AI 中文总结
本文针对随机MIMO-OFDM信号，提出三维模糊函数并推导其统计特性，明确星座图四阶矩对模糊旁瓣的影响，扩展得到快-慢时间近似，为ISAC系统感知模糊性提供统计表征。
AI 中文摘要
集成感知与通信（ISAC）系统可利用随机通信符号的有效载荷信号进行感知，但匹配滤波响应会随传输数据变化。现有针对随机正交频分复用（OFDM）波形感知的统计分析多聚焦于时延与多普勒维度，而多输入多输出（MIMO）阵列与预编码引入的空间维度却鲜有研究。本文针对时延、多普勒与角度域的随机MIMO-OFDM波形，提出三维模糊函数（3D-AF）。对于点目标感知，将3D-AF表示为随机通信符号的二次型，其中确定性矩阵捕获时延与多普勒偏移、收发阵列响应及不同子载波上的预编码。基于此表示，推导得到期望平方3D-AF的闭式表达式，明确星座图四阶矩（或峰度）对模糊旁瓣的影响。该表征还可得到时延-多普勒-角度混合搜索域上的期望积分旁瓣电平（EISL）与期望旁瓣电平（ESL）指标。该框架进一步扩展至含慢时间多普勒的相干多符号处理，得到对应的快-慢时间（FST）近似。上述结果为随机MIMO-OFDM通信信号在时延、多普勒与角度域诱导的感知模糊性提供了统计表征。
英文摘要
Random communication symbols allow integrated sensing and communications (ISAC) systems to exploit payload signals for sensing, but the resulting matched-filter response varies with the transmitted data. Existing statistical analyses of sensing with random orthogonal frequency division multiplexing (OFDM) waveforms have largely focused on delay and Doppler, while the spatial dimension introduced by multi-input multi-output (MIMO) arrays and precoding has received much less attention. This paper develops a three-dimensional ambiguity function (3D-AF) for random MIMO-OFDM waveforms over delay, Doppler, and angle domains. For point-target sensing, we express the 3D-AF as a quadratic form of the random communication symbols, with a deterministic matrix that captures the delay and Doppler shifts, the transmit and receive array responses, and the precoders on different subcarriers. Based on this representation, we derive a closed-form expression for the expected squared 3D-AF and show explicitly how the constellation fourth-order moment (or kurtosis) affects the ambiguity sidelobes. The same characterization yields expected integrated sidelobe level (EISL) and expected sidelobe level (ESL) metrics over mixed delay-Doppler-angle search domains. The framework is further extended to coherent multi-symbol processing with slow-time Doppler, leading to the corresponding fast-slow time (FST) approximation. These results provide a statistical characterization of the sensing ambiguity induced by random MIMO-OFDM communication signals in delay, Doppler, and angle.
Comments15 pages, 6 figures, 1 table
