A Time Domain Noise Measurement and Analysis for Broadband Indoor Power Line Communications

PLC noise can be divided into different classes, depending on its source as well as its physical properties [2, 8]. Figure 1 shows the categories of noise scenario in PLC. The power line noise can be classified into two major groups which are; background noise and impulsive noise [2].

2.1 Background noise

The major causes of background noise emanate from common domestic appliances such as light dimmers, desktop and laptop computers, etc. It is also caused by the summation of different noise sources of infinitesimal power. The power present in the signal of a background noise which is a function of frequency per unit frequency otherwise known as power spectral density (PSD) [9]. It is very low and hence, to a large extent increases towards lower range of frequencies [2, 7, 9]. The average range is between -140 and -125dBm/Hz [2, 10]. On the other hand, narrow-band noise is produced from electrical devices connected to the network terminals, and also from industrial equipments in relative vicinity. The periodic impulsive noise is produced by switching power supplies and is usually impulsive and periodically asynchronous to the mains frequency [2]. The range of the spectrum repetition rate is between 50 to 200kHz [11].

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Figure 1. Noise scenario

2.2 Impulsive noise

The impulsive noise is caused by switching of rectifier diode. It has a varying time from microseconds to milliseconds, random in nature and has high power spectral densities [12]. The rise in PSD of impulsive noise causes bit errors in data transmission [2, 7]. In addition, it has a repetition rate of 50 or 100Hz and is of short duration, about 10 - 100$\boldsymbol{\mu} \mathrm{s}$. Research has shown that noise is very hard to be characterized using pure analytical derivation method. Hence, all of the existing noise models are obtained based on empirical measurements. The impulsive noise is characterized by three random variables which are: Interarrival time, amplitude and width [13]. However, the background noise and the impulsive noise have peculiar characteristics. The background noise is time variant in nature and the latter cannot be considered stationary simply because it has high PSD [2, 14]. The overall system noise as given in Eq. (1), can be modeled as the sum of the background noise, and the impulsive noise denoted as $n_{b}(t)$, and the impulsive noise, denoted as $n_{i m p}(t)$[2].

$n\lfloor(t)\rfloor=n_{b}(t)+n_{i m p}(t)$  (1)

The results of the time domain noise measurements show that noise has periodic features as well as randomness for a few seconds to minutes. This remained periodic, stationary, and cyclic for long periods of observation. The noise waveform obtained in the laboratories that have a several desktop computers, Television set, soldering iron, laptop computer with charger, and fluorescent lamps etc., are shown in Figures 7-11. The noise waveform exhibits different characteristics. Out of numerous measurements taken, only a few measurements are shown due to space constraint. The practical measurements in power lines found that the typical strength of a single impulsive is more than 10 dB above the background noise level and can occasionally exceed 40dB [15, 16]. Similar behavior can be observed from our measurements where impulsive strength rises well above the background noise as shown in Figure 6(b). The impulsive amplitudes reached value that is well above the background noise level, as high as 0.75. For meaningful interpretation of the impulsive energy, a threshold value needs to be defined that represent background noise [13].

In Figure 6, we determined the background noise level to be 0.03V. Using this value as reference, the amount of increase in the noise level beyond this value is as follows [13].

$L_{v}=20 \log \left[\frac{V_{i}}{V_{b}}\right]$  (2)

where, $L_{v}$ represent the voltage level in decibel; $V_{i}$ represent the impulsive noise voltage, and $V_{b}$ represent the background noise voltage. Therefore, $L_{v}$ is equal to 27.95 dB.

Hence, the results are shown in Table 2. The analysis of the mathematical function of measured signals with respect to time is known as time domain [17]. The signal is actually a narrative of how a factor is related to another. The two factors that form a signal are generally not exchangeable (Noise amplitude and Time). The noise amplitude-axis which is known as dependent variables is a function of time on time-axis known as independent variable.

However, the independent variable (Time) describes when and how the sample is taken, while the amplitude-axis is the actual measurements. Therefore, any signal that makes use of time as the independent variables is said to be in time domain. Under no load condition, the measurement was performed in an isolated PLC network where there were no users at all in the network. The typical size or number of nodes in the network was very small and no equipment’s was left ON. Hence, isolating the network or depriving other users of the network sometimes is always difficult to enforce. There is a noticeable portion of interference emanate from electronic devices connected to the electrical power line terminals in relative proximity by radiation and conduction. Figure 7 to 12 show measurements of electrical loads connected to the electrical power line outlets. The different noise waveforms are observed with their respective amplitudes. All the electrical loads induced noise of different amplitudes into the power network. Therefore, electrical equipment’s connected to the power networks are a source of noise most especially during switching ON and OFF and exhibit different characteristics.

