Upstream power back-off

[0001] CROSS REFERENCE TO RELATED APPLICATIONS

[0002] Priority is claimed of commonly assigned copending U.S. Provisional patent application, Ser. No. 60/166,092, filed Nov. 17, 1999, entitled “Proposal to Use The Noise Floor Method for Upstream Power Backoff In VDSL, ” the teachings included herein by reference.

[0003] 1. Technical Field of the Invention

[0004] The present invention relates generally to the field of broadband communications and, more particularly, to a method and system of upstream power back-off within a broadband communication system.

[0005] 2. Background of the Invention

[0006] It is becoming increasingly clear that telephone companies around the world are making decisions to include existing twisted-pair loops in their next generation broadband access networks. One attractive alternative, known as fiber-to-the-neighborhood (FTTN), is a combination of fiber cables feeding neighborhood Optical Network Unites (ONUs) and last leg premises connections by existing or new cooper. One of the enabling technologies for FTTN is very high rate Digital Subscriber Line (VDSL). VDSL transmits high speed data over short reaches of twisted-pair copper telephone lines, with a range of speeds depending upon actual line length and direction of transmission.

[0007] A VDSL requirement to use power back-off in the upstream direction arises because distributed topologies must be presumed for VDSL. In general, power back-off causes decreases in data rates relative to when all loops are the same length and only equal-length crosstalk results. However, it is difficult to project what the data rate loss will be with a particular power back-off algorithm. The data rates are a function of the loop topology and power back-off parameters.

[0008] Referring now to FIG. 1, there is illustrated a broadband access network with a plurality of varying length transmission lines in which the lines terminate at an ONU 10. Projections of downstream VDSL performance that assume self-FEXT are pessimistic when lines of varying lengths reside in the same binder as in FIG. 1. The assumption of self-FEXT is more accurate for short lines, on which FEXT levels are highest. For long lines, the assumption of self-FEXT is pessimistic because the shorter lines do not couple over the entire length of the long lines.

[0009] In the upstream direction, however, the assumption of self-FEXT is optimistic for longer lines. If all VTU-Rs transmit at their maximum power spectral density (PSD) levels, signals on shorter lines will detrimentally affect the upstream performance on longer lines. To illustrate, assume the maximum VDSL transmit PSD is −60 dBm/Hz. Referring to FIG. 1, the signal transmitted by the VTU-R on L_N at this level will be attenuated significantly by the time it travels a distance (d_N-d_l). At this point, transmissions from the VTU-R on L_l may begin to couple into L_N. If the transmit PSD of the VTU-R on L_l is −60 dBm/Hz, then it is significantly higher than the attenuated level of the desired signal on L_N. The result of the relatively high-power interference is a degradation in achievable upstream rate on L_N.

[0010] Simulations to project VDSL performance generally assume that any far-end crosstalk at the VDSL receiver is due to disturbers that are identical to the line under consideration. In other words, it is assumed that all disturbers span the same distance and transmit the same power spectrum as the line under consideration, and “self-FEXT” results. In reality, lines emanating from a single ONU, CO or LEx may span a variety of distances in a distributed topology, as shown by the example in FIG. 1.

[0011] The near-far problem is most severe when a very long line is degraded by FEXT caused by shorter lines on which “too high” an upstream transmit PSD is used. Loosely speaking, the transmit PSD on a short line is “too high” if its level is significantly higher than the level of the signal on the long line at the point at which the shorter line begins to couple into the longer line.

[0012] The present invention achieves technical advantages as a system and method of power back-off in a broadband communication system and more particularly for a very high rate digital subscriber line (VDSL) system. The present invention defines a global desired receive power spectral density (GDR PSD). Further, a line termination (LT) enables transmission of the determined GDR PSD to a network termination (NT). The NT determines an upstream transmit power spectral density for data transmission using the received GDR PSD and a determined insertion loss of the loop on which it resides. A management interface can also enable operator configuration of GDR PSD parameters. In some cases, depending on the power back-off algorithm being implemented, normalization by a well-defined factor is also necessary. Specific advantages include enabling power back-off by the NTs without data feedback to the LT but still allows the power back-off parameters, or even the algorithm itself, to be modified via the management system.

