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

Abstract

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 SFET 1 , SFET 2 and SFET 3 . It is shown that the SFET 1 using the maximum likelihood estimation (MLE) of SF is equal to the generalised likelihood ratio test. The SFET 2 and SFET 3 are proposed to reduce the computational complexity of SFET 1 , 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 SFET 3 outperforms the SFET 1 and SFET 2 and the decreasing rate of miss detection against the number of snapshots for SFET 3 is higher than that for SFET 1 and SFET 2 .