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Robust Resource Management for SAGIN using DNN-Driven Channel Uncertainty Learning

Haonan Zhang, Weihua Wu, Qi Zhang, Runzi Liu, Zewei Jing, Weijia Han

arXiv:2609.34728v1cs.ITmath.IT

TL;DR

Imperfect CSI can cause insufficient transmit power, frequent QoS violations, service interruptions, and outages, motivating statistical CSI modeling and uncertainty sets that bound estimation errors for robust transmission. A DNN learns asymmetric CSI uncertainty sets, which are used in a robust resource-management framework with iterative joint power allocation and beamforming optimization. The proposed DNN method achieves the lowest power consumption among robust schemes and an effective trade-off between energy efficiency and robust reliability.

  • Problem

    Imperfect CSI can cause insufficient transmit power, frequent QoS violations, service interruptions, and outages, motivating statistical CSI modeling and uncertainty sets that bound estimation errors for robust transmission.

    Source: §I · p. 2

  • Method

    A DNN learns asymmetric CSI uncertainty sets, which are used in a robust resource-management framework with iterative joint power allocation and beamforming optimization.

    Source: §I · p. 2

  • Results

    The proposed DNN method achieves the lowest power consumption among robust schemes and an effective trade-off between energy efficiency and robust reliability.

    Source: §V · pp. 13–14, §VI · p. 14

  • Takeaways & Limitations

    The learned uncertainty sets enclose irregular CSI error distributions and alleviate over-conservatism in resource allocation.

    Source: §VI · p. 14

Abstract

from arXiv · show

This paper focuses on the joint robust beamforming and resource allocation for space-air-ground integrated networks (SAGIN) under uncertain channel state information (CSI). In SAGIN, uncertain CSI undermines the precise adjustment of beamforming and resource allocation, posing a major challenge to meeting heterogeneous users' strict quality of service (QoS) requirements. To address this challenge, we first formulate a chance-constrained optimization problem to minimize the total transmit power while satisfying QoS requirements under a predefined outage probability. By leveraging semidefinite relaxation (SDR), the objective function is transformed into a linear function of the traces of the beamforming matrices. Then, we propose a deep neural network (DNN)-driven channel uncertainty learning to dynamically learn and model the uncertain CSI as an asymmetric uncertainty set. Under the constructed CSI uncertainty set, a robust counterpart method based on pre-trained network parameters is developed. It characterizes the uncertainty set as a finite union of convex sets, thereby providing a tractable approximation for the original chance constraints. Finally, we design an adaptive iterative algorithm to jointly optimize the resource allocation and beamforming vectors. Simulation results show that our proposed DNN-driven method outperforms traditional robust and non-robust methods, achieving a superior energy efficiency and robust reliability in SAGIN.

I. INTRODUCTION

The paper addresses resource management and beamforming in SAGIN when imperfect CSI complicates reliable QoS provisioning. It proposes DNN-driven uncertainty modeling and robust optimization, while prior approaches are described as limited by idealized CSI, rigid uncertainty shapes, or data and acquisition demands.

I. INTRODUCTION

  • Satellite links face CSI errors from long propagation delays and Doppler shifts, while channel underestimation can waste resources and overestimation can cause QoS violations and outages.Source: §I · pp. 1–2
  • The heterogeneous SAGIN formulation combines satellite NOMA and aerial-platform LDM under full frequency reuse, accounting for cross-tier interference and heterogeneous QoS requirements.Source: §I · p. 2
  • The proposed framework jointly manages resources and beamforming under uncertain CSI, minimizing total transmit power while guaranteeing heterogeneous users’ QoS requirements.Source: §I · p. 2
  • DNN-driven uncertainty modeling uses piecewise-affine activations to partition CSI uncertainty into convex regions and characterize asymmetric sets with reduced geometric redundancy.Source: §I · p. 2
  • A two-layer iterative algorithm searches NOMA power-allocation coefficients and solves robust beamforming subproblems with the cutting plane method.The method converts semi-infinite constraints into a sequence of finite constraints.Source: §I · p. 2

II. RELATED WORKS

  • Prior robust methods use symmetric or worst-case uncertainty models, while stochastic methods may require high-frequency CSI and SVC methods rely on a single convex hull.The paper identifies the resulting challenge as capturing irregular CSI distributions without redundant regions.Source: §II · pp. 2–3

III. SYSTEM MODEL

The system model combines a low Earth orbit satellite and a low-altitude aerial platform to serve satellite terminals and ground IoT devices. The two tiers use different access schemes suited to their users.

