---
title: Multi-Beam HAPS Optimization
url: https://www.emergentmind.com/topics/multi-beam-haps-optimization
type: topic
---

# Multi-Beam HAPS Optimization

A high-altitude platform station (HAPS) equipped with beamforming arrays is a transformative architecture for wide-area wireless coverage, vertical heterogeneous networking, and integrated sensing-and-communication (ISAC) missions in 6G and beyond. Multi-beam HAPS optimization refers to the joint design of beamforming, user/resource allocation, and—where relevant—platform deployment and trajectory, with the goal of maximizing network performance metrics (throughput, fairness, beampattern, cost, and energy efficiency) subject to stringent constraints on power, backhaul, coverage, and user quality-of-service. Optimization in this context is fundamentally high-dimensional, non-convex, and frequently mixed-integer, and underpins the ability of new HAPS infrastructure to simultaneously deliver equitable communication, robust sensing, and energy-resilient operation over large geographic areas.

## 1. System Models for Multi-Beam HAPS Architectures

A typical system comprises a quasi-stationary or mobile HAPS at 18–24 km altitude, equipped with a uniform planar array (UPA), hemispherical array, or custom multi-beam FSO banks, serving ground users via multi-antenna downlink and, in some cases, uplink or ISAC signaling. Users may be single-antenna communication users (CUs), ground-based sensors, or targets for SAR imaging or radar missions. The propagation model is generally a Rician fading channel for air-to-ground links, often incorporating LoS-dominance for HAPS–UE channels and NLoS components for terrestrial links [2507.18764], [2406.02254], [2409.03474].

Beamforming architectures may include:

- UPA or vertical/horizontal arrays with digital/analog (hybrid) beamforming [2507.18764], [2406.02254].
- Hemispherical arrays for hemisphere-shaped coverage, supporting uniform capacity footprint by strategic placement of elements [2409.03474].
- Multi-beam free-space-optical (FSO) banks for optical links to ground terminals, where coverage is determined by principal plus supplementary beams, each with specific divergence and steering [2301.08642].
- Hybrid satellite-HAPS-ground or HAPS-UAV networks, incorporating terrestrial BSs or UAVs as sub-tiers, with HAPS additionally managing backhaul or as a computation hub [2204.13257], [2507.14310].

The multi-beam nature arises as the array forms spatially distinct, high-gain boresight beams aimed at user clusters, sensing targets, or probe points, with the number and geometry of beams determined subject to hardware, coverage, and interference trade-offs [2406.02254], [2409.03474], [2301.08642].

## 2. Joint Beamforming, User Association, and Sensing Design

Central to multi-beam HAPS optimization is the problem of selecting and shaping downlink (and, in ISAC, sensing) beams, while associating users to beams and allocating transmit power in order to optimize the target metric. The problem is formalized as a joint decision over:

- Digital/analog beamformer vectors for downlink to each user or user group [2507.18764], [2409.03474].
- Sensing beamformers (ISAC): spatially selective transmission toward ground targets using pilot signals and additional array weightings [2507.18764], [2507.14310].
- User-grouping: partitioning the user set into clusters, each served by a distinct beam or spot, with grouping determined by geometric disk cover techniques or association optimization [2406.02254].
- User association: assignment of each user to a unique or shared beam/platform, leveraging binary association variables in mixed-integer programming formulations [2511.06339], [2204.13257], [2307.08202].
- Platform trajectory: for dynamic HAPS, 3D flight trajectory or quasi-stationary positioning is optimized jointly with the beamformers and schedule [2506.11294], [2203.00363].

For ISAC-enabled platforms, both communication and sensing objectives/constraints are addressed. For example, the transmit signal may be 
$$
x[n] = \sum_{k=1}^K w_k[n] s_k[n] + \sum_{j=1}^J r_j[n] s'_j[n]
$$
where \(\{w_k\}\) are communication beamformers and \(\{r_j\}\) are sensing beamformers; constraints are imposed both on SINR to all CUs and sensing beampattern gain to designated ground locations [2507.18764].

## 3. Optimization Problems and Solution Methods

The underlying optimization problems are highly non-convex, involving quadratic or fractional quadratic forms (e.g., SINRs), mixed-integer association variables, and, for ISAC, max-min or weighted sum-of-log objectives for fairness and sum-rate [2507.18764], [2511.06339], [2307.08202].

Canonical formulations include:

- Max-min fairness: maximize the minimum SINR across users or the minimum beampattern gain across targets, under power and QoS constraints [2507.18764], [2511.06339], [2409.03474].
- Weighted sum-rate maximization: maximize total throughput with per-user minimum rate constraints and power budgets [2204.13257], [2511.06339].
- Multi-objective optimization (ISAC): jointly maximize worst-case SINR, minimum beampattern, and/or echo reception from targets, using Pareto trade-off parameterization [2507.14310].
- Resource-constrained multi-beam coverage: minimize platform or network cost subject to solar budget, energy, and hardware constraints [2301.08642].

Solution techniques include:

- Metaheuristic algorithms: genetic algorithm (GA) optimizes beamformer coefficients directly, especially in non-convex ISAC fairness formulations [2507.18764], [2507.14310].
- Successive Convex Approximation (SCA): handles non-convex quadratic–fractional constraints iteratively, replacing them with convex surrogates at each iteration [2511.06339], [2307.08202].
- Semidefinite Relaxation (SDR): relaxes rank-one constraints on beamforming weight matrices to convexify the problem [2506.11294].
- Block-coordinate methods: alternating between user association (solved as a generalized assignment problem or ILP) and beamforming (via quadratic programming, WMMSE, or SCA/SDR) [2204.13257], [2511.06339].
- Distributed optimization: augmented Lagrangian and multi-block ADMM decompositions for cell-free and large-scale settings, facilitating scalable and provably convergent distributed solutions [2507.08299].
- Closed-form analysis and sequential geometric algorithms for FSO coverage, disk cover, and beam center optimization [2301.08642], [2406.02254].

