Decision Statistics for Incoherent Signal Detection in Multi-Element Antenna Arrays

We present a detailed study of the characteristics of the exact decision statistic for the optimal incoherent signal detection in a multielement antenna array. The exact decision statistic is derived from a rigorous expression for the likelihood ratio in the case where the useful-signal amplitudes at the antenna-array elements are identical, whereas the phases are random. The analysis is carried out in the space of the variables which are observed at the outputs of the incoherent matched filters performing the initial signal processing at each antenna-array element. Variation in the signal-to-noise ratio is shown to deform the boundary of partitioning of the multidimensional observation space, which results in a variation in the threshold values of the exact decision statistic when the Neyman–Pearson criterion is used. The characteristics of the exact decision statistic and various approximate decision statistics are compared in detail. For the antenna arrays with a large number of elements, the influence of the used decision statistic on the target-missing probability is shown to become rather significant. A new combined decision statistic with the characteristics that are close to those of the exact decision statistic is introduced for a wide signal-to-noise ratio range.