Distributionally Robust Ultra-Reliable Resource Allocation via Double Tail Waterfilling Under Fading Risk

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Optimal resource allocation in wireless systems remains a fundamental challenge due to the inherent adversities caused by channel fading. Modern wireless applications require efficient allocation schemes that maximize total network utility ensuring robust and reliable system performance. Although optimal on average, ergodic-optimal policies, commonly realized via stochastic waterfilling schemes, are susceptible to statistical dispersion of commonly heavy-tailed or highly volatile fading channels, particularly in terms of both instantaneous power policy fluctuations <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">and</i> frequent service outages (due to deep fade events), violating established power-level and quality-of-service specifications, essentially sabotaging fulfillment of provider-specific power/energy targets on the one hand, and user-perceived system reliability on the other. At the other extreme, short-term-optimal policies, commonly relying on deterministic waterfilling, or maximally averse minimax-optimal policies, strictly satisfy specifications but are computationally demanding, impractical, while also being suboptimal in any long-term regime. To address these challenges, we introduce a distributionally robust formulation of the constrained stochastic resource allocation problem in the classical point-to-point interference-free multi-terminal network by leveraging Conditional Value-at- Risk (CVaR) as a coherent measure of fading and/or fluctuation risk relevant to both transmission power and achievable rate distributions. We derive a closed-form parameterized expression for the CVaR-optimal resource policy which is of remarkably simple and interpretable form, along with subgradient-based update schemes for the corresponding CVaR quantile levels to both transmission power and achievable rates. Building on this, we develop a primal-dual <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">double tail waterfilling</i> scheme which iteratively computes <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">globally optimal policies achieving ultra-reliable long-term rate performance, but with near-short-term characteristics</i>. Extensive numerical experiments corroborate the effectiveness of the proposed approach.