Power back-off for multiple target bit rates. Authors: Frank Sjöberg, Rickard Nilsson, Sarah Kate Wilson, Daniel Bengtsson, Mikael Isaksson

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1 T1E1.4/ (8) Standards Project: T1E1.4 VDSL Title : Power bac-off for multiple target bit rates Source : Telia Research AB Contact: Göran Övist Telia Research AB, Aurorum 6, SE Luleå, Sweden Fax: Authors: Fran Sjöberg, Ricard Nilsson, Sarah Kate Wilson, Daniel Bengtsson, Miael Isasson Distribution: T1E1.4 Technical subcommittee woring group Status: Information Abstract: This contribution describes a new efficient method to perform power bac-off in the upstream of a VDSL-system. The method gives higher data rates than the earlier proposals, i.e., the constant bac-off method and the reference length method. One conceptual difference with this new method is that we are not using just one design parameter as with the reference frequency and reference length methods. With this new method all users are assigned a certain service class, a target bit rate. The method then performs the power bac-off such that it tries to maximize the bit rate (the system margin) for all the other users. The method tries to create FEXT, at each NT, that has the same spectral shape as the bacground noise. Between 5% and % improvement in bit rates is achieved with this new method when using the FSAN models for cable, crosstal and bacground noise. The larger improvements over the other methods appear when non-flat bacground is present. This is because the PSD of the bacground noise is included in the model used by method. For thinner wires, lie the TP1 wire, the method can give more than % higher data rate for almost all users. This contribution has been prepared to assist ANSI Standards Subcommittee T1E1.4. This document (T1E1.4/98-371) is offered as a basis for discussions and is not a binding proposal of Telia Research AB. Telia Research AB specifically reserves the right to add to, amend or withdraw the statements contained herein.

2 T1E1.4/ (8) 1 Introduction The need for power bac-off in the upstream direction of VDSL is recently recognized in several contributions [1-5]. When the users are distributed along the cable, as in Figure 1, those far out in the networ will get almost no capacity if all users were to use maximal allowed transmit power. This is due to the very strong far-end crosstal (FEXT) that users on short wires introduce to the system. Power bac-off is a way to reduce this problem and get a more even distribution of the available capacity among users with different wire lengths. Figure 1 - Distributed cable topology. In [1], three different methods for how to do power bac-off were proposed. Two of these were considered potential candidates: the reference frequency method (constant bac-off) and the reference length method. In this contribution we present a new power bac-off method with higher performance. This new method is based on all users having an assigned target bit rate (a certain service class) which they will try to achieve. If a user achieves this target bit rate with an overhead system margin, the goal is to lower his transmit power in such way that the capacity (system margin) of the other users is maximized. We start out by deriving an optimal algorithm for a two-user case in Section. The optimal method is too complex to be used in practice, even in the two user case, so a simpler suboptimal method is derived. One big advantage with this method is that it can be designed for non-flat bacground noise, lie the FSAN-noise. In Section 3 we loo at the case with more than two users and conclude that the method derived in Section (for the two user case) can be directly applied to a multi-users case. In section 4 we show simulation results for this new method. These simulations are made using the same scenario as in [1], where the FSAN models were used for the cable, crosstal and noise. We will show results both when FSAN-noise is excluded and included. No duplexing-scheme is considered is this contribution. This means that the results are directly applicable to time division duplex (TDD). There are however reasons to believe that frequency divided systems will benefit from this method in the very same way or even better, depending on the allocation of frequency bands. A simple case with two users We start by looing at a simple case with only two users in the same cable. We assume that user 1 wants a certain service class, e.g. 5 Mbps. The problem is then to find a power-distribution for user 1, that maximizes the capacity for user (the system margin) while ensuring that user 1 gets the desired bit rate. The bit rate, R j, that user j gets can be calculated with [6] f max P ( f ) H ( f j j ) Rj = log 1+ df N j( f ) Γ fmin, (1) H f is the transfer function of the wire, where N( f ) is the spectral density of the total noise (FEXT, AWGN, etc), ( ) P( f ) is the transmit power spectral density (PSD) and Γ is the combined SNR-gap and system+coding margin (= 14.8 db) [1]. Lets divide the available bandwidth (between f min and f max ) into N equally wide subbands (this corresponds to a DMT-system with N subcarriers). Since we only have two users, then the bit rate of user 1 will be N P H 1 1 R1 = 1+ log,, 1 ( + P F = σ,, ) Γ, () where H 1, is the wire transfer function for user 1, F, is the FEXT transfer function from user to user 1, and σ is the variance of the bacground noise. The expression for the bit rate of user will be similar.

