16

Smart Beamforming: Improving PLC Electromagnetic Interference

Daniel M. Schneider and Andreas Schwager

16.1  Introduction

16.2  Measurement and System Setup

16.3  Difference between Eigen- and Spotbeamforming

16.4  Results: Radiation Depending on Beamforming

16.5  EMI-Friendly Beamforming

16.6  Obtaining EMI Properties without Measuring Field Levels

16.7  Conclusions

References

16.1  Introduction

Multiple-input multiple-output (MIMO) technology enhances the performance of PLC systems by utilising multiple ports for sending and receiving signals (see Chapters 8, 9, 12, 14 and 24). Beamforming or precoding is used in several current power line communication (PLC) systems (see Chapters 12 and 14) and significantly improves their performance as seen in Chapters 8 and 9. The influence of MIMO transmission on electromagnetic interference (EMI) is addressed in Chapter 7. In particular, the influence on EMI, when feeding signals on transmit ports other than the traditional differential feeding between L and N, is compared and analysed. However, Chapter 7 does not touch on the effects on EMI in detail, when using a particular MIMO scheme at the transmitter and simultaneous transmission on several ports. A comparison of MIMO schemes for PLC can be found in Chapter 8. This chapter discusses how precoding or beamforming influences EMI. The analysis, in this chapter, is based on the MIMO EMI measurements performed at the ETSI STF410 measurement campaign (see Chapters 5, 7 and [1,2,3]). Section 16.2 briefly recalls the EMI measurement setup. Section 16.3 provides a theoretical analysis of expected EMI for different beamforming modes based on the correlation of transmit signals. Next, a detailed statistical analysis of EMI for different beamforming modes is given in Section 16.4. A point of interest is whether appropriate precoding can mitigate EMI effects. This question opens the second part of this chapter where ideas and first results of an EMI-friendly beamforming are presented (see Section 16.5). Section 16.6 addresses the issue of how PLC modems can obtain information about EMI properties of the PLC network.

16.2  Measurement and System Setup

The EMI measurement setup is described in detail in Chapter 7, Figure 7.1. Figure 16.1 is a block diagram of the basic setup, focusing on the functional aspects of the transmitter. The left-hand side of the block diagram shows the eigenbeamforming transmitter with two spatial streams (Figure 16.1a), spotbeamforming with one spatial stream (Figure 16.1b) and single input single output (SISO) (Figure 16.1c), respectively. Figure 16.1a and b depict typical MIMO-orthogonal frequency division multiplexing (OFDM) transmitters as introduced in Chapter 8. The right-hand side of each block diagram depicts the antenna used to evaluate the EMI of the MIMO transmission. The k-factor for each MIMO feeding option was measured, in magnitude and phase, for frequencies up to 100 MHz in horizontal and vertical polarisation of the antenna, during the ETSI STF 410 measurement campaign (see Chapter 7). The k-factor is measured in dBμV/m-dBm. This factor can be used to calculate the electrical field strength in dBμV/m assuming a given transmit power level (in dBm). In case of MIMO transmission (see Figure 16.1a and b), the EMI of the two signals fed in the two transmit ports interfere with each other. Let h₁ be the k-factor of the first transmit port to the antenna location and h₂ the k-factor of the second transmit port of a given frequency. Assume further that s₁ and s₂ are signals of a given frequency, where the two signals are combined into the vector $s=\left[\begin{array}{c}{\text{s}}_1\\ {\text{s}}_2\end{array}\right]$ (e.g. the symbols of one OFDM subcarrier as shown in Figure 16.1a and b or one frequency measurement point of the network analyser [NWA]). Then, the resulting field at the antenna location of the given frequency is given by h₁s₁ + h₂s₂.