[0018] The numerous innovative teachings of the present application will be described with particular reference to the presently preferred exemplary embodiments. However, it should be understood that this class of embodiments provides only a few examples of the many advantageous uses and innovative teachings herein. In general, statements made in the specification of the present application do not necessarily delimit any of the various claimed inventions. Moreover, some statements may apply to some inventive features, but not to others.

[0019] Several power back-off algorithms are described for use in VDSL. In all cases, a PSD mask constraint S_max(f) is assumed. Hence, it is necessary always to take the minimum of the computed PSD and the PSD mask. Using a constant power back-off method, the upstream transmit PSDs on shorter lines are reduced equally across the upstream frequency band. Thus, the transmit PSD, which may or may not be flat, is reduced by a constant factor such that it resides no higher than the maximum allowed VDSL level within the frequency band(s) allocated for upstream transmission. The amount by which the PSD is reduced is computed using a desired receive PSD at a reference frequency and either a model or measurements of the actual loop transfer function, which provides the loop attenuation at the reference frequency. The required transmit PSD level is then simply the desired received PSD at the reference frequency divided by the attenuation of the loop at the reference frequency. Using this method, the upstream PSD level is set so the received PSD level at the reference frequency is the same at the optical network unit (ONU) for every loop.

[0020] The desired receive PSD at the reference frequency can be computed using some reference loop, typically the longest loop in the binder. Alternatively, an arbitrary desired receive PSD level can be selected.

[0021] Denoting the reference frequency as f_r and the desired receive PSD at that frequency as S_r(f_r), the constant power back-off algorithm sets the transmit PSDs to $\begin{array}{cc}{S}_i\left(f\right)=\min \left(\frac{S_r\left(f_r\right)}{{H_i\left(f_r\right)}^2},S_{\max }\left(f\right)\right),& \mathrm{Equation}1\end{array}$

[0022] where |H_i(f_r)²| is the value of the loop insertion loss at the reference frequency.

[0023] A reference length method is a generalization of the constant power back-off method. In contrast to the constant power back-off method, where a desired receive PSD is established at only a single frequency, the reference length method sets the upstream transmit PSD so that the received PSD at all frequencies is equal to the PSD that would be received if some known PSD were transmitted on a loop of length L_r. To compute the required transmit PSD, the desired receive PSD and loop attenuation within the upstream frequency bands must be known to the NT. The required transmit PSD is then simply the desired receive PSD divided by the loop attenuation profile.

[0024] Denoting the required transmit PSD as S_i(f), the desired receive PSD as S_r(f), and the loop attenuation as |H_i(f)²|, the required transmit PSD is $\begin{array}{cc}{S}_i\left(f\right)=\min \left(\frac{S_r\left(f\right)}{{H_i\left(f\right)}^2},S_{\max }\left(f\right)\right).& \mathrm{Equation}2\end{array}$

[0025] Applied strictly as defined above, the reference length method backs off the upstream transmit PSDs at all frequencies without taking into account the data-carrying capabilities of those frequencies on different length loops. As a result, all loops shorter than L_r support approximately the same upstream rate as a loop of length L_r. Thus, support of mixed services is not readily enabled. Although some operators will choose not to provide mixed services in a binder, the power back-off algorithm should provide this capability, if possible.

[0026] The upstream bit rates on shorter loops can be improved by introducing a modification to the reference length method. The modification results from the observation that although systems on short loops transmit data in most or all of the available upstream bandwidth, systems on long loops use only the lower frequencies. Because higher-frequency bands are too attenuated to support data on longer loops that are most susceptible to near-far FEXT, allowing higher transmit PSD levels in these bands on shorter loops will not affect upstream bit rates on longer loops. Thus, the concept of a frequency-dependent reference length is introduced. The reference length should decrease with increasing frequency: it should be long at low frequencies and short at high frequencies. For example, at the lowest frequencies, a reference length of 1500 meters might be used, while at the highest frequencies a reference length of 300 or even 150 meters might be chosen.

