Analysis of a generalized coding/decoding method using FIR digital filters for radar waveform design

Previous results dealing with radar systems utilizing complementary coded pulse compression waveforms are extended. The objective is to show how the generation and compression of such codes can be based on a specific single-input/multiple-output FIR (finite-impulsive-response) digital filter structure. Driving this filter with a unit pulse yields all members of a complementary code set sequence simultaneously. A decoder is then derived as an FIR digital filter and is matched to the coder filter. The significance of this technique lies in the relative ease with which the decoder structure may be identified for an arbitrary coder structure. Structures are presented for complementary code pairs and sets, as well as for generalized codes. Use of these structures leads to decoding algorithms with reduced computational requirements. The author presents an example that shows how calculations on the order of M² may be reduced to on the order of M log₂M