Sparse approximation based resource allocation in DSL/DMT transceivers with per-tone equalization

• Sparse approximation techniques has been shown to perform better than the previously reported variable order filter techniques.
• The performance can be further improved by performing the transmit power loading alongside the sparse filter computation.
• Both filter tap allocation and the transmit power loading can be represented as optimization problem and can be efficiently solved.
• The number of non-zero filter taps can be significantly reduced by using this method without significant performance loss.

Per-tone equalization has been proposed as an alternative to time domain equalization for DMT receivers in DSL modems. It optimizes the bit rate performance of the receiver as each tone can be equalized independently. It has also been shown that using variable length equalizers can significantly reduce the total number of equalizer taps and hence the run-time complexity, without compromising performance. For a given transmit power loading, it has been shown that the equalizer taps can be allocated optimally using a dual decomposition based approach with per-tone exhaustive searches over all possible equalizer lengths. However, a more general approach is needed when optimal transmit power allocation is also considered to maximize the overall bit rate, where in addition the per-tone exhaustive searches are replaced by a more efficient procedure. In this paper, a sparse approximation based resource allocation algorithm is presented to allocate equalizer taps and transmit power over tones and maximize the overall bit rate. This algorithm is shown to provide efficient allocations at a relatively low computational cost.