Efficient calculation of the MMSE-GDFE decoding order in non-ideal DSL multiple-access channels

The minimum mean squared error (MMSE)-generalized decision feedback equalizer (GDFE) provides a high multi-user crosstalk cancellation performance in upstream digital subscriber lines (DSL) scenarios. The weighted sum rate maximization approach can be used to find the points located on the boundary of the corresponding rate region (RR). The performance of the MMSE-GDFE depends on the decoding order of the users. Unfortunately, unlike in ideal multiple access channels (MAC), the optimal decoding order is not determined by the order of weight factors in practical DSL MACs. To reach the boundary of the RR, a tonal exhaustive search (TES) with computational complexity O(N²N!) is required for each tone, where N is the number of users. In this paper, we investigate the main deviations of the DSL receiver from the ideal MAC receiver and model their effects as a set of update factors on the weight factors. The order of the updated weight factors is then used to determine the decoding order of the users in an iterative fashion. The computational complexity of our updated weight factor ordering (UWFO) algorithm is O(N⁴) which is significantly smaller than that of TES. Moreover, our simulation results show that the algorithm achieves bit rates very close to the boundary of the RR leading to approximately the same performance as TES. UWFO can be applied to wireless MACs and zero-forcing GDFEs as well.