Improving the multiple access method of home networks over the electrical wiring

Abstract

Data communications on domestic low-voltage powerlines benefit from an ubiquitous and already existent infrastructure. Nevertheless, high-speed communications on this environment faces obstacles such as attenuation and noise. The HomePlug standard defines Media Access Control (MAC)- and physical (PHY)-layer protocols for home electrical wiring networks. Its MAC protocol has introduced the deferral counter (DC) mechanism, which adapts the contention of the nodes for the medium according to the network load. This article proposes the Contention window Pro-active Increase (CPI) mechanism to enhance the performance of HomePlug. The CPI mechanism is based on DC and improves the HomePlug efficiency by faster increasing the contention window size. As a consequence, there are fewer collisions and the aggregated throughput increases. Under high network load, our simulation results show a tradeoff concerning throughput and jitter. CPI improves HomePlug throughput by up to 3% with no jitter increase and by up to 15% at the cost of additional jitter.

1 HomePlug 1.0 maximum throughput

This appendix derives a simple mathematical expression for HomePlug 1.0 maximum throughput, which can be used as sanity check for our HomePlug 1.0 simulation module.

The HomePlug 1.0 standard uses the spectral band from 4.49 to 20.7 MHz. Orthogonal Frequency Division Multiplexing (OFDM) is used with 84 sub-carriers evenly spaced. Among these 84 sub-carriers, eight can be disabled to avoid interference with amateur bands. Each OFDM symbol has a duration of 8.4 μs.

The PHY payload of HomePlug consists of a number of blocks with 20 or 40 OFDM symbols each, encoded on a link-by-link basis using Reed–Solomon and convolutional concatenated codes. The division in blocks is employed to avoid the impulsive noise that can damage symbol sequences. The damage can be more severe especially when using differential modulation because at least two symbols are lost at a time. The convolutional encoder has constraint length 7 and code rates of $\frac{1}{2}$ or $\frac{3}{4}$, selected during the channel adaptation. The Reed–Solomon code, which is used next, has coding rates ranging from $\frac{23}{39}$ to $\frac{238}{254}$.

Taking into account all the above PHY transmission parameters, the physical layer can offer up to 139 different rate combinations, ranging from 1 to 14 Mbps. Additionally, HomePlug has a especial mode, called ROBO (ROBust OFDM), which uses greater redundancy to operate under noisy conditions. The ROBO mode uses DBPSK (Differential Binary Phase Shift Keying) modulation, with a redundancy level that reduces the symbol rate to $\frac{1}{4}$ bit/symbol/sub-carrier. It also uses a Reed–Solomon code with different code rates, which range from $\frac{31}{39}$ to $\frac{43}{51}$. The ROBO mode reduces the maximum transmission rate to 0.9 Mbps.

The maximum 14-Mbps transmission rate of HomePlug 1.0 is obtained using the maximum number of sub-carriers and the parameters of error correction codes that produce the minimum redundancy. The eight sub-carriers that can be disabled due to amateur band are also used. Hence, as the symbol rate per second is equal to $\frac{1}{8.4 \mu {\rm s}}$, using 84 sub-carriers, a 10⁷ symbols/s rate is obtained. Using DQPSK (Differential Quadrature Phase Shift Keying) modulation, which employs 2 bits per symbol, a 20 Mbps maximum rate is reached. Nevertheless, the error correction codes use some of these bits to offer higher robustness to HomePlug. Therefore, the maximum throughput taking the error correction redundancies out is 14 Mbps, which is approximately $20~{\rm Mbps}\times\frac{3}{4}\times\frac{238}{254}$. This is not yet the effective data transmission rate since it neglects the overhead due to delimiters, interframe spaces, backoff, headers, and other required fields as seen in Fig. 13.

Fig. 13

Times needed for a HomePlug 1.0 frame transmission

We make the following assumptions for simplicity to compute the maximum throughput of HomePlug 1.0:

• there is one node transmitting and one node receiving;

• there is always one frame about to be transmitted;

• the bit error rate is null;

• frames are always successfully transmitted.