III. SYSTEM MODEL

  • The modeled SAGIN contains a LEO satellite, an aerial platform, satellite terminals, and IoT devices.Source: §III · p. 3, Figure 1 · p. 3
  • The satellite serves multiple satellite terminals in each beam using NOMA, superimposing their signals in the power domain.Source: §III · p. 3
  • The aerial platform provides coverage for ground IoT devices, and full frequency reuse between it and the satellite introduces cross-tier interference.The model treats interference from the aerial platform to satellite terminals as significant, but satellite interference to IoT devices as negligible.Source: §III · p. 3

A. Channel Model

The channel model distinguishes uncertain satellite links from aerial-platform links with assumed perfect CSI. It specifies satellite-channel factors and aerial-platform antenna and propagation characteristics.

A. Channel Model

  • Satellite-to-terminal channel modeling includes rain attenuation, free-space path loss, and satellite and terminal antenna gains.Source: A. Channel Model · p. 3
  • The aerial-platform channel model incorporates LoS and NLoS components and UPA directional gain, with the gain capped by the side-lobe parameter.Source: A. Channel Model · p. 4
  • The aerial-platform array steering vectors are specified along its X and Y axes, with element counts and spacings defining the array geometry.Source: A. Channel Model · p. 4
  • The satellite channel estimate includes an additive error term representing channel aging and measurement inaccuracies.The model assumes perfect CSI for aerial-platform links, whose short ranges and frequent pilot estimation yield small estimation errors.Source: A. Channel Model · p. 4

B. Signal Model

The signal model assigns power and beamforming across satellite and aerial-platform transmissions. It describes NOMA successive interference cancellation for satellite users and sequential multicast-unicast decoding for IoT devices.

B. Signal Model

  • Satellite transmission assigns each user a power-allocation coefficient constrained to [0, 1], with coefficients summing to one in each beam.Source: B. Signal Model · p. 4
  • The aerial platform uses LDM to send a common multicast stream and user-specific unicast streams, which IoT devices decode sequentially.An IoT device first decodes the multicast stream while treating unicast transmissions as interference, then decodes its unicast stream after subtracting the multicast signal.Source: B. Signal Model · pp. 4–5
  • Satellite users use successive interference cancellation, decoding and canceling higher-power users before treating stronger users’ signals as background noise.Source: B. Signal Model · p. 5
  • Satellite-terminal SINR accounts for intra-beam, inter-beam, and aerial-platform interference, with the latter considered significant.Satellite interference to IoT devices is treated as negligible in the model.Source: B. Signal Model · p. 5

C. Problem Formulation and simplification

The section formulates transmit-power minimization under heterogeneous QoS and outage constraints, then uses uncertainty sets and relaxation to obtain a tractable robust problem. Its robust constraints are presented as a sufficient condition for the original chance constraints.

C. Problem Formulation and simplification

  • The objective minimizes the sum of traces of the satellite and aerial-platform beamforming matrices, subject to user QoS and outage constraints.The outage probability is bounded by ϵ, the maximum interruption probability users can tolerate.Source: C. Problem Formulation and… · p. 5
  • The robust constraints based on an uncertainty set are a sufficient condition for the chance constraints, supporting the subsequent robust optimization framework.The original problem is difficult because its chance constraints create a semi-infinite problem and its coupled variables and non-convex constraints complicate optimization.Source: C. Problem Formulation and… · p. 5
  • The chance constraints are addressed by requiring QoS constraints to hold throughout uncertainty sets designed to capture channel vectors at confidence level 1 − ϵ.The passage describes this as a way to guarantee satisfaction of the chance constraints.Source: C. Problem Formulation and… · p. 6
  • After dropping rank-one constraints, the problem is reformulated as a deterministic robust convex optimization problem.The remaining challenge is constructing a compact, distribution-matched uncertainty set.Source: C. Problem Formulation and… · p. 6

IV. DNN-DRIVEN ROBUST RESOURCE MANAGEMENT FRAMEWORK

The framework uses historical CSI and a pre-trained DNN to form an asymmetric uncertainty set, transform robust constraints, and jointly optimize beamforming and power allocation.

IV. DNN-DRIVEN ROBUST RESOURCE MANAGEMENT FRAMEWORK

  • The framework has four stages: input and inference, uncertainty-set formation, robust-counterpart transformation, and robust resource management.The stages use historical CSI with a pre-trained DNN, derive a tightly fitted asymmetric set, convert constraints into solvable convex constraints, and jointly optimize beamforming matrices and power-allocation coefficients.Source: §IV · p. 6

A. Input and Inference Stage for CSI Uncertainty

The input and inference stage learns channel uncertainty from historical CSI samples using a DNN. Quantile-based training targets the prescribed coverage level, and the resulting feature-space center and radius define the uncertainty set.

