Optimal Spectrum Management (OSM) computes the optimal PSD for all modems in Digital Subscriber Lines (DSL) systems to achieve the maximum possible data rates. Unfortunately, its complexity grows exponentially in the number of users N and becomes computationally intractable for large N. This paper shows that the non-convex optimization problem in OSM can be reformulated as an equivalent global concave minimization problem by representing its objective function as a difference of two convex functions (d.c.). A prismatic branch and bound algorithm is applied to find the global optimum that only requires solving a sequence of linear programming sub-problems with a substantial reduction in complexity, especially for large N.

This paper presents efficient multiuser margin optimization algorithms suitable for multicarrier digital subscriber line (DSL) systems using Dynamic Spectrum Management (DSM). The favorable monotonicity and fairness properties of multiuser margin are employed to formulate a box-constrained nonlinear least squares (NLSQ) problem for multiuser margin maximization, which is efficiently solved by using a scaled-gradient trust-region approach with Broyden Jacobian update. Based on this NLSQ formulation, a multiuser harmonized margin (MHM) optimization algorithm for resource allocation is developed. A Newton-Raphson method is also developed for fast margin estimation and used within the MHM. The MHM algorithm converges efficiently to a solution for the best common equal margin to all users, while explicitly guaranteeing their target rate requirements. (This is the reason for the term harmonized.) Furthermore, its predominantly distributed structure can be implemented in DSL/DSM scenarios with only Level 1 coordination. Simulation results of various cases verify the convergence to the unique optimal solution within 5-10 iterations.

Multiuser margin maximization algorithms are developed for multi-carrier digital subscriber loops (DSL) employing dynamic spectrum management (DSM). Margin maximization is desirable for constant bit rate applications and provides protection against various non-stationary and bursty noise sources. Most single-user margin maximization algorithms rely on a fixed crosstalk assumption, which does not hold in DSM. Thus with direct extension of single-user algorithms in DSM scenarios, one user's margin maximization can lead to the failure of other users in meeting their target rates. In this paper, we explore the favorable monotonicity and fairness properties in multiuser margin and use them to formulate a box-constrained non-linear least squares (NLSQ) problem that can be solved by using a scaled gradient trust region approach with Broyden Jacobian update. This algorithm efficiently converges to a solution providing the best common equal margin to all users while explicitly guaranteeing that each user's target rate requirement is satisfied. The algorithm can be implemented in practical DSL-DSM scenarios with only Level-1 coordination.

In this paper, we present a fine granularity loading scheme using joint optimization of modulation and coding for discrete multitone (DMT) modulation towards achieving maximum information rate conveyed. While most existing algorithms strived for the optimal energy distribution to maximize rate, the bits loaded were always constrained to integers. It was initially believed that most (not all) of the granularity losses could be recovered through 'bit-rounding' and 'energy re-scaling' after an optimal 'water-filling' approach. But this was observed only for the total power constrained case. With the advent of peak power constraint, we show that the room for optimization in the energy domain severely constrained and granularity losses constitute a significant percentage of the achievable data rate. To recover these losses, we propose a loading scheme that integrates the coding scheme with the bit-loading algorithm. For achieving near-continuous rate adaptation, the family of Reed-Solomon (RS) codes has been used for their low redundancy, high flexibility in correction capability and highly programmable architecture. Simulation results with very high bit rate digital subscriber line (VDSL)-DMT system show more than 20% improvement in most cases.