Multiple-Tone Signals and Detection Probabillities

An analysis technique is presented for multiple-tone signals insystems employing noncoherent integration of a square-law detectoroutput. It is shown how the characteristic function for the teststatistic can be found from the easily determined "coherent"characteristic function defined in the two-dimensional signal space.This result is applied to two detection problems, the detection of multiple-tone signals in Gaussian noise and the detection of a Gaussian signal in multiple-tone plus Gaussian noise interference.The detection curves are compared to an approximation that is often used in practice to estimate performance. It is found that detection performance in the presence of multiple-tone interferences can be significantly different from that in the presence of Gaussian noise alone.