CHAPTER 4 ADAPTIVE BIT-LOADING WITH AWGN FOR PLAIN LINE AND LINE WITH BRIDGE TAPS 4.1 Introduction The transfer function for power line channel was obtained for defined test loops in the previous chapter. In this chapter the issue of data rates achievable over Power line Communication (PLC) for DMT signals in the presence of Additive White Gaussian Noise (AWGN) is addressed. The received Signal to Noise Ratio (SNR) profiles in the presence of AWGN only are presented for typical Power line channels, since there no significant Near End Cross Talk (NEXT) and Far End Cross Talk (FEXT) present like in telephone cable bundles. Rate adaptive tone loading using the SNR profile is obtained. The dominant sources of impairment in PLC are time varying and frequency dependent channel attenuation, frequency dependent attenuation and impulse noise. These phenomenon are unique to PLC environment.The principal problem is frequency-selective attenuation, with deep notches in the frequency response resulting in very poor system performance. Hence a variant of Multi Carrier Modulation (MCM), viz Discrete Multi-Tone (DMT) is employed in which a channel is divided into many independent ISI-free sub channels. Power and bits are allocated adaptively in the sub channels according to the channel characteristics. In this chapter channel capacity estimation has been obtained by computing SNR for test loops. The SNR is obtained by considering the signal PSD as per the ITU standards (G 992.3) for VDSL2 upstream and downstream [49] along with AWGN of -140dBm/Hz and channel transfer function H(f). Water filling algorithm is employed to load the appropriate number of bits into each tone determined by the SNR of that particular tone. Finally channel capacity is obtained by adding the bits in each tone or sub channel for up to 7000 tones or 30 MHz bandwidth. Simulation results have been presented for the test loops described in the figure 3.11. SNR and bit-loading profile has been obtained for the upstream and downstream for all the test loops.
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CHAPTER 4
ADAPTIVE BIT-LOADING WITH AWGN FOR PLAIN
LINE AND LINE WITH BRIDGE TAPS
4.1 Introduction
The transfer function for power line channel was obtained for defined test
loops in the previous chapter. In this chapter the issue of data rates achievable over
Power line Communication (PLC) for DMT signals in the presence of Additive White
Gaussian Noise (AWGN) is addressed. The received Signal to Noise Ratio (SNR)
profiles in the presence of AWGN only are presented for typical Power line channels,
since there no significant Near End Cross Talk (NEXT) and Far End Cross Talk
(FEXT) present like in telephone cable bundles. Rate adaptive tone loading using the
SNR profile is obtained.
The dominant sources of impairment in PLC are time varying and frequency
dependent channel attenuation, frequency dependent attenuation and impulse noise.
These phenomenon are unique to PLC environment.The principal problem is
frequency-selective attenuation, with deep notches in the frequency response resulting
in very poor system performance. Hence a variant of Multi Carrier Modulation
(MCM), viz Discrete Multi-Tone (DMT) is employed in which a channel is divided
into many independent ISI-free sub channels. Power and bits are allocated adaptively
in the sub channels according to the channel characteristics.
In this chapter channel capacity estimation has been obtained by computing
SNR for test loops. The SNR is obtained by considering the signal PSD as per the
ITU standards (G 992.3) for VDSL2 upstream and downstream [49] along with
AWGN of -140dBm/Hz and channel transfer function H(f). Water filling algorithm is
employed to load the appropriate number of bits into each tone determined by the
SNR of that particular tone. Finally channel capacity is obtained by adding the bits in
each tone or sub channel for up to 7000 tones or 30 MHz bandwidth. Simulation
results have been presented for the test loops described in the figure 3.11. SNR and
bit-loading profile has been obtained for the upstream and downstream for all the test
loops.
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4.2 Channel Capacity Estimation
Theoretically channel capacity can be achieved by distributing the energy
according to water-filling bit-loading algorithm. Channel capacity estimation is based
on the Modified version of Shannon’s theorem. To apply Shannon’s theorem,
specifications of usable bandwidth B, noise power spectral density, transmit signal
power spectral density and transfer function are needed. Here a bandwidth of up to 30
MHz has been considered, with signal power spectral density as per VDSL2 (G993.2)
[49] with a noise power of -140dbm/Hz. Transfer function H(f) of the channel is
computed in the previous chapter for the test cases.
4.2.1 Channel Signal-to-Noise Ratio
In Discrete Multi-Tone (DMT) the transmitted symbol is divided into many
independent sub channels in the frequency domain with each sub channel carrying a
QAM carrier [36] as shown in the figure 4.1. Each sub channel has their Transmitted
power and bits allocated adaptively according to the SNR and channel characteristics.
Figure 4.1: VDSL2 Band plan
To find the rates supported, the SNR for different line topologies is needed.
SNR is computed from the equation (4.1). A bandwidth of up to 30 MHz has been
considered, with transmit signal Power Spectral Density (PSD) as per VDSL2
(G993.2) [49] as shown in the figure 4.2 for upstream and in figure 4.3 for
downstream. Noise spectral density and channel transfer function H(f), which has
been obtained for different test loops in the previous chapter are also considered for
SNR computation .