[0027] With different reference lengths defined in different upstream frequency bands, the required transmit PSD is then computed as $\begin{array}{cc}{S}_i\left(f\right)=\min \left(\frac{S_r\left(f\right)}{{H_i\left(f\right)}^2},S_{\max }\left(f\right)\right)& \mathrm{Equation}3\end{array}$

[0028] where S_r(f) is the piece-wise defined desired receive PSD.

[0029] Ideally, the PSD transmitted on reference-length loops should be the maximum allowed. However, current standards have defined transmit PSD masks that far exceed the levels that can be supported under the total power constraint of 11.5 dBm set in current standards.

[0030] An equalized-FEXT method attempts to equalize, using a known FEXT model, the level of FEXT received on each line at the ONU/CO. The upstream transmit PSDs are adjusted so that all lines affect each other approximately equally. The method is similar in approach to the reference length method, however, the equalized FEXT method allows higher transmit PSDs at lower frequencies because FEXT coupling at these frequencies is less than at higher frequencies.

[0031] Using the equalized-FEXT method, a reference length is first chosen. Let the reference length be denoted L_r. The PSD received on loops of length L_r is thus
S_r(f)=|H_r(f)|²·S_max(f).  Equation 4

[0032] Hence, the transmit PSD on any loop should be $\begin{array}{cc}{S}_i\left(f\right)=\min \left(\frac{L_r}{L_i}·\frac{S_r\left(f\right)}{{H_i\left(f\right)}^2},S_{\max }\left(f\right)\right),& \mathrm{Equation}5\end{array}$

[0033] where L_l is the length of the loop under consideration.

[0034] Thus, the required upstream transmit PSD on any line is the PSD transmitted on the reference loop times the ratio of the product of the reference loop length and insertion loss the product of the loop's own length and insertion loss.

[0035] It should be noted that the equalized-FEXT method can also be modified like the reference length method so that different reference lengths are used in different frequency bands. The expression for the desired receive PSD then takes a form similar to Equation 3.

[0036] Using a reference noise method, the upstream transmit PSD level is set such that the FEXT it would inject into another line of the same length is equal to an assumed reference noise. The upstream transmit PSDs are computed as $\begin{array}{cc}{S}_i\left(f\right)=\min \left(\frac{L_r}{L_i}·\frac{S_r\left(f\right)}{{H_i\left(f\right)}^2},S_{\max }\left(f\right)\right),& \mathrm{Equation}6\end{array}$

[0037] where $\begin{array}{cc}{S}_r\left(f\right)=\frac{\eta \left(f\right)}{L_r·K_{\mathrm{FEXT}}·f^2}.& \mathrm{Equation}7\end{array}$

[0038] In the expression for S_r(f), η(f) is an assumed reference noise, K_FEXT is a constant representing the coupling from one loop to an adjacent loop in the cable, and L_r is a nominal loop length. Note that L_r cancels from the expression for S_i(f). As discussed below, it will become clear why L_r has been added to the equations for S_i(f) and S_r(f).

[0039] A comparison of Equations 1, 2, 3, 5 and 6 reveals that all the expressions for the upstream transmit PSD have generally the same form. All require the division of some desired receive PSD by the loop insertion loss. In some cases, multiplication and/or division by the loop length is also necessary.

[0040] The present invention defines and uses a global desired receive PSD (GDR PSD), denoted as S_GDR(f). By defining a GDR PSD, virtually any power back-off algorithm can be accommodated. More importantly, the power back-off algorithm can be changed via the management interface simply by changing the GDR PSD that is sent to NTs during initialization.

[0041] Ignoring the maximum PSD mask constraint for the time being, we now examine how the GDR PSD is used with each of the aforementioned power back-off algorithms.

