Physics-Inspired Deep Learning Anti-Aliasing Framework in Efficient Channel State Feedback

TL;DR

The paper tackles aliasing caused by undersampling of downlink CSI pilots in FDD massive MIMO. It introduces a physics-inspired CSI upsampling framework at the gNB that leverages uplink CSI, the DFT shifting theorem, and multipath reciprocity to suppress aliasing, complemented by a rule-based UL Masking bandpass design and a learning-based SRCsiNet. It further integrates SRCsiNet with ISTA-Net in a SRISTA-Net to handle non-uniform sampling and improve recovery when virtual pilots supplement CSI-RS pilots. Experimental results on outdoor QuaDRiGa channels show substantial NMSE improvements over traditional interpolation and existing DL approaches, highlighting practical gains for DL CSI feedback efficiency and accuracy in outdoor environments.

Abstract

Acquiring downlink channel state information (CSI) at the base station is vital for optimizing performance in massive Multiple input multiple output (MIMO) Frequency-Division Duplexing (FDD) systems. While deep learning architectures have been successful in facilitating UE-side CSI feedback and gNB-side recovery, the undersampling issue prior to CSI feedback is often overlooked. This issue, which arises from low density pilot placement in current standards, results in significant aliasing effects in outdoor channels and consequently limits CSI recovery performance. To this end, this work introduces a new CSI upsampling framework at the gNB as a post-processing solution to address the gaps caused by undersampling. Leveraging the physical principles of discrete Fourier transform shifting theorem and multipath reciprocity, our framework effectively uses uplink CSI to mitigate aliasing effects. We further develop a learning-based method that integrates the proposed algorithm with the Iterative Shrinkage-Thresholding Algorithm Net (ISTA-Net) architecture, enhancing our approach for non-uniform sampling recovery. Our numerical results show that both our rule-based and deep learning methods significantly outperform traditional interpolation techniques and current state-of-the-art approaches in terms of performance.

Figures (13)

• Figure 1: Illustration of the total discrepancy related to the losses at different stages. ${\Delta}_1$, ${\Delta}_2$ and ${\Delta}_3$ denote the distortions from channel estimation at UE side, feedback from UE to gNB, and upsampling, respectively.
• Figure 2: Illustration of CSI upsampling with side information. (A) shows the original CSI magnitude in delay domain. (B) demonstrates the CSIRS CSI magnitude in delay domain when $D_\text{RS} = 2$. We can find that the high negative delay peak wraps around ($R=1$) into the low delay region, leading aliasing effect. (C) shows the DS CSI magnitude in delay domain by inserting zero inbetween samples of CSIRS CSI in frequency domain. The green curve represents an ideal binary bandpass filter $\mathbf{\Phi}$ to be the side information. (D) is the resulting DL CSI magnitude in delay domain after applying the binary bandpass filter $\mathbf{\Phi}$.
• Figure 3: Illustration of multipath reciprocity between UL and DL propagation channels.
• Figure 4: Comparison of SRS and CSI-RS placement density.
• Figure 5: General architecture of the proposed physic-inspired AI-driven aliasing suppression framework. This framework consists of two parts. The first part is CSI compression and recovery which are deployed at UE and base station sides, respectively. The other part is the SR operation for the LR CSIs.