Preambles for Massive Random Access: Kronecker-Product Structured Sequences and Low-Complexity Detection

To accommodate emerging technologies such as the Internet of Things and low-altitude economy, future wireless networks are expected to support millions of users (UEs) per square kilometer. Such massive connectivity imposes stringent requirements on the design of physical random access channel preambles, which are generally desired to possess strong Doppler resilience, low auto-/cross-correlation, and a huge capacity. However, existing sequence designs that satisfy these criteria usually suffer from high detection complexity. To address this issue, we investigate a Kronecker-product structured (KPS) sequence family, which possesses an inherent segment structure that facilitates the simplification of the detection algorithm. Moreover, the closed-form expression of its ambiguity function is derived, explicitly revealing how the overall characteristics are governed by the two component sequences and providing useful design guidelines. Based on the obtained insights, two new high-capacity sequence sets, namely m-ZC KPS and m-Alltop KPS, are constructed. Leveraging the intrinsic segment structure of KPS sequences, we develop a low-complexity detection scheme that separates the correlation operations into inner- and outer-layer processing and simplifies the Doppler compensation to reduce the complexity. Building upon this proposed scheme, we further introduce an enhanced version of the algorithm that incorporates a fine-grained detection among potential candidate UEs, thereby substantially improving the detection accuracy. Simulation results demonstrate that the proposed KPS sequences exhibit favorable correlation properties and low peak-to-average power ratio (PAPR). In addition, when combined with the proposed detection algorithm, they achieve approximately an 80% reduction in computational complexity while retaining reliability comparable to that of conventional algorithms.