Price of Fairness in Digital Subscriber Line Systems Using Dynamic Spectrum Management

Bit rate fairness is an important concern in current G.fast and the forthcoming fifth generation DSL systems where the frequency is extended to hundreds of MHz and crosstalk couplings reach unprecedented levels. In this paper, we study the price of fairness (PoF) in dynamic spectrum management (DSM) enabled DSL systems. We propose optimal low complexity PoF-constrained max-min fairness (MMF), weighted max-min fairness (WMMF), proportional fairness (PF), and (p,α)-PF algorithms. The proposed algorithms inherently provide weight factors which can be used to reduce the computational complexity of user encoding or decoding order optimizing algorithms used in nonlinear vectoring. Our simulation results show that although PoF grows exponentially with the minimum bit rate, fairness can be improved considerably with a relatively small price in DSM level 2 spectrum balancing and particularly in DSM level 3 using minimum mean square error (MMSE) generalized decision feedback equalizer (GDFE). It is also seen that the proposed optimal PoF-constrained MMF algorithm can reach the solutions of PF and (p,α)-PF measures for some PoF. That is, the PoF-constrained MMF or WMMF algorithms can be used instead of the non-linear PF and (p,α)-PF measures, which often result in computationally intensive solutions.