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.