A. Input and Inference Stage for CSI Uncertainty

  • The DNN is trained on D independent and identically distributed historical samples of the actual channel vector to model CSI uncertainty.The passage identifies these samples as the training dataset.Source: A. Input and Inference Stage for CSI… · p. 6
  • The network uses continuous piecewise-affine activations, whose intersecting hyperplanes partition feature space into polyhedral regions.ReLU is given as an example, and other piecewise-affine activation functions can also be modeled.Source: A. Input and Inference Stage for CSI… · pp. 6–7
  • Quantile-based training targets a feature mapping that encloses normal CSI samples while excluding outliers at the prescribed coverage level 1 − ϵ.The loss weights penalize boundary shrinkage to avoid under-coverage and boundary expansion to reduce redundant space and conservatism.Source: A. Input and Inference Stage for CSI… · p. 7
  • The feature-space center is fixed, and the radius is set from the prescribed outage probability so that CSI samples fall within the uncertainty set with probability at least 1 − ϵ.The center may be the average network representation of training samples after an initial forward pass.Source: A. Input and Inference Stage for CSI… · p. 7

B. Formation Stage of Asymmetric Boundaries

The formation stage represents the DNN-defined uncertainty set through feasible activation patterns. Each pattern yields a convex region constrained by the uncertainty radius, and the full set is their union.

B. Formation Stage of Asymmetric Boundaries

  • For a fixed activation pattern, each piecewise-affine activation becomes linear, so the network reduces to a single affine transformation.The composite weight matrix and bias vector are derived recursively by composing layer-wise affine functions.Source: B. Formation Stage of Asymmetric… · p. 8
  • Each region P(u) imposes linear inequalities consistent with activation pattern u together with the uncertainty-radius constraint.The union over feasible activation patterns forms the complete uncertainty set.Source: B. Formation Stage of Asymmetric… · p. 8
  • The DNN-defined uncertainty set is a finite union of convex regions, each a polyhedron intersected with a norm ball.The paper characterizes this as the structural form of the DNN-bounded set.Source: B. Formation Stage of Asymmetric… · p. 8

C. Robust Counterpart Transformation Stage

The robust counterpart makes the DNN-defined CSI uncertainty set tractable by searching activation patterns observed in training data. For each retained pattern, the adversarial subproblem becomes a convex SDP, and solving across patterns yields a robust feasibility check.

C. Robust Counterpart Transformation Stage

  • For each activation pattern, the uncertainty set is a polyhedral region intersected with a norm constraint, and the least-favorable channel is found by minimizing the QoS expression over that set.The overall adversarial search compares the minima across patterns.Source: C. Robust Counterpart Transformation… · p. 8
  • Dropping the rank-one constraint and applying a Schur-complement LMI turns the adversarial subproblem into a mixed-integer semidefinite program.The quadratic terms are handled by introducing an auxiliary matrix.Source: C. Robust Counterpart Transformation… · p. 8
  • Training samples define a deduplicated set of active DNN patterns, reducing the search from all possible binary combinations to patterns observed in the data.Each pattern fixes the activation variables and makes the corresponding constraints linear.Source: C. Robust Counterpart Transformation… · p. 9
  • For a fixed pattern, the adversarial subproblem becomes a convex SDP that can be solved independently for each pattern, including in parallel.Its SDR objective provides a global lower bound to the original non-convex subproblem.Source: C. Robust Counterpart Transformation… · p. 9
  • The robust counterpart is solved by iterating over the finite pattern set, converting the original semi-infinite constraints into a tractable finite collection of convex problems.The resulting convex constraints address the chance constraints before the remaining beamforming–power-allocation coupling is handled iteratively.Source: C. Robust Counterpart Transformation… · p. 9

D. Robust Resource Management and Algorithm

The algorithm alternates between NOMA power allocation and robust beamforming, using a coarse-to-fine search for power coefficients and cutting planes to find adverse channel scenarios. Its SDP master problem has rank-one unicast solutions under the stated feasibility assumption, while rank-one satellite and multicast solutions have a checkable sufficient condition.

