An optimal spectrum‐balancing algorithm for digital subscriber lines based on particle swarm optimization

This paper presents a new algorithm for optimal spectrum balancing in modern digital subscriber line (DSL) systems using particle swarm optimization (PSO). In DSL, crosstalk is one of the major performance bottlenecks, therefore various dynamic spectrum management algorithms have been proposed to reduce excess crosstalks among users by dynamically optimizing transmission power spectra. In fact, the objective function in the spectrum optimization problem is always nonconcave. PSO is a new evolution algorithm based on the movement and intelligence of swarms looking for the most fertile feeding location, which can solve discontinuous, nonconvex and nonlinear problems efficiently. The proposed algorithm optimizes the weighted rate sum. These weights allow the system operator to place differing qualities of service or importance levels on each user, which makes it possible for the system to avoid the selfish‐optimum. We can show that the proposed algorithm converges to the global optimal solutions. Simulation results demonstrate that our algorithm can guarantee fast convergence within a few iterations and solve the nonconvex optimization problems efficiently. Copyright © 2008 John Wiley & Sons, Ltd.