Weighted Sum-Rate Maximization for RIS-UAV-assisted Space-Air-Ground Integrated Network with RSMA

Abstract: In this paper, a rate-splitting multiple access (RSMA) based joint optimization framework for the space-air-ground integrated network (SAGIN) is proposed, where the satellite and base stations employ uniform planar array (UPA) antennas for signal transmission, and unmanned aerial vehicles (UAVs) relay the satellite signals. Earth stations (ESs) and user equipments (UEs) receive signals from satellite and base stations (BSs), respectively, resulting in mutual interference. We first model the channels and signals in this scenario and analyse the interference at BSs and UEs. Then, We formulate a joint optimization problem aimed at maximizing the weighted sum-rate, involving beamforming, RIS-UAV deployment and phase shifts, and rate splitting. However, this problem is highly non-convex. To tackle this challenge, we apply a block coordinate descent (BCD) approach to decompose the problem and employ the weighted minimum mean square error (WMMSE) method to transform the non-convex objective function. For the rate-splitting sub-problem, a greedy algorithm is proposed and a successive convex approximation (SCA) algorithm is used for beamforming. Besides, the alternating direction method of multipliers (ADMM) algorithm is employed for the RIS phase-shift problem with unit-modulus constraints, and an exhaustive search method is adopted for the complex UAV positioning and orientation. Simulation results validate that the proposed algorithm achieves superior performance in terms of user weighted sum-rate.

• The paper develops a block coordinate descent framework combining WMMSE, successive convex approximation, ADMM, and greedy rate allocation to jointly optimize beamforming, RIS phases, UAV geometry, and RSMA rates.
• The proposed method converges in simulations and consistently outperforms no-RSMA and no-RIS benchmarks in a 28 GHz, three-cell SAGIN, although the study reports no numerical gain percentages.
• The framework improves cross-tier interference management but remains limited by exhaustive UAV deployment search, perfect-CSI assumptions, restricted RIS geometry, and the absence of mobility or robustness analysis.

This paper presents a joint resource allocation framework for a space–air–ground integrated network (SAGIN) in which a LEO satellite and terrestrial base stations (BSs) share the same 28 GHz band, and RIS-equipped UAVs relay satellite transmissions to earth stations (ESs). The authors formulate a weighted sum-rate maximization problem over satellite and BS beamforming, RIS-UAV deployment (position and orientation), RIS phase shifts, and RSMA rate splitting, and develop a block coordinate descent (BCD)-based iterative algorithm combining WMMSE, SCA, ADMM, and exhaustive search (2603.28176).

System model

The network consists of $K$ cells, each containing a BS with an $8\times8$ uniform planar array (UPA) serving $L$ single-antenna UEs, one ES served by a LEO satellite also equipped with an $N_{\text{S}}$-element UPA, and one RIS-UAV with $N_{\text{R}}=64$ reflecting elements dedicated to that ES. Because satellite and terrestrial tiers share the same carrier, each ES receives interference from its co-located BS and each UE receives interference from the satellite, in addition to intra-tier multi-user interference. The satellite channel incorporates free-space path loss, log-normally distributed rain attenuation, and the ITU-R S.465 parabolic receive-antenna pattern; the RIS creates an equivalent cascaded channel $$\tilde{\mathbf{h}}^{H}_k = \mathbf{h}^{H}_k + \mathbf{g}^{H}_{k} \mathbf{\Psi}_{k} \mathbf{G}_k$$ with unit-modulus phase matrix $\mathbf{\Psi}_k$.

Both the satellite and each BS employ one-layer RSMA, transmitting a common stream plus private streams. The paper derives SINR expressions for the common and private streams at ESs and UEs, where cross-tier interference appears in the denominators of both tiers' SINRs. Notably, energy leakage from the BS to the RIS-UAV is assumed negligible, justified either by deploying the UAV at high altitude or by orienting the RIS toward the ES with the BS on its backside — an assumption that simplifies the model but restricts the geometry.

