Channel fingerprint (CF) is considered a key enabler for facilitating the acquisition of channel state information (CSI) in massive multiple-input multiple-output (MIMO) communication systems. In this work, we investigate a novel type of CF that stores statistical CSI (sCSI) at each potential location, referred to as statistical CF (sCF). Specifically, we reveal the relationship between sCSI, namely the channel spatial covariance matrix (CSCM), and the channel power angular spectrum (CPAS). Building on this foundation, we construct a unified tensor representation of the sCF and further reduce its dimension by exploiting the eigenvalue decomposition of the CSCM and its correlation with the PAS. Considering the practical constraints imposed by measurement cost, privacy, and security, we focus on three representative scenarios and uniformly formulate them as tensor restoration tasks. To this end, we propose a unified tensor-based learning architecture, termed LPWTNet. The architecture incorporates a closed-form Laplacian pyramid (LP) decomposition and reconstruction framework that replaces the traditional encoder-decoder structure, enabling efficient inference while capturing multi-scale frequency subband characteristics of the sCF. Additionally, a shared mask learning strategy is introduced to adaptively refine high-frequency sCF components through level-wise adjustments. To achieve a larger receptive field without over-parameterization, we further propose a small-kernel convolution mechanism based on the wavelet transform (WT), which decouples convolution across different frequency components of the sCF and enhances feature extraction efficiency. Extensive experiments show that the proposed approach delivers competitive reconstruction accuracy and computational efficiency across various sCF construction scenarios when compared with state-of-the-art baselines.

翻译：信道指纹（CF）被视为促进大规模多输入多输出（MIMO）通信系统中信道状态信息（CSI）获取的关键技术。本文研究了一种新型CF——统计CF（sCF），它在每个潜在位置存储统计CSI（sCSI）。具体而言，我们揭示了sCSI（即信道空间协方差矩阵CSCM）与信道功率角谱（CPAS）之间的关系。基于此，我们构建了sCF的统一张量表示，并通过利用CSCM的特征值分解及其与PAS的相关性进一步降低其维度。考虑到测量成本、隐私和安全性带来的实际限制，我们聚焦于三种代表性场景，并将其统一建模为张量恢复任务。为此，我们提出了一种基于张量的统一学习架构，称为LPWTNet。该架构采用闭式拉普拉斯金字塔（LP）分解与重建框架替代传统的编码器-解码器结构，在高效推理的同时捕获sCF的多尺度频率子带特征。此外，引入共享掩码学习策略，通过逐级调整自适应地细化sCF的高频分量。为在不造成过度参数化的情况下获得更大感受野，我们进一步提出基于小波变换（WT）的小核卷积机制，该机制将sCF不同频率分量上的卷积解耦，提升了特征提取效率。大量实验表明，与现有先进基线方法相比，所提方法在各种sCF构建场景中均能提供具有竞争力的重建精度和计算效率。