Doppler Tolerant and Detection Capable Polyphase Good Code Sets Based on Linear FM Waveforms

This paper introduces Doppler tolerant and detection capable polyphase good code sets based on frequency-shifted linear FM (LFM) waveforms. A polyphase smart extended matched filter, constructed by extending the LFM slope on either side and can detect the higher energy distribution within the filter before summation (i.e., the Hadamard product), is developed to detect the entire code set. It is shown that this higher energy distribution location maps to the frequency shift in the received waveform. Thus, identifying a particular set member or the Doppler shift of an LFM based polyphase code. This results in Doppler detection of an LFM based polyphase code or detection of a polyphase good code set based on frequency-shifted LFM waveforms. The frequency offset between the different members of the set is chosen such that the Doppler shifts of individual code members could also be detected.