Dynamic Spectrum Management With Spherical Coordinates

Multiuser interference, i.e., crosstalk, is the main bottleneck for digital subscriber lines (DSL) technology. Dynamic spectrum management (DSM) mitigates crosstalk by focusing on the multiuser power/frequency resource allocation problem, and it can provide formidable gains in performance. In this paper, we look at the DSM problem from a different perspective. We formulate the problem with the power allocation vectors defined with spherical coordinates, i.e., as a function of a radius and angles. We see that this reformulation permits us to exploit structure in the problem. We propose two algorithms. In the first of them, we use the fact that the DSM problem is concave in the radial dimension and perform an exhaustive search for the angles. The second algorithm uses a block coordinate descent approach, i.e., a sequence of line searches. We show that there is structure to be found in the radial dimension (it is always concave) and in the angle dimensions. For the latter, we provide conditions for the line searches to be concave or convex for each of the angles. The fact that we use structure leads to large savings in computational complexity. For example, we see that our first algorithm can be up to 60 times faster than a corresponding previously proposed algorithm. Our second algorithm is 2-15 times faster than a relevant previously proposed algorithm.