chapter 4 adaptive bit-loading with awgn for...

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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

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Shannon’s theorem as in the equation (4.3).

• Channel capacity is calculated by summing the bits loaded in each sub-

channel from the equation (4.5) as per the band plan shown in figure4.4 for

upstream and downstream.

4.3 Simulation Results and Analysis

In this section the channel capacity of power line test topologies with varying

lengths, varying number of BTs with varying lengths as shown in the figure 3.11

(A,B,C,D, E & F) are considered and the simulation results are presented.

4.3.1 Simulation Conditions

• The SNR as explained in the section 4.2.1 is obtained for the test loops in the

figure 3.11 from the equation 4.1

• Transmit signal PSD is considered as per ITU standard 993.2 for VDSL as

shown in figure 4.2 & 4.3 for upstream and downstream respectively.

• Noise of -140dBm/Hz and the channel transfer function H(f) as discussed in

chapter 3 is considered to obtain SNR.

• � = 9.8+6 = 14.8db. Here 9.8 assures that a bit error rate (BER) of 10 -7

would

be met in the channel and a 6db degradation margin has been provided.

• SNR as explained above, tone-loading profile for upstream and downstream is

obtained for the test loops from equation 4.2 as explained in the section 4.2.2.

Simulations results are given below for the test loops shown in figure 3.11 (A,

B, C, D, E & F). SNR profile for upstream and downstream are presented for plain

line with length 600mts, 1200mts and 3000mts in the next section along with line

with one, two, five and ten taps, later the tone loading profiles are presented for the

same test loops for upstream and downstream.

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4.3.2 SNR & Tone-loading profile

Test loop1: plain line with the length of 600mts, 1200mts & 3000mts

The SNR profile of the plain length of line shown in figure 3.11A, loop1 with the

power line lengths 600mts, 1200mts and 3000mts is shown in the figure 4.6 & 4.7 for

upstream and downstream. As seen the SNR decreases as the line length increases. As

the line length doubles the SNR also decreases by two times.

Figure 4.6: Upstream signal PSD & SNR of loop 1

Figure 4.7: Downstream signal PSD & SNR of loop 1

0 1000 2000 3000 4000 5000 6000 7000-150

-100

-50

0

50

100

150

SN

R &

sig

nal P

SD

Tones

PSD

600mt

1200mt

3000mt

0 1000 2000 3000 4000 5000 6000 7000-150

-100

-50

0

50

100

150

SNR &

sig

nal PSD

Tones

PSD

600mt

1200mt

3000mt

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Bit-loading profile for the testloop1, for the plain length of line of 600mts is shown in

figure 4.8 & 4.9 for up & downstream. Since it is a plain line there are no dips in the

SNR profile, hence there is also not much variation in the bits loaded in the upstream

band. Since there is gradual decrease in the SNR in the downstream bands, there is

also a monotonic decrease in the numbers of bits as the frequency increases. Since a

rounding operation would floor or ceil the ‘bi’, the increase or decrease in SNRi for

that tone ‘ SNRi’ would be less than 3db. Hence a constant bit loading pattern is seen

in fig. 4.8 & 4.9.

Figure 4.8: Upstream bit-loading in loop1

0 1000 2000 3000 4000 5000 6000 70000

5

10

15

20

25

30

35

tones

bit p

att

ern

for

uplo

adin

g in b

its p

er

tone.

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Figure 4.9: Downstream bit-loading in loop1

Test loop 2: Line with BT at the rear end

SNR profile for the loop2 and loop3 are plotted in the figure 4.10 & 4.14 for upstream

and in figure4.11 & 4.15 for downstream along with the signal PSD. As observed

from the simulation results, the attenuation is same for the loop2 and loop3 viz due to

the tap in the front end and rear end. A bridge tap causes reflections at the open circuit

end producing dips in the transfer function of the loop to which it is attached. The

bridge tap has an effect on the SNR in downstream due to the change in attenuation

profile.

0 1000 2000 3000 4000 5000 6000 70000

5

10

15

20

25

30

tones

bit p

att

ern

ford

ow

nlo

adin

g in b

its p

er

tone.

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Figure 4.10: Upstream PSD & SNR of loop 2

Figure 4.11: Downstream PSD & SNR of loop 2

Bit-loading profile for the test loop 2 & 3, line of 600mts with one tap in the rear and

front end are shown in figure 4.12, 4.13, 4.16 & 4.17. The ripples in the SNR due to

the tap introduces variation in the bits loaded in the two upstream bands, which in turn

0 1000 2000 3000 4000 5000 6000 7000-150

-100

-50

0

50

100

150

Tones

SN

R &

Sig

nal P

SD

PSD

SNR

0 1000 2000 3000 4000 5000 6000 7000-150

-100

-50

0

50

100

150

Tones

SN

R &

Sig

nal P

SD

PSD

SNR

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reduces the channel capacity compared to the plain line. The dip in the SNR in the

downstream is coinciding with the second transmit band due to which there is as deep

notch in the second band which significantly reduces the channel capacity in the

downstream.

