Separating function estimation tests for narrowband signal activity detection using linear array

This study addresses the narrowband signal detection with unknown frequency, direction of arrival, complex amplitude and noise variance. The authors find a separating function (SF) using the maximal invariant of induced group of transformations. Then three separating function estimation tests (SFETs) are proposed which called SFET₁, SFET₂ and SFET₃. It is shown that the SFET₁ using the maximum likelihood estimation (MLE) of SF is equal to the generalised likelihood ratio test. The SFET₂ and SFET₃ are proposed to reduce the computational complexity of SFET₁, based on a proposed estimation named by averaged MLE. The authors show that the proposed tests are constant false alarm rate. Moreover it is shown that the proposed tests are asymptotically optimal by increasing the number of snapshots and antennas. The simulation results show that the SFET₃ outperforms the SFET₁ and SFET₂ and the decreasing rate of miss detection against the number of snapshots for SFET₃ is higher than that for SFET₁ and SFET₂.