  Channel knowledge map (CKM) has received widespread attention as an emerging
enabling technology for environment-aware wireless communications. It involves
the construction of databases containing location-specific channel knowledge,
which are then leveraged to facilitate channel state information (CSI)
acquisition and transceiver design. In this context, a fundamental challenge
lies in efficiently constructing the CKM based on a given wireless propagation
environment. Most existing methods are based on stochastic modeling and
sequence prediction, which do not fully exploit the inherent physical
characteristics of the propagation environment, resulting in low accuracy and
high computational complexity. To address these limitations, we propose a
Laplacian pyramid (LP)-based CKM construction scheme to predict the channel
knowledge at arbitrary locations in a targeted area. Specifically, we first
view the channel knowledge as a 2-D image and transform the CKM construction
problem into an image-to-image (I2I) inpainting task, which predicts the
channel knowledge at a specific location by recovering the corresponding pixel
value in the image matrix. Then, inspired by the reversible and closed-form
structure of the LP, we show its natural suitability for our task in designing
a fast I2I mapping network. For different frequency components of LP
decomposition, we design tailored networks accordingly. Besides, to encode the
global structural information of the propagation environment, we introduce
self-attention and cross-covariance attention mechanisms in different layers,
respectively. Finally, experimental results show that the proposed scheme
outperforms the benchmark, achieving higher reconstruction accuracy while with
lower computational complexity. Moreover, the proposed approach has a strong
generalization ability and can be implemented in different wireless
communication scenarios.
