Split SR-RLS for the Joint Initialization of the Per-Tone Equalizers and Per-Tone Echo Cancelers in DMT-Based Receivers

In asymmetric digital subscriber lines (ADSL), the available bandwidth is divided in subcarriers or tones which are assigned to the upstream and/or downstream transmission direction. To allow efficient bidirectional communication over one twisted pair, echo cancellation is required to separate upstream and downstream channels. In addition, intersymbol interference and intercarrier interference have to be reduced by means of equalization. In this paper, a computationally efficient algorithm for adaptively initializing the per-tone equalizers (PTEQ) and per-tone echo cancelers (PTEC) is presented. For a given number of equalizer and echo canceler taps per-tone, it was shown that the joint PTEQ/PTEC receiver structure is able to maximize the signal-tonoise ratio (SNR) on each subcarrier and hence also the achievable bit rate. The proposed initialization scheme is based on a modification of the square root recursive least squares (SR-RLS) algorithm to reduce computational complexity and memory requirement compared to full SR-RLS, while keeping the convergence rate acceptably fast. Our performance analysis will show that the proposed method converges in the mean and an upper bound for the step size is given. Moreover, we will indicate how the presented initialization method can be reused in several other ADSL applications.