D. Robust Resource Management and Algorithm

  • The two-layer algorithm addresses coupled beamforming and power allocation with an outer coefficient search and an inner cutting-plane method for robust beamforming.The inner method adds adverse channel scenarios as cuts to the master problem.Source: D. Robust Resource Management and… · pp. 9–10
  • The outer loop alternates power allocation and beamforming, refining a local NOMA coefficient grid from coarse to fine around the previous best value.Each candidate coefficient is passed to the inner robust beamforming loop.Source: D. Robust Resource Management and… · p. 10
  • The inner cutting-plane loop solves a finite-cut SDP master, searches activation patterns for the least-favorable channel, and adds violating scenarios as new cuts.Independent pattern-specific SDPs can be solved in parallel.Source: D. Robust Resource Management and… · pp. 10–11
  • Under strict feasibility, every optimal master-problem unicast beamformer is rank one, regardless of the learned uncertainty set.The paper states strict feasibility holds whenever the QoS targets are jointly achievable.Source: D. Robust Resource Management and… · p. 11
  • Satellite and multicast beamformers are rank one when the largest generalized eigenvalue is simple, a sufficient condition verifiable from the optimum's dual-slack matrix.The condition was verified in all experiments; it cannot be dropped for the general model.Source: D. Robust Resource Management and… · p. 11
  • If that condition fails, deterministic rank reduction precedes Gaussian randomization, which is used only as a final recovery step.The paper notes that an unconditional rank-one guarantee would imply an exact polynomial-time solver for an NP-hard multicast problem unless P = NP.Source: D. Robust Resource Management and… · p. 11
  • Online complexity grows with search stages, grid candidates, cutting-plane iterations, and the costs of the master and pattern-specific adversarial SDPs.The stated bound is O(S(Kgrid + 1)Imax[C(nMP, mMP) + (P m,n |Sm,n|)C(Ns, mASP)]).Source: D. Robust Resource Management and… · p. 12

V. SIMULATION RESULTS

The DNN-driven method combines adaptive CSI uncertainty sets with optimized resource allocation to achieve lower power among robust schemes while maintaining reliability. Its results show that set adaptability matters most under uncertain satellite links; with perfect AP CSI, method differences are negligible.

V. SIMULATION RESULTS

  • Across CSI datasets, DNN uncertainty sets fit irregular sample distributions more closely than ellipsoids or KL-SVC, reducing geometric dead space while maintaining the required confidence level.Ellipsoids form expansive symmetric hulls, while KL-SVC boundaries are tighter but less able to capture complex non-convex structure.Source: §V · pp. 12–13
  • For satellite users, DNN SINR distributions hug QoS thresholds and remain continuous for clustered CSI; with perfect AP CSI, all methods perform nearly identically.Arg satisfies SINR requirements for only about 50–60% of first-beam channel realizations, while WC-CC can show a step-like CDF for clustered second-beam CSI.Source: §V · p. 13
  • As ST QoS thresholds rise, DNN consumes less power than other robust schemes, while Arg's lower power comes with severe QoS violations.WC-CC shows the steepest power increase as Γ rises; the proposed method is reported to trade off reliability and energy efficiency.Source: §V · pp. 13–14
  • Stricter outage requirements expand DNN uncertainty sets to cover tail errors, whereas relaxing the requirement shrinks them toward the core data distribution.The passage contrasts ϵ = 0.1 with ϵ = 0.5 and describes the boundary adapting to the reliability demand.Source: §V · p. 14
  • The DNN method achieves the lowest power among robust schemes while preserving reliability; dynamically optimizing NOMA power coefficients also reduces power versus static allocations across all schemes.The non-robust Arg method uses less absolute power but incurs QoS violations, while WC-CC is robust but wastes power.Source: §V · p. 14

VI. CONCLUSIONS

The proposed DNN-driven approach trades off energy efficiency and robustness in SAGIN while addressing joint beamforming and resource allocation under uncertain CSI. It uses asymmetric uncertainty sets and an SDR-based iterative method to handle probabilistic QoS constraints.

VI. CONCLUSIONS

  • The proposed method achieves an effective trade-off between energy efficiency and robustness in SAGIN.Source: §VI · p. 14
  • The framework jointly optimizes robust beamforming and resource allocation to minimize total transmit power under probabilistic QoS constraints.Source: §VI · p. 14
  • DNN-constructed asymmetric uncertainty sets capture complex CSI variations and alleviate over-conservatism in resource allocation.Source: §VI · p. 14
  • SDR-based matrix analysis and a coarse-to-fine two-layer iterative algorithm convert the non-convex chance-constrained problem into solvable finite constraints.The algorithm employs the CPM.Source: §VI · p. 14
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