Deep Learning-Driven Atomic Norm Optimization for Accurate Downlink Channel Estimation in FDD Systems

In this paper, we propose a downlink (DL) channel estimation scheme for frequency-division duplex (FDD) multi-antenna orthogonal frequency-division multiplexing (OFDM) systems, leveraging atomic norm minimization (ANM) and deep neural networks (DNN). Unlike time-division duplex (TDD) systems, where uplink (UL) and DL channels are reciprocal, FDD systems do not share this reciprocity, leading to increased channel training overhead. However, both theoretical analyses and empirical evidence reveal that key channel characteristics—such as angles of arrival and departure, path delays, and the number of propagation paths—exhibit partial reciprocity between UL and DL. Building on this insight, we design a DL channel estimation scheme that exploits frequency-independent UL parameters along with estimated DL channel gains. Our method integrates ANM with DNN to enhance estimation accuracy and efficiency. Specifically, ANM formulates the estimation problem while avoiding the off-grid errors inherent in traditional grid-based methods. To further mitigate performance degradation in clustered-path channels and reduce computational complexity, we introduce a DNN-based architecture that predicts channel parameters. The DNN captures hidden relationships between received pilot signals and frequency-independent channel parameters, enabling accurate estimation with linear time complexity. During training, ANM assists in serving users, ensuring reliable performance. Once the DNN is fully trained, it takes over to balance quality of service (QoS) and latency, providing an efficient and accurate solution for DL channel estimation in FDD-OFDM systems.