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Figure 6. a) Asynchronous impulsive noise; b) Synchronous impulsive noise

Table 2. Parameters of impulsive and background noise

Figure 7. Phone charger noise waveform

Figure 8. TV Set plus phone charger noise waveform

Figure 9. Laptop Computer noise waveform

Figure 10. Fluorescent lamp noise waveform

Figure 11. Laptop and TV loads waveform

Figure 12. Sum of all the noise in Figures 7-11

The noise induced into the power line network by the fluorescent lamp and phone charger are higher in amplitude than the other noises induced into the network. Hence, Figure 12 shows the summation of all the noises produced by different appliances. The noise at any power outlet of power network is the sum of all noises produced by different appliances connected to the power line plus background noises [13].

As Table 3 shows, there is a significant difference between the loads in terms of its Mean amplitude and the standard deviations. The measured values are the Mean, which is found by the addition of all the samples together and divide by the total number of samples (N). For the calculation of a signal’s Mean, the signal is contained in $X_{0}$ through $X_{N-1}$, where i is an index that runs through these values, and µ is the mean.

$\mu=\frac{1}{N} \sum_{i}^{N-1} X_{i}$  (3)

The standard deviation (SD) represents noise and other interference. SD is comparison to the mean. The SD is calculated as:

$\delta^{2}=\frac{1}{N-1} \sum_{I=0}^{N-1}[X i-\mu]^{2}$  (4)

The signal is stored in $\mathrm{X}_{\mathrm{i}}$, where $\mu$ is the mean, N is the number of samples, and $\delta$ is the standard deviation. The results of this study indicate that noise signals are spread out over a wider range of values. The amplitude of Mean values obtained from different electrical loads range from (33.0-798) mV. Therefore, the average amplitude Mean for all the loads is 441 mV. Likewise, amplitude standard deviation values range from (58.5-200.03) mV, with an average of 100mV respectively. This can have severe destructive impact on PLC signals and hence need for robust noise coding techniques and modulation schemes that can ease the effect of noise signal. The findings observed in this study mirror those of the previous studies that have measured noise in PLC. We compared our results to that of literature elsewhere as shown in Table 4. The result of the standard deviation of duration is quite large and different from the previous research results. This can be attributed to varied environment under study which has unpredictable noise source, structure, topology and unknown characteristics of the power cables. Hence, standard deviation of noise durations described the noise in terms of duration of occurrence which is of short duration and range from microseconds to a few miliseconds.

Table 3. Statistical parameters of impulsive noise amplitude

Table 4. Impulsive noise parameters compared with literature elsewhere

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Figure 13. a) Sum of all the noise produced by different appliances connected to the line; b) Sum of all the noise using MATLAB

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Figure 14. a) Indoor noise summation; b) Indoor noise summation using MATLAB

In addition, noise measurements were taken from digital electronics laboratory. The equipements connected to the power line are: Digital Multimeter MAS-TEK MS80550 (125 Watts), Oscilloscope GW instek GDS-1052U (18 Watts), ED-LAB CES505 electronic lab system (25 Watts), CISCO Router 2900 (240 Watts), and Functional generator (25 Watts) respectively. These appliances induced noise into the power line. The noise produced at the power outlet is the sum of all the noises produced by these appliances connected to the line plus background noise as shown in Figure 13 (a). Figure 13(b) shows the replica of the wave form using MATLAB.

The output waveform of indoor appliances that comprises of blender, microwave oven, electric cooker, electric kettle, standing fan and water dispenser are shown in Figure 14 with their amplitudes.

The waveforms show the summation of noise induced into the power line outlet by all the appliances.

