Multiple Access Channel Optimal Spectrum Balancing for Upstream DSL Transmission

Linear and Nonlinear Precoding Based Dynamic Spectrum Management for Downstream Vectored G.fast Transmission

“…the user with the largest weight is to be encoded first [9], [22]). P mask k is the spectral mask for every line and for tone k, which is typically kept low in G.fast in order not to generate too much interference into other technologies.…”

“…it uses an exhaustive discrete bit loading search to solve the US Lagrange dual function (24)), BC-DSB is more practical for large scenarios due to its significantly reduced complexity (see also section V-B). For instance, for 4 users, BC-OSB already takes more than a week [22], compared to only a few minutes for BC-DSB. Furthermore, the continuous bit loading of BC-DSB results in slightly better (<1%) line rates compared to the discrete bit loading of BC-OSB (illustrated in Fig.…”

Optimal Power Allocation for Downstream xDSL With Per-Modem Total Power Constraints: Broadcast Channel Optimal Spectrum Balancing (BC-OSB)

“…The w j 's are the weights assigned to the different users. In the MAC, the optimal detection order is actually defined by the weights and the user with the largest weight is decoded last [10], [11]. Assuming a decreasing order of weights w 1 > · · · > w K , as the MAC-BC duality dictates a reverse of the decoding/encoding order, in the BC the user with the largest weight has indeed to be encoded first.…”

“…The weighted rate sum function in the MAC for the decoding order N,N-1,...,1 (i.e. user 1 is decoded last) with Successive Interference Cancellation (SIC) is: (6) has been addressed in [10], [11]. The MAC-OSB algorithm has been derived based on a dual decomposition approach with a Lagrange formulation.…”

“…Therefore the maximization of the Lagrangian can be done by an exhaustive/iterative search on a per-tone basis [10] or by convex programming techniques such as interior point methods [11]. For further details, we refer to [10], [11].…”