DNN-Enabled Multi-User Beamforming for Throughput Maximization under Adjustable Fairness

Kaifeng Lu; Markus Rupp; Stefan Schwarz

cs.LGFeb 17, 2026

DNN-Enabled Multi-User Beamforming for Throughput Maximization under Adjustable Fairness

Authors: Kaifeng Lu, Markus Rupp, Stefan Schwarz

Organizations: Institute of Telecommunications, Technische Universität (TU) Wien

Abstract

Ensuring user fairness in wireless communications is a fundamental challenge, as balancing the trade-off between fairness and sum rate leads to a non-convex, multi-objective optimization whose complexity grows with network scale. To alleviate this conflict, we propose an optimization-based unsupervised learning approach based on the wireless transformer (WiT) architecture that learns from channel state information (CSI) features. We reformulate the trade-off by combining the sum rate and fairness objectives through a Lagrangian multiplier, which is updated automatically via a dual-ascent algorithm. This mechanism allows for a controllable fairness constraint while simultaneously maximizing the sum rate, effectively realizing a trace on the Pareto front between two conflicting objectives. Our findings show that the proposed approach offers a flexible solution for managing the trade-off optimization under prescribed fairness.

Figures & tables

Fig. 1: Transformer-DNN architecture for throughput maximization under adjustable fairness

Total Learnable Parameters. $N_{\text{L}}=8.73\times 10^{5}$
WiT parameters		Training parameters
Emb. Factor ( $N_{e}$ )	4	Batch size ( $N_{b}$ )	$2^{8}$
Blocks ( $N_{\text{att}}$ )	8	Init. LR	0.002
Heads ( $N_{\text{head}}$ )	4	Tolerance ( $\epsilon$ )	0.003
Feature dim. ( $N_{f}$ )	33	Dual step ( $\eta_{\lambda}$ )	0.01

TABLE I: Hyperparameters of the DNN

wSLNR		DNN
$\alpha_{\ell}$	Mean SR	$J_{LB}$	$J_{\mathrm{DNN}}$	$\lambda$	Mean SR
0	30.48	0.60	0.658	0.000	29.99
0.5	29.47	0.70	0.693	0.897	29.53
0.7	27.94	0.75	0.746	1.274	28.75
0.85	26.29	0.80	0.801	2.200	27.36
1.0	24.59	0.86	0.861	2.212	25.58

TABLE II: Performance comparison: adaptive fairness training vs. wSLNR , where Mean SR denotes the achievable mean sum rate in bit/s/Hz.

Fig. 2: Cross comparison on mean achievable rate and fairness between wSLNR $(\alpha_{\ell})$ and DNN trained with target $J_{LB}$ .

Fig. 3: User-rate ECDF at selected target fairness values from Table II ; DNN (dashed) vs. wSLNR (solid).

Fig. 4: Sum-rate ECDF at selected target fairness values from Table II ; DNN (dashed) vs. wSLNR (solid).

Fig. 5: Per-user rate comparison with users ordered by index (weakest to strongest) at selected matched-fairness pairs from Table II : DNN (darker bars) vs. wSLNR (lighter bars).

Fig. 6: Mean sum rate comparison at selected matched-fairness pairs from Table II : DNN (darker bars) vs. wSLNR (lighter bars).

Wireless Resource Allocation

Wireless resource allocation assigns spectrum, power, beams, and computing capacity to meet throughput, latency, fairness, and energy goals.

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Multi-User mmWave Beam and Rate Adaptation via Combinatorial Satisficing Bandits

Emre Özyıldırım, Barış Yaycı, Umut Eren Akturk, Cem Tekin

Department of Electrical and Electronics Engineering, Bilkent University, Ankara, Türkiye

Multi-Armed Bandits Combinatorial Semi-Bandits Wireless Communications Wireless Resource Allocation Millimeter-Wave Communications

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We study downlink beam and rate adaptation in a multi-user mmWave MISO system where multiple base stations (BSs), each using analog beamforming from finite codebooks, serve multiple single-antenna user equipments (UEs) with a unique beam per UE and discrete data transmission rates. BSs learn about transmission success based on ACK/NACK feedback. To encode service goals, we introduce a satisficing throughput threshold

τ_r

and cast joint beam and rate adaptation as a combinatorial semi-bandit over beam-rate tuples. Within this framework, we propose SAT-CTS, a lightweight, threshold-aware policy that blends conservative confidence estimates with posterior sampling, steering learning toward meeting

τ_r

rather than merely maximizing. Our main theoretical contribution provides the first finite-time regret bounds for combinatorial semi-bandits with satisficing objective: when

τ_r

is realizable, we upper bound the cumulative satisficing regret to the target with a time-independent constant, and when

τ_r

is non-realizable, we show that SAT-CTS incurs only a finite expected transient outside committed CTS rounds, after which its regret is governed by the sum of the regret contributions of restarted CTS rounds, yielding an

O((\log T)^2)

standard regret bound. On the practical side, we evaluate the performance via cumulative satisficing regret to

τ_r

alongside standard regret and fairness. Experiments with time-varying sparse multipath channels show that SAT-CTS consistently reduces satisficing regret and maintains competitive standard regret, while achieving favorable average throughput and fairness across users, indicating that feedback-efficient learning can equitably allocate beams and rates to meet QoS targets without channel state knowledge.

Abstract

Wireless Resource Allocation

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