Stochastic Resource Allocation via Dual Tail Waterfilling

Optimal resource allocation in wireless systems still stands as a rather challenging task due to the inherent statistical characteristics of channel fading. On the one hand, minimax/outage-optimal policies are often overconservative and analytically intractable, despite advertising maximally reliable system performance. On the other hand, ergodic-optimal resource allocation policies are often susceptible to the statistical dispersion of heavy-tailed fading channels, leading to relatively frequent drastic performance drops. We investigate a new risk-aware formulation of the classical stochastic resource allocation problem for point-to-point power-constrained communication networks over fading channels with no cross-interference, by leveraging the Conditional Value-at-Risk (CV@R) as a coherent measure of risk. We rigorously derive closed-form expressions for the CV@R-optimal risk-aware resource allocation policy, as well as the optimal associated quantiles of the corresponding user rate functions by capitalizing on the underlying fading distribution, parameterized by dual variables. We then develop a purely dual tail waterfilling scheme, achieving significantly more rapid and assured convergence of dual variables, as compared with the primal-dual tail waterfilling algorithm, recently proposed in the literature. The effectiveness of the proposed scheme is also readily confirmed via detailed numerical simulations.