Welch PSD method was used for the noise power spectral density estimation. This method provides a good estimate of the noise spectral and signal power at different frequencies [9]. Welch is computed as the magnitude squared of the Fourier Transform of a continuous time and finite power signal. For a Continuous stochastic process,

$X_{T}(t)=\left\{\begin{array}{c}x(t),|t| \leq \frac{T}{2} \\ 0,|t|>\frac{T}{2}\end{array}=X(t) \operatorname{rect}\left(\frac{t}{T}\right)\right.$  (5)

The Fourier Transform is

$F\left(X_{T}(t)\right)=\int_{-\infty}^{\infty} X_{T}(t) e^{-j 2 \pi f t} d t, \quad T<\infty$  (6)

Hence, using Parseval’s theorem,

$\left.\int_{\frac{-T}{2}}^{\frac{T}{2}}\left|X_{T}\right|(t)\right|^{2} d t=\int_{-\infty}^{\infty}\left|F\left(X_{T}(t)\right)\right|^{2} d f$  (7)

Dividing through by T,

$\frac{1}{T} \int_{-\frac{T}{2}}^{\frac{T}{2}} X_{T}^{2}(t) d t=\frac{1}{T} \int_{-\infty}^{\infty}\left|F\left(X_{T}(t)\right)\right|^{2} d f$  (8)

Hence, Eq. (8) is the average signal power over time, T.

The equation at the left side becomes the average power as T, approaches infinity. The FT at the right side equation is not defined in that limit. Therefore,

$E\left(\frac{1}{T} \int_{-\frac{T}{2}}^{\frac{T}{2}} X_{T}^{2}(t) d t\right)=E\left(\frac{1}{T} \int_{-\infty}^{\infty}\left|F\left(X_{T}\right)\right|^{2} d f\right)$  (9)

$\left.\lim _{T \rightarrow \infty} \frac{1}{T} \int_{-T / 2}^{T / 2} E\left(X^{2}\right) d t=\left.\lim _{T \rightarrow \infty} \frac{1}{T} \int_{-\infty}^{\infty} E\left[| F\left(X_{T}(t)\right)\right]\right|^{2}\right] d f$  (10)

$\left\langle E\left(X^{2}\right)\right\rangle=\int_{-\infty}^{\infty} \lim _{T \rightarrow \infty} E\left(\left|F\left(\frac{X_{T}(t)}{T}\right)\right|^{2}\right) d f$  (11)

Figure 15 and 16 show the power spectral density of the computer and television (TV) set.

The integrand on the right side is identified as Power Spectral Density (PSD).

$G_{x}(f)=\lim _{T \rightarrow \infty} E\left(\left|F\left(\frac{X_{T}(t)}{T}\right)\right|^{2}\right)$  (12)

Average power of $\{X(t)\}=\int_{-\infty}^{\infty}(f) d f$  (13)

The noise power spectral density of the laptop varied between -2dBm (Hz) and 23dBm (Hz) and the high frequency noise process overlaid the low frequency noise process. The total noise spectral density of the computer (Samsung) has a maximum of 23dBm (Hz) at 0.13MHz. The noise spectral density of TV reaches a maximum level of 22dBm (Hz) at 0.15MHz. Between 0MHz and 0.4MHz the noise density spectral oscillate in the range from -2dBm (Hz) to 22dBm (Hz) in the frequency band from 0.5MHz to 0.9MHz.

As shown in Figure 17, the power spectral density of the noises produced by summations of all the appliances connected to the network were estimated using welch method.

Figure 15. Noise density spectrum of a computer

Figure 16. Noise density spectrum of a TV

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Figure 17. Noise PSD summation

Different methods can be used for generating a noise PSD, among which are; periodogram and welch methods [18]. The periodogram is computed by taking Fourier Transform of the time and squaring the output. In comparison, both Welch and periodogram methods are good estimate of noise spectral density but, Welch method is better for good estimate of the noise spectral density and signal power at different frequencies. The noise PSD summation describes the variation of a signals power versus frequency. Background noise is generally characterized by a reasonably low power spectral density and this PSD tends to decrease as the frequency increases [17]. Our findings revealed that at low frequencies, the noise power is significantly higher and it is within the range of 0.1MHz to 0.35MHz. Hence, at higher frequencies, the noise power decreases. The results of this study indicate that transients that occur majorly are due to switching ON and OFF in different parts of electrical network and are the major causes of asynchronous impulsive noise. The durations of the impulsive noise ranges from few microseconds to milliseconds. The noise is sporadic and this can have severe impact on PLC communication systems. This however, calls for a very robust and accurate noise coding techniques and modulation schemes that can ease the effect of the PLC channel noise on the signal.