Grant-free access is a key enabler for connecting wireless devices with low latency and low signaling overhead in massive machine-type communications (mMTC). For massive grant-free access, user-specific signatures are uniquely assigned to mMTC devices. In this paper, we first derive a sufficient condition for the successful identification of active devices through maximum likelihood (ML) estimation in massive grant-free access. The condition is represented by the coherence of a signature sequence matrix containing the signatures of all devices. Then, we present a design framework of non-orthogonal signature sequences in a deterministic fashion. The design principle relies on unimodular masking sequences with low correlation, which are applied as masking sequences to the columns of the discrete Fourier transform (DFT) matrix. For example constructions, we use four polyphase masking sequences represented by characters over finite fields. Leveraging algebraic techniques, we show that the signature sequence matrix of proposed non-orthogonal sequences has theoretically bounded low coherence. Simulation results demonstrate that the deterministic non-orthogonal signatures achieve the excellent performance of joint activity and data detection by ML- and approximate message passing (AMP)-based algorithms for massive grant-free access in mMTC.

翻译：免授权访问是连接大规模机器类通信（mMTC）中低时延、低信令开销无线设备的关键技术。针对大规模免授权访问，用户特定签名被唯一分配给mMTC设备。本文首先推导了在大规模免授权访问中通过最大似然（ML）估计成功识别活跃设备的充分条件，该条件由包含所有设备签名的签名序列矩阵的相干性表示。随后，我们提出了一种确定性非正交签名序列的设计框架。该设计原理依赖于具有低相关性的单模掩码序列，这些序列作为掩码应用于离散傅里叶变换（DFT）矩阵的列。在示例构造中，我们使用了由有限域字符表示的四相多相掩码序列。利用代数技术，我们证明所提出的非正交序列的签名序列矩阵具有理论上有界的低相干性。仿真结果表明，基于ML和近似消息传递（AMP）算法，所提出的确定性非正交签名在大规模免授权mMTC中实现了优异的联合活动与数据检测性能。