Smart Extended Matched Filter for Linear FM based good code sets

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This paper introduces a good code set consisting of frequency shifted Linear FM (LFM) waveforms. It is shown that the entire set can be detected with one Smart Extended Matched Filter (SEMF), constructed by extending the frequency sweep of the LFM waveform on either side, which has an additional ability to detect the energy pattern following the multiplication of the incoming data with the filter coefficients (i.e. the Hadamard product) before the summation. This allows for associating a peak at the filter output with the location of the higher energy distribution within the filter, prior to summation. The location of this higher energy region determines the frequency shift which could identify a particular member of the proposed good code set or Doppler shift of a LFM waveform. Thus, resulting in Doppler detection for a LFM waveform or detection of a good code set comprised of frequency shifted LFM waveforms. The frequency offset between the members of the set is chosen such that Doppler shifts for individual code members could also be detectable by the SEMF. Such good code sets are generated using LFM waveforms with increasing instantaneous frequencies (or up-chirps) or LFM waveforms with decreasing instantaneous frequencies (or down-chirps) or both resulting in a larger set. However, in the case of the combined set, a receiver with two SEMF's: one for the up-chirp based set, and another for the down-chirp based set, is required.