Computationally Efficient Partial Crosstalk Cancellation in Fast Time-Varying DSL Crosstalk Environments

Line selection (LS), tone selection (TS), and joint tone-line selection (JTLS) partial crosstalk cancellers have been proposed to reduce the online computational complexity of far-end crosstalk (FEXT) cancellers in digital subscriber lines (DSL). However, when the crosstalk profile changes rapidly over time, there is an additional requirement that the partial crosstalk cancellers, particularly the LS and JTLS schemes, should also provide a low preprocessing complexity. This is in contrast to the case for perfect crosstalk cancellers. In this paper, we propose two novel channel matrix inversion methods, the approximate inverse (AI) and reduced inverse (RI) schemes, which reduce the recurrent complexity of the LS and JTLS schemes. Moreover, we propose two new classes of JTLS algorithms, the subsort and Lagrange JTLS algorithms, with significantly lower computational complexity than the recently proposed optimal greedy JTLS scheme. The computational complexity analysis of our algorithms shows that they provide much lower recurrent complexities than the greedy JTLS algorithm, allowing them to work efficiently in very fast time-varying crosstalk environments. Moreover, the analytical and simulation results demonstrate that our techniques are close to the optimal solution from the crosstalk cancellation point of view. The results also reveal that partial crosstalk cancellation is more beneficial in upstream DSL, particularly for short loops.