[0042] For constant power back-off, the GDR PSD is defined for only one frequency, f_r. Thus, the GDR PSD becomes S_GDR(f_r), and the upstream transmit PSD on the i th loop is computed as $\begin{array}{cc}{S}_i\left(f\right)=\frac{S_{\mathrm{GDR}}\left(f_r\right)}{{H_i\left(f_r\right)}^2}.& \mathrm{Equation}8\end{array}$

[0043] In the case of the reference length method, the GDR PSD is defined as the PSD that would be received if a known PSD were transmitted on a loop of length L_r. The computed, required transmit PSD on the i th loop is simply $\begin{array}{cc}{S}_i\left(f\right)=\frac{S_{\mathrm{GDR}}\left(f\right)}{{H_i\left(f\right)}^2}.& \mathrm{Equation}9\end{array}$

[0044] In the multiple reference lengths method, the GDR PSD is defined piece-wise, with a different reference length in each defined frequency band. However, the expression for the computed upstream transmit PSD on the i th loop remains the same: $\begin{array}{cc}{S}_i\left(f\right)=\frac{S_{\mathrm{GDR}}\left(f\right)}{{H_i\left(f\right)}^2}.& \mathrm{Equation}10\end{array}$

[0045] For the equalized-FEXT method, the computed upstream transmit PSDs are then given by $\begin{array}{cc}{S}_i\left(f\right)=\frac{L_r}{L_i}·\frac{S_{\mathrm{GDR}}\left(f\right)}{{H_i\left(f\right)}^2}.& \mathrm{Equation}11\end{array}$

[0046] Note that the NT must normalize the GDR PSD by the ratio of the reference length to its own loop length when it computes the transmit PSD. Alternatively, if the loop length is determined via some procedure when the NT is installed, then the LT can perform the normalization. Then, however, the GDR PSD is no longer really “global”, instead, it will vary from line to line. Hence, the GDR PSDs transmitted to different NTs will differ.

[0047] In a preferred embodiment, the reference noise method with GDR PSD is used for power back-off because performance degradations caused by use of the reference noise method can be shown to be bounded. As shown below, when two lines of arbitrary lengths are considered, the reference noise method results in an upstream performance degradation that is less than 3dB relative to when the two VTU-Rs reside on loops of the same length and transmit at ihe maximum allowed PSD. This result is significant because it means the performance degradation due to applying this power back-off algorithm is bounded regardless of the distribution of line lengths in a binder.

[0048] With the reference noise method, the upstream transmit PSDs are set to $\begin{array}{cc}{S}_i\left(f\right)=\frac{\eta \left(f\right)}{K_{\mathrm{FEXT}}·{H_i\left(f\right)}^2·f^2·L_i},& \mathrm{Equation}12\end{array}$

[0049] where η(f) is an assumed noise floor, K_FEXT is a constant representing the coupling from one loop to an adjacent loop in the cable, |H_i(f)|² is the insertion loss of Loop i, and L_i is the length of Loop i. All S_i(f) are limited by the maximum allowable transmit PSD, which is denoted by S_max(f). If the computed value of S_i(f) exceeds S_max(f), then the transmit PSD is constrained to S_max(f).

[0050] An examination of Equation 12 reveals that the upstream transmit PSD level is such that the FEXT it would inject into another line of the same length is equal to the noise floor. Clearly, setting the PSD in this manner results in a 3 dB increase in the noise profile on a loop of the same length. Hence, the degradation to that line is 3 dB. In the following description, it is shown that even when two lines of different lengths are considered, the degradation to performance using this method is no greater than 3 dB relative to the performance with self-FEXT.

[0051] With this method, selection of an appropriate noise floor is required to compute the upstream transmit PSDs. If all upstream VDSL signals reside above approximately 2 MHz, then the total noise at each VTU-O should be composed only of VDSL FEXT and whatever noise is added by the transceiver itself. Clearly, impulse noise and radio-frequency interference cannot be assumed as part of the noise floor. If all transceivers are designed to have the same noise floor, then η(f) should be this level. If all upstream VDSL signals do not reside above 2 MHz, then it is possible that noise other than FEXT and the receiver noise floor appears at the VTU-O. In this case, the noise floor has components that should be added to the receiver noise.