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Figure 4.2: US transmitter PSD mask (VDSL2 standard, ITU G993.2)
Figure 4.3: DS transmitter PSD mask (VDSL2 standard, ITU
G993.2)
0 1000 2000 3000 4000 5000 6000 7000-110
-100
-90
-80
-70
-60
-50
-40
-30
tones
PS
D in d
bm
US transmitter PSD mask
0 1000 2000 3000 4000 5000 6000 7000-110
-100
-90
-80
-70
-60
-50
-40
-30
tones
PS
D in d
bm
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The SNR [32] at the receiver is given by
2))(()( fHNoisepower
werTxSignalpofSNR =
(4.1)
• H(f) is obtained from equation (3.35) for different power line topologies shown
in figure 3.11.
• The ‘Txsignalpower’ PSD profile is provided for the 30 MHz VDSL2 band in
[49] as shown in figure 4.2 for upstream(US) and figure 4.3 for
downstream(DS). These are non-echo cancelled PSD masks specified in
G993.2. Each frequency is equal to a tone number multiplied with 4.3125 KHz.
• The noise power considered is Additive White Gaussian Noise (AWGN) of -
140dbm/Hz across all the tones.
• SNR is now an array with elements indexed to tones which can now be
employed in the Shannon’s theorem.
• SNR profiles across tones are obtained using equation (4.1) for the test loops
shown in figure 3.11.
4.2.2 Tone-loading Algorithm
The bits per tone that can be loaded on the ith
channel is given by Shannon’s
theorem [33]
�2 � ���!�E ���2� (4.2)
Where �2 is bits /dimension
Shannon theorem has been modified with the addition of ‘�’ the SNR gap,
which is a function of probability of symbol error and the line encoding system as
given in equation 4.3. For a symbol error probability of 10-7
(for QAM), the SNR gap
is 9.8dB. With a designed SNR margin of 6dB, � = (9.8+6) dB is used in this bit
profile calculation.
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�2 � ���! HE �,�\G I (4.3)
Where SNRi is the SNR of tone ‘i’.�The ‘bi’ so obtained is a rational number and needs
to be converted to integers as given in the equation 4.4.
��� � ����� '���! HE �,�\G I( (4.4)
Notice that addition or removal of one bit corresponds to an increase or
decrease of 3db in SNR. A rounding operation would floor or ceil the ‘bi’ that
corresponds to an increase or decrease in SNRi for the tone. This incremental ‘ SNRi’
is referred to fine gains. Water filling of energy across all the tones ensures that the
total energy does not exceed the standards specified limit of +21dbm across all usable
tones. Fine gains across all tones ensure that the surplus energies are redistributed
among the tones as shown in figure.4.4.
There is a need to allocate an amount of energy to each of the subchannel
such that the overall capacity C=�i ci is maximized, subject to a total energy constraint
E= �iEi.. This is accomplished with water filling algorithm. The energy is viewed as
water poured into a bowl that represents essentially the inverse SNR of the
transmission medium until no more water (energy) is left. Flip the channel and keep
pouring energy. Maximum power that can be transmitted is computed for a particular
frequency. The channel treats different frequencies differently, viz different
frequencies experience different attenuation. The problem is whether more power has
to be transmitted where there is more noise or a threshold for making a decision. It is
not prudent to keep pumping power into those frequencies which have high
attenuation. So a threshold ‘K’ is fixed, and if the threshold is crossed, no power is
allocated to that frequency. Continued to do so, not all the available power is used
because of the fractional bits. So with all the remaining power, reallocate evenly over
the frequencies so that they add up to ‘K’ and that’s where the term water filling
comes up.
The water filling solution is represented by flowchart given in the figure 4.4
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Figure 4.4: Flow chart for water filling algorithm with fine gain adjustment
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As seen in the band plan shown in figure 4.5 there are different frequency
bands allocated for the upstream and downstream. Hence the bits are loaded
accordingly in the upstream band by considering the SNR at that tone, and bits are not
loaded in the other frequency bands as specified in ITU 993.2. Similarly bits are
loaded in the downstream band and zero bits are loaded in the other frequency bands.
With the DMT symbol rate 4000 symbols/sec as for DSL the total channel
capacity can now be obtained from the equation (4.5) by summing the bits loaded in
each sub-channel considering the usable frequency bands for up-stream (US) and
down-stream (DS) transmitted signal PSD as specified in the band plan for VDSL in
G993.2 [49] shown below in the figure 4.5. Channel capacity for US and DS is
separately computed.
US0 DS1 US1 DS2 US2 DS3 US3
Figure 4.5: Band plan for VDSL2
Channel capacity is given by
� � �� ��� ���:::�� ¡� (4.5)
The channel capacity estimation is done as follows:
• The channel transfer function is computed using equations (3.8), (3.9) and
(3.10) with the knowledge of channel parameters.
• The SNR at the receiver is obtained from the equation (4.1), with the channel
transfer function, noise considered is AWGN and the signal PSD for VDSL2
band.
• Bits per tone that can be loaded on the ith channel is obtained by modified