Method and apparatus for multiple signal identification and finding the basis functions of the received signal

A method is disclosed to detect a broad class of signals in Gaussian noise using higher order statistics. The method detects a number of different signal types. The signals may be in the base-band or the pass-band, single-carrier or multi-carrier, frequency hopping or non-hopping, broad-pulse or narrow-pulse etc. In a typical setting this method provides an error rate of 3% at a signal to noise ratio of 0 dB. This method gives the time frequency detection ratio which may be used to determine if the detected signal falls in Class Single-Carrier of Class Multi-Carrier. Additionally, this method may be used for a number of different applications such as multiple signal identification, finding the basis functions of the received signal.