[0052] To simplify the problem, only two lines are considered. Of course, real cables will support more than two lines in a binder. Due to the manner in which cables are manufactured, however, it can be argued that the upstream performance on each loop will be most affected by, at most, 2 or 3 other loops. Thus, consideration of only two loops (i.e., one disturber) will provide some insight.

[0053] For performance with self-FEXT, we first establish the achievable performance when two lines of equal length reside in a binder, that is, with self-FEXT. FIG. 2 shows such a loop configuration. Two VTU-Rs 210, 220 are located on loops of length L, where the loop insertion losses of the two loops are denoted as |H(f)|². An ONU 230 is also located on the loops.

[0054] In the upstream direction, the PSD of FEXT caused by either line into the other is expressed by:
N_FEXT(f)=K_FEXT·|H(f)|²·f²·L·S(f),  Equation 13
where K_FEXT is a constant representing the coupling from one loop to an adjacent loop in the cable, and S(f) is the upstream transmit PSD, which is assumed to be the same on both loops. The total noise received by the VTU-O on either loop is
N_i(f)=K_FEXT·|H(f)|²·f²·L·S(f)+η(f),  Equationl 14
where η(f) is the noise floor.

[0055] Without loss of generality, assume S(f)=S_max(f). The upstream SNRs on both loops are written as $\begin{array}{cc}{\mathrm{SNR}}_{i,\mathrm{self}}\left(f\right)=\frac{S_{\max }\left(f\right)·{H\left(f\right)}^2}{N_i\left(f\right)}=\frac{1}{K_{\mathrm{FEXT}}·{H\left(f\right)}^2·f^2·L·S_{\max }\left(f\right)+\eta \left(f\right)}.& \mathrm{Equation}15\end{array}$

[0056] Note that $\begin{array}{cc}{\mathrm{SNR}}_{i,\mathrm{self}}\left(f\right)=\frac{1}{K_{\mathrm{FEXT}}·f^2·L·\left(1+\frac{\eta \left(f\right)}{N_{\mathrm{FEXT}}\left(f\right)}\right)}<\frac{1}{K_{\mathrm{FEXT}}·f^2·L}.& \mathrm{Equation}16\end{array}$

[0057] Hence, the SNR with self-FEXT is less than $\frac{1}{K_{\mathrm{FEXT}}·f^2·L}$
in the two-line case because both η(f) and N_FEXT(f) are non-negative functions.

[0058] Referring now to FIG. 3 there is illustrated a broadband communication configuration when two unequal-length lines support VDSL. Two VTU-Rs 310, 320 are located on the loops which also terminate at an ONU 330. Loop 1 and Loop 2 are lengths L₁ and L₂, respectively, where L₁<L₂ without loss of generality.

[0059] The upstream transmit PSDs on the two lines are denoted as S₁(f) and S₂(f). The insertion losses of the two loops are denoted as |H₁(f)|² and |H₂(f)|².

[0060] As before, the FEXT received by the VTU-O on each line is due entirely to upstream transmissions on the other loop. The FEXT received by the VTU-O on Loop 1 is
N_1,FEXT(f)=K_FEXT·|H₂(f)|²·f₂·L₁·S₂(f),  Equation 17
and the FEXT on Loop 2 is
N_2,FEXT(f)=K_FEXT·|H₁(f)|²·f²·L₁·S₁(f).  Equationl 18
The received noise profiles at the VTU-O are then
N_i(f)=K_FEXT·|H₂(f)|²·f²·L₁·S₂(f)+η(f),  Equationl 19
and
N₂(f)=K_FEXT·|H₁(f)|²·f²·L₁·S₁(f)+η(f).  Equation 20

