CHAPTER 4 ADAPTIVE BIT-LOADING WITH AWGN FOR PLAIN LINE AND LINE WITH BRIDGE TAPS

Transcription

1 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 -14dBm/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 7 or 3 MHz bandwidth. Simulation results have been presented for the test loops described in the figure SNR and bit-loading profile has been obtained for the upstream and downstream for all the test loops.

2 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 3 MHz has been considered, with signal power spectral density as per VDSL2 (G993.2) [49] with a noise power of -14dbm/Hz. Transfer function H(f) of the channel is computed in the previous chapter for the test cases 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 3 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.

3 -3 US transmitter PSD mask -4 - PSD in dbm Figure 4.2: US transmitter PSD mask (VDSL2 standard, ITU G993.2) PSD in dbm Figure 4.3: DS transmitter PSD mask (VDSL2 standard, ITU G993.2)

4 The SNR [32] at the receiver is given by TxSignalpower SNR ( f ) = ( H ( f )) 2 Noisepower (4.1) H(f) is obtained from equation (3.3) for different power line topologies shown in figure The Txsignalpower PSD profile is provided for the 3 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 G Each frequency is equal to a tone number multiplied with KHz. The noise power considered is Additive White Gaussian Noise (AWGN) of - 14dbm/Hz across all the. SNR is now an array with elements indexed to which can now be employed in the Shannon s theorem. SNR profiles across are obtained using equation (4.1) for the test loops shown in figure Tone-loading Algorithm The bits per tone that can be loaded on the i th channel is given by Shannon s theorem [33] (4.2) Where 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 1-7 (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.

5 (4.3) Where SNR i is the SNR of tone i.the b i so obtained is a rational number and needs to be converted to integers as given in the equation 4.4. (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 b i that corresponds to an increase or decrease in SNR i for the tone. This incremental SNR i is referred to fine gains. Water filling of energy across all the ensures that the total energy does not exceed the standards specified limit of +21dbm across all usable. Fine gains across all ensure that the surplus energies are redistributed among the 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 c i is maximized, subject to a total energy constraint E= i E i.. 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

6 Figure 4.4: Flow chart for water filling algorithm with fine gain adjustment

7 As seen in the band plan shown in figure 4. 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 Similarly bits are loaded in the downstream band and zero bits are loaded in the other frequency bands. With the DMT symbol rate 4 symbols/sec as for DSL the total channel capacity can now be obtained from the equation (4.) 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.. Channel capacity for US and DS is separately computed. US DS1 US1 DS2 US2 DS3 US3 Figure 4.: Band plan for VDSL2 Channel capacity is given by (4.) The channel capacity estimation is done as follows: The channel transfer function is computed using equations (3.8), (3.9) and (3.1) 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

8 Shannon s theorem as in the equation (4.3). Channel capacity is calculated by summing the bits loaded in each subchannel from the equation (4.) 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 Simulation Conditions The SNR as explained in the section 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 for VDSL as shown in figure 4.2 & 4.3 for upstream and downstream respectively. Noise of -14dBm/Hz and the channel transfer function H(f) as discussed in chapter 3 is considered to obtain SNR. = = 14.8db. Here 9.8 assures that a bit error rate (BER) of 1-7 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 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 6mts, 12mts and 3mts 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.

9 4.3.2 SNR & Tone-loading profile Test loop1: plain line with the length of 6mts, 12mts & 3mts The SNR profile of the plain length of line shown in figure 3.11A, loop1 with the power line lengths 6mts, 12mts and 3mts 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. 1 PSD 6mt 12mt 3mt SNR & signal PSD Figure 4.6: Upstream signal PSD & SNR of loop 1 1 PSD 6mt 12mt 3mt SNR & signal PSD Figure 4.7: Downstream signal PSD & SNR of loop 1

10 Bit-loading profile for the testloop1, for the plain length of line of 6mts 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 SNR i for that tone SNR i would be less than 3db. Hence a constant bit loading pattern is seen in fig. 4.8 & bit pattern for uploading in bits per tone Figure 4.8: Upstream bit-loading in loop1

11 3 bit pattern fordownloading in bits per tone 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 4.1 & 4.14 for upstream and in figure4.11 & 4. 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.

