Abstract:

Aiming at the problem that the locally optimal detector (LOD) has complex structure and is difficult to perform constant false alarm processing under the background of symmetric α stable (SαS) distribution, an adaptive cumulative distribution detector (CDD) is proposed. The detector performs nonlinear transformation on the received signal based on the cumulative distribution function, and then performs matched filtering processing. The SαS distribution is approximated according to the bi-parameter Cauchy-Gaussian mixture model (BCGM), and based on this, the detection performance of CDD is systematically analyzed, and its constant false alarm characteristics is proved. The detector is further simplified by the sigmoid function, and an near CDD (NCDD) is obtained. Both theoretical and simulation results show that NCDD has similar performance with LOD when the value of α is large, but the structure is simpler and it is easier to deal with the constant false alarm ratio.

Key words: symmetric α stable (SαS) distribution, cumulative distribution function, signal detection, constant false alarm ratio