[0061] It now is shown that in the two-line case, the maximum degradation to each line due to this power back-off algorithm is less than or equal to 3dB relative to the equal-length FEXT case. Three cases must be examined in the proof. Case 1 is when the computed values of both S_i(f) and S₂(f) lie under S_max(f). Case 2 is when S₁(f) lies under S_max(f), but S₂(f)=S_max(f). Case 3 is when the computed values of both S₁(f) and S₂(f) exceed S_max(f) and are thus limited to S_max(f).
Case 1: S₁(f)<S_max(f) and S₂(f)<S_max(f)

[0062] In this case, S₁(f)<S_max(f) and S₂(f)<S_max(f), with S₁(f) and S₂(f) as defined in Equation 12. Substituting for S₁(f) and S₂(f), after some algebra, the SNRs at the VTU-O become $\begin{array}{cc}\begin{array}{c}{\mathrm{SNR}}_1\left(f\right)=\frac{S_1\left(f\right)·{H_1\left(f\right)}^2}{K_{\mathrm{FEXT}}·{H_2\left(f\right)}^2·f^2·L_i·S_2\left(f\right)+\eta \left(f\right)}\\ =\frac{1}{K_{\mathrm{FEXT}}·f^2·L_1\left(1+\frac{L_1}{L_2}\right)}\end{array}& \mathrm{Equation}21\end{array}$
and $\begin{array}{cc}{\mathrm{SNR}}_2\left(f\right)=\frac{S_2\left(f\right)·{H_2\left(f\right)}^2}{K_{\mathrm{FEXT}}·{H_1\left(f\right)}^2·f^2·L_i·S_1\left(f\right)+\eta \left(f\right)}=\frac{1}{2K_{\mathrm{FEXT}}·f^2·L_2}& \mathrm{Equation}22\end{array}$

[0063] Now we compare Equations 21 and 22 to the maximum SNRs in Equation 16. Relative to when L=L₁, we see that $\begin{array}{cc}{\mathrm{SNR}}_1\left(f\right)>\frac{1}{2}·{\mathrm{SNR}}_1,\mathrm{self}\left(f\right)& \mathrm{Equation}23\end{array}$

[0064] and, relative to when L=L₂, $\begin{array}{cc}{\mathrm{SNR}}_2\left(\left(f\right)>\frac{1}{2}·{\mathrm{SNR}}_2,\mathrm{self}\left(f\right)\right).& \mathrm{Equation}24\end{array}$

[0065] Therefore, relative to when both loops are length LI the loss on Loop 1 due to setting the upstream PSDs using this method is less than 3 dB. Relative to when both loops are length L₂ the loss on Loop 2 is less than 3 dB.
Case 2: S₁(f)<S_max(f), S₂(f)=S_max(f)

[0066] In this case, S₁(f) lies under S_max(f), but S₂(f)=S_max(f). We know that in this case the computed value of S₂(f) was greater than allowed by S_max(f). Hence,
K_FEXT·|H₂(f)|²·f²·L₁·S_max(f)<η(f).  Equation 25

[0067] Using this observation, the SNR at the VTU-O on Loop 1 becomes $\begin{array}{cc}{\mathrm{SNR}}_1\left(f\right)=\frac{S_1\left(f\right)·{H_1\left(f\right)}^2}{K_{\mathrm{FEXT}}·{H_2\left(f\right)}^2·f^2·L_1·S_{\max }\left(f\right)+\eta \left(f\right)}>\frac{S_1\left(f\right)·{H_1\left(f\right)}^2}{\eta \left(f\right)+\eta \left(f\right)}& \mathrm{Equation}26\end{array}$

[0068] Substituting for S₁(f) and simplifying, we find that $\begin{array}{cc}{\mathrm{SNR}}_1\left(f\right)>\frac{1}{2K_{\mathrm{FEXT}}·f^2·L_1}& \mathrm{Equation}27\end{array}$

[0069] Thus, $\begin{array}{cc}{\mathrm{SNR}}_1\left(f\right)>\frac{1}{2}·{\mathrm{SNR}}_{1,\mathrm{self}}\left(f\right)& \mathrm{Equation}28\end{array}$

