Crosstalk profile detection for use in multiuser detection

Profile detection in multiuser digital subscriber line systems

“…If the crosstalk channels have been stored from recent measurements, then except for the timing offsets that the crosstalk channels have with respect to some nominal reference, the multiuser transmission scheme can be loaded appropriately just by detecting the presence of the crosstalker profile. Timing issues can be addressed separately and are left considered in future work [11]. So, a detection scheme that is independent of timing issues is desired.…”

“…The determination of the conditional probabilities is not straightforward due to the possibly different sampling rates used by the different users and due to the unknown timing offsets between users. There are various ML criteria based on different assumptions for the input data [11], [13], [14]. In our problem, the simplest of these criteria is the Gaussian maximum likelihood (GML) detector, which treats input symbols as Gaussian random variables, so that the output waveform is a Gaussian random variable.…”

“…where represents a normal random vector with mean and covariance matrix and (10) where is the expectation operator, and is the identity matrix. Then, the GML test can be written as: (11) where is the determinant of matrix . While GML is less complex than the other ML criteria, it is still very complex due to the effects of the timing information.…”