Sum-Rate Maximization in SAGIN With an IRS-Equipped HAP via Unsupervised DNN With Lagrange Dual
Year: 2026
Type: article
Abstract: This paper studies sum-rate maximization in a space-air-ground integrated network (SAGIN) where a terrestrial base station (BS) and an IRS-equipped high-altitude platform (HAP) jointly serve ground user equipment (GUEs) and satellite user equipment (SUEs). We formulate the joint BS transmit power and IRS phase-shift optimization, rigorously establish its non-convexity by proving strict convexity of the satellite-user rate in the transmit power, and analyze the problem through its Lagrange dual to obtain weak duality, concavity of the dual function, the explicit KKT system, and an $O(\epsilon ^{-4})$ projected-gradient iteration complexity bound. This analysis motivates a gradient-descent Lagrange-dual (GD-LD) iterative method and a Lagrange-based training loss for an unsupervised deep neural network (DNN). The DNN satisfies the phase-shift constraint by construction via sigmoid activation, enforces the power constraint through a Lagrange penalty term, and exhibits training-time gradient consistency with the Lagrangian. As a result, it produces near-feasible, near-optimal solutions in a single forward pass, satisfying the phase-shift constraint by construction, while approximately satisfying the power constraint through a Lagrange penalty. Simulations show that the proposed DNN achieves near-optimal sum-rate with substantially lower complexity than exhaustive search and WMMSE, and consistently outperforms GD-LD across varying BS transmit power and cell radius.
Source: IEEE Access
Authors: Kimchheang Chhea, Jung-Ryun Lee
Institution: Ministry of Economy and Finance
Language: English
Subfield: Electrical and Electronic Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,075
OpenAlex ID: W7204469285