[0070] The upstream SNR on Loop 2 is $\begin{array}{cc}{\mathrm{SNR}}_2\left(f\right)=\frac{S_{\max }\left(f\right)·{H_2\left(f\right)}^2}{K_{\mathrm{FEXT}}·{H_1\left(f\right)}^2·f^2·L_1·S_1\left(f\right)+\eta \left(f\right)}=\frac{S_{\max }\left(f\right)·{H_2\left(f\right)}^2}{\eta \left(f\right)+\eta \left(f\right)}& \mathrm{Equation}29\end{array}$

[0071] We note that $\begin{array}{cc}\frac{1}{2}·{\mathrm{SNR}}_{2,\mathrm{self}}\left(f\right)=\frac{S_{\max }\left(f\right)·{H_2\left(f\right)}^2}{2K_{\mathrm{FEXT}}·{H_2\left(f\right)}^2·f^2·L_2·S_{\max }\left(f\right)+2\eta \left(f\right)}.& \mathrm{Equation}30\end{array}$

[0072] Thus, $\begin{array}{cc}{\mathrm{SNR}}_2\left(f\right)>=\frac{1}{2}·{\mathrm{SNR}}_{2,\mathrm{self}}\left(f\right).& \mathrm{Equation}31\end{array}$

[0073] Again, the degradations relative to the self-FEXT cases are limited to less than 3 dB.

 Case 3: S₁(f)=S₂(f)=S_max(f)

[0074] In this case, the computed values of S₁(f) and S₂(f) both exceed S_max(f). Thus both transmit PSDs are set to smax S_max(f). Therefore,
K_FEXT·|H₁(f)|²·f²·L₁·S_max(f)<η(f)  Equation 32

[0075] and
K_FEXT·|H₂(f)|²·f²·L₁·S_max(f)<η(f).  Equation 33

[0076] The upstream SNR on Loop 1 is $\begin{array}{cc}{\mathrm{SNR}}_1\left(f\right)=\frac{S_{\max }\left(f\right)·{H_1\left(f\right)}^2}{K_{\mathrm{FEXT}}·{H_2\left(f\right)}^2·f^2·L_1·S_{\max }\left(f\right)+\eta \left(f\right)}>\frac{S_{\max }\left(f\right)·{H_1\left(f\right)}^2}{\eta \left(f\right)+\eta \left(f\right)}& \mathrm{Equation}34\end{array}$

[0077] while the upstream SNR on Loop 2 is $\begin{array}{cc}{\mathrm{SNR}}_2\left(f\right)=\frac{S_{\max }\left(f\right)·{H_2\left(f\right)}^2}{K_{\mathrm{FEXT}}·{H_1\left(f\right)}^2·f^2·L_1·S_{\max }\left(f\right)+\eta \left(f\right)}>\frac{S_{\max }\left(f\right)·{H_2\left(f\right)}^2}{\eta \left(f\right)+\eta \left(f\right)}& \mathrm{Equation}35\end{array}$

[0078] which leads directly to the results that $\begin{array}{cc}{\mathrm{SNR}}_1\left(f\right)>=\frac{1}{2}·{\mathrm{SNR}}_{1,\mathrm{self}}\left(f\right).& \mathrm{Equation}36\end{array}$

[0079] and $\begin{array}{cc}{\mathrm{SNR}}_2\left(f\right)>=·\frac{1}{2}{\mathrm{SNR}}_{2,\mathrm{self}}\left(f\right).& \mathrm{Equation}37\end{array}$

[0080] Thus, we have shown that in the two-line case, the maximum degradation relative to the self-FEXT case is less than 3 dB using the reference noise method of upstream power back-off. We hypothesize that when additional lines are considered, the bound will increase slightly.

[0081] When the reference noise method is used, the GDR PSD must be normalized by the ratio of a nominal loop length to the loop length to compute the required transmit PSD: $\begin{array}{cc}{S}_i\left(f\right)=\frac{L_r}{L_i}·\frac{S_{\mathrm{GDR}}\left(f\right)}{{H_1\left(f\right)}^2}.& \mathrm{Equation}38\end{array}$

[0082] Again, the normalization can be absorbed into the GDR PSD if transmission of a different GDR PSD to each NT is acceptable. It should be clear to the reader now why the factor L_r was incorporated into the expression for S_i(f). Without this factor, the GDR PSD is not actually a PSD.