Figure 16.1a shows beamforming in the precoding matrix F. If $b=\left[\begin{array}{c}{b}_1\\ b_2\end{array}\right]$ is the vector of the two signals of a given frequency before precoding, then the vector of the two transmit signals is given by s = Fb (refer also to Chapter 8). In the case of spotbeamforming (refer to Figure 16.1b), only one spatial stream is used, that is, b = b₁, and the precoding matrix simplifies to a precoding vector f. Figure 16.1c shows SISO transmission.

FIGURE 16.1
Setup: transmitter and EMI measurement. (a) Two-stream MIMO: Eigenbeamforming, (b) one-stream MIMO: Spotbeamforming, and (c) SISO.

The total transmit signal energy is identical for all setups (Figure 16.1a through c). OFDM and the precoding blocks are also identical in the three setups. The quadrature amplitude modulation (QAM) mapper is the source of the transmit signals and defines the level of transmit energy. The output energy of spotbeamforming (Figure 16.1b) and SISO (Figure 16.1c) configurations has been boosted by 3 dB to make the comparison more clear, as each configuration only has one QAM mapper. MIMO precoding splits input energy into two output ports but does not amplify or attenuate the signals. The OFDM units also do not change the energy between input and output. This is how identical transmit signal energy is guaranteed for all three setups.

16.3  Difference between Eigen- and Spotbeamforming

The relation or correlation between the signals transmitted on the two transmit ports influences the electrical field levels at the antenna and determines if the signals interfere constructively or destructively. The following is a discussion of the spatial correlation of transmitted signals where beamforming has been applied. Note that there is a similar discussion already in Section 8.5.2, which is recalled here for convenience to describe the special case of two transmit ports.

In Figure 16.1a, both MIMO streams are modulated independently by the two QAM mappers. If each MIMO stream is modulated independently, the signals are spatially uncorrelated

$E\left\{b{b}^H\right\}=I_2,$

(16.1)

where

$E\{\cdot \}$ represents expectation over time samples

I₂ is the 2 × 2 identity matrix

Thus, where no precoding is applied, s = b, the transmitted signals are also uncorrelated $E\left\{s{s}^H\right\}=E\left\{b{b}^H\right\}=I_2$. If precoding is applied and the entries of b are uncorrelated, the correlation matrix results in

$E\left\{s{s}^H\right\}=E\left\{\left(Fb\right){\left(Fb\right)}^H\right\}=FE\left\{b{b}^H\right\}{F}^H=F{F}^H.$

(16.2)

For eigenbeamforming (two spatial streams) with F = V, the unitary property of V simplifies Equation 16.2 to VV^H = I₂ and the transmit signals remain uncorrelated. Thus, eigenbeam-forming does not influence the electrical field levels. Spatial multiplexing without precoding and beamforming with an arbitrary unitary precoding matrix results in the same EMI.

If one-stream beamforming (spotbeamforming) is used with F = v₁ (where v₁ is the first column vector of V), the simplification $v{v}_1^H=I_2$ is not valid. This causes a correlation between the transmit signals, which means that the precoding vector influences the electrical field levels (see next section).

16.4  Results: Radiation Depending on Beamforming

The unitary precoding matrix V can be represented by two angles ψ and ϕ:

$V=\left[v_1{v}_2\right]=\left[\begin{array}{cc}\cos \left(\text{ψ}\right)& \sin \left(\text{ψ}\right)\\ -e^{j\varphi }\sin \left(\text{ψ}\right)& e^{j\varphi }\cos \left(\text{ψ}\right)\end{array}\right],$

(16.3)