12 1 PSD SNR SNR & Signal PSD Figure 4.1: Upstream PSD & SNR of loop 2 1 PSD SNR SNR & Signal PSD Figure 4.11: Downstream PSD & SNR of loop 2 Bit-loading profile for the test loop 2 & 3, line of 6mts with one tap in the rear and front end are shown in figure 4.12, 4.13, 4.16 & The ripples in the SNR due to the tap introduces variation in the bits loaded in the two upstream bands, which in turn

13 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. bit loading pattern for line length 6mts 3 bit pattern for uploading in bits per tone Figure 4.12: Upstream bit-loading in loop2 22 bit pattern fordownloading in bits per tone Figure 4.13: Downstream bit-loading in loop2

14 Test loop3: Line with BT at the front end 1 PSD SNR SNR & signal PSD Figure 4.14: Upstream PSD & SNR of loop 3 1 PSD SNR SNR & Signal PSD Figure 4.: Downstream PSD & SNR of loop 3

15 3 bit pattern for uploading in bits per tone Figure 4.16: Upstream bit-loading in loop bit pattern fordownloading in bits per tone Figure 4.17: Downstream bit-loading in loop 3

16 Test loop4: Line with two BT s of equal length SNR profile for the loop 4, with two bridge taps of equal lengths 1mts are shown in figure 4.18 and 4.19 for up and down stream and with two bridge taps of different lengths 1 & 2mts are shown in figure 4.22 & 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. 1 SNR & Signal PSD Figure 4.18: Upstream PSD & SNR of loop 4

17 1 SNR & Signal PSD Figure 4.19: Downstream PSD & SNR of loop 4 Bit-loading profile for the test loop 4, for the line of 6mts with two bridge taps of equal length(1mts) are shown in the figure 4.2 & 4.21 and two taps of different lengths(1 & 2mts) are shown in the figure 4.24 & 4.2. 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. 3 bit pattern for uploading in bits per tone Figure 4.2: Upstream bit-loading in loop 4

18 bit loading pattern for downloading for line length 6mts with two taps after 2mts 3 bit loading pattern for downloading for line length 6mts with two taps after 2mts 22 bit pattern fordownloading in bits per tone bit pattern fordownloading in bits per tone Figure 4.21: Downstream bit-loading in loop 4 Test loop4: Line with two BT s of unequal length (1 & 2mts) 1 SNR & Signal PSD Figure 4.22: Upstream PSD & SNR of loop 4

19 DS: line length of 6mts,taps after 2mts 1 SNR & Signal PSD Figure 4.23: Downstream PSD & SNR of loop 4 3 bit pattern for uploading in bits per tone Figure 4.24: Upstream bit-loading in loop 4 with tap length of 1 & 2mts

20 bit pattern fordownloading in bits per tone bit pattern fordownloading in bits per tone Figure 4.2: Downstream bit-loading in loop 4 with tap length of 1 & 2mts Test loop : Line with five BT s SNR profile of test loop with taps are shown in figure 4.26 & 4.27for up & downstream and similarly for loop6 with 1 taps are shown in figure 4.3 & The dips are stronger with 1taps compared to taps, hence the SNR is worse with the increasing number of taps.

21 2 1 PSD SNR SNR & Signal PSD Figure 4.26: Upstream PSD & SNR of loop 2 1 DS:line length(6mt) with a tap after 1mt PSD SNR SNR & Signal PSD Figure 4.27: Downstream PSD & SNR of loop

22 Bit-loading profile for the test loops, line of length 6mts with five taps are shown in figure 4.28 & & 6, Bit-loading profile for the test loops 6, line of 1mts with ten taps are shown in figure 4.32 & 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 bit pattern for uploading in bits per tone Figure 4.28: Upstream bit-loading in loop

23 3 2 bit pattern fordownloading in bits per tone Figure 4.29: Downstream bit-loading in loop Test loop 6: Line with ten BT s 2 PSD SNR SNR & Signal PSD Figure 4.3: Upstream PSD & SNR of loop 6

24 2 PSD SNR SNR & Signal PSD Figure 4.31: Downstream PSD & SNR of loop bit pattern for uploading in bits per tone Figure 4.32: Upstream bit-loading in loop 6

25 3 18 bit pattern fordownloading in bits per tone Figure 4.33: Downstream bit-loading in loop 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 4Mbps. 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 db typically so that the bits in stop band reduce to zero. In any case the

26 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 (6mts) Mbits Mbits Loop1(12mts) Mbits.772 Mbits Loop1(3mts) Mbits Mbits Loop Mbits Mbits Loop Mbits Mbits Loop Mbits Mbits Loop 4 (unequal tap length) 91.3Mbits Mbits Loop 9. Mbits Mbits Loop Mbits Mbits

27 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 3 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 -14dbm/Hz across all the. 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 db.