This study focuses on (traditional and unsourced) multiple-access communication over a single transmit and multiple ($M$) receive antennas. We assume full or partial channel state information (CSI) at the receiver. It is known that to fully achieve the fundamental limits (even asymptotically) the decoder needs to jointly estimate all user codewords, doing which directly is computationally infeasible. We propose a low-complexity solution, termed coded orthogonal modulation multiple-access (COMMA), in which users first encode their messages via a long (multi-user interference aware) outer code operating over a $q$-ary alphabet. These symbols are modulated onto $q$ orthogonal waveforms. At the decoder a multiple-measurement vector approximate message passing (MMV-AMP) algorithm estimates several candidates (out of $q$) for each user, with the remaining uncertainty resolved by the single-user outer decoders. Numerically, we show that COMMA outperforms a standard solution based on linear multiuser detection (MUD) with Gaussian signaling. Theoretically, we derive bounds and scaling laws for $M$, the number of users $K_a$, SNR, and $q$, allowing to quantify the trade-off between receive antennas and spectral efficiency. The orthogonal signaling scheme is applicable to unsourced random access and, with chirp sequences as basis, allows for low-complexity fast Fourier transform (FFT) based receivers that are resilient to frequency and timing offsets.

翻译：本研究聚焦于单发射天线与多（$M$）接收天线场景下的（传统与无源）多址通信。我们假设接收端已知完全或部分信道状态信息（CSI）。现有研究表明，为实现（包括渐近情形下的）基本极限的完全可达，译码器需要联合估计所有用户的码字，而直接进行联合估计在计算上不可行。本文提出一种低复杂度方案，称为编码正交调制多址接入（COMMA），其中用户首先通过基于$q$元字母表的长（多用户干扰感知）外码对其消息进行编码，并将这些符号调制到$q$个正交波形上。在译码端，多测量向量近似消息传递（MMV-AMP）算法为每个用户估计多个候选值（最多$q$个），剩余的不确定性由单用户外码译码器消除。数值结果表明，COMMA方案优于基于高斯信号线性多用户检测（MUD）的标准方案。理论上，我们推导了关于$M$、用户数$K_a$、信噪比及$q$的界限和标度律，从而量化接收天线与频谱效率之间的权衡关系。该正交信号方案适用于无源随机接入场景，并以线性调频序列作为基函数，可实现基于快速傅里叶变换（FFT）的低复杂度接收机，且对频率偏移和时间偏移具有鲁棒性。