where the range of ψ and ϕ to represent all possible beamforming matrices is $0\le \text{ψ}\le \text{π/2}$ and $-\text{π}\le \varphi \le \text{π}$ (refer also to Chapter 14). The precoding vector for spotbeamforming is given by $v_1=\left[\begin{array}{c}\cos \left(\text{ψ}\right)\\ -e^{j\varphi }\sin \left(\text{ψ}\right)\end{array}\right]$. Figure 16.2 shows an example of one measurement at one frequency. The x-and y-axes represent the angles ψ and ϕ in the range described earlier. The contour lines in the figure show the level of the electrical field relative to SISO (D1 port of the triangle style coupler when feeding at the same outlet, see Chapter 5) depending on the precoding vector represented by ψ and ϕ. The distance between the contour lines is 1 dB. If the signals of the two transmit ports interfere destructively, almost complete signal elimination may be achieved (see ψ = 1.1 and ϕ = −2.8). On the other hand, the signals may interfere constructively for some precoding vectors. This is the case especially for ψ < 1.1 and −1 < ϕ < 1. The bold contour line marks the median line, that is, 50% of the beamforming angles result in an electrical field level higher than the median value of −3.5 dB (relative to SISO), while 50% of the beamforming angles result in lower radiation compared to the median value. The maximum (−0.5 dB) is 3 dB higher than the median value. In Figure 16.2, there is a small peak denoting that the electrical fields have been completely eliminated, while the flat area describes levels slightly higher than the median value. The phenomena of deep canyons and flat hills in signal level readings can be monitored with many applications with multipath fading channels (e.g. HF radio broadcast transmissions; see Chapter 22, Figure 22.2).

FIGURE 16.2
Electrical field levels relative to SISO depending on the precoding vector, one channel at one frequency.

Figure 16.3 shows the cumulative distribution frequency (CDF) of the radiation compared to SISO with the same channel and frequency as in Figure 16.2. To obtain this CDF, all possible precoding vectors of one-stream beamforming were used. Figure 16.3 comprises the 20%, 80% and 50% (median) values. The median value shows a radiation of 3.5 dB less than the SISO case seen in Figure 16.1c for this channel and frequency. The maximum radiation is reached with low statistical probability and is 3 dB higher than the median value (see upper right corner in Figure 16.3). Here, the radiation level of the SISO transmission is never reached. On the other hand, signal elimination (−18 dB) may be achieved with a very low statistical probability (see lower left corner in Figure 16.3). The median value of spotbeamforming radiation is equal to the radiation levels of two-stream MIMO (eigen-beamforming or spatial multiplexing without precoding). This was validated for every measurement (see next section).

The calculation as shown for Figure 16.3 was performed for each measurement (i.e. each measurement site, each frequency and each antenna location). Overall, 100,863 measurement points are used in these statistics (1,601 frequency points between 1 and 100 MHz at 63 sweeps). Figure 16.4 shows the CDF of the radiation for all measurements using different MIMO setups where D1 and D3 (see Chapter 1, Figure 1.2) were used as feeding ports. The level of radiation is given relative to the radiation of SISO (D1 port) where the difference between MIMO and SISO is calculated for each pair of measurements before determining the CDF. As shown in Section 16.3, the radiation of two-stream MIMO is independent of the beamforming matrix and is the same as spatial multiplexing without precoding. Since these cases all yield the same levels of radiation, they are shown by only one single line (indicated by ‘no precoding or two-stream BF’ in Figure 16.4). The min, 20%, 50%, 80% and max lines of spotbeamforming (one-stream BF) are related to the corresponding CDF values of the different beamforming angles (refer also to Figures 16.2 and 16.3). The median value of spotbeamforming is also identical to two-stream MIMO or spatial multiplexing. The maximum radiation of spotbeamforming is shifted by +3 dB compared to two-stream MIMO but is only 2.4 dB higher compared to SISO. This is depicted in the zoomed version of the graph in Figure 16.4. The figure also comprises the special spotbeamforming $f\text{\hspace{0.17em}=}\left[\begin{array}{c}1/\sqrt{2}\\ 1/\sqrt{2}\end{array}\right]$ where the signal is transmitted via both transmit ports with the same power and no phase offset (denoted by ‘equal BF’ in the figure). Identical signals are transmitted here via both transmit ports. Interestingly, the electrical field level is significantly reduced compared to two-stream MIMO and SISO.

FIGURE 16.3
CDF of the electrical field levels of all possible one-stream beamforming vectors relative to SISO, one channel at one frequency, same channel as in Figure 16.2.