Figure 4.12: Upstream bit-loading in loop2

Figure 4.13: Downstream bit-loading in loop2

0 1000 2000 3000 4000 5000 6000 70000

5

10

15

20

25

30

35

tones

bit p

attern

for uplo

adin

g in b

its p

er to

ne.

bit loading pattern for line length 600mts

0 1000 2000 3000 4000 5000 6000 70000

5

10

15

20

25

30

tones

bit p

attern

ford

ow

nlo

adin

g in b

its p

er to

ne.

1200 1400 1600 1800 2000 2200 2400

10

12

14

16

18

20

22

tones

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Test loop3: Line with BT at the front end



0 1000 2000 3000 4000 5000 6000 7000-150

-100

-50

0

50

100

150

Tones

SN

R &

sig

nal P

SD

PSD

SNR

0 1000 2000 3000 4000 5000 6000 7000-150

-100

-50

0

50

100

150

Tones

SN

R &

Sig

nal P

SD

PSD

SNR

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Figure 4.16: Upstream bit-loading in loop 3

Figure 4.17: Downstream bit-loading in loop 3

0 1000 2000 3000 4000 5000 6000 70000

5

10

15

20

25

30

35

tones

bit p

attern

for uplo

adin

g in b

its p

er to

ne.

0 1000 2000 3000 4000 5000 6000 70000

5

10

15

20

25

30

tones

bit p

att

ern

ford

ow

nlo

adin

g in b

its p

er

tone.

1200 1400 1600 1800 2000 2200 2400

8

10

12

14

16

18

20

22

24

tones

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Test loop4: Line with two BT’s of equal length

SNR profile for the loop 4, with two bridge taps of equal lengths 10mts are shown in

figure 4.18 and 4.19 for up and down stream and with two bridge taps of different

lengths 10 & 20mts are shown in figure 4.22 & 4.23. It is observed that the

attenuation at the dips is increased with two taps compared to the single tap. The

numbers of dips are more with the taps of unequal lengths due to mismatch of

impedance.


0 1000 2000 3000 4000 5000 6000 7000-150

-100

-50

0

50

100

150

Tones

SN

R &

Sig

nal P

SD

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Bit-loading profile for the test loop 4, for the line of 600mts with two bridge taps of

equal length(10mts) are shown in the figure 4.20 & 4.21 and two taps of different

lengths(10 & 20mts) are shown in the figure 4.24 & 4.25. Since the ripples in the

SNR is more for the two taps with different lengths, there is reduction in the channel

capacity compared to the two taps of equal length.


0 1000 2000 3000 4000 5000 6000 7000-150

-100

-50

0

50

100

150

Tones

SNR &

Sig

nal PSD

0 1000 2000 3000 4000 5000 6000 70000

5

10

15

20

25

30

35

tones

bit p

attern

for uplo

adin

g in b

its p

er to

ne.

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Test loop4: Line with two BT’s of unequal length (10 & 20mts)


0 1000 2000 3000 4000 5000 6000 7000-150

-100

-50

0

50

100

150

Tones

SN

R &

Sig

nal P

SD

0 1000 2000 3000 4000 5000 6000 70000

5

10

15

20

25

30

tones

bit p

att

ern

ford

ow

nlo

adin

g in b

its p

er

tone.

bit loading pattern for downloading for line length 600mts with two taps after 200mts

1000 1200 1400 1600 1800 2000 2200 2400

6

8

10

12

14

16

18

20

22

tones

bit p

att

ern

ford

ow

nlo

adin

g in b

its p

er

tone.

bit loading pattern for downloading for line length 600mts with two taps after 200mts

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Figure 4.24: Upstream bit-loading in loop 4 with tap length of 10 &

20mts

0 1000 2000 3000 4000 5000 6000 7000-150

-100

-50

0

50

100

150DS: line length of 600mts,taps after 200mts

Tones

SN

R &

Sig

nal P

SD

0 1000 2000 3000 4000 5000 6000 70000

5

10

15

20

25

30

35

tones

bit p

att

ern

for

uplo

adin

g in b

its p

er

tone.

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Figure 4.25: Downstream bit-loading in loop 4 with tap length of 10 & 20mts

Test loop 5: Line with five BT’s

SNR profile of test loop5 with 5taps are shown in figure 4.26 & 4.27for up &

downstream and similarly for loop6 with 10 taps are shown in figure 4.30 & 4.31. The

dips are stronger with 10taps compared to 5 taps, hence the SNR is worse with the

increasing number of taps.

0 1000 2000 3000 4000 5000 6000 70000

5

10

15

20

25

30

tones

bit p

att

ern

ford

ow

nlo

adin

g in b

its p

er

tone.

