This paper investigates the energy efficiency of massive unsourced random access~(URA) in multiple-input multiple-output quasi-static Rayleigh fading channels. Specifically, we derive achievability and converse bounds on the minimum required energy-per-bit under the per-user probability of error constraint, where the converse bounds contain two parts: one is general and the other is a weaker ensemble bound. Numerical evaluation shows that the gap between our achievability and converse bounds is less than $5$~dB in the considered regime. Some practical schemes are energy-inefficient compared with our bounds especially when there are many users. Moreover, we observe that in contrast to the sourced random access paradigm, the URA paradigm achieves higher spectral efficiency.

翻译：本文研究了多输入多输出准静态瑞利衰落信道中大规模无源随机接入(URA)的能量效率问题。具体而言，我们在每用户错误概率约束下推导了每比特所需最小能量的可达性边界与不可达性边界，其中不可达性边界包含两部分：一部分是通用边界，另一部分为较弱的集总边界。数值评估表明，在所考虑的范围内，我们的可达性边界与不可达性边界之间的差距小于5分贝。与我们的边界相比，一些实际方案在用户数量较多时存在能量效率不足的问题。此外，我们观察到，与有源随机接入范式相比，URA范式能够实现更高的频谱效率。