FIGURE 16.4
CDF of the radiation of all feeding outlets, all antenna positions and all frequencies, D1 and D3 feeding.

Figure 16.5 shows a similar plot as Figure 16.4 where T1 and T2 are used as feeding ports. The figure basically shows the same properties as the D1 and D3 feeding in Figure 16.4. The zoom in Figure 16.5 confirms the worst-case 3 dB increase but an optimum case signal elimination of 12 dB relative to two-stream MIMO.

The CDFs of Figures 16.4 and 16.5 show records of some channels providing higher EMI in the MIMO cases, while the majority of measurements in the SISO configuration show higher radiation. Figure 16.6 shows an example of the k-factor of one measurement sweep over the frequency. The figure compares the k-factor of SISO (solid line, feeding port D1) and spotbeamforming (dashed line, one-stream BF, D1 and D3 feeding). At this channel, SISO radiates higher at some frequencies, while at other frequencies MIMO provides higher EMI. This explains the CDF shape of Figures 16.4 and 16.5.

FIGURE 16.5
CDF of the radiation of all feeding outlets, all antenna positions and all frequencies, T1 and T2 feeding.

It is assumed that MIMO PLC modems operate in eigenbeamforming mode at almost all channels and frequencies. Spotbeamforming is used only at high attenuated channels or frequencies. Simulations were performed to investigate how many channels and frequencies use spotbeamforming if the signal to noise ratio (SNR) conditions do not support eigenbeamforming. The following assumptions are used for these simulations:

FIGURE 16.6
Example of the k-factor depending on the frequency of one measurement, comparison between SISO and spotbeamforming.

•  The transmit to noise power ratio is set to 75 dB, corresponding to a transmit power level of −55 dBm/Hz and a flat noise power spectral density of −130 dBm/Hz (which is the median value of noise below 30 MHz; see Chapter 5).

•  The system parameters are the same as described in Chapter 9.

•  The channels of the ETSI measurement campaign were used (more than 340 channels; see Chapter 5).

As a result of these simulations, 5% of the subcarriers of all channels use spotbeamforming due to the insufficient SNR of the second stream. 95% of these subcarriers support eigenbeamforming.

16.5  EMI-Friendly Beamforming

As shown in the previous section, beamforming may be used to improve interference (EMI) from PLC by eliminating signals at some locations or reducing the electrical or magnetical field of the radiated signals in the air. If the level of interference is improved as described earlier, experimentally, the level of transmit power of PLC modems may be enhanced to have the equivalent EMI potential. The beamforming vector for minimising EMI will usually not be the optimum beamforming vector for a PLC receiver on the network. Thus, there is a loss of throughput rates compared to beamforming optimised for the communication link. On the other hand, the gain of increased feeding levels might compensate for this loss. Of course, given EMC regulatory requirements have to be considered before bringing such an experiment to maturation.

Figure 16.7 shows the electrical field in the air (solid contour lines, denoted by ‘E-field depending on precoding’ in the legend), radiated from the power lines. The field depends on the precoding vector described by the two angles ψ and ϕ (similar to the plot shown in Figure 16.2). The level of the E-field is shown relative to the E-field of SISO-PLC radiation at 30 MHz. The antenna was located indoors. The highest increase of radiation (less than +3 dB compared to SISO in this example) is obtained by the precoding vector marked with the black square ■. The maximal signal elimination (maximal reduction compared to SISO’s transmission E-field, −14 dB) is obtained by the precoding vector marked with grey star ★. (see ψ ≈ 1 and ϕ ≈ −3 in the figure). The communication links to other outlets in the building were also measured for the feeding outlet where the E-field measurements were performed. Two links are available in this example. The optimum (spotbeamforming) precoding vector for these two receiving outlets is marked by the two diamond symbols ♦ labelled 1 and 2. The dashed contour lines in Figure 16.7 show the available SNR for the first link depending on the precoding vector. Of course, the highest SNR of 30 dB (see the grey circle • in Figure 16.7) is achieved if the precoding vector is optimised for this link. The SNR decreases when ‘moving away’ from this optimum precoding. The precoding vector optimised for the communication link and the precoding vector optimised to reduce the E-field are usually not identical. The example shown in Figure 16.7 provides quite some distance between the two vectors: The subscript number (0.88) at the first diamond symbol indicates a measure of distance to the optimum precoding vector to minimise the E-field. This distance might vary between 0 (same precoding vector) and 1 (most distant precoding vector or orthogonal vector); details of the definition of this distance may be found in [4].