The selection of method depends on the structure and dimensionality of the constraints, the presence of binary/integer variables, and the system scalability requirements.

## 4. Key Performance Results and Trade-offs

Extensive simulation studies across these works provide the following validated findings for multi-beam HAPS optimization:

- Multi-beam HAPS with large UPAs (>64 elements) substantially improves both minimum user rates and worst-case sensing gain, yielding near-flat beampattern coverage over footprints and uniform per-user throughput [2507.18764], [2409.03474].
- HAPS-based ISAC achieves simultaneous fairness in communication (max-min SINR) and strong, uniform sensing (via beampattern optimization), outclassing UAV-based or non-joint schemes [2507.18764], [2507.14310], [2506.11294].
- Fairness-oriented optimization (max-min) ensures equitable distribution but trades off some aggregate throughput; sum-rate maximization can increase total rates by up to 20% but decreases fairness (Jain’s index from ~0.9 to ~0.7) [2511.06339].
- More beams and larger arrays increase both spatial multiplexing and uniformity but risk higher sidelobe/inter-beam interference if not controlled by judicious design (e.g., antenna selection, phase steering) [2409.03474], [2406.02254].
- HAA architectures outperform RAA/CAA in area-uniformity, coverage, and sum-rate; e.g., HAA achieves up to 14 Gbps throughput at 50 dBm, 60%+ higher than RAA at the same power [2409.03474].
- In hybrid and cell-free deployments, adding a HAPS augments capacity, matches the performance of multiple terrestrial BSs, and enables both "super-connecting" urban users and "connecting the unconnected" rural users [2204.13257], [2507.08299].
- Energy-constrained multi-beam FSO design demonstrates that increasing the number of beams can up to double coverage and halve network cost, provided solar and hardware budgets permit [2301.08642].
- NOMA-based HAPS schemes, jointly optimizing user grouping, beam width, and power offer 20–30% energy and throughput gains over OFDMA/OMA, with outage probability falling by more than an order of magnitude at high SNR [2406.02254], [2203.00363].

## 5. Hardware and Architectural Innovations

Recent advances in multi-beam HAPS optimization are enabled by novel platform and array architectures:

- Hemispherical Antenna Array (HAA): Provides hemispheric placements of antennas aligned with ground coverage, leveraging selection algorithms for analog phase-shifted beamforming and achieving near-uniform user rates across wide areas [2409.03474].
- Flexible multi-FSO transceiver bundles: Optimal placement and divergence of supplementary FSO beams for wide ground footprint, analytically deriving coverage and cost-minimization formulas, with 14-beam bundles found optimal with current platform parameters [2301.08642].
- Dynamic HAPS deployment strategies: Alternating between "stop-and-go" (quasi-stationary) and continuous circular trajectories, optimizing 3D positioning and beamforming to maximize both sum-rate and SAR imaging fidelity [2506.11294].
- HAPS-UAV ISAC integration: Divides computation (with HAPS as CPU) and analog beamforming (UAV APs), balancing energy efficiency, fairness, and beam pattern performance through joint optimization [2507.14310].

## 6. Complexity, Scalability, and Distributed Implementation

Given the scale and dimensionality of multi-beam HAPS systems, special attention is required to computational complexity:

- Mixed-integer and non-convex QCQP problems scale exponentially in the number of beams/users, requiring decomposition and distributed methods for tractability (e.g., distributed SOCP, ALM-ADMM) [2511.06339], [2507.08299].
- User association solved via GAP admits decentralized implementation, with only interference summaries exchanged, supporting hundreds of users per HAPS [2511.06339], [2507.08299].
- Distributed PF beamforming frameworks achieve near-centralized performance with order-of-magnitude reductions in signaling overhead and local computation [2507.08299].
- Genetic algorithms are preferred for global, highly non-convex fairness/ISAC formulations, exploring millions of candidate solutions under high-dimensional constraints [2507.18764].

## 7. Design Principles and Insights

Empirical and theoretical studies establish the following principles for multi-beam HAPS design:

- Maximize spatial degrees-of-freedom (using large and/or flexible arrays) to support both user multiplexing and sharp beam patterning.
- Jointly optimize beamforming—both at the analog and digital level—with resource assignment (user association, power allocation) and deployment (position/trajectory).
- For ISAC systems, control trade-offs between communication SINR and beampattern gain by either max-min objectives or scalarization (Pareto weighting), with explicit auxiliary variables [2507.18764], [2507.14310].
- When FSO is used, balance between coverage extension and platform energy budget to select optimal number and divergence of beams [2301.08642].
- Leverage fairness-driven optimization (e.g., max-min SINR) to ensure digital equity, particularly in rural/underserved regions, while switching to sum-rate maximization as capacity permits [2511.06339].
- Implement distributed solution architectures in multi-access and cell-free HAPS–terrestrial networks to permit scalable computation and near-optimal performance [2507.08299], [2307.08202].

Each of these operational facets is substantiated with analytically specified algorithms and simulation studies in the referenced works, and together they define the rigorous framework for multi-beam HAPS optimization in current and future wide-area wireless, ISAC, and hybrid network deployments.

Source: https://www.emergentmind.com/topics/multi-beam-haps-optimization