3 T1E1.4/ (8) Our problem is to maximize R under the constraint that R 1 equals the target bit rate ( R1 = R target ). There are N 1,, 1,, K. This can be solved with the help of a Lagrange multiplier λ. The problem can then be written in mathematical notation as variables to solve for and those are the transmit power levels on each tone, P { N} ( R( 1) ( R1( 1) R )) where R j ( P 1 ) is short hand notation for Rj( P11, P1, P1, N) P 1, P λ P target =, (3),,...,. We have now N+1 unnowns and N+1 equations: P, H, P1, H1, log 1+ λ log R { N} 1 1,, ( σ + P1, F1, ) + + ( σ + P, F, ) target = K (4) Γ Γ and R1 = R target. This problem can be solved numerically but it is very hard to solve analytically. Since we want to extend this method to a case with more than users some simplifications are required. If we assume that the signal-tonoise ratio (SNR) is fairly high on all our subcarriers, then (4) can be simplified by removing the 1 within the logarithm functions, giving F1, 1 λ =, { 1,, KN}, σ + P1, F1, P1, (5) which leads to the following solution σ λ P1, =, { 1,, KN}, F1, 1 λ (6) where the value of λ has to be determined so that the constraint equation is fulfilled, R1 = R target. Looing at this expression for the optimal (suboptimal) way of determining the power distribution, we see that the FEXT introduced to the other user will have the same spectral shape as the bacground noise. If we only have AWGN noise, this means that the FEXT will be flat. The level of the FEXT is determined by the target bit rate R1 = R target. There is actually one more constraint which has not been considered so far, and that is that P 1, must never exceed the maximal allowable PSD-level for VDSL ( P max ). Taing that into consideration (6) can be rewritten as P 1, σ σ λ if λ < P F1, F1, = σ Pmax if λ P F1, If a too large target rate R target is chosen it can happen then P1, = Pmax for all and still the target bit rate is not achieved. Figure shows an example on how the PSD will loo for different wire lengths. Shorter wires use less transmit power in general, and tend to load more power on the higher frequencies. - max max (7) -55 Power Spectral Density (dbm/hz) m m 9m m m subcarrier index Figure - Simple example on how the transmit PSD will be for some different wire lengths.

4 T1E1.4/ (8) 3 A model for several users In a more realistic case more than two users will interfere with each other. This is a much more complicated problem, but it turns out that the model we derived in the previous section is applicable to this case also. We will try to show this in an iterative way, lie a proof by induction. If a new user comes into the system, and all other users have already performed power-bac off according to (7), then we will show that the best way the new user can do power bac-off is as in (7). For a two user case, the power-loading should be done is such way that the FEXT is spectrally shaped as the bacground noise (7). We will assume that all users have the same spectral shape as the bacground noise, but not necessarily the same level. Let s consider a system with two active users who both use the power bac-off method from (7). Let s also assume that there is no upper limit for the transmit PSD, P max = (even though this is no the case in reality). Now we introduce a third user into the networ. Due to the FEXT that the third user will introduce, the first and second user will get lower system margin, or lower bit rates. The third user should do his power-loading such that the bit rates of user 1 and user are jointly maximized (the system margins are maximized). The achievable bit rate for user is N P H R = log 1+ (,, 1 + P1 F1 + P3 F (8) = σ,,, 3, ) Γ Since user 1 has performed power bac-off according to (8) we now that P 1, F 1, =σ λ 1, i.e. the FEXT from user 1 has the same spectral shape as the bacground noise. Using this in () we get N P, H, R = log 1+ (9) = 1 ( σ( 1+ λ1) + P3 F3 ),, Γ The combined bacground noise and FEXT from user 1 has the same spectral shape as the bacground noise alone. Thus, considering only user 3 and user, the expression given in (7), determines how user 3 shall do