FIGURE 16.7
Electrical field levels relative to SISO (solid contour lines) and SNR (dashed contour lines) depending on different precoding vectors, 30 MHz.

Assume that the precoding vector is optimised to achieve elimination of the E-field (star symbol in Figure 16.7). The radiated E-field is E_reduced = 2 dB −(−14 dB) = 16 dB below the radiation level of the case where the precoding vector is used, which has been optimised for this link. Meaning, the level of transmit power may be increased by this amount to obtain the same E-field level. On the other hand, the loss in SNR by not using the optimum precoding vector for this link is SNR_loss = 8 dB (30 dB −22 dB), as observed by the intersection of the dashed contour lines with the star symbol. Overall, an SNR increase of SNR_gain = E_reduced −SNR_loss = 8 dB may be obtained in this example which results in an increased bitrate.

Figure 16.8 shows similar plots as Figure 16.7, with the same transmitting outlet location, building and two different antenna locations 10 m from the exterior wall at the outside of the building. The E-field contour lines are quite similar to Figure 16.7 (the E-field maximum ■ is in the centre of the figure, while the minimum precoding vector ★ is also centralised but nearer the bottom line). However, the distance between the two optimum E-field vectors ★ is not large. This indicates that the optimal E-field precoding is independent, to an extent, of the antenna location.

In the United States, the assessment of the PLC product certification (see also Chapter 6) is done by checking the electrical field level on the outside of a building. If this level is lowered by, for example, 10 dB by smart beamforming, the transmit level of PLC modems may also be increased by 10 dB.

FIGURE 16.8
Same settings as in Figure 16.7 at two different outdoor antenna locations at 10 m distance (compared to the indoor antenna location in Figure 16.7). (a) First antenna location at 10 m distance and (b) second antenna location at 10 m distance

FIGURE 16.9
CDF of SNR gain due to EMI-friendly beamforming.

Per Figures 16.7 and 16.8, the EMI could be mitigated completely, as shown by the deep notches. Theoretically, as an extreme example, the electrical field level of the MIMO modems could be lower than the ambient noise level. As a result, the feeding level could be increased accordingly. Of course, in reality, several limiting factors have to be considered. The EMI information has to be quite accurate and the beamforming angles are usually quantised to a set of certain values. To investigate the potential of EMI-friendly beamforming and corresponding SNR gain, the algorithm earlier is applied to all available EMI and corresponding S21 measurements. The quantisation of the beamforming angles is set to 12 bits (5 bits for ψ and 7 bits for ϕ) which are the beamforming parameters of HomePlug AV2 (see Chapter 14). The SNR gain of each frequency and measurement site is influenced by two factors. First, the loss of SNR due to non-optimised beamforming of this link, and second, feeding level gain from EMI-friendly beamforming. If the SNR gain is less than 0 dB, classical spotbeamforming is applied in the following simulations. Figure 16.9 shows the CDF of the signal to noise level gain SNR_gain for all measurements. In median, an SNR gain of almost 10 dB is observed. At the 90% point, that is, for 10% of the sweeps, the SNR gain is 20 dB and higher. The SNR gain is always larger than 0 dB as the scheme defaults to normal spotbeamforming if no SNR gain is achieved from EMI-friendly beamforming.

