arXiv subjects

Guijun Liu

Publications and source records attributed to Guijun Liu.

3 recordsLinked to original sources

arXiv2026

Bergman Kernels and Hankel Operators on Weighted Fock Spaces in Several Complex Variables

We introduce a class of plurisubharmonic weights on \mathbb C^n and develop a theory of the associated weighted Fock spaces F_φ^p. The curvature assumptions are imposed on a \mathcal C^2-regularization at bounded distance from the original weight. Thus the original weight need not be smooth or strictly plurisubharmonic, and, even when it is of class \mathcal C^2, its complex Hessian eigenvalues need not be uniformly comparable. This provides a counterpart of Christ's doubling theory in several complex variables. We establish a global upper estimate with decay away from the diagonal and a uniform lower estimate near the diagonal for the weighted Bergman kernel. These estimates yield L^p bounds for the kernel functions, boundedness of the Bergman projection, and duality and complex interpolation for the associated Fock spaces. For a certain class of weights beyond the uniformly controlled curvature setting, we construct an integral solution operator for the \bar\partial equation and establish scale-adapted weighted L^p estimates for 1\leq p\leq\infty. As an application, for all 1\leq p,q<\infty, we characterize the boundedness and compactness of Hankel operators from F_φ^p to L_φ^q with possibly unbounded symbols in terms of weighted IDA spaces.

math.CV↗

arXiv2025

Generative Model-Aided Continual Learning for CSI Feedback in FDD mMIMO-OFDM Systems

Deep autoencoder (DAE) frameworks have demonstrated their effectiveness in reducing channel state information (CSI) feedback overhead in massive multiple-input multiple-output (mMIMO) orthogonal frequency division multiplexing (OFDM) systems. However, existing CSI feedback models struggle to adapt to dynamic environments caused by user mobility, requiring retraining when encountering new CSI distributions. Moreover, returning to previously encountered environments often leads to performance degradation due to catastrophic forgetting. Continual learning involves enabling models to incorporate new information while maintaining performance on previously learned tasks. To address these challenges, we propose a generative adversarial network (GAN)-based learning approach for CSI feedback. By using a GAN generator as a memory unit, our method preserves knowledge from past environments and ensures consistently high performance across diverse scenarios without forgetting. Simulation results show that the proposed approach enhances the generalization capability of the DAE framework while maintaining low memory overhead. Furthermore, it can be seamlessly integrated with other advanced CSI feedback models, highlighting its robustness and adaptability.

cs.LG↗

arXiv2025

Distributed Gossip-GAN for Low-overhead CSI Feedback Training in FDD mMIMO-OFDM Systems

The deep autoencoder (DAE) framework has turned out to be efficient in reducing the channel state information (CSI) feedback overhead in massive multiple-input multipleoutput (mMIMO) systems. However, these DAE approaches presented in prior works rely heavily on large-scale data collected through the base station (BS) for model training, thus rendering excessive bandwidth usage and data privacy issues, particularly for mMIMO systems. When considering users' mobility and encountering new channel environments, the existing CSI feedback models may often need to be retrained. Returning back to previous environments, however, will make these models perform poorly and face the risk of catastrophic forgetting. To solve the above challenging problems, we propose a novel gossiping generative adversarial network (Gossip-GAN)-aided CSI feedback training framework. Notably, Gossip-GAN enables the CSI feedback training with low-overhead while preserving users' privacy. Specially, each user collects a small amount of data to train a GAN model. Meanwhile, a fully distributed gossip-learning strategy is exploited to avoid model overfitting, and to accelerate the model training as well. Simulation results demonstrate that Gossip-GAN can i) achieve a similar CSI feedback accuracy as centralized training with real-world datasets, ii) address catastrophic forgetting challenges in mobile scenarios, and iii) greatly reduce the uplink bandwidth usage. Besides, our results show that the proposed approach possesses an inherent robustness.

eess.SP↗