Extending the unambiguous range of CW polyphase radar systems using number theoretic transforms

Abstract

Polyphase continuous waveform (CW) radar systems often use the popular Frank code and P4 code due to their linear time-frequency characteristics as well as their low periodic ambiguity sidelobes. The phase relationship of the Frank code corresponds to a sawtooth folding waveform. The phase relationship of the P4 code is symmetrical with a parabolic distribution. The radar system's unambiguous target detection range is limited by the number of subcodes within the code period (code length). Increasing the code length to extend the unambiguous range results in a larger range-Doppler correlation matrix processor in the receiver, a longer compression time and an increase in the receiver's bulk memory requirements. In addition, the entire code period may not be returned from the target due to a limited time-on-target resulting in significant correlation loss. To significantly extend the unambiguous range beyond a single code period, this thesis explores the relationship between the polyphase codes (Frank and P4) and the number theoretic transforms (NTT) where the residues exhibit the same distribution as the polyphase values. The unambiguous range is extended from the number of subcodes within a single code period to the dynamic range of the transform without requiring a large increase in correlation processing. The dynamic range of a NTT is defined as the greatest length of combined phase sequences that contain no ambiguities or repeated paired terms. By transmitting N 2 coprime code periods, the unambiguous range can be extended by considering the paired values from each sequence. A new Frank phase code formulation is derived as a function of the residue number system (RNS) where each residue corresponds to a phase value within the code period (modulus) sequence. Based on the symmetrical distribution of the P4 code, a new phase code expression is derived using both the symmetrical number system (SNS) and the robust symmetrical number system (RSNS). Here each phase value within the code period corresponds to a symmetrical residue. MATLAB simulations are used to verify the new expressions for the RNS, SNS and RSNS phase codes. Implementation considerations of the new approach are also addressed.