The wireless channel is undergoing continuous changes, and the block-fading assumption, despite its popularity in theoretical contexts, never holds true in practical scenarios. This discrepancy is particularly critical for user activity detection in grant-free random access, where joint processing across multiple resource blocks is usually undesirable. In this paper, we propose employing a low-dimensional approximation of the channel to capture variations over time and frequency and robustify activity detection algorithms. This approximation entails projecting channel fading vectors onto their principal directions to minimize the approximation order. Through numerical examples, we demonstrate a substantial performance improvement achieved by the resulting activity detection algorithm.

翻译：无线信道持续变化，尽管块衰落假设在理论研究中被广泛采用，但在实际场景中从未成立。这一出入对于无授权随机接入中的用户活动检测尤为关键，因为通常需要避免跨多个资源块的联合处理。本文提出采用信道的低维近似来捕捉其时频变化特征，并增强活动检测算法的鲁棒性。该近似通过将信道衰落向量投影至主方向，以最小化近似阶数。数值示例表明，由此产生的活动检测算法实现了显著的性能提升。