A Particle-Swarm-Assisted Gradient Meta-Learning Algorithm for Joint Transmit Precoding and STAR-RIS Coefficient Optimization

Kang Zhou

cs.LGSep 24, 2026

A Particle-Swarm-Assisted Gradient Meta-Learning Algorithm for Joint Transmit Precoding and STAR-RIS Coefficient Optimization

Authors: Kang Zhou

Organizations: School of Artificial Intelligence, Mianyang City College, Mianyang 621000, China

Abstract

This paper investigates the joint optimization of the transmit precoder and the transmission/reflection coefficients of a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) to maximize the weighted sum rate (WSR) in a multi-user downlink. We propose a particle-swarm-assisted gradient meta-learning (PSA-GML) algorithm for this non-convex problem. The original problem is first equivalently transformed via an amplitude-split parameterization and a collapsed precoder representation, which automatically satisfy the energy-conservation constraint and reduce the search dimension. Particle swarm optimization (PSO) then performs a global search over the STAR-RIS coefficients to yield a high-quality, initialization-robust warm start, with the transmit precoder obtained in closed form. Departing from conventional alternating optimization (AO), a coordinate-wise long short-term memory (LSTM) meta-optimizer trained by first-order gradient meta-learning further refines the coefficients and precoder jointly, learning per-coordinate adaptive update rules from data. The meta-optimizer is trained offline and applied to unseen channels without further adaptation. Numerical results show that PSA-GML attains an 11.06 bits/s/Hz WSR at 10 dB with N=32 elements and K=4 users, exceeding AO by 13.1% (and by 6.2% even with multiple random restarts) and the random-phase scheme by 35.1%. In the interference-limited regime it reaches 83.9% of the hand-designed Adam refinement without manual hyper-parameter tuning, and it transfers zero-shot across regimes, indicating that the learned update rule captures the intrinsic WSR landscape structure.

Figures & tables

Fig. 4: Convergence behavior of the proposed PSA-GML algorithm and the baselines.

Fig. 5: WSR performance comparison versus the transmit SNR.

Method	Main	Intf
PSO only	10.85	4.31
PSO + SGD refinement	10.85	4.32
PSO + learned optimizer	11.06	4.73
PSO + Adam refinement	11.12	5.64

TABLE I: WSR (bits/s/Hz) of the PSO warm start followed by different refinement optimizers, in the main regime (SNR

=10

dB,

K=4

) and the interference-limited regime (SNR

=0

dB,

K=8

)

Fig. 6: Average WSR convergence of the PSO warm start followed by different refinement optimizers (SGD, the learned optimizer, and Adam) in the interference-limited regime.

Fig. 7: WSR performance comparison versus the number of STAR-RIS elements $N$ .

Fig. 8: Sum-rate performance comparison versus the number of users $K$ .

Fig. 9: Gain of the PSO warm start versus $N$ under i.i.d. Rayleigh and Saleh-Valenzuela channels.

Fig. 10: Average runtime comparison of the proposed algorithm and the baselines.

	AO	Proposed PSA-GML
Per-Iteration Complexity	$\mathcal{O}(NN_{t}K+K^{3})$	$\mathcal{O}(NN_{t}K+K^{3})$
Refinement Per-Step Overhead	–	$\mathcal{O}(DH^{2})$
Offline Training	–	$N_{c}\left[PI_{\mathrm{PSO}}\,\mathcal{O}(NN_{t}K+K^{3})+S\left(\mathcal{O}(NN_{t}K+K^{3})+\mathcal{O}(DH^{2})\right)\right]$
Online Inference: PSO stage	–	$PI_{\mathrm{PSO}}\,\mathcal{O}(NN_{t}K+K^{3})$
Online Inference: refinement / AO iterations	$N_{\mathrm{AO}}\,\mathcal{O}(NN_{t}K+K^{3})$	$S\left[\mathcal{O}(NN_{t}K+K^{3})+\mathcal{O}(DH^{2})\right]$

TABLE II: Computational Complexity Comparison

Fig. 11: Optimized amplitude-split and phase-shift coefficients of the STAR-RIS.

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