16.6  Obtaining EMI Properties without Measuring Field Levels

One important question has to be answered if beamforming is adjusted to mitigate the EMI: How does a modem know the EMI properties? Usually the modem cannot measure the radiation or the EMI properties of the actual power line grid. One interesting approach could be to use current probes to measure the currents on each wire. According to Biot-Savart’s law, the CM current is responsible for radiation. The current probe might be located in the transmitter or somewhere else on the network, depending on how the EMI depends on the outlet properties or on the properties of the power line grid. In a training phase, the transmitting modem toggles all possible precoding vectors in a predefined way and the probes signal which precoding vector gives balanced currents on the three wires.

To investigate the potential of this idea, measurements were performed in an anechoic chamber. Figure 16.10 shows the setup. An artificial mains network including a fuse cabinet, wires with similar length as in a small flat, power strips and several appliances or impedances connected was laid out in the chamber. The electrical field probe [5] was located at a distance of approximately 3 m from the artificial mains. The MIMO current probe consists of three inductors, inserted into the live (L), the neutral (N) and the protective earth (PE) wire and connected at various locations in the network. The probe’s transfer impedance is

$Z_T\left(\text{dB}\text{Ω}\right)=V\left(\text{dBμV}\right)-I\left(\text{dBμA}\right)=21.5\text{dB}\text{Ω}.$

(16.4)

A multiport NWA feeds signals using the PLC coupler described in Chapter 1 into the mains and simultaneously records the E-field, as well as the currents on the wires. The coupling factor (k-factor in dBμV/m -dBm) in the chamber is derived using Equation 7.1 in Chapter 7. The current I_wire is calculated as

$I_{\text{wire}}=P_{\text{Tx}}+{\text{S}}_{21}-Z_T+{\text{Conv}}_{\text{dBm2dbμV}},$

(16.5)

where

P_Tx = 12 dBm is the NWA’s injected feeding power

S₂₁ is the scatter factor recorded by the NWA

Conv_dBm2dBμV = 107 dBm −dBμV is the conversion factor from dBm to dBμV

Figure 16.11a shows the currents on L, N and PE of the current probe placed somewhere on the mains grid. Equal beamforming was applied in this example, that is, the same signal is transmitted on both transmit ports. In a next step, the beamforming is adjusted to balance the currents on N and PE by minimising the current on L. Minimising the current on L is selected, since D1 (L–N) and D3 (L–PE) are used for feeding. Figure 16.11b shows the influence of this beamforming on the currents measured by the current probe. As expected, the current on L is minimised, while the currents on N and PE have the same magnitude.

FIGURE 16.10
Setup of EMI current measurements.

FIGURE 16.11
Magnitude of currents on L, N and PE for different precoding. (a) Equal precoding, (b) precoding to balance currents on N and PE by minimising current on L.

Figure 16.12 shows the k-factor versus frequency of the two different beamforming vectors introduced before, that is, equal precoding (solid line) and precoding to balance currents on N and PE (dashed line). For most frequencies, the k-factor is decreased by the beamforming based on the balanced currents.

FIGURE 16.12
k-factor for different types of beamforming: equal precoding and precoding based on balanced currents.

Figure 16.13 shows the corresponding CDF, that is, the CDF of the k-factor of Figure 16.12. In median, an improvement of 4 dB is observed for beamforming based on balanced currents compared to equal beamforming.

Another idea is to use the S11 parameter at the transmitting modem to identify the optimum beamforming vector in order to mitigate the EMI. The S11 parameter measures the reflected energy. By toggling all possible beamforming vectors (or a subset of beamforming vectors) and monitoring the corresponding S11 value, a correlation to the expected EMI might be revealed in future research.

The transfer functions to other modems on the network might also give an indication of the beamforming to mitigate EMI. Beamforming vectors providing minimal signal level at one or more receiving PLC modems are assumed to cause low signal radiation. Beamforming vectors providing maximal signal level at one or more receiving PLC modems are assumed to cause higher signal radiation. There are devices or resistors on the network which absorb communication signal energy. If beamforming is directed to these devices, radiation is also reduced. The variation of signal level at the receiving modem might indicate how much energy is lost due to signal radiation. An antenna or level meter providing a feedback channel might check the level of interference for different beamforming vectors and indicate the optimum beamforming vector.

