Spectrum balancing methods decide what should be the spectral assignment for each user, given their channel line and signal spectra. It is well known that for the single-user case the optimal solution is a 'water-filling' power spectral density. For the multiuser case, performance evaluation and/or optimization become much more complex. For multiple users, performance improvement can occur with the use of iterative/ad hoc methods that often lead to an optimal solution or to some acceptable sub optimal solution. Performance improvements over static spectrum management can be very large.
In current DSL deployment, an Incumbent Local Exchange Carrier (ILEC) allows a Competing Local Exchange Carrier (CLEC) to place modulated signals for the DSL service directly on their leased copper pair phone line. If those lines emanate from a telephone company central office, the carriers involved try to ensure mutual spectrum compatibility using some sort of fixed spectrum management based on worst-case crosstalk scenarios. When lines emanate from a remote location (often fed by fiber), co-location or unbundling is not mandated nor practiced at present. To improve performance, the Network Maintenance Center (NMC) can collect channel information and adaptively determine those lines that have significant mutual crosstalk. This NMC can then use an appropriate spectrum-balancing technique to recommend how better to assign the available resources.
The spectrum-balancing problem in DSL differs from the widely studied power-control problem in wireless systems in certain key aspects. The DSL environment varies from loop to loop, but it does not vary over time. Since the wireless' time variation is not of concern, spectrum balancing can make use of more accurate channel knowledge provided by Channel Identification. Better channel knowledge can allow implementation of sophisticated centralized power control schemes. On the other hand, DSL channels are heavily frequency selective, unlike the wireless scenario where designers often assume flat fading.
Keeping these differences in mind, we developed an iterative algorithm for spectrum and power assignment in DSL systems based on the novel ideas in , . Reference  describes an efficient iterative water-filling method that achieves the sum capacity in a Gaussian vector multiple-access channel, given a total power constraint for each user. This paper shows that if each user successively employs single-user water-filling regarding all crosstalk from other users as noise, then ultimately the system converges to a sum capacity point. Such an algorithm can thus be implemented in a distributed manner.
A DSL system may have a set of user-rate specifications to achieve. Reference  shows a method to meet these specifications by adding an outer control mechanism to the iterative water-filling method in . This control mechanism finds the optimal total power constraint for each user. After each inner iterative water-filling, the control mechanism adjusts the user powers based on the current rates and the target rates. For example, if the user's data rate is much above its target rate, its power is decreased. This procedure is continued until the target rates are achieved. This method gave significant performance enhancements over other power control algorithms for DSL. See  and the T1E1.4 contribution "Example Improvements of Dynamic Spectrum Management" for some example cases supporting this claim.
In some systems, the FDMA capacity (capacity assuming different transmitters use non overlapping frequency bands) may be of interest rather than the actual capacity. An example is a VDSL system which uses frequency division duplex to separate upstream and downstream transmission. The optimal frequency assignment between upstream and downstream is an optimal FDMA capacity problem for a multiple-access channel with two users. Keeping this in mind  studies the FDMA-capacity problem for gaussian multiple-access channel. It gives efficient numerical methods for the general problem and provides some additional insight into the two-user VDSL scenario.
Because of the general nature of the underlying ideas in the methods described, similar analysis can be done in the wireless case. Refer to our Wireless Research section for more. Also, refer to our T1E1.4 contribution "Unbundled DSL evolution" to get a perspective on these methods with respect to DSL current practices and regulations. All publications referred in this page are listed in the 'Publications on Spectrum Balancing' page.
the above discussion did not assume that the different signals are
coordinated. Common sense suggests that if coordination between the line
signals are possible, performance can improve yet further. This line of
argument leads to the development of Vectored Transmission Methods.