The optimization problem (P1) maximizes the weighted sum rate $\tilde{f}(\mathbf{\Xi})$ over beamformers $\mathbf{w}^{\text{S}}, \mathbf{w}^{\text{B}}$, rate splits $\mathbf{r}^{\text{E}}, \mathbf{r}^{\text{U}}$, RIS phases $8\times8$0, and UAV rotation matrices and positions $8\times8$1, subject to common-rate feasibility, transmit power limits at both satellite and BSs, unit-modulus RIS constraints, valid rotation matrices (constraint P1.h), position constraints, half-space visibility constraints (P1.j), and per-user QoS minimum rates (P1.k). The coupling of continuous beamforming, discrete-ish geometric variables, and unit-modulus constraints renders the problem highly non-convex.

Proposed algorithm

The solution follows a two-layer structure. In the outer loop, BCD decomposes P1 into four sub-problems:

• Rate splitting (P1.1): a linear program solved by a greedy algorithm — allocate the minimum rates required by the lower-bound constraints, then assign all remaining common-rate budget to the user with the highest weight.
• Beamforming (P3.1): the non-convex weighted sum-rate is transformed via WMMSE into a weighted MSE minimization; QoS and common-rate constraints are recast as SINR constraints linearized by first-order Taylor expansions (SCA), yielding a QCQP solvable as an SOCP via CVX.
• RIS phase shifts (P3.2/P3.3): the objective is rearranged into a quadratic form in $8\times8$2 (the vector of RIS coefficients); unit-modulus constraints are handled by ADMM with penalty parameter $8\times8$3, where the auxiliary variable $8\times8$4 admits a closed-form projection onto the unit-modulus set, and iterations terminate on primal/dual residual thresholds.
• UAV deployment (P3.4): no low-complexity method is available, so an exhaustive search is adopted. Dimensionality is reduced by Euler-angle decomposition of $8\times8$5 (three rotation angles) and by restricting the RIS position to lie along the ES antenna's central axis, parametrized by a scalar $8\times8$6 with bounds derived from altitude limits.

Complexity: the SOCP sub-problems scale as $8\times8$7 and $8\times8$8, while the exhaustive deployment search scales as $8\times8$9, i.e., polynomial in the reciprocal of the search grid resolution — this is the dominant and least scalable component of the algorithm.

Numerical results

Simulations use $L$0 cells, $L$1 UEs per cell, 64-element UPAs at both satellite and BSs, 64-element RIS, $L$2 GHz, $L$3 dBm, $L$4 W, and noise power $L$5 dBm, with ITU-R rain-attenuation parameters $L$6, $L$7. Two benchmarks are compared: a no-rate-splitting scheme (pure SDMA/private beamforming) and a no-RIS scheme.

The reported findings are qualitative rather than quantified in the text: the proposed BCD algorithm converges within a finite number of iterations across all tested settings; the weighted sum rate decreases with more UEs (both increased interference and per-UE power dilution) and with lower transmit power; and the proposed scheme consistently outperforms both benchmarks, indicating that RSMA rate splitting and RIS-UAV assistance each contribute non-trivial gains. The paper does not report specific gain magnitudes (e.g., percentage improvements or rate values), nor does it isolate the individual contributions of rate splitting versus RIS assistance through an ablation beyond the two benchmarks.

Limitations and open questions

Several limitations are acknowledged or implicit. The exhaustive search for UAV position and orientation is computationally prohibitive for large networks or fine search grids, and the authors concede that a low-complexity alternative is difficult to design; the reduction to a one-dimensional position search along the ES antenna axis is a modeling restriction rather than a general solution. The assumption that BS-to-RIS leakage is negligible constrains feasible geometries. The channel model assumes perfect channel state information, deterministic LoS-dominated links, and static UAV positions — mobility, hovering-induced orientation jitter, and channel estimation errors are not addressed. Finally, convergence is to a Karush–Kuhn–Tucker-type point of the non-convex problem, with no global optimality guarantee, and the numerical evaluation does not quantify the size of the gains over the benchmarks.

Conclusion

The paper contributes a complete optimization pipeline for RSMA-based interference management in a co-channel satellite-terrestrial SAGIN assisted by RIS-UAVs, combining WMMSE, SCA, ADMM, and greedy rate allocation within a BCD framework, with demonstrated convergence and consistent superiority over no-RSMA and no-RIS baselines. The principal open issues left by the work are scalable UAV deployment optimization, robustness to channel uncertainty and UAV mobility, and empirical quantification of the RSMA and RIS gains.