Extending the unambiguous range of polyphase P4 CW radar using the robust symmetrical number system

Polyphase continuous waveform radar systems often use polyphase P4 modulation because of the periodic autocorrelation zero sidelobes and good Doppler tolerance. The P4´s unambiguous detection range is equal to the number of subcodes within a code period. To extend the unambiguous detection range beyond a single-code period, this study develops a novel relationship between the polyphase P4 code and the robust symmetrical number system (RSNS) where the P4 phase values within the code period match the symmetrical residues within an RSNS sequence. By transmitting N≥2 coprime P4 code periods, the unambiguous range is extended by considering the paired values from each sequence. With this new approach, the unambiguous range is extended to the greatest length of combined coprime phase sequences that contain no repeated paired terms. The flexibility of the RSNS allows the unambiguous range to be extended using a fewer number of subcodes within each code period. The combined phase sequences also have an inherent integer Gray code property to control range detection errors. Examples are shown to demonstrate the feasibility of the approach and to compare the unambiguous detection range to that of a single P4 code period.