power bac-off so that user get as high bit rate as possible. This also ensures that user 3 creates FEXT that has the same spectral shape as the bacground noise, P 3, F 3, =σ λ 3. Analogously this is the also best solution if we consider user 3 and user 1. Thus, it is optimal for user 3 to use the method in (7). This way of reasoning can then be extended to four or more users. So the method derived for the two user case gives the optimal solution in the multi-user case also (under the assumptions that we have relatively high SNR, the same shape of the bacground noise, and no restriction on transmit PSD levels). One important constraint we have used above is that P max =, which ensures that the FEXT is spectrally shaped as the bacground noise. When this is not the case we cannot use the reasoning above because some users will create FEXT that does not loo lie the bacground noise. Trying to solve the problem optimally in this case in very hard, and there is also an issue of how the performance of the other users shall be weighted since one single power distribution is probably not optimal for all the other user. Despite this, the simulation shows in Section 4, that our simple method (7) gives quite good performance even when the transmit PSD is limited, P max = dbm / Hz. Our method is based on the fact that the FEXT have the same spectral shape as the bacground noise. For this we need to now the PSD of the bacground noise. There are essentially two different ways to implement this. On way is to use a fixed design noise-psd, e.g. -1 dbm/hz if we have only AWGN, and another, ad-hoc, way is to is to let each user measure the bacground noise individually. The problem with the latter method is that we don t now in advance when the power bac-off will it converge. As soon as new users come into the system and start transmitting, the total noise will change for all the other users. They will measure this and adapt their loading algorithm accordingly. When that is done the FEXT has changed again, and all users will redo their loading again, and so on. We have tested this in some simulation and it did converge in all cases after just a few iterations. 4 Performance simulations To evaluate the performance of this new method we have used the scenario from [1]. This means that we are using the FSAN models for the cable, crosstal and bacground noise, and the networ topology in Figure 1 with users per node. The FSAN crosstal combination method is also implemented. The entire bandwidth (.3-MHz) is used all the time, and is divided into 4 subbands. No duplex is considered and we have assumed % efficiency. We have

5 T1E1.4/ (8) looed at the performance both with and without the FSAN-noise (model B, the exchange scenario). When FSAN-noise is included this is taen into consideration with the new method by using the PSD of the FSAN-noise as noise variance in (7). We have also looed at the performance on a TP1-cable, which has more attenuation than the FSAN-cable. One issue that is not discussed is how to find the right λ j :s to get the desired data rates. This has to be done simultaneously for all users and can be solved with some numerical method. Here we do it in the following way. All users start with maximum transmit power ( P max = dbm / Hz ). Then user 1 (at shortest range) starts doing power bac-off. This will reduce the FEXT for all other users. Then user performs bac-off, and so on until the last user has done his bac-off. Then the procedure starts over again, since user 1 now has lower noise (higher system margin) and he can do bac-off again. After a few iteration the process converges. By starting with max-power on all users, the results will never be to optimistic. If the iteration is stopped to early some users will have lower rates than what they actually can get. Between 5 and 15 iteration turned to out be sufficient. 