可移动天线增强的MIMO-OFDM ISAC：模糊函数分析、波形设计与天线位置优化

中文摘要 AI 辅助

多输入多输出正交频分复用（MIMO-OFDM）为集成感知与通信（ISAC）提供了丰富的空间和时频自由度，而可移动天线（MAs）通过阵列几何调整进一步引入了可重构的空间自由度。然而，阵列几何和信息承载的MIMO-OFDM波形如何共同塑造三维（3D）模糊响应仍未得到充分理解，且传统的二维（2D）距离-多普勒度量无法完全表征这种耦合。本文研究了MA增强的MIMO-OFDM ISAC，并联合设计发射MA位置和符号级预编码（SLP）波形。首先推导了离散周期角度-距离-多普勒模糊函数，并基于波形秩刻画了其结构。证明秩一波形产生的3D模糊响应在角度维与距离-多普勒平面之间是可分离的，而更高秩波形则在不同候选角度上以不同权重组合多个空间分量，使得距离-多普勒响应随候选角度变化，从而使MA位置能够进一步塑造3D模糊响应。基于此分析，定义了3D积分旁瓣电平比（ISLR），构建了MA位置与SLP波形的联合优化问题，并开发了一种基于惩罚对偶分解的交替优化算法。对于仅雷达情形，证明了至少存在一个秩一的全局最优解，从而能够将原始高维MIMO-OFDM波形设计无损地降维为空间波束与MA位置的低维联合设计。

英文摘要

Multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) provides abundant spatial and time-frequency degrees of freedom for integrated sensing and communication (ISAC), while movable antennas (MAs) further introduce reconfigurable spatial freedom through array geometry adjustment. However, how the array geometry and information bearing MIMO-OFDM waveform jointly shape the three dimensional (3D) ambiguity response remains insufficiently understood, and conventional two dimensional (2D) range-Doppler metrics cannot fully characterize this coupling. This paper investigates MA-enhanced MIMO-OFDM ISAC with joint design of the transmit MA positions and symbol-level precoding (SLP) waveform. The discrete periodic angle-range-Doppler ambiguity function is first derived, and its structure is characterized in terms of waveform rank. It is proved that a rank one waveform yields a 3D ambiguity response that is separable between the angular dimension and the range-Doppler plane, whereas a higher rank waveform combines multiple spatial components with different weights across candidate angles, allowing the range-Doppler response to vary with the candidate angle and enabling the MA positions to further shape the 3D ambiguity response. Based on this analysis, a 3D integrated sidelobe level ratio (ISLR) is defined, the joint optimization of the MA positions and SLP waveform is formulated, and a penalty dual decomposition based alternating optimization algorithm is developed. For the radar-only case, the existence of at least one rank one globally optimal solution is established, enabling a lossless reduction from the original high dimensional MIMO-OFDM waveform design to a low dimensional joint design of the spatial beam and MA positions.

发表机构

• Beijing Institute of Technology（北京理工大学）
• School of Information and Electronic Engineering, Beijing University of Posts and Telecommunications（北京邮电大学信息工程学院）

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