Although routinely utilized in literature, orthogonal waveforms may lose orthogonality in distributed multi-input multi-output (MIMO) radar with spatially separated transmit (TX) and receive (RX) antennas, as the waveforms may experience distinct delays and Doppler frequency offsets unique to different TX-RX propagation paths. In such cases, the output of each waveform-specific matched filter (MF), employed to unravel the waveforms at the RXs, contains both an auto term and multiple cross terms, i.e., the filtered response of the desired and, respectively, undesired waveforms. We consider the impact of non-orthogonal waveforms and their cross terms on target detection with or without timing, frequency, and phase errors. To this end, we present a general signal model for distributed MIMO radar, examine target detection using existing coherent/non-coherent detectors and two new detectors, including a hybrid detector that requires phase coherence locally but not across distributed antennas, and provide a statistical analysis leading to closed-form expressions of false alarm and detection probabilities for all detectors. Our results show that cross terms can behave like foes or friends, respectively, if they and the auto term add destructively or constructively, depending on the propagation delay, frequency, and phase offsets. Regarding sync errors, we show that phase errors affect only coherent detectors, frequency errors degrade all but the non-coherent detector, while all are impacted by timing errors, which result in a loss in the signal-to-noise ratio (SNR).

中文翻译：

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分布式 MIMO 雷达中具有非正交波形和同步误差的信号检测


尽管正交波形在文献中经常使用，但在具有空间分离的发射 (TX) 和接收 (RX) 天线的分布式多输入多输出 (MIMO) 雷达中，正交波形可能会失去正交性，因为波形可能会经历独特的延迟和多普勒频率偏移。不同的 TX-RX 传播路径。在这种情况下，用于解析 RX 处波形的每个特定于波形的匹配滤波器 (MF) 的输出包含自项和多个交叉项，即分别对所需波形和不需要波形进行滤波的响应。我们考虑非正交波形及其交叉项对有或没有定时、频率和相位误差的目标检测的影响。为此，我们提出了分布式 MIMO 雷达的通用信号模型，使用现有的相干/非相干检测器和两个新检测器（包括需要本地相位相干但不需要跨分布式天线的混合检测器）检查目标检测，并提供统计数据分析得出所有探测器的误报和探测概率的封闭式表达式。我们的结果表明，如果交叉项和自动项根据传播延迟、频率和相位偏移进行破坏性或建设性相加，则交叉项可以分别表现得像敌人或朋友。关于同步误差，我们表明相位误差仅影响相干检测器，频率误差会降低除非相干检测器之外的所有检测器的性能，而所有检测器都会受到定时误差的影响，从而导致信噪比（SNR）损失。