4.1 The FSAN scenario In this case we use exactly the same setup as in [1], but we will also include results for the case with the FSAN bacground noise. To see that this new method, which we will refer to as the multi-rate method, does perform at least as well as the other two existing proposals we start by comparing it with both the reference frequency method and the reference length method. The reference frequency is set to. MHz and the reference length is set to m (node 8). For the multi-rate method we need to define target bit rates. When comparing to the reference frequency method the target rates used are those achieved with the reference frequency method +% when there is no FSAN-noise, and +% when the FSAN-noise is included. Figure 3 shows the achievable bit rates for both methods. The target rates were achieved for all but the m node, at which the multi-rate method gave 11% higher bit rates with FSAN-noise and 1% less bit rate without FSAN-noise. The multi-rate method performs relatively better in the presence of FSAN-noise because it taes into consideration the spectral shape of the bacground noise. Comparing the multi-rate method with the reference length method, the target bit rates were 5% higher than those achieved with the reference length method. Figure 4 shows the achievable bit rates for this case. In the case with FSANnoise the multi-rate method reached the target rates for all nodes but the one at 13m, where it gave 3% less bit rate. Without FSAN-noise the target rates were achieved for all nodes with shorter wires than the reference length (m). The multi-rate method gave 3% less bit rate rates for the m node, and a few percentage higher rates the last two nodes. Since this new multi-rate method gives us the freedom to gives the users any bit rates we want, we have included a case where multiples of 6.5 Mbps are used as possible service classes. The target rates were set to (5, 5, 39, 39, 39, 3.5, 3.5, 3.5, 6, 6) respectively for all nodes when there is no FSAN-noise. For the case with FSAN-noise, the target rates were (39, 3.5, 6, 19.5, 19.5, 19.5, 19.5, 19.5, 13, 6.5). In Figure 5 the bit rates can be compared with those achieved with the other two methods. Without FSAN-noise the target rates were achieved for all but the last node (m), but with FSAN-noise the last three nodes did not fully reach their target bit rates. In Figure 6, the FEXT that is generated at each node and the FEXT that is received on each wire is shown for the case without FSAN-noise. Since the bacground noise consists only of AWGN, the FEXT should be flat when our method is used. As we can see in the top picture the FEXT is flat for many of the nodes, but for those nodes that must use full transmit power this is not the case. This leads to that the FEXT received at the CO on each wire will not be flat (spectrally shaped as the bacground noise), which can be seen in the lower picture in Figure 6. The assumption made in Section 3 in order to extended the method from two to several users does not hold any longer then. But the performance is still quite good. An ad-hoc way to deal with this problem is to measure the bacground noise on each individual wire instead of using a fixed design bacground noise level, as mentioned in Section 3. Figure 5 shows the performance for this ad-hoc method as well, which is seen as a split of the upper solid line at meters. The ad-hoc method performs slightly better.

6 T1E1.4/ (8) 7 7 Frequency No Bac-off Length No Bac-off Figure 3. Achievable bit rates on the FSAN-cable with AWGN and FSAN-noise. Reference frequency compared with multi-rate. 8 Figure 4. Achievable bit rates on the FSAN-cable with AWGN and FSAN-noise. Reference length compared with multi-rate Amount of FEXT generated from each node 3 Frequency Length FEXT PSD (dbm/hz) Frequency (MHz) -15 Amount of FEXT received on each wire FEXT PSD (dbm/hz) Figure 5. Achievable bit rates on the FSANcable. Service classes in steps of 6.5 Mbps for the multi-rate method Frequency (MHz) Figure 6. FEXT generated and received with the multi-rate method with fixed design bacground noise level Frequency No Bac-off Transmit PSD (dbm/hz) Frequency (MHz) Figure 7. Transmit PSD for the case with service classes in step of 6.5 Mbps and no FSAN-noise. 8 Figure 8. Achievable bit rates on the TP1- cable with AWGN and FSAN-noise. Reference frequency compared with multi rate.