Figure 13 illustrates the overhead incurred in the transmission of a HomePlug frame. Expression 5 computes the HomePlug maximum throughput (R).

$$ \label{eq:taxa} R = \frac{d}{o+t}\ {\rm Mbps}, $$

(5)

where d is the payload size in bits, o is the overhead time in microseconds, and t the payload transmission time in microseconds. A HomePlug frame is composed of the header, the variable field, the FCS (Frame Check Sequence), the start and the end-of-frame delimiters, and the End-of-Frame Gap (EFG), as depicted in Fig. 13. The End-of-Frame Gap is a delay allocated for the processing of the frame received. The time spent with overhead, o, is given by:

$$ \begin{array}{rll} \label{eq:sc} o &=& \left({\rm CIFS} + {\rm PR}0 + {\rm PR}1 + \overline{\rm backof\/f} + 3\times {\rm delim.} \right.\\ &&{\kern6pt}\left.+ {\rm RIFS} + {\rm EFG}{\vphantom{\overline{\rm backof\/f} + 3\times {\rm delim.}}}\right)\ {\mathrm \mu} {\rm s} \\ o &=& (35.84 + 35.84 + 35.84 + 3.5\times35.84 + 3 \\ &&{\kern6pt}\times72 + 26 + 1.5)\ {\mathrm \mu} {\rm s} \\ o &=& 476.46\ {\mathrm \mu} {\rm s}. \end{array} $$

(6)

All stations must correctly receive the delimiters as well as the priority resolution signals. Therefore, they are sent using all the sub-carriers, with the same modulation and the same codification, regardless the data sender or receiver. The term $\overline{\rm backof\/f}$ of Expression 6 represents the average backoff time taking into account the initial size of the contention window. Hence, $\overline{\rm backof\/f}=\frac{{\rm CW}_{\rm min}}{2}\times (\rm slot~time)=\frac{7}{2}\times 35.84~\mu {\rm s}$ since we are assuming neither contention nor bit error rate. The header, the FCS, the encryption control (E _Ctl), the encryption padding (E _Pad), and the Integrity Check Value, which is the Ethernet FCS, are included in the data transmission time because they are sent at the same rate as the data. The HomePlug header is composed by a segment control plus the Ethernet source and destination addresses (SA and DA). The E _Pad is required because the encryption algorithm employed uses blocks of 8 bytes. Thus, besides the data, there is a 34-byte overhead plus the E _Pad added to the number of symbols to be transmitted. The number of symbols transmitted is denoted by n _s . The payload transmission time, t, is equal to the number of symbols, n _s , multiplied by the time needed to transmit one symbol, 8.4 μs.

$$ \label{eq:td} t = n_s{\times}8.4\ {\mathrm \mu} {\rm s}. $$

(7)

The value of n _s depends on the number of bits per symbol (m) which is a function of the used modulation, the number of sub-carriers (n _c ), the multiplication of the two error correction code rates (c), and the number of symbols per block (n _b ) as shown in Expression 8. The data are transmitted into 20- or 40-OFDM symbol transmission blocks to combat impulse noise. Thus, the block padding fills the last physical transmission block with zeros if the number of symbols of the frame is not a multiple of the used block size. Thus, in Expression 8, the number of blocks must be rounded up. Larger block sizes are more robust against noise, however, may lead to higher overhead.

$$ \label{eq:ns} n_s = \left\lceil\frac{1}{n_b}\times\frac{d + (34+E_{\rm Pad})\times 8}{m\times n_c\times c}\right\rceil{\times}n_b\ \mbox{\rm symbols.} $$

(8)

The encryption padding, E _Pad, is calculated as shown in Expression 9. The payload size (d + E _Pad) must be a multiple of 8 bytes. Thus,

$$ \label{eq:epad} E_{\rm Pad} = \left\lceil\frac{d}{8\times8}\right\rceil\times 8 - \frac{d}{8}\ {\rm bytes}. $$

(9)

Replacing 6, 7 and 8 into 5 the maximum throughput of HomePlug 1.0 is obtained:

$$ \label{eq:eg} R = \frac{d}{476.46 + \lceil \frac{1}{n_b}\times\frac{d + (34+E_{\rm Pad})\times8}{m\times n_c\times c} \rceil \times n_b\times 8.4}\ {\rm Mbps}. $$

(10)

For the maximum throughput, m = 2 bits/symbol, n _c = 84 sub-carriers, c = $\frac{3}{4}\times\frac{238}{254}$ and n _b = 20 symbols per block. Figure 14 plots the maximum throughput obtained with Expression 10 for different payload sizes. In Fig. 14, the full line represents the theoretical values whereas the dots are the values obtained through simulation. We observe that the simulation points match the theoretical curve.

Fig. 14

Maximum throughput of the HomePlug MAC protocol

The maximum throughput has a saw-tooth shape due to the padding inserted in the frames to keep the number of symbols per block always a multiple of 20. The periodic falls happen when another block of symbols is needed. As the payload increases, the padding decreases and the throughput grows until another block is needed.

A more precise calculation of the HomePlug maximum throughput must consider medium contention and bit error rates. This is not our purpose in this article, however, we encourage readers to take a look at [9, 19].