This paper tackles the problem of building a spatial correlation map for multi-antenna wireless systems from a small number of measurements. A spatial correlation map records how the signals at different antenna elements relate to each other at every location. That information matters for tasks such as beamforming and channel estimation, and it can cut the need for repeated real-time measurements in future systems like 6G.

The authors convert the hard problem of estimating a large correlation matrix into two lower‑dimensional image tasks. They break the high‑dimensional matrix into a path gain map (PGM), which records the strength of propagation paths, and a path angle map (PAM), which records the arrival angles of those paths. They treat completion of these maps from sparse samples as an image super‑resolution problem and build a neural network called E-SRResNet to fill in the missing values.

E-SRResNet is based on an existing super‑resolution network but adds modules designed for wireless channels. It uses multi‑head attention (MHA) to capture long‑range relationships across the map, and multi‑scale feature fusion (MSFF) to combine broad, smooth patterns (common in line‑of‑sight areas) with fine, complex details (near buildings). The model also takes simple prior maps as input: a line‑of‑sight (LoS) indicator, a binary building map, and the base station (BS) location map. For training and testing the method the authors used the CKMImageNet dataset, and the network outputs completed PGMs and PAMs that are recombined to form the full spatial correlation map.

The paper also explains the physical simplifications behind the approach. Under a sparse multipath assumption and basic phase assumptions (phases independent and uniformly distributed), the spatial correlation matrix can be written as a sum of steering vectors weighted by average path powers. That lets the authors focus on a small number of dominant paths (L much smaller than the antenna count N). On the architecture side, the backbone has 16 residual blocks, with four‑headed attention in each block and MSFF modules placed after the 4th, 8th and 12th blocks. The MSFF uses a dilation pyramid to cover effective receptive fields from about 7×7 to 15×15 without many extra parameters.