Massive MIMO based grant-free random access (mGFRA) is a promising RA technique for massive access with low signaling overhead. However, due to a limited orthogonal preamble size, preamble collision is a key factor that constrains the success probability of mGFRA. In this paper, we examine the potential of applying non-orthogonal preambles to mitigate the issue, where two typical non-orthogonal sequences, i.e., Gaussian distribution sequences and Zadoff-Chu (ZC) sequences, are taken into account. Asymptotic behaviors of the success probabilities with the non-orthogonal preamble sequences are analyzed and compared using derived closed-forms. Through the analysis we reveal that ZC sequences outperform Gaussian ones. However, though non-orthogonal sequences are able to reduce or even alleviate the preamble collision, they do not necessarily provide better performance than the orthogonal counterpart. In addition, regarding orthogonal sequences as a single-root case of ZC sequences, we show that there exists an optimal number of ZC roots that maximizes the success probability for mGFRA, which is low-bounded by orthogonal baseline. Simulation results evaluate the performance of non-orthogonal sequences in mGFRA under various practical system parameters, and validate our analysis.

中文翻译：

---

具有大规模 MIMO 的免授权 RA 的非正交序列分析

基于大规模 MIMO 的无授权随机接入 (mGFRA) 是一种很有前途的 RA 技术，用于以低信令开销进行大规模接入。然而，由于有限的正交前导码大小，前导码冲突是限制 mGFRA 成功概率的关键因素。在本文中，我们研究了应用非正交前同步码来缓解该问题的潜力，其中考虑了两个典型的非正交序列，即高斯分布序列和 Zadoff-Chu (ZC) 序列。使用导出的封闭形式分析和比较非正交前导序列成功概率的渐近行为。通过分析我们发现ZC序列优于高斯序列。然而，尽管非正交序列能够减少甚至减轻前导冲突，它们不一定提供比正交对应物更好的性能。此外，将正交序列视为 ZC 序列的单根情况，我们表明存在一个最优数量的 ZC 根，使 mGFRA 的成功概率最大化，这是正交基线下限的。仿真结果评估了 mGFRA 中非正交序列在各种实际系统参数下的性能，并验证了我们的分析。