This paper analyzes the detection of a M-dimensional useful signal modeled as the output of a M xK MIMO filter driven by a K-dimensional white Gaussian noise, and corrupted by a M-dimensional Gaussian noise with mutually uncorrelated components. The study is focused on frequency domain test statistics based on the eigenvalues of an estimate of the spectral coherence matrix (SCM), obtained as a renormalization of the frequency-smoothed periodogram of the observed signal. If N denotes the sample size and B the smoothing span, it is proved that in the high-dimensional regime where M, B, N converge to infinity while K remains fixed, the SCM behaves as a certain correlated Wishart matrix. Exploiting well-known results on the behaviour of the eigenvalues of such matrices, it is deduced that the standard tests based on linear spectral statistics of the SCM fail to detect the presence of the useful signal in the high-dimensional regime. A new test based on the SCM, which is proved to be consistent, is also proposed, and its statistical performance is evaluated through numerical simulations.

翻译：本文分析一个MxK MIMO过滤器的MxK 有用信号的探测,该信号的模型是由K-Seet Gausian噪音驱动的MxK MIMO过滤器的输出由K-Seet Gausian噪音驱动,并被一个M-Seut Gaussian噪音以相互不相干的组成部分腐蚀。研究的重点是基于光谱一致性矩阵估计值的频率域域测试统计,该模型是作为观测到的信号的频谱间段图的重新统一而获得的。如果N表示样本大小和B的光滑度,则证明在高维系统中,M、B、N在K保持固定时会趋同于无限度,SCM作为某种相关的Wishart矩阵进行行为。挖掘这种矩阵的光值的已知结果,由此推论,基于SCM的线光谱期图的标准测试无法检测高维系系统中是否有有用的信号。基于SCM的新测试证明是一致的,也是通过模拟来评估其统计性。