Conjugate Equivariant Neural Network for Precoder Learning

Exploiting mathematical properties of wireless policies in deep neural network (DNN) design can improve learning performance and generalizability while reducing training complexity. Permutation equivariance and permutation invariance have been incorporated into DNN architectures. In this paper, we investigate conjugation equivariance (CE) and propose a general conjugation-equivariant neural network (CENN) framework for precoder learning. We first establish that the optimal policies for a unified class of precoding problems satisfy CE, i.e., when the channel matrices are conjugated, the conjugate of an optimal precoder remains optimal. We then show that, for DNNs with linear processing functions, enforcing CE restricts their ability to learn optimal precoding policies. To overcome this limitation, we develop a general nonlinear construction and prove that it converts an arbitrary base function into a CE processing function while preserving the base function's original equivariance properties. This construction enables existing equivariant networks to incorporate CE without adding learnable parameters. Simulations for fully digital and RIS-aided precoding show that the resulting CE-enhanced networks improve learning and generalization performance while requiring fewer training samples and shorter training time than their original counterparts.

Learning-Based Beamforming for Energy Efficiency of Continuous Aperture Array Systems

This paper jointly optimizes the base-station (BS) continuous aperture array (CAPA) dimensions and beamforming functions to maximize energy efficiency (EE) of the downlink multiuser multi-CAPA system, where both the BS and the users are equipped with CAPAs. Since the beamforming functions are continuous current distribution over the BS CAPA, the resulting EE maximization problem is a nontrivial functional optimization problem that couples aperture sizing and beamforming design. To address this challenge, we propose a cascaded network architecture consisting of a graph neural network (GNN) and a functional-gradient based implicit neural representation (FGB-INR) to learn the BS CAPA dimensions and beamforming functions, respectively. Both networks exploit the permutation equivariance of the optimal optimization policy, and the update equations of FGB-INR are designed according to the functional-gradient structure of the EE objective. Simulation results show that the proposed method approaches the EE of the numerical method while substantially reducing inference latency. They also demonstrates that the functional-gradient structure in FGB-INR improves EE while reducing sample complexity and training time.

Implicit Neural Representation for Multiuser Continuous Aperture Array Beamforming

Implicit neural representations (INRs) can parameterize continuous beamforming functions in continuous aperture arrays (CAPAs) and thus enable efficient online inference. Existing INR-based beamforming methods for CAPAs, however, typically suffer from high training complexity and limited generalizability. To address these issues, we first derive a closed-form expression for the achievable sum rate in multiuser multi-CAPA systems where both the base station and the users are equipped with CAPAs. For sum-rate maximization, we then develop a functional weighted minimum mean-squared error (WMMSE) algorithm by using orthonormal basis expansion to convert the functional optimization into an equivalent parameter optimization problem. Based on this functional WMMSE algorithm, we further propose BeamINR, an INR-based beamforming method implemented with a graph neural network to exploit the permutation-equivariant structure of the optimal beamforming policy; its update equation is designed from the structure of the functional WMMSE iterations. Simulation results show that the functional WMMSE algorithm achieves the highest sum rate at the cost of high online complexity. Compared with baseline INRs, BeamINR substantially reduces inference latency, lowers training complexity, and generalizes better across the number of users and carrier frequency.

A Model-based DNN for Learning HMIMO Beamforming

Holographic MIMO (HMIMO) is a promising technique for large-scale MIMO systems to enhance spectral efficiency while maintaining low hardware cost and power consumption. Existing alternating optimization algorithms can effectively optimize the hybrid beamforming of HMIMO to improve the system performance, while their high computational complexity hinders real-time application. In this paper, we propose a model-based deep neural network (MB-DNN), which leverages permutation equivalent properties and the optimal beamforming structure to jointly optimize the holographic and digital beamforming. Simulation results demonstrate that the proposed MB-DNN outperforms benchmark schemes and requires much less inference time than existing alternating optimization algorithms.

Learn to Optimize Resource Allocation under QoS Constraint of AR

This paper studies the uplink and downlink power allocation for interactive augmented reality (AR) services, where live video captured by an AR device is uploaded to the network edge and then the augmented video is subsequently downloaded. By modeling the AR transmission process as a tandem queuing system, we derive an upper bound for the probabilistic quality of service (QoS) requirement concerning end-to-end latency and reliability. The resource allocation with the QoS constraints results in a functional optimization problem. To address it, we design a deep neural network to learn the power allocation policy, leveraging the structure of optimal power allocation to enhance learning performance. Simulation results demonstrate that the proposed method effectively reduces transmit powers while meeting the QoS requirement.