Next-generation wireless communication systems are unifying large-scale multiple-input multiple-output (MIMO) and integrated sensing and communication (ISAC) to enhance sensing and communication performance. In this paper, the signal detection problem for MIMO-ISAC systems is modeled as a mixed-integer least squares (MILS) problem. To solve it efficiently, we propose a projection-based neighborhood search-aided alternating direction method of multipliers (P-NS-ADMM) detection scheme. By theoretical analysis, we demonstrate that P-NS-ADMM achieves the same received diversity order as maximum likelihood (ML) detection. For further complexity reduction, an iteration-based NS-ADMM (I-NS-ADMM) is proposed to remove the complex projection operation. Complexity analysis shows its complexity advantage compared with P-NS-ADMM. Moreover, to better estimate the sensing signals for I-NS-ADMM, a flexible mechanism of ADMM iterations is given. Finally, simulations demonstrate the proposed NS-aided ADMM detection schemes have significant performance advantages in terms of both BER and NMSE.

翻译：下一代无线通信系统正通过统一大规模多输入多输出（MIMO）与集成感知与通信（ISAC）技术来增强感知与通信性能。本文将MIMO-ISAC系统的信号检测问题建模为混合整数最小二乘（MILS）问题。为高效求解该问题，提出一种基于投影的邻域搜索辅助交替方向乘子法（P-NS-ADMM）检测方案。理论分析表明，P-NS-ADMM能够达到与最大似然（ML）检测相同的接收分集阶数。为进一步降低复杂度，提出基于迭代的NS-ADMM（I-NS-ADMM）以去除复杂的投影操作。复杂度分析显示了其相较于P-NS-ADMM的复杂度优势。此外，为优化I-NS-ADMM对感知信号的估计，给出了ADMM迭代的灵活机制。最后，仿真结果表明所提出的NS辅助ADMM检测方案在误码率（BER）与归一化均方误差（NMSE）方面均具有显著性能优势。