论文标题
最佳相关器和波形不匹配检测
Optimal Correlators and Waveforms for Mismatched Detection
论文作者
论文摘要
We consider the classical Neymann-Pearson hypothesis testing problem of signal detection, where under the null hypothesis ($\calH_0$), the received signal is white Gaussian noise, and under the alternative hypothesis ($\calH_1$), the received signal includes also an additional non-Gaussian random signal, which in turn can be viewed as a deterministic waveform plus zero-mean, non-Gaussian noise.但是，我们通常强加了（不匹配的）相关检测器（相对易于实现），而不是很难实施的经典似然比测试检测器，我们以最佳的相关权重为特征，这是False-Alarm误差指数与错过检测错误指数之间的最佳权衡。那些最佳的相关权重取决于（通常是非线性的），在$ \ calh_1 $下的基础确定波形上。然后，我们假设确定性波形也可以自由进行优化（受功率限制），并与相关器共同进行，并表明最佳波形和最佳相关器权重可以在通常不超过两到四个级别的少量有限的少量集中，取决于非高斯噪声组件的分布。最后，我们概述了基于相关性和接收信号的能量的线性组合的范围扩展到更宽的检测器。
We consider the classical Neymann-Pearson hypothesis testing problem of signal detection, where under the null hypothesis ($\calH_0$), the received signal is white Gaussian noise, and under the alternative hypothesis ($\calH_1$), the received signal includes also an additional non-Gaussian random signal, which in turn can be viewed as a deterministic waveform plus zero-mean, non-Gaussian noise. However, instead of the classical likelihood ratio test detector, which might be difficult to implement, in general, we impose a (mismatched) correlation detector, which is relatively easy to implement, and we characterize the optimal correlator weights in the sense of the best trade-off between the false-alarm error exponent and the missed-detection error exponent. Those optimal correlator weights depend (non-linearly, in general) on the underlying deterministic waveform under $\calH_1$. We then assume that the deterministic waveform may also be free to be optimized (subject to a power constraint), jointly with the correlator, and show that both the optimal waveform and the optimal correlator weights may take on values in a small finite set of typically no more than two to four levels, depending on the distribution of the non-Gaussian noise component. Finally, we outline an extension of the scope to a wider class of detectors that are based on linear combinations of the correlation and the energy of the received signal.