7 T1E1.4/ (8) 4. The TP1 cable To test another environment we have used the TP1-cable with the same scenario as in subsection 4.1. The TP1-wire is a.4 mm wire that has more attenuation than the FSAN-wire. As in the previous cases, with the FSAN-cable, we will compare the performance of the multi-rate method with the other two methods, and see what can be achieved when some certain service classes are used. The reference frequency is now set to 1.5 MHz when there is no FSAN-noise, and. MHz when the FSAN-noise is included. With the reference length method, node 7 (m) and node 5 (7m) is used for the cases without and with FSAN-noise, respectively. Without FSAN-noise the multi-rate method can deliver % higher bit rates than the reference frequency method, on all but the last node, which gets % less bit rate, see Figure 8. When adding the FSAN bacground noise we let the node at meters use full transmit power for the reference frequency method, since there is almost no capacity for wires longer than that. With the multi-rate method, 3% higher bit rates can be achieved for all nodes up to meters, see Figure 8. When comparing to the reference length method we use the rates give by the reference-length model +% as target rates for the multi-rate model. Figure 9 shows the achievable bit rates both with and without FSAN-noise. Up to the reference length the multi-rate method is able to deliver % higher rates. For the reference node and the nodes further away the difference is smaller. Finally we loo at the possible performance when we (as for the FSAN-cable) use multiples of 6.5 Mbps as possible service classes. The target rates were set to (39, 3.5, 3.5, 3.5, 3.5, 3.5, 6, 19.5, 13, 13) respectively for all nodes when there is no FSAN-noise. In the case with FSAN-noise the target rates were (3.5, 3.5, 3.5, 3.5, 3.5, 13, 6.5, 6.5, 6.5, 6.5). In Figure the bit rates can be compared with those achieved with the other two methods. Without FSAN-noise the target rates were achieved for all but the last node (m), but with FSAN-noise only the first four nodes reached their target bit rates. This is due to the strong attenuation in the TP1-cable for long wires. Even without VDSL self-fext there is not much capacity on wires longer than m if the FSAN-noise is used. 7 7 Length No Bac-off Frequency Length Figure 9. Achievable bit rates on the TP1-cable with AWGN and FSAN-noise. Reference length compared with multi-rate. 8 Figure. Achievable bit rates on the TP1- cable. Service classes in steps of 6.5 Mbps for the multi-rate method.

8 T1E1.4/ (8) 5 Conclusions In this contribution we have derived a new method for power bac-off in upstream VDSL. Our starting assumption is that each user belong to a certain services class, i.e., has a certain target bit rate he/she will try to achieve. If this rate can be achieved with an overhead in the system margin, then power bac-off should be performed so that the other users receive as little disturbance (FEXT) as possible. That is, our optimization criteria, when determining the power bac-off, is to maximize the system margin for the other users. In a two user case this means that we optimize the bit rate for the one user, when fixing the bit rate of the other user. The optimal solution is very hard to calculate even for a two user case, so we derive a suboptimal method that then is extended to deal with the multi-user case. With our suboptimal method the transmit PSD should be set so that the FEXT generated by that user has the same spectral shape as the bacground noise (assuming that every user have the same bacground noise). If the bacground noise is only AWGN then the generated FEXT should be flat. There are essentially two different ways to implement this. Either a fixed model of the bacground noise is used, e.g. - 1 dbm/hz for the AWGN case, or the users can measure the bacground noise themselves individually and use that to determine the shape of the transmit PSD. The latter one seems to give slightly better performance, since it deals better with the problem that the limit in allowable PSD-levels maes it impossible to shape the FEXT as needed. The problem with the second way is that we are not sure how well the transmit PSD-levels will converge. With simulation we have shown that this new power bac-off method performs, at least as well as, but most often much better than the reference-frequency and reference-length method. On the FSAN-cable, -% higher bit rates could be achieved on 9 out of nodes compared with the reference frequency method, and around 5% higher bit rates than with the reference length method. On wires with more attenuation, lie TP1-cable, the multi-rate method has an even bigger advantage over the other two methods. The simulation also showed that the multi-rate method deals with non-flat noise, lie the FSAN-noise, much better than the reference frequency method. One important advantage with this new method is that we can assign the users to different services classes, and then perform power bac-off in an efficient way, given the target bit rates. References [1] FSAN VDSL woring group, Power bac-off methods for VDSL, ETSI TM6, 983T17A, Luleå, Sweden, June [] T. Sartenaer, P. Reusens, Upstram Power Cut-bac needed for solidarity between VDSL modems distributed along the calbes, ETSI TM6, 981T19, Madris, Spain, January [3] J. Coo, Power Bacoff for VDSL upstream: a study with simulations, FSAN VDSL woring group, Bern, Switzerland, Feb 98. [4] J. Coo, Power Bacoff Comparison, FSAN VDSL woring group, London, UK, May 98. [5] T. Kessler, M. Friese and M. Schlipp, Achievable bitrates with the constant power bac-off method, ETSI TM6, 984T35A, Vienna, Austria, Sept [6] P. Chow, J. Cioffi and J. Bingham, A Practical Discrete Multitone Transceiver Loading Algorithm for Data Transmission over Spectrally Shaped Channels, IEEE Transactions on Communications, vol. 43, no. /3/4, February/March/April 1995.