Max-Min Fairness Rate Control in Wireless Networks: Optimality and Algorithms by Perron-Frobenius Theory - 2018


Rate adaptation and power control are two key resource allocation mechanisms in multiuser wireless networks. In the presence of interference, how do we have a tendency to jointly optimize finish-to-finish supply rates and link powers to realize weighted max-min rate fairness for all sources in the network? This optimization downside is tough to solve as physical layer link rate functions are nonlinear, nonconvex, and paired in the transmit powers. We have a tendency to show that the weighted max-min rate fairness downside can, in fact, be decoupled into separate fairness problems for flow rate and power management. For a large class of physical layer link rate functions, we have a tendency to characterize the optimal resolution analytically by a nonlinear Perron-Frobenius theory through solving a conditional eigenvalue downside that captures the interaction of multiuser interference. We propose an iterative algorithm to compute the optimal flow rate that converges geometrically quick while not any parameter configuration. Numerical results demonstrate that our iterative algorithm is computationally quick for the Shannon capability, CDMA, and piecewise link rate functions.

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