Where to Perform Channel Measurements for CKM Construction: A Random Field Theory Analysis

2026-07-27

AI Summary

This work addresses the challenge of efficiently constructing channel gain maps (CGMs) under limited measurements by optimizing sensor placement to minimize global reconstruction error. The physical space is discretized through a combinatorial optimization framework, and an adaptive spatial discretization strategy grounded in Gaussian random field theory is proposed to minimize, in the mean-square sense, the information loss incurred when approximating the continuous channel field with a discrete representation. By integrating a greedy algorithm with simulated annealing to determine optimal measurement locations, the proposed method substantially outperforms conventional uniform sampling schemes. It achieves lower average mean-square error while overcoming the traditional trade-off between accuracy and computational complexity, thereby offering both theoretical insights and practical guidance for environment-aware communications in 6G systems.

Abstract

Channel knowledge map (CKM) is regarded as a promising technology for future sixth-generation (6G) networks, facilitating environmental-aware wireless communication, sensing, and localization. Research works on CKM construction can be classified as model-based methods and data-based approaches. Specifically, data-based CKM construction exploits the fundamental principle of spatial correlation to complete CKM based on limited measurement data, leading to the question of "where to perform channel measurements". In this paper, we study the spatial measurement strategy for efficient data-based CKM construction, and consider a specific type of CKM named channel gain map (CGM). The general objective is to select a subset of locations for channel measurements, so as to minimize the average mean-squared-error (AMSE) of the global CGM construction. In order to reduce the infinite measurement locations to a finite set, we discretize the underlying physical space into a finite number of cubic grid points, and formulate a combinatorial optimization problem to select measurement locations from them. In order to solve the proposed problem, we employ two representative algorithms, namely the greedy algorithm and the simulated annealing (SA), and discuss their respective advantages. To overcome the accuracy-complexity trade-off of traditional uniform discretization, we develop an adaptive discretization strategy from the viewpoint of Gaussian random field theory to minimize the information loss from the original continuous field to its approximated discrete representation in the mean-squared sense. Compared to uniform discretization, the proposed adaptive discretization strategy achieves a significant performance gain in terms of AMSE-reduction, establishing the theoretical framework of spatial measurement and providing practical guidance for implementation.

Problem

• Channel Knowledge Map
• spatial measurement strategy
• mean-squared-error
• adaptive discretization
• Gaussian random field

Innovation

• adaptive discretization
• Gaussian random field
• channel knowledge map
• spatial measurement strategy
• mean-squared error