  We present asymptotic expressions for user throughput in a multi-user
wireline system with a linear decoder, in increasingly large system sizes. This
analysis can be seen as a generalization of results obtained for wireless
communication. The features of the diagonal elements of the wireline channel
matrices make wireless asymptotic analyses inapplicable for wireline systems.
Further, direct application of results from random matrix theory (RMT) yields a
trivial lower bound. This paper presents a novel approach to asymptotic
analysis, where an alternative sequence of systems is constructed that includes
the system of interest in order to approximate the spectral efficiency of the
linear zero-forcing (ZF) and minimum mean squared error (MMSE) crosstalk
cancelers. Using works in the field of large dimensional random matrices, we
show that the user rate in this sequence converges to a non-zero rate. The
approximation of the user rate for both the ZF and MMSE cancelers are very
simple to evaluate and does not need to take specific channel realizations into
account. The analysis reveals the intricate behavior of the throughput as a
function of the transmission power and the channel crosstalk. This unique
behavior has not been observed for linear decoders in other systems. The
approximation presented here is much more useful for the next generation G.fast
wireline system than earlier digital subscriber line (DSL) systems as
previously computed performance bounds, which are strictly larger than zero
only at low frequencies. We also provide a numerical performance analysis over
measured and simulated DSL channels which show that the approximation is
accurate even for relatively low dimensional systems and is useful for many
scenarios in practical DSL systems.
