented here considering the noise as a cyclostationary non-white Gaussian random process. Performance of a power line communication system is severely deteriorated by fading and multipath effect. The impulsive noise has been considered time variant, has short duration, random occurrence with a high power spectral density (PSD). It causes bit error in the signal. Using orthogonal frequency division multiplexing (OFDM) technique, the effect of impulsive noise and fading can be improved greatly. An analytic approach is presented to evaluate the performance of a power line communication link in the presence of the above limitations. The simulation results show that there is deterioration in system BER due to time and frequency dependence of noise and the degradation is found to be significant at higher bit rates and bandwidth. The system suffers penalty in receiver sensitivity due to non-white nature of the noise process. In this paper, an analytical approach using diversity reception is carried out to examine the performance improvement of a power line channel in fading and impulsive noise. The system bit error rate (BER) is compared numerically for both binary phase shift keying (BPSK) and OFDM system. The BER results show that there is significant improvement in OFDM. Also the performance is remarkably upgraded using diversity reception.


Introduction
The main source of Power-line noise is caused by Electric appliances connected to the line (Janse, 2008;Ma, So, & Gunawan, 2005;Ezio, 2006).Essentially, the power-lines or associated hardware improperly generate unwanted radio signals that override or compete with desired radio signals.Power-line noise can impact radio and television reception -including cable TV head-end pick-up and Internet service.Disruption of radio communications, such as amateur radio, can also occur (Massaki, 2001).Loss of critical communications, such as police, fire, military and other similar users of the radio spectrum can result in even more serious consequences.Virtually all power-line noise, originating from utility company equipment, is caused by a spark or arcing across some power-line related hardware (Janse, 2008;Tachikawa, Hokari, & Marubayashi, 1989).
During the last two decades several research works has been reported on the modeling and characterization of power line noise (Article from john nosotti.doc, 2004).Noise in a power line results due to the effect of corona, impulse voltages, electric arc between the lines, and affect the communication link severely (Voglgsang, Langguth, Koerner, Steckenbiller, & Krnorr, 2000).The nature of power line noise is found to be a non-white cyclostationary process (Masaaki, Takaya, & Hiraku, 2006).The modeling and simulation of PLC system using several types of noise are also reported (Zimmermann & Dostert, 2002;Meng, Guan, & Chen, 2005;Katayama, Itou, Yamazato, & Ogawa, 2005;Hooijen, 1997).
In a Power-line, the bit error rate (BER) performance of a communication link impaired by power line noises.These noises consist of stationary background noise and time variant impulsive noise.Impulsive noise appears as Poisson distribution.The multipath delay spread is a time dispersion characteristics of the channel.The signal is made up of the sum of many signals, each traveling over a separate path.Since these path lengths are not the This is an important relation because the time dependent or non stationary features of noise are represent mathematically in the closed form of PDF.
Let the received signal is given by, Let us assume that the power of signal is constant for a short duration , so the reference signal for this time duration can be expressed as: The power P S can be calculated as, The signal is processed in a narrow band with band-pass and band-rejection filters of centre frequency C f .

Cyclostationary Noise
A cyclostationary additive Gaussian noise whose mean is zero and variance is synchronous to the AC voltage of the mains the PDF of such noise at the instance t = iT s can be expressed as, Here, equals instantaneous variance of the noise and E(.) equals ensemble average.
Based on the assumption that 2 ( ) t  is a periodic function the ensemble average is replaced by the average instantaneous power of the normalized waveform taken at every 2 ac T .Then for 0 2 In a cyclostationary noise characteristics Now, this function can be approximated a sample function with a small number of parameters.For this purpose the model employs the following periodic function to approximate Here, l = 0, 1, 2 ....

. (L-1)
Al, l  and nl denotes the characteristics of the noise.
By Fourier series expansion we get, where, P n = Mean of the variance within a bit period = σ 2

Ber Calculation
We know

Effect of Non-white Gaussian Noise
In preceding sections, a simple method of representing the performance of a power line communication link in the presence of the noise in broadband and narrow band communication channel has been demonstrated.The main purpose of this demonstration is to find out the BER in the presence of non-white additive Gaussian noise.
In this work, we have proposed a model for BER for both frequency dependent and frequency independent cases, which cannot be represented by conventional models.It can be a useful tool for the performance evaluation of Power Line Communication (PLC).It can be used as a tool for the design and evaluation of power line communication system, and also as a powerful mean for the studies in interference and fading environment of the noise in power lines.

Diversity Reception
So far, we have analyzed the BER performance of a power line system in the presence of non-white additive Gaussian noises.So, the transmitted signal traveling in the channel is subjected to this impulsive noise, fading, time dispersion, and other degradations.To overcome all those impairments and improve signal quality, we propose diversity reception technique.In diversity technique the receiver has more than one version of the transmitted signal is received through a distinct channel.When several version of the signal, carrying the same information are received over multiple channels that exhibit independent fading with comparable strengths, the chances that all the independently faded signal components experience the same fading simultaneously can be greatly reduced.