1200 1400 1600 1800 2000 2200

13

14

15

16

17

18

19

20

21

22

23

tones

bit p

att

ern

ford

ow

nlo

adin

g in b

its p

er

tone.

�

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0 1000 2000 3000 4000 5000 6000 7000-500

-400

-300

-200

-100

0

100

200

Tones

SN

R &

Sig

nal P

SD

PSD

SNR

0 1000 2000 3000 4000 5000 6000 7000-500

-400

-300

-200

-100

0

100

200

Tones

SN

R &

Sig

nal P

SD

DS:line length(600mt) with a tap after 100mt

PSD

SNR

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Bit-loading profile for the test loops 5, line of length 600mts with five taps are shown

in figure 4.28 & 4.29. & 6, Bit-loading profile for the test loops 6, line of 1000mts

with ten taps

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are shown in figure 4.32 & 4.33. Since the deep notches are present

along with the ripples in the SNR of the test loops with five and ten taps the channel

capacity is reduced to a greater extent in the up and down stream.


0 1000 2000 3000 4000 5000 6000 70000

5

10

15

20

25

30

35

tones

bit p

att

ern

for

uplo

adin

g in b

its p

er

tone.

1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900

8

10

12

14

16

18

20

22

tones

�

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Test loop 6: Line with ten BT’s


0 1000 2000 3000 4000 5000 6000 7000-1000

-800

-600

-400

-200

0

200

Tones

SN

R &

Sig

nal P

SD

PSD

SNR

0 1000 2000 3000 4000 5000 6000 70000

5

10

15

20

25

30

tones

bit p

att

ern

ford

ow

nlo

adin

g in b

its p

er

tone.

1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 21000

5

10

15

20

tones

�

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0 1000 2000 3000 4000 5000 6000 7000-1000

-800

-600

-400

-200

0

200

Tones

SN

R &

Sig

nal P

SD

PSD

SNR

0 1000 2000 3000 4000 5000 6000 70000

5

10

15

20

25

30

35

tones

bit p

att

ern

for

uplo

adin

g in b

its p

er

tone.

2000 2100 2200 2300 2400 2500 2600 2700 2800

0

2

4

6

8

10

12

14

16

18

20

tones

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4.3.3 Channel Capacity

Using the tone loading profiles the channel capacities have been computed

from the equation 4.3 and are tabulated in table 4.1. There is a fall in the channel

capacity with increase in line length due to skin effect and bridge taps. However in

actual practice rates required are typically 40Mbps. Hence from the stated full

capacity bit loading profile we need to drawback on bits per tone to realize the lower

required rates. Another observation is that the SNR is high enough to support non

zero bit loading over a portion of the stop bands as observed in SNR profiles of

upstream and downstream. This suggests that we can reduce the transmitting PSD by

a value of 15 dB typically so that the bits in stop band reduce to zero. In any case the

0 1000 2000 3000 4000 5000 6000 70000

5

10

15

20

25

30

tones

bit p

att

ern

ford

ow

nlo

adin

g in b

its p

er

tone.

1000 1200 1400 1600 1800 2000

0

2

4

6

8

10

12

14

16

18

tones

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gain value for the stop band would be set to zero to ensure no energy is transmitted in

that band.

Table 4.1: Capacity estimation for test loops.

Line Topology

Upstream Capacity

Downstream

Capacity

Loop1 (600mts)

111.964 Mbits

173.140 Mbits

Loop1(1200mts)

106.872 Mbits

155.772 Mbits

Loop1(3000mts)

87.660 Mbits

137.592 Mbits

Loop 2

102.420 Mbits

159.692 Mbits

Loop 3

101.828 Mbits

160.160 Mbits

Loop 4

97.612 Mbits

122.312 Mbits

Loop 4

(unequal tap length)

91.053Mbits

129.796 Mbits

Loop 5

90.500 Mbits

97.660 Mbits

Loop 6

71.736 Mbits

85.688 Mbits

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4.4 Conclusion

In this chapter SNR profile and tone-loading are computed for a line with and

without bridge taps. For SNR computation the ‘Transmit signal power’ PSD profile

provided for the 30 MHz VDSL2 band specified in G993.2 for upstream and

downstream are utilised which is not found in the literature. The noise power

considered is Additive White Gaussian Noise (AWGN) of -140dbm/Hz across all the

tones. Bits are loaded in each tone depending on the SNR. Finally channel capacity is

obtained by summing up the bits in each tone. According to the simulation results it is

observed that attenuation increases with the increase in the line length and with the

bridge taps. The channel capacity also reduces with the bridge taps. Another

observation is that the SNR is high enough to support non zero bit loading over a

portion of the stop bands. This suggests that the transmitting PSD of ADSL/VDSL2

can be reduced by a value of at least 15db.

chapter 4 adaptive bit-loading with awgn for...

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