The location where the interference should be reduced might also be another PLC modem operating in a neighbour’s flat. This PLC modem might signal the channel parameters to the interfering transmit modem. The transmitter might easily calculate the beamforming angles to eliminate interference at the neighbour’s flat.

FIGURE 16.13
CDF of the k-factor for different types of beamforming: equal precoding and precoding based on balanced currents, measurement in anechoic chamber of an artificial mains network.

16.7  Conclusions

This chapter aimed to answer the question how MIMO and especially beamforming influence the levels of the electrical field compared to SISO. The results showed that in median MIMO radiates less compared to SISO. This result suggests that the transmit power level of each MIMO port may not have to be reduced by 3 dB compared to SISO but may be chosen to be less. It was shown that the levels of the electrical field are identical for

•  Two-stream MIMO (independent of any arbitrary unitary precoding matrix, eigenbeamforming)

•  Spatial multiplexing without precoding (special case of two-stream MIMO)

•  Median of one-stream beamforming

Spatial multiplexing and eigenbeamforming yield the same probability of EMI. In the case of one-stream beamforming or spotbeamforming, the precoding vector influences the EMI. The beam may result in a destructive or constructive interference. The worst-case constructive interference results in a 3 dB higher radiation compared to two-stream MIMO. However, this special case is unlikely since only one special beamforming vector may give this result. It is also assumed that MIMO PLC modems operate in eigenbeamforming mode most of the time and for almost all channels. On the other hand, beamforming may be used to almost eliminate the radiation.

This conclusion motivated the second part of this chapter: Beamforming may be used in future PLC systems to mitigate the effects of EMI and unwanted radiation. If beamforming is optimised to minimise the radiation, the question arises how this would influence the modem’s throughput performance. Usually, beamforming is used at the transmitter to maximise the performance (throughput) to the receiver. However, if beamforming is chosen to minimise EMI, the transmit power level might be increased which leads to an increase in performance. First results were presented which showed an SNR gain when this concept is applied. This gives another degree of freedom in the design of the PLC modem.

An interesting question for future research is the following: How does a modem obtain the properties of EMI, in order to correctly adjust beamforming to mitigate it? One interesting approach could be to use a current probe to measure the currents on each wire and to toggle the beamforming vectors until the currents on the wires are balanced. First measurements in the laboratory indicated that there is a relation between the currents on the wires and EMI which can be used to adapt the beamforming to reduce EMI.

Applying this concept to remove interferences at PLC modems in a neighbour’s flat, optimal beamforming can be calculated using the channel parameter’s feedback information from a neighbour’s modem.

References

1.  ETSI, TR 101 562-1 v1.3.1, PowerLine Telecommunications (PLT), MIMO PLT, Part 1: Measurement methods of MIMO PLT, Technical Report, 2012.

2.  ETSI, TR 101 562-2 v1.2.1, PowerLine Telecommunications (PLT), MIMO PLT, Part 2: Setup and statistical results of MIMO PLT EMI measurements, Technical Report, 2012.

3.  ETSI, TR 101 562-3 v1.1.1, PowerLine Telecommunications (PLT), MIMO PLT, Part 3: Setup and statistical results of MIMO PLT channel and noise measurements, Technical Report, 2012.

4.  D. Schneider, Inhome power line communications using multiple input multiple output principles, Dr.-Ing. dissertation, Verlag Dr. Hut, Munich, Germany, January 2012.

5.  SCHWARZBECK MESS-ELEKTRONIK; EFS 9218: Active electric field probe with biconical elements and built-in amplifier 9 kHz–300 MHz. http://www.schwarzbeck.com/Datenblatt/m9218.pdf, accessed 16 October 2013.