Signal Combining for Diversity Reception
Diversity techniques can increase the system capacity and improve communication reliability (Tachikawa & Takuma, 2010).By transmitting and receiving multiple copies of data, a MIMO system can effectively combat x  is the transmitted energy signal.Solving the above expression by taking the derivation with respect to i w provides maximum combining values.In other words, each branch is multiplied with its signal-to-noise ratio.The resulting SNR can be written as When adding up the branches of SNR, the total SNR will be accomplished.

Analysis of Impulsive Noise
As mentioned earlier, PLC noise can be termed as background noise and impulsive noise.The background noise is assumed to be additive white Gaussian noise (AWGN) with zero mean and variance w 2  .The arrival of impulsive noise follows a Poisson process (Massaki, 2001) with a rate of λ units per second, so that the event of k arrivals in t seconds has the probability distribution (Tachikawa, Hokari, & Marubayashi, 1989), The duration time of the impulsive noise T noise and time period is T. Pi is defined as the total average occurrence of the impulsive noise duration in time T and P 0 is the average duration without impulsive noise in time T, in which duration only AWGN is present (Massaki, 2001).From (1),

BER of Single Carrier BPSK under Impulsive Noise
If the BER under impulsive noise is P bi and BER under AWGN is P bw , then the BER of a single carrier BPSK is given by (Voglgsang et al., 2000), and, Where E b is the signal energy per bit, N i and N 0 are the power spectral density of the impulsive noise and AWGN respectively.We get BER in BPSK under impulsive noise as

BER of Single Carrier OFDM under Impulsive Noise
For OFDM, let the PSD of overall noise (includes impulsive noise and AWGN) be N m where N m is given by (Voglgsang et al., 2000), If AWGN noise power is N 0 and impulsive noise power is N i , then µ is defined as and BER of OFDM system under AWGN and impulsive noise is

Performance Improvement through Diversity Reception
For OFDM, we assume that in case of diversity reception L is equal to the number of receiver, then P b is given by (Masaaki, Takaya, & Hiraku, 2006;Zimmermann & Dostert, 2002) assuming 0.5(1+µ) ≈ 1 and 0.5 where, and the ratio of Impulsive noise power (N i ) to AWGN noise power (N 0 ) µ is given by, P b is calculated taking 2   = 0.1, 0.5 and 1.0, and L = 2, 4, 6 and 8.

Simulation Results
In order to investigate the BER performance in a power line communication system in the presence of non-white additive Gaussian noise based on the formulas derived in the previous sections, we used computer simulation with MATLAB.The expression of the signal to noise ratio is developed considering the frequency and time dependence of the cyclostationary noise.The system bit error rate (BER) is then evaluated numerically for several system parameters like system bit rate, Fourier coefficients of the non-white Gaussian noise process etc.The simulation result is shown in Figure 3, Figure 4, Figure 5 and Figure 6.

Discussion on Results
Following the theoretical approach presented in section II, we evaluate the bit error rate (BER) performance of a power line communication system with white and non-white power spectral density of noise.The results are presented in Figure 3 through Figure 6 for various system parameters.Figure 3 shows the plot of BER versus P S for different values of Fourier coefficients of the noise variance.It is noticed that there is significant improvement in BER performance depending on the values of Fourier coefficients A l and B l .Optimum performance corresponds to a set of values of A l and B l .Similar results are depicted in Figure 4 for data rate 1000 kbps.Comparison of Figure 3 and Figure 4 shows that there is deterioration in system BER due to higher data rate.
Results for frequency dependent noise PSD are depicted in Figure 5 and Figure 6 considering the Fourier coefficients as above.It is noticed that system performance is improved in the case of frequency dependent noise which is considered as a narrowband noise.

OFDM System with Diversity Reception
The BER performance is analyzed and compared for both BPSK and OFDM channel in single carrier receiver.The results show that the performance is significantly improved in OFDM.Results for diversity reception system are discussed in the following sections.

BER Performance in Impulsive Noise
Three noise scenarios is considered, namely 'Heavily disturbed', 'Moderately disturbed' and 'Lightly disturbed' (Ma, So, & Gunawan, 2005;Meng, Guan, & Chen, 2005).For plotting Equation (36), the parameters are taken from (Ma, So, & Gunawan, 2005) where IAT is the inter arrival time of the impulsive noise, which is the reciprocal of the arrival rate λ.The parameters as listed in Table 1.The BER performance in impulsive noise is shown in Figure 7, Figure 8 and Figure 9.

Table 1 .
Parameters of the impulsive noise scenario