We derive finite-blocklength bounds on the minimum achievable energy per bit over a Gaussian unsourced multiple access (UMA) channel in the presence of heterogeneous path-loss conditions. We consider a setting in which the path loss is known to the users, which enables the use of location-based codebook partitioning [Çakmak et al., 2025]. Through numerical simulations and a large-system analysis based on the replica method, we quantify the performance gain of this strategy relative to the conventional UMA approach in which all users employ a common codebook.

翻译：针对异构路径损耗条件下的高斯无源多址接入信道，我们推导了可实现每比特最小能量的有限分组长度界限。研究场景中用户已知路径损耗信息，从而能够采用基于位置的码本划分策略 [Çakmak 等，2025]。通过数值仿真与基于复制方法的大系统分析，我们量化了该策略相较于所有用户使用公共码本的传统无源多址接入方法的性能增益。