[0083] As above-described, all aforementioned upstream power back-off methods can be defined using the GDR PSD. In some cases, the upstream transmit PSD is computed simply by dividing the GDR PSD by the loop insertion loss. Other methods derived from FEXT equations require normalization by a ratio of loop lengths. By choosing the appropriate GDR PSD, operators can tailor the power back-off to meet their service requirements, including mixed services known in the art.

[0084] Referring now to FIG. 4 there is shown a method for upstream power back-off in a broadband communication system in accordance with the present invention. According to the present invention, power back-off is applied in the upstream direction, NT→LT, so that crosstalk from systems on short lines does not unduly compromise service on long lines. The global desired receive power spectral density (GDR PSD) is determined 410 and denoted S_GDR(f) defined as $\begin{array}{cc}{S}_{\mathrm{GDR}}\left(f\right)=\frac{\eta \left(f\right)}{L_r·K_{\mathrm{FEXT}}·f^2},& \mathrm{Equation}39\end{array}$
where η(f) is an assumed reference noise profile, L_i is a determined nominal loop length 420, and K_FEXT is a constant representing the coupling from one loop to an adjacent loop in the cable.

[0085] The GDR PSD and a nominal loop length L_r are transmitted 430 by the LT and is received 440 by the NT during initialization. If the value of L_r is non-zero, the NT uses an estimate of the length of the loop, L_i, and determines the upstream transmit power spectral density 450 as, $\begin{array}{cc}S\left(f\right)=\frac{L_r}{L_i}\frac{S_{\mathrm{GDR}}\left(f\right)}{{H\left(f\right)}^2},& \mathrm{Equation}40\end{array}$
where |H(f)|² is the estimated insertion loss of the loop. Transmission by the LT of a value of 0 for L_r shall indicate no normalization of the GDR PSD is necessary, and the NT determnines the upstream transmit power spectral density 450 as, $\begin{array}{cc}S\left(f\right)=\frac{S_{\mathrm{GDR}}\left(f\right)}{{H\left(f\right)}^2}.& \mathrm{Equation}41\end{array}$

[0086] The estimation of the loop length can occur during initialization or, if that is deemed too risky, during the installation procedure. Alternatively, all loops can be assumed to be the same length, such as 1km. Simulations show this approximation does not dramatically degrade the performance of at least the reference noise method. If a reasonable estimation of the loop length is not possible, a back-off algorithm that is independent of the loop length (such as multiple reference lengths) can be selected.

[0087] In either case, the upstream transmit PSD shall be no greater than
min(S(f), S_max(f)),  Equation 42
where S_max(f) is the maximum allowed upstream transmit PSD.

[0088] In a preferred embodiment, the NT performs power back-off autonomously, that is, without sending any information to the LT until back-off has been applied, however, the management system provides the facility to change parameters of the S_GDR(f) and L_r, Hence, the reference noise profile η(f) and nominal loop length is operator-configurable via the management system. The same GDR PSD and nominal length are used by all NTs in the same binder.

[0089] This proposal offers a number of benefits, and particularly the following: (1) Power back-off can be performed by the NT before it transmits any data to the LT. Defining the GDR PSD enables the NT to perform a simple computation to determine the required transmit PSD; and (2) The power back-off parameters can be changed via the management system. Operators can change power back-off parameters using the management system. By defining a GDR PSD, the back-off parameters, and even the algorithm itself, can be changed. Hence, operators are not “locked in” to a specific back-off algorithm or parameter set.

[0090] Although a preferred embodiment of the method and system of the present invention has been illustrated in the accompanied drawings and described in the foregoing Detailed Description, it is understood that the invention is not limited to the embodiments disclosed, but is capable of numerous rearrangements, modifications, and substitutions without departing from the spirit of the invention as set forth and defined by the following claims.